subject:"Re\: Bruno's mathematical reality"



On 30 Dec 2013, at 09:01, meekerdb wrote:


On 12/29/2013 11:42 PM, Bruno Marchal wrote:


On 29 Dec 2013, at 20:25, meekerdb wrote:


On 12/29/2013 5:56 AM, Bruno Marchal wrote:


On 28 Dec 2013, at 22:23, meekerdb wrote:


On 12/28/2013 4:09 AM, Bruno Marchal wrote:
For a long time I got opponent saying that we cannot generate  
computationally a random number, and that is right, if we want  
generate only that numbers. but a simple counting algorithm  
generating all numbers, 0, 1, 2,  6999500235148668, ...  
generates all random finite incompressible strings,


How can a finite string be incompressible?  6999500235148668 in  
base 6999500235148669 is just 10.



You can define a finite string as incompressible when the shorter  
combinators to generate it is as lengthy as the string itself.
This definition is not universal for a finite amount of short  
sequences which indeed will depend of the language used (here  
combinators).


Then you can show that such a definition can be made universal by  
adding some constant, which will depend of the universal language.


It can be shown that most (finite!) numbers, written in any base,  
are random in that sense.


Of course, 10 is a sort of compression of any string X in some  
base, but if you allow change of base, you will need to send the  
base with the number in the message. If you fix the base, then  
indeed 10 will be a compression of that particular number base,  
for that language, and it is part of incompressibility theory  
that no definition exist working for all (small) numbers.


Since all finite numbers are small, I think this means the theory  
only holds in the limit.


The definition will work for all numbers reasonably bigger than the  
code of the universal machine used. That is what determine the  
constant. Not all numbers are small relatively to the size of the  
universal number/machine used to compress information.


Maybe you can clarify this point which seemed to arise in my  
discussion with JR.  Are you talking about numbers or about strings  
of digits that name numbers?


I am talking about string of digits (naming or not numbers). Sometimes  
I call them number, as all strings on a fixed alphabet can be seen as  
a number written in the base defined by that alphabet. But compression  
is a notion concerning strings of symbols.


Bruno




Brent

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Re: Bruno's mathematical reality



On 30 Dec 2013, at 06:28, Jason Resch wrote:

In the space of all possible movies, the ones that are watchable or  
meaningful to human viewers would all be highly compressible. The  
ones that are random snow, despite containing more information,  
would not make interesting movies.  So maybe there is something to  
your idea that interesting is related to short descriptions. We did  
evolve to find entirely predictable and entirely unpredictable  
things boring, there may be some ideal blend of predictability and  
unpredicability that we find most engaging.



Yes, it is the redundancy of the information related to the notion of  
universal machine. It is contained in Post numbers, which is a sort of  
UD by itself (when seen in some way): 0,  
00110001011000100101001001110 ... with nth digit = 0 or 1  
according to the fact that the nth programs (with 0 input) stop or  
not. (It is an halting oracle, and of course is not computable, but it  
is compressible).


The non computable maximal compression of Post number gives Chaitin  
Omega number, which delete all redundancies in the UD, and thus the  
whole physics!


Anything interesting and beautiful is highly redundant, like the  
Mandelbrot set for example.


In recursion theory, it is the difference between two  
complementarities: the simple/immune complementarity discovered by  
Post (and rediscovered by Chaitin in term of algorithmic compression)  
on one par, and the creative/productive complementarity, also  
discovered by Post, where "creative" has been shown later to be  
equivalent with Turing universality (or sigma_1 completeness) by John  
Myhill, (using Kleene second recursion theorem).


Bruno







http://iridia.ulb.ac.be/~marchal/



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Re: Bruno's mathematical reality



On 30 Dec 2013, at 05:54, meekerdb wrote:


On 12/29/2013 7:45 PM, Jason Resch wrote:




On Sun, Dec 29, 2013 at 6:58 PM, meekerdb   
wrote:

On 12/29/2013 3:49 PM, Jason Resch wrote:




On Sun, Dec 29, 2013 at 5:42 PM, meekerdb   
wrote:

On 12/29/2013 2:08 PM, Jason Resch wrote:




On Sun, Dec 29, 2013 at 4:51 PM, meekerdb   
wrote:

On 12/29/2013 1:28 PM, Jason Resch wrote:




On Sun, Dec 29, 2013 at 2:25 PM, meekerdb   
wrote:

On 12/29/2013 5:56 AM, Bruno Marchal wrote:


On 28 Dec 2013, at 22:23, meekerdb wrote:


On 12/28/2013 4:09 AM, Bruno Marchal wrote:
For a long time I got opponent saying that we cannot generate  
computationally a random number, and that is right, if we  
want generate only that numbers. but a simple counting  
algorithm generating all numbers, 0, 1, 2,   
6999500235148668, ... generates all random finite  
incompressible strings,


How can a finite string be incompressible?  6999500235148668  
in base 6999500235148669 is just 10.



You can define a finite string as incompressible when the  
shorter combinators to generate it is as lengthy  
as  the  
string itself.
This definition is not universal for a finite amount of short  
sequences which indeed will depend of the language used (here  
combinators).


Then you can show that such a definition can be made universal  
by adding some constant, which will depend of the universal  
language.


It can be shown that most (finite!) numbers, written in any  
base, are random in that sense.


Of course, 10 is a sort of compression of any string X in some  
base, but if you allow change of base, you will need to send  
the base with the number in the message. If you fix the base,  
then indeed 10 will be a compression of that particular number  
base, for that language, and it is part of incompressibility  
theory that no definition exist working for all (small) numbers.


Since all finite numbers are small, I think this means the  
theory only holds in the limit.


Brent


Brent,

It is easy to see with the pigeon hole principal.  There are  
more 2 digit numbers than 1 digit numbers, and more 3 digit  
numbers than 2 digit numbers, and so on.  For any string you can  
represent using a shorter string,  
another   
"shorter string" must necessarily be displaced.  You can't keep  
replacing things with shorter strings because there aren't  
enough of them, so as a side-effect, every compression strategy  
must represent some strings by larger ones.  In fact, the  
average size of all possible compressed messages (with some  
upper-bound length n) can never be smaller than the average size  
of all uncompressed messages.


The only reason compression algorithms are useful is because  
they are tailored to represent some class of messages with  
shorter strings, while making (the vast majority of) other  
messages slightly larger.


A good explanation.

Thanks.

But just because you cannot compress all numbers of a given size  
doesn't imply that any particular number is incompressible.


That is true if you consider the size of the compression program  
to be of no relevance.  In such a case, you can of course have a  
number of very small strings map directly to very large ones.


  So isn't it the case that every finite number string is  
compressible in some algorithm?  So there's no sense to saying  
6999500235148668 is random, but 11 is not, except  
relative to some given compression algorithm.


Right, but this leads to the concept of Kolmogorov complexity. If  
you consider the size of the minimum string and algorithm  
together, necessary to represent some number, you will find there  
are some patterns of data that are  
more  compressible  
than others.  In your previous example with base  
6999500235148668, you would need to include  
both  that base, and  
the string "10" in order to encode 6999500235148669.


But that seems to make the randomness of a number dependent on the  
base used to write it down? Did I have to write down "And this is  
in base 10" to show that 6999500235148668 is random?  There seems  
to be an equivocation here on "computing a number" and "computing  
a representation of a number".




A number containing regular patterns in some base, will also  
contain regular patterns in some other base (even if they are not  
obvious to us), compression algorithms are good at recognizing them.


The text of this sentence may not seem very redundant, but english  
text can generally be compressed somewhere between 20% - 30% of  
its original size.  If you convert a number like "555" to  
base 2, its patterns should be more evident in the pattern of bits.


 For the majority of numbers, you will find the Kolmogorov  
complexity of the number to almost always be on the order of the

Re: Bruno's mathematical reality



On 29 Dec 2013, at 23:42, meekerdb wrote:


On 12/29/2013 2:08 PM, Jason Resch wrote:




On Sun, Dec 29, 2013 at 4:51 PM, meekerdb   
wrote:

On 12/29/2013 1:28 PM, Jason Resch wrote:




On Sun, Dec 29, 2013 at 2:25 PM, meekerdb   
wrote:

On 12/29/2013 5:56 AM, Bruno Marchal wrote:


On 28 Dec 2013, at 22:23, meekerdb wrote:


On 12/28/2013 4:09 AM, Bruno Marchal wrote:
For a long time I got opponent saying that we cannot generate  
computationally a random number, and that is right, if we want  
generate only that numbers. but a simple counting algorithm  
generating all numbers, 0, 1, 2,  6999500235148668, ...  
generates all random finite incompressible strings,


How can a finite string be incompressible?  6999500235148668 in  
base 6999500235148669 is just 10.



You can define a finite string as incompressible when the shorter  
combinators to generate it is as lengthy as the string itself.
This definition is not universal for a finite amount of short  
sequences which indeed will depend of the language used (here  
combinators).


Then you can show that such a definition can be made universal by  
adding some constant, which will depend of the universal language.


It can be shown that most (finite!) numbers, written in any base,  
are random in that sense.


Of course, 10 is a sort of compression of any string X in some  
base, but if you allow change of base, you will need to send the  
base with the number in the message. If you fix the base, then  
indeed 10 will be a compression of that particular number base,  
for that language, and it is part of incompressibility theory  
that no definition exist working for all (small) numbers.


Since all finite numbers are small, I think this means the theory  
only holds in the limit.


Brent


Brent,

It is easy to see with the pigeon hole principal.  There are more  
2 digit numbers than 1 digit numbers, and more 3 digit numbers  
than 2 digit numbers, and so on.  For any string you can represent  
using a shorter string, another "shorter string" must necessarily  
be displaced.  You can't keep replacing things with shorter  
strings because there aren't enough of them, so as a side-effect,  
every compression strategy must represent some strings by larger  
ones.  In fact, the average size of all possible compressed  
messages (with some upper-bound length n) can never be smaller  
than the average size of all uncompressed messages.


The only reason compression algorithms are useful is because they  
are tailored to represent some class of messages with shorter  
strings, while making (the vast majority of) other messages  
slightly larger.


A good explanation.

Thanks.

But just because you cannot compress all numbers of a given size  
doesn't imply that any particular number is incompressible.


That is true if you consider the size of the compression program to  
be of no relevance.  In such a case, you can of course have a  
number of very small strings map directly to very large ones.


  So isn't it the case that every finite number string is  
compressible in some algorithm?  So there's no sense to saying  
6999500235148668 is random, but 11 is not, except  
relative to some given compression algorithm.


Right, but this leads to the concept of Kolmogorov complexity. If  
you consider the size of the minimum string and algorithm together,  
necessary to represent some number, you will find there are some  
patterns of data that are more compressible than others.  In your  
previous example with base 6999500235148668, you would need to  
include both that base, and the string "10" in order to encode  
6999500235148669.


But that seems to make the randomness of a number dependent on the  
base used to write it down? Did I have to write down "And this is in  
base 10" to show that 6999500235148668 is random?  There seems to be  
an equivocation here on "computing a number" and "computing a  
representation of a number".


Only for the numbers or strings with size similar to the size of the  
universal number use for the compression. This means it works for  
almost all numbers (= all except a finite number of exception).






 For the majority of numbers, you will find the Kolmogorov  
complexity of the number to almost always be on the order of the  
number of digits in that number.  The exceptions like 11  
are few and far between.


1 looks a lot messier in base 9.


Sure.

Bruno


http://iridia.ulb.ac.be/~marchal/



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Re: Bruno's mathematical reality



On 29 Dec 2013, at 22:51, meekerdb wrote:


On 12/29/2013 1:28 PM, Jason Resch wrote:




On Sun, Dec 29, 2013 at 2:25 PM, meekerdb   
wrote:

On 12/29/2013 5:56 AM, Bruno Marchal wrote:


On 28 Dec 2013, at 22:23, meekerdb wrote:


On 12/28/2013 4:09 AM, Bruno Marchal wrote:
For a long time I got opponent saying that we cannot generate  
computationally a random number, and that is right, if we want  
generate only that numbers. but a simple counting algorithm  
generating all numbers, 0, 1, 2,  6999500235148668, ...  
generates all random finite incompressible strings,


How can a finite string be incompressible?  6999500235148668 in  
base 6999500235148669 is just 10.



You can define a finite string as incompressible when the shorter  
combinators to generate it is as lengthy as the string itself.
This definition is not universal for a finite amount of short  
sequences which indeed will depend of the language used (here  
combinators).


Then you can show that such a definition can be made universal by  
adding some constant, which will depend of the universal language.


It can be shown that most (finite!) numbers, written in any base,  
are random in that sense.


Of course, 10 is a sort of compression of any string X in some  
base, but if you allow change of base, you will need to send the  
base with the number in the message. If you fix the base, then  
indeed 10 will be a compression of that particular number base,  
for that language, and it is part of incompressibility theory that  
no definition exist working for all (small) numbers.


Since all finite numbers are small, I think this means the theory  
only holds in the limit.


Brent


Brent,

It is easy to see with the pigeon hole principal.  There are more 2  
digit numbers than 1 digit numbers, and more 3 digit numbers than 2  
digit numbers, and so on.  For any string you can represent using a  
shorter string, another "shorter string" must necessarily be  
displaced.  You can't keep replacing things with shorter strings  
because there aren't enough of them, so as a side-effect, every  
compression strategy must represent some strings by larger ones.   
In fact, the average size of all possible compressed messages (with  
some upper-bound length n) can never be smaller than the average  
size of all uncompressed messages.


The only reason compression algorithms are useful is because they  
are tailored to represent some class of messages with shorter  
strings, while making (the vast majority of) other messages  
slightly larger.


A good explanation.  But just because you cannot compress all  
numbers of a given size doesn't imply that any particular number is  
incompressible.  So isn't it the case that every finite number  
string is compressible in some algorithm?  So there's no sense to  
saying 6999500235148668 is random, but 11 is not, except  
relative to some given compression algorithm.


It works up to a constant related to the choice of the universal base  
to do the compression. "11" is probably random in the SK  
combinator language. But for strings which are greater than the  
description of the universal bases used, the same strings will be  
random or not.


Bruno




Brent

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Re: Bruno's mathematical reality

2013-12-30 Thread meekerdb


On 12/29/2013 11:42 PM, Bruno Marchal wrote:


On 29 Dec 2013, at 20:25, meekerdb wrote:


On 12/29/2013 5:56 AM, Bruno Marchal wrote:


On 28 Dec 2013, at 22:23, meekerdb wrote:


On 12/28/2013 4:09 AM, Bruno Marchal wrote:
For a long time I got opponent saying that we cannot generate computationally a 
random number, and that is right, if we want generate only that numbers. but a 
simple counting algorithm generating all numbers, 0, 1, 2,  6999500235148668, 
... generates all random finite incompressible strings,


How can a finite string be incompressible? 6999500235148668 in base 6999500235148669 
is just 10.



You can define a finite string as incompressible when the shorter combinators to 
generate it is as lengthy as the string itself.
This definition is not universal for a finite amount of short sequences which indeed 
will depend of the language used (here combinators).


Then you can show that such a definition can be made universal by adding some 
constant, which will depend of the universal language.


It can be shown that most (finite!) numbers, written in any base, are random in that 
sense.


Of course, 10 is a sort of compression of any string X in some base, but if you allow 
change of base, you will need to send the base with the number in the message. If you 
fix the base, then indeed 10 will be a compression of that particular number base, for 
that language, and it is part of incompressibility theory that no definition exist 
working for all (small) numbers.


Since all finite numbers are small, I think this means the theory only holds in 
the limit.


The definition will work for all numbers reasonably bigger than the code of the 
universal machine used. That is what determine the constant. Not all numbers are small 
relatively to the size of the universal number/machine used to compress information.


Maybe you can clarify this point which seemed to arise in my discussion with JR.  Are you 
talking about numbers or about strings of digits that name numbers?


Brent

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Re: Bruno's mathematical reality



On 29 Dec 2013, at 20:25, meekerdb wrote:


On 12/29/2013 5:56 AM, Bruno Marchal wrote:


On 28 Dec 2013, at 22:23, meekerdb wrote:


On 12/28/2013 4:09 AM, Bruno Marchal wrote:
For a long time I got opponent saying that we cannot generate  
computationally a random number, and that is right, if we want  
generate only that numbers. but a simple counting algorithm  
generating all numbers, 0, 1, 2,  6999500235148668, ...  
generates all random finite incompressible strings,


How can a finite string be incompressible?  6999500235148668 in  
base 6999500235148669 is just 10.



You can define a finite string as incompressible when the shorter  
combinators to generate it is as lengthy as the string itself.
This definition is not universal for a finite amount of short  
sequences which indeed will depend of the language used (here  
combinators).


Then you can show that such a definition can be made universal by  
adding some constant, which will depend of the universal language.


It can be shown that most (finite!) numbers, written in any base,  
are random in that sense.


Of course, 10 is a sort of compression of any string X in some  
base, but if you allow change of base, you will need to send the  
base with the number in the message. If you fix the base, then  
indeed 10 will be a compression of that particular number base, for  
that language, and it is part of incompressibility theory that no  
definition exist working for all (small) numbers.


Since all finite numbers are small, I think this means the theory  
only holds in the limit.


The definition will work for all numbers reasonably bigger than the  
code of the universal machine used. That is what determine the  
constant. Not all numbers are small relatively to the size of the  
universal number/machine used to compress information.


Bruno






Brent

Each particular language will have some exception on the  
incompressibility issue. That should be part of the role of the  
variable constant in the general universal definition.


Bruno




http://iridia.ulb.ac.be/~marchal/



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Re: Bruno's mathematical reality

On Sun, Dec 29, 2013 at 11:54 PM, meekerdb  wrote:

>  On 12/29/2013 7:45 PM, Jason Resch wrote:
>
>
>
>
> On Sun, Dec 29, 2013 at 6:58 PM, meekerdb  wrote:
>
>>   On 12/29/2013 3:49 PM, Jason Resch wrote:
>>
>>
>>
>>
>> On Sun, Dec 29, 2013 at 5:42 PM, meekerdb  wrote:
>>
>>>   On 12/29/2013 2:08 PM, Jason Resch wrote:
>>>
>>>
>>>
>>>
>>> On Sun, Dec 29, 2013 at 4:51 PM, meekerdb  wrote:
>>>
  On 12/29/2013 1:28 PM, Jason Resch wrote:




 On Sun, Dec 29, 2013 at 2:25 PM, meekerdb  wrote:

>  On 12/29/2013 5:56 AM, Bruno Marchal wrote:
>
>
>  On 28 Dec 2013, at 22:23, meekerdb wrote:
>
>  On 12/28/2013 4:09 AM, Bruno Marchal wrote:
>
> For a long time I got opponent saying that we cannot generate
> computationally a random number, and that is right, if we want generate
> only that numbers. but a simple counting algorithm generating all numbers,
> 0, 1, 2,  6999500235148668, ... generates all random finite
> incompressible strings,
>
>
> How can a finite string be incompressible?  6999500235148668 in base
> 6999500235148669 is just 10.
>
>
>
>  You can define a finite string as incompressible when the shorter
> combinators to generate it is as lengthy as the string itself.
> This definition is not universal for a finite amount of short
> sequences which indeed will depend of the language used (here 
> combinators).
>
>  Then you can show that such a definition can be made universal by
> adding some constant, which will depend of the universal language.
>
>  It can be shown that most (finite!) numbers, written in any base,
> are random in that sense.
>
>  Of course, 10 is a sort of compression of any string X in some base,
> but if you allow change of base, you will need to send the base with the
> number in the message. If you fix the base, then indeed 10 will be a
> compression of that particular number base, for that language, and it is
> part of incompressibility theory that no definition exist working for all
> (small) numbers.
>
>
>  Since all finite numbers are small, I think this means the theory
> only holds in the limit.
>
> Brent
>


  Brent,

  It is easy to see with the pigeon hole principal.  There are more 2
 digit numbers than 1 digit numbers, and more 3 digit numbers than 2 digit
 numbers, and so on.  For any string you can represent using a shorter
 string, another "shorter string" must necessarily be displaced.  You can't
 keep replacing things with shorter strings because there aren't enough of
 them, so as a side-effect, every compression strategy must represent some
 strings by larger ones.  In fact, the average size of all possible
 compressed messages (with some upper-bound length n) can never be smaller
 than the average size of all uncompressed messages.

  The only reason compression algorithms are useful is because they are
 tailored to represent some class of messages with shorter strings, while
 making (the vast majority of) other messages slightly larger.


  A good explanation.

>>>
>>>  Thanks.
>>>
>>>
  But just because you cannot compress all numbers of a given size
 doesn't imply that any particular number is incompressible.

>>>
>>>  That is true if you consider the size of the compression program to be
>>> of no relevance.  In such a case, you can of course have a number of very
>>> small strings map directly to very large ones.
>>>
>>>
   So isn't it the case that every finite number string is compressible
 in some algorithm?  So there's no sense to saying 6999500235148668 is
 random, but 11 is not, except relative to some given
 compression algorithm.

>>>
>>>  Right, but this leads to the concept of Kolmogorov complexity. If you
>>> consider the size of the minimum string and algorithm together, necessary
>>> to represent some number, you will find there are some patterns of data
>>> that are more compressible than others.  In your previous example with base
>>> 6999500235148668, you would need to include both that base, and the string
>>> "10" in order to encode 6999500235148669.
>>>
>>>
>>>  But that seems to make the randomness of a number dependent on the
>>> base used to write it down? Did I have to write down "And this is in base
>>> 10" to show that 6999500235148668 is random?  There seems to be an
>>> equivocation here on "computing a number" and "computing a representation
>>> of a number".
>>>
>>>
>>>
>>  A number containing regular patterns in some base, will also contain
>> regular patterns in some other base (even if they are not obvious to us),
>> compression algorithms are good at recognizing them.
>>
>>  The text of this sentence may not seem very redundant, but english text
>> can generally be compressed somewhere betwee

Re: Bruno's mathematical reality


On 12/29/2013 7:45 PM, Jason Resch wrote:




On Sun, Dec 29, 2013 at 6:58 PM, meekerdb > wrote:


On 12/29/2013 3:49 PM, Jason Resch wrote:




On Sun, Dec 29, 2013 at 5:42 PM, meekerdb mailto:meeke...@verizon.net>> wrote:

On 12/29/2013 2:08 PM, Jason Resch wrote:




On Sun, Dec 29, 2013 at 4:51 PM, meekerdb mailto:meeke...@verizon.net>> wrote:

On 12/29/2013 1:28 PM, Jason Resch wrote:




On Sun, Dec 29, 2013 at 2:25 PM, meekerdb mailto:meeke...@verizon.net>> wrote:

On 12/29/2013 5:56 AM, Bruno Marchal wrote:


On 28 Dec 2013, at 22:23, meekerdb wrote:


On 12/28/2013 4:09 AM, Bruno Marchal wrote:

For a long time I got opponent saying that we cannot generate
computationally a random number, and that is right, if we want
generate only that numbers. but a simple counting algorithm
generating all numbers, 0, 1, 2,  6999500235148668, ...
generates all random finite incompressible strings,


How can a finite string be incompressible? 6999500235148668 in 
base
6999500235148669 is just 10.



You can define a finite string as incompressible when the 
shorter
combinators to generate it is as lengthy as the string itself.
This definition is not universal for a finite amount of short
sequences which indeed will depend of the language used (here
combinators).

Then you can show that such a definition can be made universal 
by
adding some constant, which will depend of the universal 
language.

It can be shown that most (finite!) numbers, written in any 
base,
are random in that sense.

Of course, 10 is a sort of compression of any string X in some 
base,
but if you allow change of base, you will need to send the base 
with
the number in the message. If you fix the base, then indeed 10 
will
be a compression of that particular number base, for that 
language,
and it is part of incompressibility theory that no definition 
exist
working for all (small) numbers.


Since all finite numbers are small, I think this means the 
theory
only holds in the limit.

Brent



Brent,

It is easy to see with the pigeon hole principal.  There are more 2 
digit
numbers than 1 digit numbers, and more 3 digit numbers than 2 digit
numbers, and so on.  For any string you can represent using a 
shorter
string, another "shorter string" must necessarily be displaced.  You
can't keep replacing things with shorter strings because there 
aren't
enough of them, so as a side-effect, every compression strategy must
represent some strings by larger ones.  In fact, the average size 
of all
possible compressed messages (with some upper-bound length n) can 
never
be smaller than the average size of all uncompressed messages.

The only reason compression algorithms are useful is because they 
are
tailored to represent some class of messages with shorter strings, 
while
making (the vast majority of) other messages slightly larger.


A good explanation.


Thanks.

But just because you cannot compress all numbers of a given size 
doesn't
imply that any particular number is incompressible.


That is true if you consider the size of the compression program to be 
of no
relevance.  In such a case, you can of course have a number of very 
small
strings map directly to very large ones.

  So isn't it the case that every finite number string is 
compressible in
some algorithm?  So there's no sense to saying 6999500235148668 is 
random,
but 11 is not, except relative to some given compression
algorithm.


Right, but this leads to the concept of Kolmogorov complexity. If you 
consider
the size of the minimum string and algorithm together, necessary to 
represent
some number, you will find there are some patterns of data that are more
compressible than others.  In your previous example with base
6999500235148668, you would need to include both that base, and the 
string
"10" in order to encode 6999500235148669.


But that seems to make the randomness of a number dependent on the base 
used to
write it down? Did I have to write down "And this is in base 10" to 
show that
6999500235148668 is random?  There seems to be an equivocation here on
"computing a number" and "computing a repre

Re: Bruno's mathematical reality

On Sun, Dec 29, 2013 at 6:58 PM, meekerdb  wrote:

>  On 12/29/2013 3:49 PM, Jason Resch wrote:
>
>
>
>
> On Sun, Dec 29, 2013 at 5:42 PM, meekerdb  wrote:
>
>>   On 12/29/2013 2:08 PM, Jason Resch wrote:
>>
>>
>>
>>
>> On Sun, Dec 29, 2013 at 4:51 PM, meekerdb  wrote:
>>
>>>  On 12/29/2013 1:28 PM, Jason Resch wrote:
>>>
>>>
>>>
>>>
>>> On Sun, Dec 29, 2013 at 2:25 PM, meekerdb  wrote:
>>>
  On 12/29/2013 5:56 AM, Bruno Marchal wrote:


  On 28 Dec 2013, at 22:23, meekerdb wrote:

  On 12/28/2013 4:09 AM, Bruno Marchal wrote:

 For a long time I got opponent saying that we cannot generate
 computationally a random number, and that is right, if we want generate
 only that numbers. but a simple counting algorithm generating all numbers,
 0, 1, 2,  6999500235148668, ... generates all random finite
 incompressible strings,


 How can a finite string be incompressible?  6999500235148668 in base
 6999500235148669 is just 10.



  You can define a finite string as incompressible when the shorter
 combinators to generate it is as lengthy as the string itself.
 This definition is not universal for a finite amount of short sequences
 which indeed will depend of the language used (here combinators).

  Then you can show that such a definition can be made universal by
 adding some constant, which will depend of the universal language.

  It can be shown that most (finite!) numbers, written in any base, are
 random in that sense.

  Of course, 10 is a sort of compression of any string X in some base,
 but if you allow change of base, you will need to send the base with the
 number in the message. If you fix the base, then indeed 10 will be a
 compression of that particular number base, for that language, and it is
 part of incompressibility theory that no definition exist working for all
 (small) numbers.


  Since all finite numbers are small, I think this means the theory only
 holds in the limit.

 Brent

>>>
>>>
>>>  Brent,
>>>
>>>  It is easy to see with the pigeon hole principal.  There are more 2
>>> digit numbers than 1 digit numbers, and more 3 digit numbers than 2 digit
>>> numbers, and so on.  For any string you can represent using a shorter
>>> string, another "shorter string" must necessarily be displaced.  You can't
>>> keep replacing things with shorter strings because there aren't enough of
>>> them, so as a side-effect, every compression strategy must represent some
>>> strings by larger ones.  In fact, the average size of all possible
>>> compressed messages (with some upper-bound length n) can never be smaller
>>> than the average size of all uncompressed messages.
>>>
>>>  The only reason compression algorithms are useful is because they are
>>> tailored to represent some class of messages with shorter strings, while
>>> making (the vast majority of) other messages slightly larger.
>>>
>>>
>>>  A good explanation.
>>>
>>
>>  Thanks.
>>
>>
>>>  But just because you cannot compress all numbers of a given size
>>> doesn't imply that any particular number is incompressible.
>>>
>>
>>  That is true if you consider the size of the compression program to be
>> of no relevance.  In such a case, you can of course have a number of very
>> small strings map directly to very large ones.
>>
>>
>>>   So isn't it the case that every finite number string is compressible
>>> in some algorithm?  So there's no sense to saying 6999500235148668 is
>>> random, but 11 is not, except relative to some given
>>> compression algorithm.
>>>
>>
>>  Right, but this leads to the concept of Kolmogorov complexity. If you
>> consider the size of the minimum string and algorithm together, necessary
>> to represent some number, you will find there are some patterns of data
>> that are more compressible than others.  In your previous example with base
>> 6999500235148668, you would need to include both that base, and the string
>> "10" in order to encode 6999500235148669.
>>
>>
>>  But that seems to make the randomness of a number dependent on the base
>> used to write it down? Did I have to write down "And this is in base 10" to
>> show that 6999500235148668 is random?  There seems to be an equivocation
>> here on "computing a number" and "computing a representation of a number".
>>
>>
>>
>  A number containing regular patterns in some base, will also contain
> regular patterns in some other base (even if they are not obvious to us),
> compression algorithms are good at recognizing them.
>
>  The text of this sentence may not seem very redundant, but english text
> can generally be compressed somewhere between 20% - 30% of its original
> size.  If you convert a number like "555" to base 2, its patterns
> should be more evident in the pattern of bits.
>
>
>> For the majority of numbers, you will find the Kolmogorov complexity
>> of the nu

Re: Bruno's mathematical reality


On 12/29/2013 3:49 PM, Jason Resch wrote:




On Sun, Dec 29, 2013 at 5:42 PM, meekerdb > wrote:


On 12/29/2013 2:08 PM, Jason Resch wrote:




On Sun, Dec 29, 2013 at 4:51 PM, meekerdb mailto:meeke...@verizon.net>> wrote:

On 12/29/2013 1:28 PM, Jason Resch wrote:




On Sun, Dec 29, 2013 at 2:25 PM, meekerdb mailto:meeke...@verizon.net>> wrote:

On 12/29/2013 5:56 AM, Bruno Marchal wrote:


On 28 Dec 2013, at 22:23, meekerdb wrote:


On 12/28/2013 4:09 AM, Bruno Marchal wrote:

For a long time I got opponent saying that we cannot generate
computationally a random number, and that is right, if we want 
generate
only that numbers. but a simple counting algorithm generating all
numbers, 0, 1, 2,  6999500235148668, ... generates all random
finite incompressible strings,


How can a finite string be incompressible? 6999500235148668 in base
6999500235148669 is just 10.



You can define a finite string as incompressible when the shorter
combinators to generate it is as lengthy as the string itself.
This definition is not universal for a finite amount of short 
sequences
which indeed will depend of the language used (here combinators).

Then you can show that such a definition can be made universal by 
adding
some constant, which will depend of the universal language.

It can be shown that most (finite!) numbers, written in any base, 
are
random in that sense.

Of course, 10 is a sort of compression of any string X in some 
base, but
if you allow change of base, you will need to send the base with the
number in the message. If you fix the base, then indeed 10 will be a
compression of that particular number base, for that language, and 
it is
part of incompressibility theory that no definition exist working 
for all
(small) numbers.


Since all finite numbers are small, I think this means the theory 
only
holds in the limit.

Brent



Brent,

It is easy to see with the pigeon hole principal.  There are more 2 
digit
numbers than 1 digit numbers, and more 3 digit numbers than 2 digit 
numbers,
and so on.  For any string you can represent using a shorter string, 
another
"shorter string" must necessarily be displaced.  You can't keep 
replacing
things with shorter strings because there aren't enough of them, so as a
side-effect, every compression strategy must represent some strings by 
larger
ones.  In fact, the average size of all possible compressed messages 
(with
some upper-bound length n) can never be smaller than the average size 
of all
uncompressed messages.

The only reason compression algorithms are useful is because they are 
tailored
to represent some class of messages with shorter strings, while making 
(the
vast majority of) other messages slightly larger.


A good explanation.


Thanks.

But just because you cannot compress all numbers of a given size 
doesn't imply
that any particular number is incompressible.


That is true if you consider the size of the compression program to be of no
relevance.  In such a case, you can of course have a number of very small 
strings
map directly to very large ones.

  So isn't it the case that every finite number string is compressible 
in some
algorithm?  So there's no sense to saying 6999500235148668 is random, 
but
11 is not, except relative to some given compression 
algorithm.


Right, but this leads to the concept of Kolmogorov complexity. If you 
consider the
size of the minimum string and algorithm together, necessary to represent 
some
number, you will find there are some patterns of data that are more 
compressible
than others.  In your previous example with base 6999500235148668, you 
would need
to include both that base, and the string "10" in order to encode 
6999500235148669.


But that seems to make the randomness of a number dependent on the base 
used to
write it down? Did I have to write down "And this is in base 10" to show 
that
6999500235148668 is random?  There seems to be an equivocation here on 
"computing a
number" and "computing a representation of a number".



A number containing regular patterns in some base, will also contain regular patterns in 
some other base (even if they are not obvious to us), compression algorithms are good at 
recognizing them.


The text of this sentence may not seem very redundant, but english text can generally be 
compressed somewhere between 20% - 30% of its original size.  If you convert a number 
like "55

Re: Bruno's mathematical reality

On Sun, Dec 29, 2013 at 5:42 PM, meekerdb  wrote:

>  On 12/29/2013 2:08 PM, Jason Resch wrote:
>
>
>
>
> On Sun, Dec 29, 2013 at 4:51 PM, meekerdb  wrote:
>
>>  On 12/29/2013 1:28 PM, Jason Resch wrote:
>>
>>
>>
>>
>> On Sun, Dec 29, 2013 at 2:25 PM, meekerdb  wrote:
>>
>>>  On 12/29/2013 5:56 AM, Bruno Marchal wrote:
>>>
>>>
>>>  On 28 Dec 2013, at 22:23, meekerdb wrote:
>>>
>>>  On 12/28/2013 4:09 AM, Bruno Marchal wrote:
>>>
>>> For a long time I got opponent saying that we cannot generate
>>> computationally a random number, and that is right, if we want generate
>>> only that numbers. but a simple counting algorithm generating all numbers,
>>> 0, 1, 2,  6999500235148668, ... generates all random finite
>>> incompressible strings,
>>>
>>>
>>> How can a finite string be incompressible?  6999500235148668 in base
>>> 6999500235148669 is just 10.
>>>
>>>
>>>
>>>  You can define a finite string as incompressible when the shorter
>>> combinators to generate it is as lengthy as the string itself.
>>> This definition is not universal for a finite amount of short sequences
>>> which indeed will depend of the language used (here combinators).
>>>
>>>  Then you can show that such a definition can be made universal by
>>> adding some constant, which will depend of the universal language.
>>>
>>>  It can be shown that most (finite!) numbers, written in any base, are
>>> random in that sense.
>>>
>>>  Of course, 10 is a sort of compression of any string X in some base,
>>> but if you allow change of base, you will need to send the base with the
>>> number in the message. If you fix the base, then indeed 10 will be a
>>> compression of that particular number base, for that language, and it is
>>> part of incompressibility theory that no definition exist working for all
>>> (small) numbers.
>>>
>>>
>>>  Since all finite numbers are small, I think this means the theory only
>>> holds in the limit.
>>>
>>> Brent
>>>
>>
>>
>>  Brent,
>>
>>  It is easy to see with the pigeon hole principal.  There are more 2
>> digit numbers than 1 digit numbers, and more 3 digit numbers than 2 digit
>> numbers, and so on.  For any string you can represent using a shorter
>> string, another "shorter string" must necessarily be displaced.  You can't
>> keep replacing things with shorter strings because there aren't enough of
>> them, so as a side-effect, every compression strategy must represent some
>> strings by larger ones.  In fact, the average size of all possible
>> compressed messages (with some upper-bound length n) can never be smaller
>> than the average size of all uncompressed messages.
>>
>>  The only reason compression algorithms are useful is because they are
>> tailored to represent some class of messages with shorter strings, while
>> making (the vast majority of) other messages slightly larger.
>>
>>
>>  A good explanation.
>>
>
>  Thanks.
>
>
>>  But just because you cannot compress all numbers of a given size doesn't
>> imply that any particular number is incompressible.
>>
>
>  That is true if you consider the size of the compression program to be
> of no relevance.  In such a case, you can of course have a number of very
> small strings map directly to very large ones.
>
>
>>   So isn't it the case that every finite number string is compressible in
>> some algorithm?  So there's no sense to saying 6999500235148668 is random,
>> but 11 is not, except relative to some given compression
>> algorithm.
>>
>
>  Right, but this leads to the concept of Kolmogorov complexity. If you
> consider the size of the minimum string and algorithm together, necessary
> to represent some number, you will find there are some patterns of data
> that are more compressible than others.  In your previous example with base
> 6999500235148668, you would need to include both that base, and the string
> "10" in order to encode 6999500235148669.
>
>
> But that seems to make the randomness of a number dependent on the base
> used to write it down? Did I have to write down "And this is in base 10" to
> show that 6999500235148668 is random?  There seems to be an equivocation
> here on "computing a number" and "computing a representation of a number".
>
>
>
A number containing regular patterns in some base, will also contain
regular patterns in some other base (even if they are not obvious to us),
compression algorithms are good at recognizing them.

The text of this sentence may not seem very redundant, but english text can
generally be compressed somewhere between 20% - 30% of its original size.
 If you convert a number like "555" to base 2, its patterns should
be more evident in the pattern of bits.


>For the majority of numbers, you will find the Kolmogorov complexity
> of the number to almost always be on the order of the number of digits in
> that number.  The exceptions like 11 are few and far between.
>
>
> 1 looks a lot messier in base 9.
>
>

base 10: 111
base 9: 73555318547116177

Re: Bruno's mathematical reality


On 12/29/2013 2:08 PM, Jason Resch wrote:




On Sun, Dec 29, 2013 at 4:51 PM, meekerdb > wrote:


On 12/29/2013 1:28 PM, Jason Resch wrote:




On Sun, Dec 29, 2013 at 2:25 PM, meekerdb mailto:meeke...@verizon.net>> wrote:

On 12/29/2013 5:56 AM, Bruno Marchal wrote:


On 28 Dec 2013, at 22:23, meekerdb wrote:


On 12/28/2013 4:09 AM, Bruno Marchal wrote:

For a long time I got opponent saying that we cannot generate
computationally a random number, and that is right, if we want generate 
only
that numbers. but a simple counting algorithm generating all numbers, 
0, 1,
2,  6999500235148668, ... generates all random finite incompressible
strings,


How can a finite string be incompressible? 6999500235148668 in base
6999500235148669 is just 10.



You can define a finite string as incompressible when the shorter 
combinators
to generate it is as lengthy as the string itself.
This definition is not universal for a finite amount of short sequences 
which
indeed will depend of the language used (here combinators).

Then you can show that such a definition can be made universal by 
adding some
constant, which will depend of the universal language.

It can be shown that most (finite!) numbers, written in any base, are 
random
in that sense.

Of course, 10 is a sort of compression of any string X in some base, 
but if
you allow change of base, you will need to send the base with the 
number in
the message. If you fix the base, then indeed 10 will be a compression 
of that
particular number base, for that language, and it is part of 
incompressibility
theory that no definition exist working for all (small) numbers.


Since all finite numbers are small, I think this means the theory only 
holds in
the limit.

Brent



Brent,

It is easy to see with the pigeon hole principal.  There are more 2 digit 
numbers
than 1 digit numbers, and more 3 digit numbers than 2 digit numbers, and so 
on.
 For any string you can represent using a shorter string, another "shorter 
string"
must necessarily be displaced.  You can't keep replacing things with shorter
strings because there aren't enough of them, so as a side-effect, every 
compression
strategy must represent some strings by larger ones.  In fact, the average 
size of
all possible compressed messages (with some upper-bound length n) can never 
be
smaller than the average size of all uncompressed messages.

The only reason compression algorithms are useful is because they are 
tailored to
represent some class of messages with shorter strings, while making (the 
vast
majority of) other messages slightly larger.


A good explanation.


Thanks.

But just because you cannot compress all numbers of a given size doesn't 
imply that
any particular number is incompressible.


That is true if you consider the size of the compression program to be of no relevance. 
 In such a case, you can of course have a number of very small strings map directly to 
very large ones.


  So isn't it the case that every finite number string is compressible in 
some
algorithm?  So there's no sense to saying 6999500235148668 is random, but
11 is not, except relative to some given compression algorithm.


Right, but this leads to the concept of Kolmogorov complexity. If you consider the size 
of the minimum string and algorithm together, necessary to represent some number, you 
will find there are some patterns of data that are more compressible than others.  In 
your previous example with base 6999500235148668, you would need to include both that 
base, and the string "10" in order to encode 6999500235148669.


But that seems to make the randomness of a number dependent on the base used to write it 
down? Did I have to write down "And this is in base 10" to show that 6999500235148668 is 
random?  There seems to be an equivocation here on "computing a number" and "computing a 
representation of a number".


 For the majority of numbers, you will find the Kolmogorov complexity of the number to 
almost always be on the order of the number of digits in that number.  The exceptions 
like 11 are few and far between.


1 looks a lot messier in base 9.

Berent

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Re: Bruno's mathematical reality

On Sun, Dec 29, 2013 at 5:03 PM, Stephen Paul King <
stephe...@provensecure.com> wrote:

> Dear Brent and Jason,
>
>   I think that this is an important idea: the relationship between
> compression algorithms and numbers. It does not look like a simple
> one-to-one and onto map!
>
>
Stephen,

For any "loss-less" (full-fidelity) compression algorithm, the mapping is
one-to-one.  There are other compression algorithms, like jpeg or mp3 which
are lossy (they discard some information in the process), and hence they
are many-to-one.

Jason

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Re: Bruno's mathematical reality

On Sun, Dec 29, 2013 at 4:51 PM, meekerdb  wrote:

>  On 12/29/2013 1:28 PM, Jason Resch wrote:
>
>
>
>
> On Sun, Dec 29, 2013 at 2:25 PM, meekerdb  wrote:
>
>>  On 12/29/2013 5:56 AM, Bruno Marchal wrote:
>>
>>
>>  On 28 Dec 2013, at 22:23, meekerdb wrote:
>>
>>  On 12/28/2013 4:09 AM, Bruno Marchal wrote:
>>
>> For a long time I got opponent saying that we cannot generate
>> computationally a random number, and that is right, if we want generate
>> only that numbers. but a simple counting algorithm generating all numbers,
>> 0, 1, 2,  6999500235148668, ... generates all random finite
>> incompressible strings,
>>
>>
>> How can a finite string be incompressible?  6999500235148668 in base
>> 6999500235148669 is just 10.
>>
>>
>>
>>  You can define a finite string as incompressible when the shorter
>> combinators to generate it is as lengthy as the string itself.
>> This definition is not universal for a finite amount of short sequences
>> which indeed will depend of the language used (here combinators).
>>
>>  Then you can show that such a definition can be made universal by
>> adding some constant, which will depend of the universal language.
>>
>>  It can be shown that most (finite!) numbers, written in any base, are
>> random in that sense.
>>
>>  Of course, 10 is a sort of compression of any string X in some base,
>> but if you allow change of base, you will need to send the base with the
>> number in the message. If you fix the base, then indeed 10 will be a
>> compression of that particular number base, for that language, and it is
>> part of incompressibility theory that no definition exist working for all
>> (small) numbers.
>>
>>
>>  Since all finite numbers are small, I think this means the theory only
>> holds in the limit.
>>
>> Brent
>>
>
>
>  Brent,
>
>  It is easy to see with the pigeon hole principal.  There are more 2
> digit numbers than 1 digit numbers, and more 3 digit numbers than 2 digit
> numbers, and so on.  For any string you can represent using a shorter
> string, another "shorter string" must necessarily be displaced.  You can't
> keep replacing things with shorter strings because there aren't enough of
> them, so as a side-effect, every compression strategy must represent some
> strings by larger ones.  In fact, the average size of all possible
> compressed messages (with some upper-bound length n) can never be smaller
> than the average size of all uncompressed messages.
>
>  The only reason compression algorithms are useful is because they are
> tailored to represent some class of messages with shorter strings, while
> making (the vast majority of) other messages slightly larger.
>
>
> A good explanation.
>

Thanks.


> But just because you cannot compress all numbers of a given size doesn't
> imply that any particular number is incompressible.
>

That is true if you consider the size of the compression program to be of
no relevance.  In such a case, you can of course have a number of very
small strings map directly to very large ones.


>   So isn't it the case that every finite number string is compressible in
> some algorithm?  So there's no sense to saying 6999500235148668 is random,
> but 11 is not, except relative to some given compression
> algorithm.
>

Right, but this leads to the concept of Kolmogorov complexity. If you
consider the size of the minimum string and algorithm together, necessary
to represent some number, you will find there are some patterns of data
that are more compressible than others.  In your previous example with base
6999500235148668, you would need to include both that base, and the string
"10" in order to encode 6999500235148669.  For the majority of numbers, you
will find the Kolmogorov complexity of the number to almost always be on
the order of the number of digits in that number.  The exceptions like
11 are few and far between.

Jason

-- 
You received this message because you are subscribed to the Google Groups 
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Re: Bruno's mathematical reality

2013-12-29 Thread Stephen Paul King

Dear Brent and Jason,

  I think that this is an important idea: the relationship between
compression algorithms and numbers. It does not look like a simple
one-to-one and onto map!


On Sun, Dec 29, 2013 at 4:51 PM, meekerdb  wrote:

>  On 12/29/2013 1:28 PM, Jason Resch wrote:
>
>
>
>
> On Sun, Dec 29, 2013 at 2:25 PM, meekerdb  wrote:
>
>>  On 12/29/2013 5:56 AM, Bruno Marchal wrote:
>>
>>
>>  On 28 Dec 2013, at 22:23, meekerdb wrote:
>>
>>  On 12/28/2013 4:09 AM, Bruno Marchal wrote:
>>
>> For a long time I got opponent saying that we cannot generate
>> computationally a random number, and that is right, if we want generate
>> only that numbers. but a simple counting algorithm generating all numbers,
>> 0, 1, 2,  6999500235148668, ... generates all random finite
>> incompressible strings,
>>
>>
>> How can a finite string be incompressible?  6999500235148668 in base
>> 6999500235148669 is just 10.
>>
>>
>>
>>  You can define a finite string as incompressible when the shorter
>> combinators to generate it is as lengthy as the string itself.
>> This definition is not universal for a finite amount of short sequences
>> which indeed will depend of the language used (here combinators).
>>
>>  Then you can show that such a definition can be made universal by
>> adding some constant, which will depend of the universal language.
>>
>>  It can be shown that most (finite!) numbers, written in any base, are
>> random in that sense.
>>
>>  Of course, 10 is a sort of compression of any string X in some base,
>> but if you allow change of base, you will need to send the base with the
>> number in the message. If you fix the base, then indeed 10 will be a
>> compression of that particular number base, for that language, and it is
>> part of incompressibility theory that no definition exist working for all
>> (small) numbers.
>>
>>
>>  Since all finite numbers are small, I think this means the theory only
>> holds in the limit.
>>
>> Brent
>>
>
>
>  Brent,
>
>  It is easy to see with the pigeon hole principal.  There are more 2
> digit numbers than 1 digit numbers, and more 3 digit numbers than 2 digit
> numbers, and so on.  For any string you can represent using a shorter
> string, another "shorter string" must necessarily be displaced.  You can't
> keep replacing things with shorter strings because there aren't enough of
> them, so as a side-effect, every compression strategy must represent some
> strings by larger ones.  In fact, the average size of all possible
> compressed messages (with some upper-bound length n) can never be smaller
> than the average size of all uncompressed messages.
>
>  The only reason compression algorithms are useful is because they are
> tailored to represent some class of messages with shorter strings, while
> making (the vast majority of) other messages slightly larger.
>
>
> A good explanation.  But just because you cannot compress all numbers of a
> given size doesn't imply that any particular number is incompressible.  So
> isn't it the case that every finite number string is compressible in some
> algorithm?  So there's no sense to saying 6999500235148668 is random, but
> 11 is not, except relative to some given compression algorithm.
>
> Brent
>
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Re: Bruno's mathematical reality


On 12/29/2013 1:28 PM, Jason Resch wrote:




On Sun, Dec 29, 2013 at 2:25 PM, meekerdb > wrote:


On 12/29/2013 5:56 AM, Bruno Marchal wrote:


On 28 Dec 2013, at 22:23, meekerdb wrote:


On 12/28/2013 4:09 AM, Bruno Marchal wrote:

For a long time I got opponent saying that we cannot generate 
computationally a
random number, and that is right, if we want generate only that numbers. 
but a
simple counting algorithm generating all numbers, 0, 1, 2,  
6999500235148668,
... generates all random finite incompressible strings,


How can a finite string be incompressible? 6999500235148668 in base
6999500235148669 is just 10.



You can define a finite string as incompressible when the shorter 
combinators to
generate it is as lengthy as the string itself.
This definition is not universal for a finite amount of short sequences 
which
indeed will depend of the language used (here combinators).

Then you can show that such a definition can be made universal by adding 
some
constant, which will depend of the universal language.

It can be shown that most (finite!) numbers, written in any base, are 
random in
that sense.

Of course, 10 is a sort of compression of any string X in some base, but if 
you
allow change of base, you will need to send the base with the number in the
message. If you fix the base, then indeed 10 will be a compression of that
particular number base, for that language, and it is part of 
incompressibility
theory that no definition exist working for all (small) numbers.


Since all finite numbers are small, I think this means the theory only 
holds in the
limit.

Brent



Brent,

It is easy to see with the pigeon hole principal.  There are more 2 digit numbers than 1 
digit numbers, and more 3 digit numbers than 2 digit numbers, and so on.  For any string 
you can represent using a shorter string, another "shorter string" must necessarily be 
displaced.  You can't keep replacing things with shorter strings because there aren't 
enough of them, so as a side-effect, every compression strategy must represent some 
strings by larger ones.  In fact, the average size of all possible compressed messages 
(with some upper-bound length n) can never be smaller than the average size of all 
uncompressed messages.


The only reason compression algorithms are useful is because they are tailored to 
represent some class of messages with shorter strings, while making (the vast majority 
of) other messages slightly larger.


A good explanation.  But just because you cannot compress all numbers of a given size 
doesn't imply that any particular number is incompressible.  So isn't it the case that 
every finite number string is compressible in some algorithm?  So there's no sense to 
saying 6999500235148668 is random, but 11 is not, except relative to some 
given compression algorithm.


Brent

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Re: Bruno's mathematical reality

On Sun, Dec 29, 2013 at 2:25 PM, meekerdb  wrote:

>  On 12/29/2013 5:56 AM, Bruno Marchal wrote:
>
>
>  On 28 Dec 2013, at 22:23, meekerdb wrote:
>
>  On 12/28/2013 4:09 AM, Bruno Marchal wrote:
>
> For a long time I got opponent saying that we cannot generate
> computationally a random number, and that is right, if we want generate
> only that numbers. but a simple counting algorithm generating all numbers,
> 0, 1, 2,  6999500235148668, ... generates all random finite
> incompressible strings,
>
>
> How can a finite string be incompressible?  6999500235148668 in base
> 6999500235148669 is just 10.
>
>
>
>  You can define a finite string as incompressible when the shorter
> combinators to generate it is as lengthy as the string itself.
> This definition is not universal for a finite amount of short sequences
> which indeed will depend of the language used (here combinators).
>
>  Then you can show that such a definition can be made universal by adding
> some constant, which will depend of the universal language.
>
>  It can be shown that most (finite!) numbers, written in any base, are
> random in that sense.
>
>  Of course, 10 is a sort of compression of any string X in some base, but
> if you allow change of base, you will need to send the base with the number
> in the message. If you fix the base, then indeed 10 will be a compression
> of that particular number base, for that language, and it is part of
> incompressibility theory that no definition exist working for all (small)
> numbers.
>
>
> Since all finite numbers are small, I think this means the theory only
> holds in the limit.
>
> Brent
>


Brent,

It is easy to see with the pigeon hole principal.  There are more 2 digit
numbers than 1 digit numbers, and more 3 digit numbers than 2 digit
numbers, and so on.  For any string you can represent using a shorter
string, another "shorter string" must necessarily be displaced.  You can't
keep replacing things with shorter strings because there aren't enough of
them, so as a side-effect, every compression strategy must represent some
strings by larger ones.  In fact, the average size of all possible
compressed messages (with some upper-bound length n) can never be smaller
than the average size of all uncompressed messages.

The only reason compression algorithms are useful is because they are
tailored to represent some class of messages with shorter strings, while
making (the vast majority of) other messages slightly larger.

Jason


>
>  Each particular language will have some exception on the
> incompressibility issue. That should be part of the role of the variable
> constant in the general universal definition.
>
>  Bruno
>
>
>
>
>http://iridia.ulb.ac.be/~marchal/
>
>
>
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Re: Bruno's mathematical reality


On 12/29/2013 5:56 AM, Bruno Marchal wrote:


On 28 Dec 2013, at 22:23, meekerdb wrote:


On 12/28/2013 4:09 AM, Bruno Marchal wrote:
For a long time I got opponent saying that we cannot generate computationally a random 
number, and that is right, if we want generate only that numbers. but a simple 
counting algorithm generating all numbers, 0, 1, 2,  6999500235148668, ... 
generates all random finite incompressible strings,


How can a finite string be incompressible? 6999500235148668 in base 6999500235148669 is 
just 10.



You can define a finite string as incompressible when the shorter combinators to 
generate it is as lengthy as the string itself.
This definition is not universal for a finite amount of short sequences which indeed 
will depend of the language used (here combinators).


Then you can show that such a definition can be made universal by adding some constant, 
which will depend of the universal language.


It can be shown that most (finite!) numbers, written in any base, are random in 
that sense.

Of course, 10 is a sort of compression of any string X in some base, but if you allow 
change of base, you will need to send the base with the number in the message. If you 
fix the base, then indeed 10 will be a compression of that particular number base, for 
that language, and it is part of incompressibility theory that no definition exist 
working for all (small) numbers.


Since all finite numbers are small, I think this means the theory only holds in 
the limit.

Brent

Each particular language will have some exception on the incompressibility issue. That 
should be part of the role of the variable constant in the general universal definition.


Bruno




http://iridia.ulb.ac.be/~marchal/ 



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Re: Bruno's mathematical reality



On 28 Dec 2013, at 22:23, meekerdb wrote:


On 12/28/2013 4:09 AM, Bruno Marchal wrote:
For a long time I got opponent saying that we cannot generate  
computationally a random number, and that is right, if we want  
generate only that numbers. but a simple counting algorithm  
generating all numbers, 0, 1, 2,  6999500235148668, ...  
generates all random finite incompressible strings,


How can a finite string be incompressible?  6999500235148668 in base  
6999500235148669 is just 10.



You can define a finite string as incompressible when the shorter  
combinators to generate it is as lengthy as the string itself.
This definition is not universal for a finite amount of short  
sequences which indeed will depend of the language used (here  
combinators).


Then you can show that such a definition can be made universal by  
adding some constant, which will depend of the universal language.


It can be shown that most (finite!) numbers, written in any base, are  
random in that sense.


Of course, 10 is a sort of compression of any string X in some base,  
but if you allow change of base, you will need to send the base with  
the number in the message. If you fix the base, then indeed 10 will be  
a compression of that particular number base, for that language, and  
it is part of incompressibility theory that no definition exist  
working for all (small) numbers. Each particular language will have  
some exception on the incompressibility issue. That should be part of  
the role of the variable constant in the general universal definition.


Bruno




http://iridia.ulb.ac.be/~marchal/



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Re: Bruno's mathematical reality



On 28 Dec 2013, at 22:19, meekerdb wrote:


On 12/28/2013 3:43 AM, Bruno Marchal wrote:


On 28 Dec 2013, at 04:36, Stephen Paul King wrote:





I loath Kronecker's claim! It is synonymous to "Man is the measure  
of all things".



What is his claim?  I am not familiar with it.

God created the Integers, all else is the invention of man.



"man is a measure of all things" is a quote from a french  
philosopher (I just forget right now his name) itself taken from a  
greek general, which cut the feet or head of all soldier having not  
the right size (!).  (Sorry for those vague memories, learn this in  
highschool)


"Man is the measure of all things." is usually attributed to  
Protagoras (a student of Plato).


Ah! Thanks. Protagoras is also the one asking if virtue are teachable.  
I define a virtue Protagorean when it is not teachable by words, but  
still by practice/example.





Procrustes, who stretched or chopped guests to fit his iron bed, was  
a metal smith, not a general.


OK, I remember! Thanks.








Now, of course, comp saves Kronecker from anthropomorphism, as with  
comp we can say that:
"God created the integers, all else is the invention of ...  
integers".


"Die ganze Zahl schuf der liebe Gott, alles Übrige ist Menschenwerk"
--- Kronecker



"Die ganze Zahl schuf der liebe Gott, alles Übrige ist Zahlenwerk"

:)

Bruno



http://iridia.ulb.ac.be/~marchal/



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Re: Bruno's mathematical reality



On 28 Dec 2013, at 22:12, meekerdb wrote:


On 12/28/2013 3:13 AM, Bruno Marchal wrote:
Perhaps; but only for nano second. you real mind overlap on  
sequence of states, with the right probabilities, and for this you  
need the complete run of the UD, because your next "moment" is  
determioned by the FPI on all computations.


That's a point that bothers me.  It seems that you require a  
completed, realized uncountable inifinity.



Not in the ontology, where I can use only 0 and its successors, and  
the numbers laws (+ and *).


What the theology and physics need from inside is indeed not bound- 
able, and is bigger than anything we can conceive. That is in part a  
reason why I use the term "theology". from inside arithmetic, we are  
eventually confronted with some thing very big.


Bruno










Brent

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http://iridia.ulb.ac.be/~marchal/



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Re: Bruno's mathematical reality



On 28 Dec 2013, at 18:43, Stephen Paul King wrote:


Dear Bruno,


On Sat, Dec 28, 2013 at 12:34 PM, Bruno Marchal   
wrote:


On 28 Dec 2013, at 07:34, LizR wrote:

On 28 December 2013 19:31, Stephen Paul King > wrote:

Computed how? By what?

I know the answer to this one! To quote Brent -- "He proposes to  
dispense with any physical computation and have the UD exist via  
arithmetical realism as an abstract, immaterial computation."


Assuming comp, there is not much choice in the matter. That is the  
point.


I will agree.



Above the substitution level: interaction between universal  
machines, including one apparently sustained from below the  
substitution level by the statistical interference between  
infinities of universal machines getting your actual states.


But the "actual states" are not just some random string from my  
point of view!



Nor for me. They are state brought by some computation above the S- 
level, and supported by infinitely many computation below the S-level.
The result is indeterminate, but not itself random. In The WM- 
duplication, the result is indeterminate or random, but W or M  
themselves are not random.






The very fact that we can (somewhat) communicate is an important  
fact. There is a selection mechanism: interaction.


That's part of the problem. Showing this.







I don't know how to avoid those infinities without reifying some God- 
of-the-gap or Matter-of-the-gap notion to singularize a computation  
for consciousness, but if that is needed for consciousness, then  
comp is false.


Umm, that is a false choice! The FPI is good enough to "do the job"  
without resorting to a 'god/matter in the gap" solution. The  
singularization of consciousness is easy, as you have shown.


No it is not! There is a lot of work to be done before we have a realm  
in which words like "interaction" can make sense.






It is the concurrent interaction problem that is not easy.


So let us concentrate on what is more easy first.




I cannot exactly predict your actions and thus can only "bet" on  
your future states, but I can constrain your possible choices of  
action with my physical behaviors even if the physical world is an  
illusion. The fact that it is a common and persistent illusion makes  
it a ground of commonality from which we can distinguish ourselves 3- 
p wise from each other.


We cannot use physics.







True, you still survive with a digital brain, but no more through  
comp, it is true from comp + some explicit magic to make disappear  
the other realities. You get an irrefutable form of cosmic solipsism.


There is no magic here, there is the SAT problem. Boolean algebras  
do not automatically pop out with global consistency over their  
arguments/propositions. One has to actually physically "run" a  
physical world to know what it will do. Claiming that it exists in  
Platonia is not a solution.


No, it is a problem. And thanks to the work done, it is (with comp) a  
problem in arithmetic. That is the result.


Bruno




http://iridia.ulb.ac.be/~marchal/



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Re: Bruno's mathematical reality



On 28 Dec 2013, at 18:10, Stephen Paul King wrote:


Dear Bruno,


On Sat, Dec 28, 2013 at 7:37 AM, Bruno Marchal   
wrote:


On 28 Dec 2013, at 05:27, LizR wrote:


On 28 December 2013 17:23, Edgar L. Owen  wrote:
Jason,

You might be able to theoretically simulate it but certainly not  
compute it in real time which is what reality actually does which  
is my point.


"In real time" ?! In comp (and many TOEs) time is emergent.


Physical times and subjective time emerge. OK. But let us be honest,  
comp assumes already a sort of time, through the natural order: à,  
1, 2, 3, ...


Then you have all UD-time step of the computations emulated by the UD:

phi_444(6) first step
...
phi_444(6) second step
... ...  (meaning greater delay  
in the UD-time steps).

ph_444(6) third  step
... ... ...
ph_444(6) fourth  step
  ... ...
ph_444(6) fifth step
etc.


This would explain the sequencing of events aspect of time, but it  
does nothing to address the concurrency problem.



Nor dark matter, nor visible matter, nor 

That is the problem I offer to you, as a result of the translation of  
he mind-body problem in arithmetic, enforced by the comp hypothesis.





We need a theory of time that has an explanation of both sequencing  
and transition. I wish you could study GR, say from Penrose's math  
book, and Prof. Hitoshi Kitada's Local Time interpretation of QM.


I did, and we have already discussed this. That can be used to  
progress, may be. If you find that it would be very nice.
Right now, we need to solve much more simpler problem in logic to  
proceed in a way such that we keep into account the communicable/non- 
communicable self-referential constraints, in the way imposed by the  
FPI.





  It gives a nice set of concepts that help solve the problem of  
time: there is no such thing as a "global" time; there is only local  
time. Local for each individual observer. Synchronizations of these  
local times generates the appearance of global time for a collection  
that is co-moving or (equivalently) have similar inertial frames.


That's physics. But physics is given by a precise equation in comp.   
You are free to use *any* papers and results to solve that equation.  
You need to study logic to make the link properly.


(Of course you can also do physics, without tackling the comp mind- 
body problem. That's what physicists do since a long time)


Bruno

http://iridia.ulb.ac.be/~marchal/



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Re: Bruno's mathematical reality



On 28 Dec 2013, at 17:43, Stephen Paul King wrote:


Dear Bruno,


On Sat, Dec 28, 2013 at 7:30 AM, Bruno Marchal   
wrote:


On 28 Dec 2013, at 05:27, Stephen Paul King wrote:


Hi LizR and Jason,

  Responding to both of you. I don't understand the claim of  
determinism is "random noise" is necessary for the computations.  
Turing machines require exact pre-specifiability. Adding noise  
oracles is cheating!


But it exist in arithmetic. Subtracting it would be cheating. the  
silmple counting algorith generates all random finite strings  
(random in the strong Chaitin sense).


Almost all numbers are random, when written in some base. And you  
can define the notion of base *in* arithmetic, so they exist in all  
models of arithmetic. We can't subtract them.


With respect: No! We cannot wait forever (literally) to obtain  
consistency of our data bases in the face of the inability to know  
in advance the arrival time of messages in the network.


  The fact that arithmetic "contains" all finite (even the random  
ones) strings is an ontological claim. I have no problem with the  
claim. My problem is that we cannot reason as if time does not exist  
when we are trying to construct real computers.


  We have to use different ideas, for example: competition for  
resources! Platonic computers do not compete for resources nor  
change. They are static and fixed eternally...


In God's eyes. We already know that from inside, except for the  
measure problem which remains to be solved, things look very dynamical  
and changing all the times. Bp & p is already a logic of (subjective)  
time. Bp & Dt gives a quantum logic, Bp & Dt & p gives a subjective or  
intuitionist quantum logic full of percepts including a time which can  
be felt.


It is a trivial exercise to show that all diophantine approximation of  
anything physical is emulated in arithmetic, so Platonia contains all  
possible competition on all conceivable resources, and actually  
anything that you can live, or not live, like the collision between  
the Milky Way and Andromeda is emulated statically in arithmetic, and  
lived temporally by its emulated persons.


Platonia is static from outside, not from inside. Arithmetic becomes a  
block universe(s), although it is more like a "block-mindscape" or a  
block multi-dreams".


Bruno



http://iridia.ulb.ac.be/~marchal/



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Re: Bruno's mathematical reality



On 28 Dec 2013, at 17:35, Stephen Paul King wrote:


Dear Bruno,


On Sat, Dec 28, 2013 at 7:09 AM, Bruno Marchal   
wrote:


On 28 Dec 2013, at 04:56, Jason Resch wrote:





On Fri, Dec 27, 2013 at 10:42 PM, Stephen Paul King > wrote:

Hi Jason,

"Any program, and whether or not it ever terminates can be  
translated to a statement concerning numbers in arithmetic. Thus  
mathematical truth captures the facts concerning whether or not any  
program executes forever, and what all of its intermediate states  
are. "


this also captures every instance of random numbers as well.

It is not clear to me what "random" means in arithmetical truth.

Randomness can appear from the perspectives of observers, but I  
don't see how it can arise in arithmetic.


?

It appears in all numbers written in any base. Most numbers are  
already random (even incompressible).
I guess you know that. In the phi_i(j) in the UD, randomness can  
appear in the many j used as input, as we usually dovetail on the  
function of one variable. (but such input can easily be internalized  
in 0-variable programs).


OK, I must agree, but can you see how this removes our ability to  
use the natural ordering of the integers as an explanation of the  
appearance of time?


Of the physical time? yes, that is right. That is a consequence of the  
delay invariance of the FPI.  But we can still use it indirectly. It  
is part of the additive-multiplicative structure of the numbers that  
we assume (through the numbers laws).




Since there are multiple and equivalent (as to their properties)  
sequences of integers that have very different orders relative to  
each other, if we use these ordering as our "time" we would have a  
different dimension of time for every one!


?
On the contrary. As you just said, the appearance of time is not  
dependent on that order.









For a long time I got opponent saying that we cannot generate  
computationally a random number, and that is right, if we want  
generate only that numbers. but a simple counting algorithm  
generating all numbers, 0, 1, 2,  6999500235148668, ...  
generates all random finite incompressible strings, and even all the  
infinite one (for the 1p view, notably).


In that (trivial) sense, arithmetic contains a lot of 3p randomness,  
even perhaps too much. Then 1p randomeness appears too, by the 1p  
indeterminacy (and that one is in the eyes of the machine).


Chaitin's results can also explain why we cannot filter out that 3p  
randomness from arithmetic.



Have you had any more thoughts on the "book keeping" problem we have  
discussed in the past?


Can you remind me? Thanks.

Bruno


http://iridia.ulb.ac.be/~marchal/



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Re: Bruno's mathematical reality

On 28 Dec 2013, at 17:30, Stephen Paul King wrote:

Dear Bruno,

On Sat, Dec 28, 2013 at 6:53 AM, Bruno Marchal
wrote:

On 28 Dec 2013, at 04:39, Stephen Paul King wrote:

Dear Jason,

ISTM that the line " For each program we have generated that has
not halted, execute one instruction of it for each (Program p in
listOfPrograms)" is buggy.

It assumes that the space of "programs that do not halt" is
accessible. How?

The space of all programs that do not halt is not Turing accessible.
The space of all programs that do halt is not Turing accessible.

The space of all programs (that do halt of do not halt) *is*
accessible.

Could you elaborate on this claim. I wish to be sure that I
understand it. Is it really a "space"?

It is a recursively enumerable set.

Would it have metrics and topological properties?

As a set, you can endow it with some structure, if you have the
motivation.

All what happen is that we have no general systematic,
computational, means to distinguish the programs that halt from the
programs that does not halt (on their inputs), and that is why the
universal dovetailer must *dovetail* on the executions of all
programs.

Not having a "general systematic, computational, means to
distinguish.." has not stopped Nature.

Nor the FPI. Right.

She solves the problem by the evolution of physical worlds.

That's too quick, especially that we don't assume "nature".

I propose that physical worlds ARE a form of non-universal
computation.

Then brain and computers cannot exist in those physical world.

I still think that the UD lives only in Platonia and is timeless and
static.

That's correct.

Only its "projections" (to use Plato's cave metaphor) are run as
physical worlds

OK. The "FPI" projections. But they are not "run", only selected. The
computation are run, not the projection from inside.

Bruno

if they can survive the challenge of mutual consistency.

Bruno

On Fri, Dec 27, 2013 at 10:09 PM, Jason Resch
wrote:

On Fri, Dec 27, 2013 at 9:31 PM, Stephen Paul King > wrote:

Hi Jason,

Could you discuss the "trace of the UD" that LizR mentioned? How
is it computed? Could you write an explicit example? I have never
been able to grok it.

Bruno has written an actual UD in the LISP programming language. I
will write a simple one in pseudo-code below:

List listOfPrograms = new List[]; # Empty list
int i = 0;
while (true)
{
# Create a program corresponding to the binary expansion of the
integer i

Program P = createProgramFromInteger(i);

# Add the program to a list of programs we have generated so far
listOfPrograms.add(P);

# For each program we have generated that has not halted,
execute one instruction of it

for each (Program p in listOfPrograms)
{
if (p.hasHalted() == false)
{
executeOneInstruction(p);
}
}

# Finally, increment i so a new program is generated the next
time through

i = i + 1;
}

Any program, and whether or not it ever terminates can be
translated to a statement concerning numbers in arithmetic. Thus
mathematical truth captures the facts concerning whether or not any
program executes forever, and what all of its intermediate states
are. If these statements are true independently of you and me, then
the executions of these programs are embedded in arithmetical truth
and have a platonic existence. The first, second, 10th,
1,000,000th, and 10^100th, and 10^100^100th state of the UD's
execution are mathematical facts which have definite values, and
all the conscious beings that are instantiated and evolve and write
books on consciousness, and talk about the UD on their Internet,
etc. as part of the execution of the UD are there, in the math.

Jason

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Re: Bruno's mathematical reality



On 28 Dec 2013, at 17:16, Stephen Paul King wrote:


Dear Bruno,


On Sat, Dec 28, 2013 at 4:54 AM, Bruno Marchal   
wrote:


On 27 Dec 2013, at 17:51, Stephen Paul King wrote:


Dear Bruno,


On Fri, Dec 27, 2013 at 11:11 AM, Bruno Marchal   
wrote:


On 25 Dec 2013, at 18:40, spudboy...@aol.com wrote:

Are we not presuming, structure, or a-priori, existence of  
something, doing this processing, this work?



In the UDA we assume a "Turing universal", or "sigma_1-complete"  
physical reality, in some local sense.



Could this "Turing universal/sigma_1-complete in a local sense" be  
the exact criteria required to define the observations 3- 
experiences of individuals or is it the 1-experiences of  
individuals (observers) in keeping with the definition of an  
observer as the intersection of infinitely many computations?


I think the UDA answers this question. You need Turing universality,  
but also the FPI, which in some sense comes from mechanism, but not  
necessarily "universality", which has, here, only an indirect  
relevance in the definition of what is a computation in arithmetic.


I suspect that the FPI results from the "underlap" or failure to  
reach exact overlap between observers. As if a small part of the  
computations that are observers is not universal. This would  
effectively induce FPI as any one observer would be forever unable  
to exactly match its experience of "being in the world" with that of  
another.


<,














We need this to just explain what is a computer, alias, universal  
machine, alias universal number (implemented or not in a physical  
reality).
Note that we do not assume a *primitive physical reality*. In comp,  
we are a priori agnostic on this. The UDA, still will explains that  
such "primitiveness" cannot solve the mind-body problem when made  
into a dogma/assumption-of-primitiveness.


It has always seemed to me that UDA cannot solve the mind-body  
problem strictly because it cannot comprehend the existence of  
"other minds".


UDA formulates the problem, and show how big the mind-body problem  
is, even before tackling the "other minds" problem. But something is  
said. In fact it is easy to derive from the UDA the following  
assertions:


comp + explicit non-solipsism entails sharable many words or a core  
linear physical reality.


I do not comprehend this. It is easy for us to "see" that solipsism  
is false,


?




but how can a computation "see" anything? I do not understand how it  
is that you can claim that computations will not be solipsistic by  
default.


The 1p is solipsist, but not in a public way, just in the trivial way  
that nobody can see that solipsism is false, as the dream argument  
justifies. Solipsism is irrefutable, and hopefully false.


Now, if you remember the definition of first person plural (which is  
just when different people enter the same annihilation-reconstitution  
box), if we add non solipsism, it means that when machine interact,  
they share the computations. So, the only way to avoid solipsism in  
comp, is that the measure is sharable by interacting machine, and so  
they have to live in a quantum-lile many worlds.










But comp in fact has to justify the non-solipsism, and this is begun  
through the nuance Bp & p versus Bp & Dt. Normally the linearity  
should allow the first person plural in the "& Dt" nuance case.


Exactly! I am looking forward to the explanation of this " nuance Bp  
& p versus Bp & Dt". :-


Keep in mind that UDA does not solve the problem, but formulate it.  
AUDA go more deep in a solution, and the shape of that solution  
(like UDA actually) provides already information contradicting the  
Aristotelian theology (used by atheists and the main part of  
institutionalized abramanic religion).


Sure. My main worry is that your wonderful result obtains at too  
high a price: the inability to even model interactions and time.



If you show that, you extend the UDA in a full proof refutation of  
comp. Good luck!
I thought this would be easy, but the simplicity of this is  
counterbalanced by the self-referential constraints. On p-sigma_1, we  
get already three arithmetical (quantum) quantizations.


Keep in mind that I offer a problem, not a solution (although I offer  
a path toward it, and some shaping of the possible solutions, notably  
that they belong to (neo)platonism and refute Aristotle).


Bruno







Bruno






Then in AUDA, keeping comp at the meta-level, I eliminate all  
assumptions above very elementary arithmetic (Robinson Arithmetic).


The little and big bangs, including the taxes, and why it hurts is  
derived from basically just


Kxy = x
Sxyz = xz(yz)

or just

x + 0 = x
x + s(y) = s(x + y)

 x *0 = 0
 x*s(y) = x*y + x





http://iridia.ulb.ac.be/~marchal/




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Re: Bruno's mathematical reality



On 28 Dec 2013, at 16:51, Jason Resch wrote:




On Dec 28, 2013, at 6:09 AM, Bruno Marchal  wrote:



On 28 Dec 2013, at 04:56, Jason Resch wrote:





On Fri, Dec 27, 2013 at 10:42 PM, Stephen Paul King > wrote:

Hi Jason,

"Any program, and whether or not it ever terminates can be  
translated to a statement concerning numbers in arithmetic. Thus  
mathematical truth captures the facts concerning whether or not  
any program executes forever, and what all of its intermediate  
states are. "


this also captures every instance of random numbers as well.

It is not clear to me what "random" means in arithmetical truth.

Randomness can appear from the perspectives of observers, but I  
don't see how it can arise in arithmetic.


?

It appears in all numbers written in any base. Most numbers are  
already random (even incompressible).

I guess you know that.


I agree most numbers are incompressible, but I was using random in a  
different sense than the unpredictability of the next digits of the  
number given previous ones.


OK. But in the iterated self-duplication, both form of indeterminacy  
can be mixed.






In the phi_i(j) in the UD, randomness can appear in the many j used  
as input, as we usually dovetail on the function of one variable.  
(but such input can easily be internalized in 0-variable programs).


For a long time I got opponent saying that we cannot generate  
computationally a random number, and that is right, if we want  
generate only that numbers.


Right, all the random numbers are there, the question is how to  
throw the dart so that it lands on one.


Of course. And here the 1-indetermlinacy provides one answer.





but a simple counting algorithm generating all numbers, 0, 1,  
2,  6999500235148668, ... generates all random finite  
incompressible strings, and even all the infinite one (for the 1p  
view, notably).


I think we are using the term in a slightly different sense.   
Certainly any number in the range 1 - N can be considered as a  
random number in that range (as it is a candidate to be output by  
some RNG), but the problem is selecting it in a random (in the sense  
of not-predictable) way.


Yes. here I just point on the fact that random number (with random  
digits) exists.






There was a joke cartoon of some computer code:

int getRandomNumber()
{
  return 4; // this number was determined by a random die roll
}



Lol
Close to my favorite infinite binary random sequence:
...

The term "random" is very large.





While a number can be interpreted as random once, it might not be  
the second time.


While selecting and using all possibilities is arguably a way to  
achieve randomness (unpredictibilty), (from some points of view) it  
is often not practical nor useful.  Consider encrypting a message  
with all possible keys and sending the recipient all possible  
messages.


Not only might you need to send 2^256 possible ciphertexts but any  
eavesdropper could use the first possible key to decrypt it. This  
achieves randomness from the POV of the cipher, but not for the user  
or the attackers.


In quantum cryptography this is essentially what is done, but it  
requires that the sender and reciever (and attackers) be duplicated  
for each possible key. So they need to be embedded in that larger  
program that provides all possible inputs for it to seem random.  
This is just FPI though, is it not?


Yes.

Bruno





Jason



In that (trivial) sense, arithmetic contains a lot of 3p  
randomness, even perhaps too much. Then 1p randomeness appears too,  
by the 1p indeterminacy (and that one is in the eyes of the machine).


Chaitin's results can also explain why we cannot filter out that 3p  
randomness from arithmetic.


Bruno




What method is deployed to ensure that a program is not just a  
"regular" random number and not some random number prefixed on a  
"real" halting program?


It don't see how it makes a difference.


Truth is not a measure zero set, or is it?

I don't understand this question..  Could you clarify?

Jason




On Fri, Dec 27, 2013 at 10:09 PM, Jason Resch  
 wrote:




On Fri, Dec 27, 2013 at 9:31 PM, Stephen Paul King > wrote:

Hi Jason,

  Could you discuss the "trace of the UD" that LizR mentioned? How  
is it computed? Could you write an explicit example? I have never  
been able to grok it.



Bruno has written an actual UD in the LISP programming language.   
I will write a simple one in pseudo-code below:


List listOfPrograms = new List[]; # Empty list
int i = 0;
while (true)
{
   # Create a program corresponding to the binary expansion of the  
integer i

   Program P = createProgramFromInteger(i);

   # Add the program to a list of programs we have generated so far
   listOfPrograms.add(P);

   # For each program we have generated that has not halted,  
execute one instruction of it

   for each (Program p in listOfPrograms)
   {
 if (p.hasHalted() == fa

Re: Bruno's mathematical reality

On Sat, Dec 28, 2013 at 8:35 PM, meekerdb  wrote:

>  On 12/28/2013 4:47 PM, Jason Resch wrote:
>
>
>
>
> On Sat, Dec 28, 2013 at 6:52 PM, meekerdb  wrote:
>
>>   On 12/28/2013 3:00 PM, Jason Resch wrote:
>>
>>
>>
>>
>> On Sat, Dec 28, 2013 at 4:23 PM, meekerdb  wrote:
>>
>>>  On 12/28/2013 4:09 AM, Bruno Marchal wrote:
>>>
>>> For a long time I got opponent saying that we cannot generate
>>> computationally a random number, and that is right, if we want generate
>>> only that numbers. but a simple counting algorithm generating all numbers,
>>> 0, 1, 2,  6999500235148668, ... generates all random finite
>>> incompressible strings,
>>>
>>>
>>>  How can a finite string be incompressible?  6999500235148668 in base
>>> 6999500235148669 is just 10.
>>>
>>
>>  It took you 2 more digits to represent that number in that way.
>>
>>
>>  But I wouldn't have if everybody knew that our numbering system was
>> base 6999500235148669.
>>
>
>  You should patent this and sell the compression algorithm to youtube. :-)
>
>
> Actually it's a commonly used one.  It's a one-time-pad; you and your
> communicant agree before hand on the basis or the pad and then you only
> have to send 10 to communicate 6999500235148668.  It's the most secure form
> of cryptography.
>

Agreeing on a base wouldn't enable you to send a message securely if you
are constrained to sending "10". With OTPs, you agree on the pad
beforehand, then combine the pad with the message before sending it where
it can be de-combined.  In your example there is no act of combining or
de-combining involved.

Jason

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Re: Bruno's mathematical reality


On 12/28/2013 4:47 PM, Jason Resch wrote:




On Sat, Dec 28, 2013 at 6:52 PM, meekerdb > wrote:


On 12/28/2013 3:00 PM, Jason Resch wrote:




On Sat, Dec 28, 2013 at 4:23 PM, meekerdb mailto:meeke...@verizon.net>> wrote:

On 12/28/2013 4:09 AM, Bruno Marchal wrote:

For a long time I got opponent saying that we cannot generate 
computationally
a random number, and that is right, if we want generate only that 
numbers. but
a simple counting algorithm generating all numbers, 0, 1, 2, 
6999500235148668, ... generates all random finite incompressible 
strings,


How can a finite string be incompressible? 6999500235148668 in base
6999500235148669 is just 10.


It took you 2 more digits to represent that number in that way.


But I wouldn't have if everybody knew that our numbering system was base
6999500235148669.


You should patent this and sell the compression algorithm to youtube. :-)


Actually it's a commonly used one.  It's a one-time-pad; you and your communicant agree 
before hand on the basis or the pad and then you only have to send 10 to communicate 
6999500235148668.  It's the most secure form of cryptography.


Brent

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Re: Bruno's mathematical reality

On Sat, Dec 28, 2013 at 6:52 PM, meekerdb  wrote:

>  On 12/28/2013 3:00 PM, Jason Resch wrote:
>
>
>
>
> On Sat, Dec 28, 2013 at 4:23 PM, meekerdb  wrote:
>
>>  On 12/28/2013 4:09 AM, Bruno Marchal wrote:
>>
>> For a long time I got opponent saying that we cannot generate
>> computationally a random number, and that is right, if we want generate
>> only that numbers. but a simple counting algorithm generating all numbers,
>> 0, 1, 2,  6999500235148668, ... generates all random finite
>> incompressible strings,
>>
>>
>>  How can a finite string be incompressible?  6999500235148668 in base
>> 6999500235148669 is just 10.
>>
>
>  It took you 2 more digits to represent that number in that way.
>
>
> But I wouldn't have if everybody knew that our numbering system was base
> 6999500235148669.
>

You should patent this and sell the compression algorithm to youtube. :-)

Jason

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Re: Bruno's mathematical reality


On 12/28/2013 3:00 PM, Jason Resch wrote:




On Sat, Dec 28, 2013 at 4:23 PM, meekerdb > wrote:


On 12/28/2013 4:09 AM, Bruno Marchal wrote:

For a long time I got opponent saying that we cannot generate 
computationally a
random number, and that is right, if we want generate only that numbers. 
but a
simple counting algorithm generating all numbers, 0, 1, 2,  
6999500235148668,
... generates all random finite incompressible strings,


How can a finite string be incompressible? 6999500235148668 in base 
6999500235148669
is just 10.


It took you 2 more digits to represent that number in that way.


But I wouldn't have if everybody knew that our numbering system was base 
6999500235148669.

Brent
"There are only 10 kind of people in the world. Those who think in binary and those who 
don't."


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Re: Bruno's mathematical reality

On Sat, Dec 28, 2013 at 4:23 PM, meekerdb  wrote:

>  On 12/28/2013 4:09 AM, Bruno Marchal wrote:
>
> For a long time I got opponent saying that we cannot generate
> computationally a random number, and that is right, if we want generate
> only that numbers. but a simple counting algorithm generating all numbers,
> 0, 1, 2,  6999500235148668, ... generates all random finite
> incompressible strings,
>
>
> How can a finite string be incompressible?  6999500235148668 in base
> 6999500235148669 is just 10.
>

It took you 2 more digits to represent that number in that way.

Jason

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Re: Bruno's mathematical reality

2013-12-28 Thread LizR

On 29 December 2013 00:26, Bruno Marchal  wrote:

>
> On 28 Dec 2013, at 03:53, Jason Resch wrote:
>
>
>
>
>> Would any "universal number do"?
>>
>
> That is what Bruno speculatively has suggested. I am not so sure.
> Sometimes I think an "if-then-else-statement" contains all that is
> fundamentally required for consciousness, or at least, to be an atom of
> consciousness.
>
>
> As the base of the UD, any universal numbers will do. That is why I can
> chose arithmetic or combinators etc.
> For raw consciousness, I am prety sure that universality is already too
> much, now just "if then else" might be not enough, I don't know, and I
> don't thinks it is important. I will not found a society to protect the
> private life of thermostat. I think.
>

Fair dos for thermostats! Like us, they have their ups and downs...

(Or is that thermometers?)

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Re: Bruno's mathematical reality


On 12/28/2013 4:37 AM, Bruno Marchal wrote:


On 28 Dec 2013, at 05:27, LizR wrote:

On 28 December 2013 17:23, Edgar L. Owen mailto:edgaro...@att.net>> 
wrote:


Jason,

You might be able to theoretically simulate it but certainly not compute it 
in real
time which is what reality actually does which is my point.

"In real time" ?! In comp (and many TOEs) time is emergent.


Physical times and subjective time emerge. OK. But let us be honest, comp assumes 
already a sort of time, through the natural order: à, 1, 2, 3, ...


Then you have all UD-time step of the computations emulated by the UD:

phi_444(6) first step
...
phi_444(6) second step
... ...  (meaning greater delay in the 
UD-time steps).
ph_444(6) third  step
... ... ...
ph_444(6) fourth  step
  ... ...
ph_444(6) fifth step
etc.



To take a parallel example that should be close to your heart, suppose you're an AI 
living in the matrix and it's simulating reality for you. You aren't aware of this but 
believe yourself to be say a human writer who is participating in an online discussion. 
Suppose it takes a million years to simulate one second of your experience. How would 
you know? You can only compare your experience of time with in-matrix clocks, which all 
run at the speed you'd expect.


It's the same for any theory which tries to compute reality.


But the physical time is not Turing emulable, and perhaps is not even existing, like in 
Dewitt-Wheeler equation: H = 0.
if it exist, it depends on all computations "instantaneously", by the delay invariance 
of the FPI.


Which seems like a flaw in trying to recover physics from comp - but maybe not, physics 
has it's own problems with time.


Brent

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Re: Bruno's mathematical reality


On 12/28/2013 4:09 AM, Bruno Marchal wrote:
For a long time I got opponent saying that we cannot generate computationally a random 
number, and that is right, if we want generate only that numbers. but a simple counting 
algorithm generating all numbers, 0, 1, 2,  6999500235148668, ... generates all 
random finite incompressible strings,


How can a finite string be incompressible? 6999500235148668 in base 6999500235148669 is 
just 10.


Brent

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Re: Bruno's mathematical reality


On 12/28/2013 3:43 AM, Bruno Marchal wrote:


On 28 Dec 2013, at 04:36, Stephen Paul King wrote:



I loath Kronecker's claim! It is synonymous to "Man is the measure of all 
things".


What is his claim?  I am not familiar with it.


God created the Integers, all else is the invention of man.



"man is a measure of all things" is a quote from a french philosopher (I just forget 
right now his name) itself taken from a greek general, which cut the feet or head of all 
soldier having not the right size (!).  (Sorry for those vague memories, learn this in 
highschool)


"Man is the measure of all things." is usually attributed to Protagoras (a 
student of Plato).
Procrustes, who stretched or chopped guests to fit his iron bed, was a metal smith, not a 
general.




Now, of course, comp saves Kronecker from anthropomorphism, as with comp we can 
say that:
"God created the integers, all else is the invention of ... integers".


"Die ganze Zahl schuf der liebe Gott, alles Übrige ist Menschenwerk"
--- Kronecker

Brent



Of course it made comp number-centered, but this we knew at the start with comp, and ... 
with christianism, in which it is important to realize our finiteness.


Bruno

http://iridia.ulb.ac.be/~marchal/ 



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Re: Bruno's mathematical reality


On 12/28/2013 3:13 AM, Bruno Marchal wrote:
Perhaps; but only for nano second. you real mind overlap on sequence of states, with the 
right probabilities, and for this you need the complete run of the UD, because your next 
"moment" is determioned by the FPI on all computations.


That's a point that bothers me.  It seems that you require a completed, realized 
uncountable inifinity.


Brent

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Re: Bruno's mathematical reality

Dear Bruno,

On Sat, Dec 28, 2013 at 12:34 PM, Bruno Marchal  wrote:

>
> On 28 Dec 2013, at 07:34, LizR wrote:
>
> On 28 December 2013 19:31, Stephen Paul King 
> wrote:
>
>> Computed how? By what?
>>
>
> I know the answer to this one! To quote Brent -- "He proposes to dispense
> with any physical computation and have the UD exist via arithmetical
> realism as an abstract, immaterial computation."
>
>
> Assuming comp, there is not much choice in the matter. That is the point.
>

I will agree.

>
> Above the substitution level: interaction between universal machines,
> including one apparently sustained from below the substitution level by the
> statistical interference between infinities of universal machines getting
> your actual states.
>

But the "actual states" are not just some random string from my point of
view! The very fact that we can (somewhat) communicate is an important
fact. There is a selection mechanism: interaction.

>
> I don't know how to avoid those infinities without reifying some
> God-of-the-gap or Matter-of-the-gap notion to singularize a computation for
> consciousness, but if that is needed for consciousness, then comp is false.
>

Umm, that is a false choice! The FPI is good enough to "do the job"
without resorting to a 'god/matter in the gap" solution. The
singularization of consciousness is easy, as you have shown. It is the
concurrent interaction problem that is not easy. I cannot exactly predict
your actions and thus can only "bet" on your future states, but I can
constrain your possible choices of action with my physical behaviors even
if the physical world is an illusion. The fact that it is a common and
persistent illusion makes it a ground of commonality from which we can
distinguish ourselves 3-p wise from each other.

> True, you still survive with a digital brain, but no more through comp, it
> is true from comp + some explicit magic to make disappear the other
> realities. You get an irrefutable form of cosmic solipsism.
>

There is no magic here, there is the SAT problem. Boolean algebras do not
automatically pop out with global consistency over their
arguments/propositions. One has to actually physically "run" a physical
world to know what it will do. Claiming that it exists in Platonia is not
a solution.

>
> Bruno
>
>
>
>
>
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Re: Bruno's mathematical reality



On 28 Dec 2013, at 07:34, LizR wrote:

On 28 December 2013 19:31, Stephen Paul King > wrote:

Computed how? By what?

I know the answer to this one! To quote Brent -- "He proposes to  
dispense with any physical computation and have the UD exist via  
arithmetical realism as an abstract, immaterial computation."


Assuming comp, there is not much choice in the matter. That is the  
point.


Above the substitution level: interaction between universal machines,  
including one apparently sustained from below the substitution level  
by the statistical interference between infinities of universal  
machines getting your actual states.


I don't know how to avoid those infinities without reifying some God- 
of-the-gap or Matter-of-the-gap notion to singularize a computation  
for consciousness, but if that is needed for consciousness, then comp  
is false. True, you still survive with a digital brain, but no more  
through comp, it is true from comp + some explicit magic to make  
disappear the other realities. You get an irrefutable form of cosmic  
solipsism.


Bruno






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Re: Bruno's mathematical reality

Dear Bruno,

On Sat, Dec 28, 2013 at 7:37 AM, Bruno Marchal  wrote:

>
> On 28 Dec 2013, at 05:27, LizR wrote:
>
> On 28 December 2013 17:23, Edgar L. Owen  wrote:
>
>> Jason,
>>
>> You might be able to theoretically simulate it but certainly not compute
>> it in real time which is what reality actually does which is my point.
>>
>> "In real time" ?! In comp (and many TOEs) time is emergent.
>
>
> Physical times and subjective time emerge. OK. But let us be honest, comp
> assumes already a sort of time, through the natural order: à, 1, 2, 3, ...
>
> Then you have all UD-time step of the computations emulated by the UD:
>
> phi_444(6) first step
> ...
> phi_444(6) second step
> ... ...  (meaning greater delay in the
> UD-time steps).
> ph_444(6) third  step
> ... ... ...
> ph_444(6) fourth  step
>   ... ...
> ph_444(6) fifth step
> etc.
>
>
This would explain the sequencing of events aspect of time, but it does
nothing to address the concurrency problem. We need a theory of time that
has an explanation of both sequencing and transition. I wish you could
study GR, say from Penrose's math book, and Prof. Hitoshi Kitada's Local
Time interpretation of QM.
  It gives a nice set of concepts that help solve the problem of time:
there is no such thing as a "global" time; there is only local time. Local
for each individual observer. Synchronizations of these local times
generates the appearance of global time for a collection that is co-moving
or (equivalently) have similar inertial frames.

>
>
> To take a parallel example that should be close to your heart, suppose
> you're an AI living in the matrix and it's simulating reality for you. You
> aren't aware of this but believe yourself to be say a human writer who is
> participating in an online discussion. Suppose it takes a million years to
> simulate one second of your experience. How would you know? You can only
> compare your experience of time with in-matrix clocks, which all run at the
> speed you'd expect.
>
> It's the same for any theory which tries to compute reality.
>
>
> But the physical time is not Turing emulable, and perhaps is not even
> existing, like in Dewitt-Wheeler equation: H = 0.
>

Indeed! The common idea of "physical time" is an illusion! See: 
http://arxiv.org/abs/gr-qc/9408027

What is and What should be Time?
Hitoshi Kitada ,
Lancelot
R. Fletcher 
(Submitted on 20 Aug 1994 (v1 ), last
revised 16 Mar 1996 (this version, v4))

The notions of time in the theories of Newton and Einstein are reviewed so
that certain of their assumptions are clarified. These assumptions will be
seen as the causes of the incompatibility between the two different ways of
understanding time, and seen to be philosophical hypotheses, rather than
purely scientific ones. The conflict between quantum mechanics and
(general) relativity is shown to be a consequence of retaining the
Newtonian conception of time in the context of quantum mechanics. As a
remedy for this conflict, an alternative definition of time -- earlier
presented in Kitada 1994a and 1994b -- is reviewed with less mathematics
and more emphasis on its philosophical aspects. Based on this revised
understanding of time it is shown that quantum mechanics and general
relativity are reconciled while preserving the current mathematical
formulations of both theories.

> if it exist, it depends on all computations "instantaneously", by the
> delay invariance of the FPI.
>
> Bruno
>
>
>
> http://iridia.ulb.ac.be/~marchal/
>
>
>
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Re: Bruno's mathematical reality



On 28 Dec 2013, at 07:30, meekerdb wrote:


On 12/27/2013 8:24 PM, Stephen Paul King wrote:

Hi Edgar,

  But here is the thing. If we assume timelessness, Bruno is  
CORRECT! THe question then becomes: What is "time"?


It's a computed partial ordering relation between events.


The 1p time looks like that, but this is of course still an open  
problem (both in comp and physics, I would say).


Such partial ordering gives models of the S4Grz logic (Bp & p).  It is  
more the subjective time than the physical time, which is just not on  
a comp horizon soon.


Bruno






Brent

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Re: Bruno's mathematical reality



On 28 Dec 2013, at 07:26, meekerdb wrote:

He proposes to dispense with any physical computation and have the  
UD exist via arithmetical realism as an abstract, immaterial  
computation.


What does a physicist? It looks outside, and seem to be believe in a  
special unique universal number, the physical TOE, describing what he  
observed.


But comp say that if we share realities, like Everett QM seems to  
suggest, then we share a rather low comp substitution level, and that  
below it we should see the trace of the interference of the infinitely  
many computations in arithmetic.


What we need to do is to compare the quantum observed multiverse with  
the comp multi-dream which is inside the head of all universal  
numbers. (That is begun in AUDA).


Bruno

http://iridia.ulb.ac.be/~marchal/



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Re: Bruno's mathematical reality

Dear Bruno,


On Sat, Dec 28, 2013 at 7:30 AM, Bruno Marchal  wrote:

>
> On 28 Dec 2013, at 05:27, Stephen Paul King wrote:
>
> Hi LizR and Jason,
>
>   Responding to both of you. I don't understand the claim of determinism
> is "random noise" is necessary for the computations. Turing machines
> require exact pre-specifiability. Adding noise oracles is cheating!
>
>
> But it exist in arithmetic. Subtracting it would be cheating. the silmple
> counting algorith generates all random finite strings (random in the strong
> Chaitin sense).
>
> Almost all numbers are random, when written in some base. And you can
> define the notion of base *in* arithmetic, so they exist in all models of
> arithmetic. We can't subtract them.
>

With respect: No! We cannot wait forever (literally) to obtain consistency
of our data bases in the face of the inability to know in advance the
arrival time of messages in the network.

  The fact that arithmetic "contains" all finite (even the random ones)
strings is an ontological claim. I have no problem with the claim. My
problem is that we cannot reason as if time does not exist when we are
trying to construct real computers.

  We have to use different ideas, for example: competition for resources!
Platonic computers do not compete for resources nor change. They are static
and fixed eternally...



>
> Bruno
>
>
>
>
>
>
> On Fri, Dec 27, 2013 at 11:22 PM, LizR  wrote:
>
>> On 28 December 2013 17:15, Jason Resch  wrote:
>>
>>> On Fri, Dec 27, 2013 at 11:06 PM, LizR  wrote:
>>>
 Clearly programmes don't have to be deterministic. They could contain a
 source of genuine randomness, in principle.

>>>
>>> That source, if it is within the program, would necessarily be
>>> deterministic.  If it is external to the program, then it is more properly
>>> treated as an input to the program rather than a part of the program itself.
>>>
>>> In practice, computers draw on sources of environmental noise such as
>>> delays between keystrokes, timing of the reception of network traffic, and
>>> delays in accessing data off of hard drives, etc. These steps are necessary
>>> precisely because programs cannot produce randomness on their own.
>>>
>>> I knew that - honest! :-)
>>
>> I was answering the question as posed. I believe that in practice all
>> real-world programmes are deterministic, and (more to the point) the UD is.
>>
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>
>
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Re: Bruno's mathematical reality

Dear Bruno,


On Sat, Dec 28, 2013 at 7:17 AM, Bruno Marchal  wrote:

>
> On 28 Dec 2013, at 05:03, Stephen Paul King wrote:
>
> I ask this because I am studying Carl Hewitt's Actor Model...
>
>
> Also know today as "object oriented" languages. c++ win against smaltalk,
> which won against the Actor model, but the idea is the same, basically. It
> is efficacious, but the math and semantics is still unclear to me. It is a
> sort of vague polymorphic lambda calculus. I did love a long time ago, the
> "actor model". It is somewhat psychologically sad that the term "object"
> replaced the term "actor".
>

Yes, Carl Hewitt claims that the Actor model has unbounded indeterminacy
as it does not assume an upper bound on the length of a path of a message
from one actor to another. We see this as a security feature, not a
problem. Our goal is "inherently secure" computation. We are using Marius
Buliga's "graphic lambda calculus" that very elegantly allows for the
construction of topological graphs that are both models of computation and
computer programs via a natural graph rewrite scheme.




>
> bruno
>
>
>
> On Fri, Dec 27, 2013 at 11:03 PM, Stephen Paul King <
> stephe...@provensecure.com> wrote:
>
>> Hi jason,
>>
>>   Do programs have to be "deterministic". What definition of
>> deterministic are you using?
>>
>>
>> On Fri, Dec 27, 2013 at 11:00 PM, Jason Resch wrote:
>>
>>>
>>>
>>>
>>> On Fri, Dec 27, 2013 at 10:54 PM, LizR  wrote:
>>>
 On 28 December 2013 16:44, Stephen Paul King <
 stephe...@provensecure.com> wrote:

> Hi Jason,
>
> "The first, second, 10th, 1,000,000th, and 10^100th, and 10^100^100th
> state of the UD's execution are mathematical facts ..." Umm, how?
> Godel and Matiyasevich would disagree! If there does not exist a program
> that can evaluate whether or not a UD substring is a faithful
> representation of a "true theorem", then how is it "a fact"?
>
> That depends on whether the UD is deterministic or not.

>>>
>>> It is. The evolution of any Turing machines is deterministic.
>>>
>>>
 If it is, then, its Nth state is a fact. (It doesn't need to be run or
 evaluated, and the Nth state may be a fact that nobody knows, like the
 googolth digit of pi, assuming no one's worked that out.)

>>>
>>> Right. :-)
>>>
>>> The fact that I remember drinking a glass of water is as much a
>>> mathematical fact about the UD, as the fact as the third decimal digit of
>>> Pi is 4.
>>>
>>> Jason
>>>
>>>
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Re: Bruno's mathematical reality



On 28 Dec 2013, at 07:35, Stephen Paul King wrote:

An observer can only experience a "reality" that is not  
contradictory to its existence.


Tell this to the dictators.

Usually a reality guarantied some local consistency by definition of a  
reality (modeled by the notion of models in logic).


Bruno




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Re: Bruno's mathematical reality

Dear Bruno,


On Sat, Dec 28, 2013 at 7:09 AM, Bruno Marchal  wrote:

>
> On 28 Dec 2013, at 04:56, Jason Resch wrote:
>
>
>
>
> On Fri, Dec 27, 2013 at 10:42 PM, Stephen Paul King <
> stephe...@provensecure.com> wrote:
>
>> Hi Jason,
>>
>> "Any program, and whether or not it ever terminates can be translated to
>> a statement concerning numbers in arithmetic. Thus mathematical truth
>> captures the facts concerning whether or not any program executes forever,
>> and what all of its intermediate states are.
>> "
>>
>> this also captures every instance of random numbers as well.
>>
>
> It is not clear to me what "random" means in arithmetical truth.
>
> Randomness can appear from the perspectives of observers, but I don't see
> how it can arise in arithmetic.
>
>
> ?
>
> It appears in all numbers written in any base. Most numbers are already
> random (even incompressible).
> I guess you know that. In the phi_i(j) in the UD, randomness can appear in
> the many j used as input, as we usually dovetail on the function of one
> variable. (but such input can easily be internalized in 0-variable
> programs).
>

OK, I must agree, but can you see how this removes our ability to use the
natural ordering of the integers as an explanation of the appearance of
time? Since there are multiple and equivalent (as to their properties)
sequences of integers that have very different orders relative to each
other, if we use these ordering as our "time" we would have a different
dimension of time for every one!



>
> For a long time I got opponent saying that we cannot generate
> computationally a random number, and that is right, if we want generate
> only that numbers. but a simple counting algorithm generating all numbers,
> 0, 1, 2,  6999500235148668, ... generates all random finite
> incompressible strings, and even all the infinite one (for the 1p view,
> notably).
>
> In that (trivial) sense, arithmetic contains a lot of 3p randomness, even
> perhaps too much. Then 1p randomeness appears too, by the 1p indeterminacy
> (and that one is in the eyes of the machine).
>
> Chaitin's results can also explain why we cannot filter out that 3p
> randomness from arithmetic.
>


Have you had any more thoughts on the "book keeping" problem we have
discussed in the past?



>
> Bruno
>
>
>
>
>> What method is deployed to ensure that a program is not just a "regular"
>> random number and not some random number prefixed on a "real" halting
>> program?
>>
>
> It don't see how it makes a difference.
>
>
>>
>> Truth is not a measure zero set, or is it?
>>
>
> I don't understand this question..  Could you clarify?
>
> Jason
>
>
>>
>>
>>
>> On Fri, Dec 27, 2013 at 10:09 PM, Jason Resch wrote:
>>
>>>
>>>
>>>
>>> On Fri, Dec 27, 2013 at 9:31 PM, Stephen Paul King <
>>> stephe...@provensecure.com> wrote:
>>>
 Hi Jason,

   Could you discuss the "trace of the UD" that LizR mentioned? How is
 it computed? Could you write an explicit example? I have never been able to
 grok it.


>>> Bruno has written an actual UD in the LISP programming language.  I will
>>> write a simple one in pseudo-code below:
>>>
>>> List listOfPrograms = new List[]; # Empty list
>>> int i = 0;
>>> while (true)
>>> {
>>># Create a program corresponding to the binary expansion of the
>>> integer i
>>>Program P = createProgramFromInteger(i);
>>>
>>># Add the program to a list of programs we have generated so far
>>>listOfPrograms.add(P);
>>>
>>># For each program we have generated that has not halted, execute one
>>> instruction of it
>>>for each (Program p in listOfPrograms)
>>>{
>>>  if (p.hasHalted() == false)
>>>  {
>>> executeOneInstruction(p);
>>>  }
>>>}
>>>
>>># Finally, increment i so a new program is generated the next time
>>> through
>>>i = i + 1;
>>> }
>>>
>>>
>>> Any program, and whether or not it ever terminates can be translated to
>>> a statement concerning numbers in arithmetic. Thus mathematical truth
>>> captures the facts concerning whether or not any program executes forever,
>>> and what all of its intermediate states are. If these statements are true
>>> independently of you and me, then the executions of these programs are
>>> embedded in arithmetical truth and have a platonic existence.  The first,
>>> second, 10th, 1,000,000th, and 10^100th, and 10^100^100th state of the UD's
>>> execution are mathematical facts which have definite values, and all the
>>> conscious beings that are instantiated and evolve and write books on
>>> consciousness, and talk about the UD on their Internet, etc. as part of the
>>> execution of the UD are there, in the math.
>>>
>>> Jason
>>>
>>>
>>>
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Re: Bruno's mathematical reality

Dear Bruno,


On Sat, Dec 28, 2013 at 6:53 AM, Bruno Marchal  wrote:

>
> On 28 Dec 2013, at 04:39, Stephen Paul King wrote:
>
> Dear Jason,
>
>   ISTM that the line " For each program we have generated that has not
> halted, execute one instruction of it for each (Program p in
> listOfPrograms)" is buggy.
>
> It assumes that the space of "programs that do not halt" is accessible.
> How?
>
>
> The space of all programs that do not halt is not Turing accessible.
> The space of all programs that do halt is not Turing accessible.
>
> The space of all programs (that do halt of do not halt) *is* accessible.
>

Could you elaborate on this claim. I wish to be sure that I understand
it. Is it really a "space"? Would it have metrics and topological
properties?



>
> All what happen is that we have no general systematic, computational,
> means to distinguish the programs that halt from the programs that does not
> halt (on their inputs), and that is why the universal dovetailer must
> *dovetail* on the executions of all programs.
>

Not having a "general systematic, computational, means to distinguish.."
has not stopped Nature. She solves the problem by the evolution of physical
worlds. I propose that physical worlds ARE a form of non-universal
computation.

I still think that the UD lives only in Platonia and is timeless and
static. Only its "projections" (to use Plato's cave metaphor) are run as
physical worlds if they can survive the challenge of mutual consistency.



>
> Bruno
>
>
>
>
>
> On Fri, Dec 27, 2013 at 10:09 PM, Jason Resch wrote:
>
>>
>>
>>
>> On Fri, Dec 27, 2013 at 9:31 PM, Stephen Paul King <
>> stephe...@provensecure.com> wrote:
>>
>>> Hi Jason,
>>>
>>>   Could you discuss the "trace of the UD" that LizR mentioned? How is it
>>> computed? Could you write an explicit example? I have never been able to
>>> grok it.
>>>
>>>
>> Bruno has written an actual UD in the LISP programming language.  I will
>> write a simple one in pseudo-code below:
>>
>> List listOfPrograms = new List[]; # Empty list
>> int i = 0;
>> while (true)
>> {
>># Create a program corresponding to the binary expansion of the
>> integer i
>>Program P = createProgramFromInteger(i);
>>
>># Add the program to a list of programs we have generated so far
>>listOfPrograms.add(P);
>>
>># For each program we have generated that has not halted, execute one
>> instruction of it
>>for each (Program p in listOfPrograms)
>>{
>>  if (p.hasHalted() == false)
>>  {
>> executeOneInstruction(p);
>>  }
>>}
>>
>># Finally, increment i so a new program is generated the next time
>> through
>>i = i + 1;
>> }
>>
>>
>> Any program, and whether or not it ever terminates can be translated to a
>> statement concerning numbers in arithmetic. Thus mathematical truth
>> captures the facts concerning whether or not any program executes forever,
>> and what all of its intermediate states are. If these statements are true
>> independently of you and me, then the executions of these programs are
>> embedded in arithmetical truth and have a platonic existence.  The first,
>> second, 10th, 1,000,000th, and 10^100th, and 10^100^100th state of the UD's
>> execution are mathematical facts which have definite values, and all the
>> conscious beings that are instantiated and evolve and write books on
>> consciousness, and talk about the UD on their Internet, etc. as part of the
>> execution of the UD are there, in the math.
>>
>> Jason
>>
>>
>>
>> --
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>
>
>
> --
>
> Kindest Regards,
>
> Stephen Paul King
>
> Senior Researcher
>
> Mobile: (864) 567-3099
>
> stephe...@provensecure.com
>
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Re: Bruno's mathematical reality



On 28 Dec 2013, at 07:32, LizR wrote:

On 28 December 2013 18:03, Stephen Paul King > wrote:

Hi Jason,

  I would like to know the definition of "reality" that you are  
using here.


I quite like "whatever doesn't go away when you stop believing in it."


I quite like too.

Bruno





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Re: Bruno's mathematical reality

Dear Bruno,


On Sat, Dec 28, 2013 at 4:54 AM, Bruno Marchal  wrote:

>
> On 27 Dec 2013, at 17:51, Stephen Paul King wrote:
>
> Dear Bruno,
>
>
> On Fri, Dec 27, 2013 at 11:11 AM, Bruno Marchal  wrote:
>
>>
>> On 25 Dec 2013, at 18:40, spudboy...@aol.com wrote:
>>
>> Are we not presuming, structure, or a-priori, existence of something,
>> doing this processing, this work?
>>
>>
>>
>> In the UDA we assume a "Turing universal", or "sigma_1-complete" physical
>> reality, in some local sense.
>>
>
>
> Could this "Turing universal/sigma_1-complete in a local sense" be the
> exact criteria required to define the observations 3-experiences of
> individuals or is it the 1-experiences of individuals (observers) in
> keeping with the definition of an observer as the intersection of
> infinitely many computations?
>
>
> I think the UDA answers this question. You need Turing universality, but
> also the FPI, which in some sense comes from mechanism, but not necessarily
> "universality", which has, here, only an indirect relevance in the
> definition of what is a computation in arithmetic.
>

I suspect that the FPI results from the "underlap" or failure to reach
exact overlap between observers. As if a small part of the computations
that are observers is not universal. This would effectively induce FPI as
any one observer would be forever unable to exactly match its experience of
"being in the world" with that of another.



>
>
>
>
>
>
>
>
>> We need this to just explain what is a computer, alias, universal
>> machine, alias universal number (implemented or not in a physical reality).
>> Note that we do not assume a *primitive physical reality*. In comp, we
>> are a priori agnostic on this. The UDA, still will explains that such
>> "primitiveness" cannot solve the mind-body problem when made into a
>> dogma/assumption-of-primitiveness.
>>
>
> It has always seemed to me that UDA cannot solve the mind-body problem
> strictly because it cannot comprehend the existence of "other minds".
>
>
> UDA formulates the problem, and show how big the mind-body problem is,
> even before tackling the "other minds" problem. But something is said. In
> fact it is easy to derive from the UDA the following assertions:
>
> comp + explicit non-solipsism entails sharable many words or a core linear
> physical reality.
>

I do not comprehend this. It is easy for us to "see" that solipsism is
false, but how can a computation "see" anything? I do not understand how it
is that you can claim that computations will not be solipsistic by default.



>
> But comp in fact has to justify the non-solipsism, and this is begun
> through the
> 
> nuance Bp & p versus Bp & Dt. Normally the linearity should allow the
> first person plural in the "& Dt" nuance case.
>

Exactly! I am looking forward to the explanation of this "

nuance Bp & p versus Bp & Dt". :-)



>
> Keep in mind that UDA does not solve the problem, but formulate it. AUDA
> go more deep in a solution, and the shape of that solution (like UDA
> actually) provides already information contradicting the Aristotelian
> theology (used by atheists and the main part of institutionalized abramanic
> religion).
>

Sure. My main worry is that your wonderful result obtains at too high a
price: the inability to even model interactions and time.



>
> Bruno
>
>
>
>
>
>>
>> Then in AUDA, keeping comp at the meta-level, I eliminate all assumptions
>> above very elementary arithmetic (Robinson Arithmetic).
>>
>> The little and big bangs, including the taxes, and why it hurts is
>> derived from basically just
>>
>> Kxy = x
>> Sxyz = xz(yz)
>>
>> or just
>>
>> x + 0 = x
>> x + s(y) = s(x + y)
>>
>>  x *0 = 0
>>  x*s(y) = x*y + x
>>
>>
>>
>>
> http://iridia.ulb.ac.be/~marchal/
>
>
>
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Re: Bruno's mathematical reality




On Dec 28, 2013, at 6:09 AM, Bruno Marchal  wrote:



On 28 Dec 2013, at 04:56, Jason Resch wrote:





On Fri, Dec 27, 2013 at 10:42 PM, Stephen Paul King > wrote:

Hi Jason,

"Any program, and whether or not it ever terminates can be  
translated to a statement concerning numbers in arithmetic. Thus  
mathematical truth captures the facts concerning whether or not any  
program executes forever, and what all of its intermediate states  
are. "


this also captures every instance of random numbers as well.

It is not clear to me what "random" means in arithmetical truth.

Randomness can appear from the perspectives of observers, but I  
don't see how it can arise in arithmetic.


?

It appears in all numbers written in any base. Most numbers are  
already random (even incompressible).

I guess you know that.


I agree most numbers are incompressible, but I was using random in a  
different sense than the unpredictability of the next digits of the  
number given previous ones.


In the phi_i(j) in the UD, randomness can appear in the many j used  
as input, as we usually dovetail on the function of one variable.  
(but such input can easily be internalized in 0-variable programs).


For a long time I got opponent saying that we cannot generate  
computationally a random number, and that is right, if we want  
generate only that numbers.


Right, all the random numbers are there, the question is how to throw  
the dart so that it lands on one.


but a simple counting algorithm generating all numbers, 0, 1,  
2,  6999500235148668, ... generates all random finite  
incompressible strings, and even all the infinite one (for the 1p  
view, notably).


I think we are using the term in a slightly different sense.   
Certainly any number in the range 1 - N can be considered as a random  
number in that range (as it is a candidate to be output by some RNG),  
but the problem is selecting it in a random (in the sense of not- 
predictable) way.


There was a joke cartoon of some computer code:

int getRandomNumber()
{
  return 4; // this number was determined by a random die roll
}

While a number can be interpreted as random once, it might not be the  
second time.


While selecting and using all possibilities is arguably a way to  
achieve randomness (unpredictibilty), (from some points of view) it is  
often not practical nor useful.  Consider encrypting a message with  
all possible keys and sending the recipient all possible messages.


Not only might you need to send 2^256 possible ciphertexts but any  
eavesdropper could use the first possible key to decrypt it. This  
achieves randomness from the POV of the cipher, but not for the user  
or the attackers.


In quantum cryptography this is essentially what is done, but it  
requires that the sender and reciever (and attackers) be duplicated  
for each possible key. So they need to be embedded in that larger  
program that provides all possible inputs for it to seem random. This  
is just FPI though, is it not?


Jason



In that (trivial) sense, arithmetic contains a lot of 3p randomness,  
even perhaps too much. Then 1p randomeness appears too, by the 1p  
indeterminacy (and that one is in the eyes of the machine).


Chaitin's results can also explain why we cannot filter out that 3p  
randomness from arithmetic.


Bruno




What method is deployed to ensure that a program is not just a  
"regular" random number and not some random number prefixed on a  
"real" halting program?


It don't see how it makes a difference.


Truth is not a measure zero set, or is it?

I don't understand this question..  Could you clarify?

Jason




On Fri, Dec 27, 2013 at 10:09 PM, Jason Resch  
 wrote:




On Fri, Dec 27, 2013 at 9:31 PM, Stephen Paul King > wrote:

Hi Jason,

  Could you discuss the "trace of the UD" that LizR mentioned? How  
is it computed? Could you write an explicit example? I have never  
been able to grok it.



Bruno has written an actual UD in the LISP programming language.  I  
will write a simple one in pseudo-code below:


List listOfPrograms = new List[]; # Empty list
int i = 0;
while (true)
{
   # Create a program corresponding to the binary expansion of the  
integer i

   Program P = createProgramFromInteger(i);

   # Add the program to a list of programs we have generated so far
   listOfPrograms.add(P);

   # For each program we have generated that has not halted,  
execute one instruction of it

   for each (Program p in listOfPrograms)
   {
 if (p.hasHalted() == false)
 {
executeOneInstruction(p);
 }
   }

   # Finally, increment i so a new program is generated the next  
time through

   i = i + 1;
}


Any program, and whether or not it ever terminates can be  
translated to a statement concerning numbers in arithmetic. Thus  
mathematical truth captures the facts concerning whether or not any  
program executes forever, and what all of its intermediate states  
are. If these statements are true independently of y

Re: Bruno's mathematical reality

On 28 Dec 2013, at 05:53, Stephen Paul King wrote:

Hi LizR,

This is fun! :-) We must remember that we are defining People as
intersections of infinitely many computations. Right?

This is a very loose way to talk. Computations are not sets, so
"intersection of computations" is very ill defined. We can say more
easily and clearly that machines cannot know which computations they
are supported by, and that the statistics will have to take into
account the distribution of 3p states in all computations.

Their perceptions of themselves as physical being having some
particular set of configuration, for example bilateral symmetry,
etc. is not really relevant to UDA.

So, if there is a change in accessibility to data, facts, etc. Where
is that "change" coming from".

From the computations (in arithmetic) which supports you,

This is my problem: We are presented with an argument that works
in Platonia and we have no explanation as to the relation it has
with the "real world" where things change and degrade and evolve,
etc. What is measuring that change?

We are already in Platonia. After Gödel + comp, we know that Platonia
(arithmetic) is full of change, when viewed from inside.
That should not seem so strange, as the 0 -> s(0) -> s(s(0)) ->
implements already a sort of atomic change.

Bruno

On Fri, Dec 27, 2013 at 11:49 PM, LizR wrote:
On 28 December 2013 17:46, Stephen Paul King > wrote:
Ah, but they do degrade. Consider your ability to access a '80s
floppy drive's data.

Well, that's because people haven't worked out how to do it
perfectly. I agree digital archaeology is a real problem, but so
would analogue be without the relevant machines to play it back
(admittedly it's easier to decode analogue from first principles).
But that is a different form of degrading. If you have a system
capable of copying the data it should be more or less 100% accurate.

On Fri, Dec 27, 2013 at 11:44 PM, LizR wrote:
On 28 December 2013 17:41, Jason Resch wrote:
On Fri, Dec 27, 2013 at 11:27 PM, Stephen Paul King > wrote:

Hi LizR and Jason,

Responding to both of you. I don't understand the claim of
determinism is "random noise" is necessary for the computations.
Turing machines require exact pre-specifiability. Adding noise
oracles is cheating!

I think you misunderstand. Computers are deterministic, but they
often need randomness to implement things such as cryptography or
monte-carlo simulations, etc. Due to this need for true
unpredictability, our computers must harness environmental noise if
they are to have any hope of being unpredictable. This is because
computers cannot generate unpredictability on their own.

They are engineered not to! This is why digital recordings don't
degrade, etc.

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Mobile: (864) 567-3099

stephe...@provensecure.com

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Re: Bruno's mathematical reality

On 28 Dec 2013, at 05:31, Stephen Paul King wrote:

Hi Jason,

On Fri, Dec 27, 2013 at 11:23 PM, Jason Resch
wrote:

On Fri, Dec 27, 2013 at 11:09 PM, Stephen Paul King > wrote:

Hi Jason,

"It is not a question of whether or not that binary string refers
to anything that is true or not, only what its particular value
happens to be." No no no! We can not make statements without showing
how their proof are accessible!

The proof is straight forward. Run the UD and see what the state is.

Run it, on what hardware? ??

Are you objecting that it does not have a definite value because you
or I are not capable of computing it?

Did the 100th digit of Pi not exist until the first human computed it?

Pfft, that is a red herring and you know it! Why even mention
humans? If numbers exist, then that existence has nothing at all to
do with humans or aliens of black clouds. It is merely the necessary
possibility that the numbers are not inconsistent. If they were
inconsistent, then all that would exist is noise. And we are back to
my question. What decodes the noise into "meaningful" strings?

The universal numbers, through the laws (in this case with arithmetic
beeing the base) of addition and multiplication. Arithmetic "dovetail"
on programs, and consciousness filter out the "meaningfull one" (as we
assume comp).

Consider the i-th through j_th values of pi's expansion in binary.
If it is a finite string, how do we know that it is a Turing machine
program?

All integers can be mapped directly to Turing machine programs.
Consider Java: it uses a byte-code where every byte is an
instruction for the Java virtual machine. Every string of bytes can
therefore be considered as a sequence of instructions for the Java
virtual machine to execute.

SO it is OK to include the java code that generates noise. There are
your oracles! Pick one. Whoops, how is the selection made?

Like in the WM duplication. By self-reference.

bruno

Jason

On Fri, Dec 27, 2013 at 11:06 PM, Jason Resch
wrote:

On Fri, Dec 27, 2013 at 10:44 PM, Stephen Paul King > wrote:

Hi Jason,

"The first, second, 10th, 1,000,000th, and 10^100th, and
10^100^100th state of the UD's execution are mathematical facts ..."
Umm, how? Godel and Matiyasevich would disagree! If there does not
exist a program that can evaluate whether or not a UD substring is a
faithful representation of a "true theorem", then how is it "a fact"?

The mathematical fact to which I am referring is only a basic and
straight-forward statement like "the binary representation of the
state of UD after executing 100..00th steps is
'101010010...0010". It is not a question of whether or not that
binary string refers to anything that is true or not, only what its
particular value happens to be.

Jason

On Fri, Dec 27, 2013 at 10:09 PM, Jason Resch
wrote:

On Fri, Dec 27, 2013 at 9:31 PM, Stephen Paul King > wrote:

Hi Jason,

Could you discuss the "trace of the UD" that LizR mentioned? How
is it computed? Could you write an explicit example? I have never
been able to grok it.

Bruno has written an actual UD in the LISP programming language. I
will write a simple one in pseudo-code below:

List listOfPrograms = new List[]; # Empty list
int i = 0;
while (true)
{
# Create a program corresponding to the binary expansion of the
integer i

Program P = createProgramFromInteger(i);

# Add the program to a list of programs we have generated so far
listOfPrograms.add(P);

# For each program we have generated that has not halted, execute
one instruction of it

for each (Program p in listOfPrograms)
{
if (p.hasHalted() == false)
{
executeOneInstruction(p);
}
}

# Finally, increment i so a new program is generated the next
time through

i = i + 1;
}

Any program, and whether or not it ever terminates can be translated
to a statement concerning numbers in arithmetic. Thus mathematical
truth captures the facts concerning whether or not any program
executes forever, and what all of its intermediate states are. If
these statements are true independently of you and me, then the
executions of these programs are embedded in arithmetical truth and
have a platonic existence. The first, second, 10th, 1,000,000th,
and 10^100th, and 10^100^100th state of the UD's execution are
mathematical facts which have definite values, and all the conscious
beings that are instantiated and evolve and write books on
consciousness, and talk about the UD on their Internet, etc. as part
of the execution of the UD are there, in the math.

Jason

Re: Bruno's mathematical reality



On 28 Dec 2013, at 05:31, LizR wrote:

On 28 December 2013 17:27, Stephen Paul King > wrote:

Hi LizR and Jason,

  Responding to both of you. I don't understand the claim of  
determinism is "random noise" is necessary for the computations.  
Turing machines require exact pre-specifiability. Adding noise  
oracles is cheating!


Who said random noise was necessary? I said the UD, at least, is  
completely deterministic.



The UD is indeed totally deterministic. but it still generates all  
random strings, and all executions of all programs on all random  
streams. This has consequences on the FPI, but is not a consequences  
of the FPI. The UD generates deterministically 3P randomness. 1p  
randomness exists too in arithmetic, but cannot be said being  
generated by the UD. That one is an "illusion" in the mind of the  
observers.


Bruno




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Re: Bruno's mathematical reality



On 28 Dec 2013, at 05:27, LizR wrote:


On 28 December 2013 17:23, Edgar L. Owen  wrote:
Jason,

You might be able to theoretically simulate it but certainly not  
compute it in real time which is what reality actually does which is  
my point.


"In real time" ?! In comp (and many TOEs) time is emergent.


Physical times and subjective time emerge. OK. But let us be honest,  
comp assumes already a sort of time, through the natural order: à, 1,  
2, 3, ...


Then you have all UD-time step of the computations emulated by the UD:

phi_444(6) first step
...
phi_444(6) second step
... ...  (meaning greater delay in  
the UD-time steps).

ph_444(6) third  step
... ... ...
ph_444(6) fourth  step
  ... ...
ph_444(6) fifth step
etc.



To take a parallel example that should be close to your heart,  
suppose you're an AI living in the matrix and it's simulating  
reality for you. You aren't aware of this but believe yourself to be  
say a human writer who is participating in an online discussion.  
Suppose it takes a million years to simulate one second of your  
experience. How would you know? You can only compare your experience  
of time with in-matrix clocks, which all run at the speed you'd  
expect.


It's the same for any theory which tries to compute reality.


But the physical time is not Turing emulable, and perhaps is not even  
existing, like in Dewitt-Wheeler equation: H = 0.
if it exist, it depends on all computations "instantaneously", by the  
delay invariance of the FPI.


Bruno



http://iridia.ulb.ac.be/~marchal/



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Re: Bruno's mathematical reality

On 28 Dec 2013, at 05:27, Stephen Paul King wrote:

Hi LizR and Jason,

But it exist in arithmetic. Subtracting it would be cheating. the
silmple counting algorith generates all random finite strings (random
in the strong Chaitin sense).

Almost all numbers are random, when written in some base. And you can
define the notion of base *in* arithmetic, so they exist in all models
of arithmetic. We can't subtract them.

Bruno

On Fri, Dec 27, 2013 at 11:22 PM, LizR wrote:
On 28 December 2013 17:15, Jason Resch wrote:
On Fri, Dec 27, 2013 at 11:06 PM, LizR wrote:
Clearly programmes don't have to be deterministic. They could
contain a source of genuine randomness, in principle.

That source, if it is within the program, would necessarily be
deterministic. If it is external to the program, then it is more
properly treated as an input to the program rather than a part of
the program itself.

In practice, computers draw on sources of environmental noise such
as delays between keystrokes, timing of the reception of network
traffic, and delays in accessing data off of hard drives, etc. These
steps are necessary precisely because programs cannot produce
randomness on their own.

I knew that - honest! :-)

I was answering the question as posed. I believe that in practice
all real-world programmes are deterministic, and (more to the point)
the UD is.

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Re: Bruno's mathematical reality

On 28 Dec 2013, at 05:06, LizR wrote:

Clearly programmes don't have to be deterministic. They could
contain a source of genuine randomness, in principle.

I don't think the UD does, however.

The UD emulates all quantum computer and many sort of non
deterministic processes, including all randomness (through the
inputs), even deterministically.

Just think about the fact that the UD does emulate infinite iteration
of the WM duplication.

Bruno

The definition of deterministic would be - gives the same output on
each run (given that the UD has no input).

On 28 December 2013 17:03, Stephen Paul King > wrote:

I ask this because I am studying Carl Hewitt's Actor Model...

On Fri, Dec 27, 2013 at 11:03 PM, Stephen Paul King > wrote:

Hi jason,

Do programs have to be "deterministic". What definition of
deterministic are you using?

On Fri, Dec 27, 2013 at 11:00 PM, Jason Resch
wrote:

On Fri, Dec 27, 2013 at 10:54 PM, LizR wrote:
On 28 December 2013 16:44, Stephen Paul King > wrote:

Hi Jason,

That depends on whether the UD is deterministic or not.

It is. The evolution of any Turing machines is deterministic.

If it is, then, its Nth state is a fact. (It doesn't need to be run
or evaluated, and the Nth state may be a fact that nobody knows,
like the googolth digit of pi, assuming no one's worked that out.)

Right. :-)

The fact that I remember drinking a glass of water is as much a
mathematical fact about the UD, as the fact as the third decimal
digit of Pi is 4.

Jason

--
Kindest Regards,

Stephen Paul King

Senior Researcher
Mobile: (864) 567-3099

stephe...@provensecure.com

http://www.provensecure.us/

“This message (including any attachments) is intended only for the
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Re: Bruno's mathematical reality

On 28 Dec 2013, at 05:03, Stephen Paul King wrote:

I ask this because I am studying Carl Hewitt's Actor Model...

Also know today as "object oriented" languages. c++ win against
smaltalk, which won against the Actor model, but the idea is the same,
basically. It is efficacious, but the math and semantics is still
unclear to me. It is a sort of vague polymorphic lambda calculus. I
did love a long time ago, the "actor model". It is somewhat
psychologically sad that the term "object" replaced the term "actor".

bruno

On Fri, Dec 27, 2013 at 11:03 PM, Stephen Paul King > wrote:

Hi jason,

Do programs have to be "deterministic". What definition of
deterministic are you using?

On Fri, Dec 27, 2013 at 11:00 PM, Jason Resch
wrote:

On Fri, Dec 27, 2013 at 10:54 PM, LizR wrote:
On 28 December 2013 16:44, Stephen Paul King > wrote:

Hi Jason,

That depends on whether the UD is deterministic or not.

It is. The evolution of any Turing machines is deterministic.

If it is, then, its Nth state is a fact. (It doesn't need to be run
or evaluated, and the Nth state may be a fact that nobody knows,
like the googolth digit of pi, assuming no one's worked that out.)

Right. :-)

The fact that I remember drinking a glass of water is as much a
mathematical fact about the UD, as the fact as the third decimal
digit of Pi is 4.

Jason

--
Kindest Regards,

Stephen Paul King

Senior Researcher
Mobile: (864) 567-3099

stephe...@provensecure.com

http://www.provensecure.us/

“This message (including any attachments) is intended only for the
use of the individual or entity to which it is addressed, and may
contain information that is non-public, proprietary, privileged,
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recipient, you are hereby notified that any use, dissemination,
distribution, or copying of this communication is strictly
prohibited. If you have received this message in error, notify
sender immediately and delete this message immediately.”

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stephe...@provensecure.com

http://www.provensecure.us/

“This message (including any attachments) is intended only for the
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Re: Bruno's mathematical reality

On 28 Dec 2013, at 05:01, Stephen Paul King wrote:

How do we distinguish a program from a string of random numbers.
(Consider OTP encryptions).

In which language?

A program fortran will be distinguished by the grammar of Fortran.

In some language all numbers will be program.

Then , for all language question like "does that progream compute this
or that" are non algorithmically solvable (and undecidable in most
theories).

Bruno

On Fri, Dec 27, 2013 at 10:56 PM, Jason Resch
wrote:

On Fri, Dec 27, 2013 at 10:42 PM, Stephen Paul King > wrote:

Hi Jason,

"Any program, and whether or not it ever terminates can be
translated to a statement concerning numbers in arithmetic. Thus
mathematical truth captures the facts concerning whether or not any
program executes forever, and what all of its intermediate states
are. "

this also captures every instance of random numbers as well.

It is not clear to me what "random" means in arithmetical truth.

Randomness can appear from the perspectives of observers, but I
don't see how it can arise in arithmetic.

What method is deployed to ensure that a program is not just a
"regular" random number and not some random number prefixed on a
"real" halting program?

It don't see how it makes a difference.

Truth is not a measure zero set, or is it?

I don't understand this question.. Could you clarify?

Jason

On Fri, Dec 27, 2013 at 10:09 PM, Jason Resch
wrote:

On Fri, Dec 27, 2013 at 9:31 PM, Stephen Paul King > wrote:

Hi Jason,

Could you discuss the "trace of the UD" that LizR mentioned? How
is it computed? Could you write an explicit example? I have never
been able to grok it.

Bruno has written an actual UD in the LISP programming language. I
will write a simple one in pseudo-code below:

List listOfPrograms = new List[]; # Empty list
int i = 0;
while (true)
{
# Create a program corresponding to the binary expansion of the
integer i

Program P = createProgramFromInteger(i);

# Add the program to a list of programs we have generated so far
listOfPrograms.add(P);

# For each program we have generated that has not halted, execute
one instruction of it

for each (Program p in listOfPrograms)
{
if (p.hasHalted() == false)
{
executeOneInstruction(p);
}
}

# Finally, increment i so a new program is generated the next
time through

i = i + 1;
}

Any program, and whether or not it ever terminates can be translated
to a statement concerning numbers in arithmetic. Thus mathematical
truth captures the facts concerning whether or not any program
executes forever, and what all of its intermediate states are. If
these statements are true independently of you and me, then the
executions of these programs are embedded in arithmetical truth and
have a platonic existence. The first, second, 10th, 1,000,000th,
and 10^100th, and 10^100^100th state of the UD's execution are
mathematical facts which have definite values, and all the conscious
beings that are instantiated and evolve and write books on
consciousness, and talk about the UD on their Internet, etc. as part
of the execution of the UD are there, in the math.

Jason

--
Kindest Regards,

Stephen Paul King

Senior Researcher
Mobile: (864) 567-3099

stephe...@provensecure.com

http://www.provensecure.us/

“This message (including any attachments) is intended only for the
use of the individual or entity to which it is addressed, and may
contain information that is non-public, proprietary, privileged,
confidential and exempt from disclosure under applicable law or may
be constituted as attorney work product. If you are not the intended
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Re: Bruno's mathematical reality

On 28 Dec 2013, at 04:56, Jason Resch wrote:

On Fri, Dec 27, 2013 at 10:42 PM, Stephen Paul King > wrote:

Hi Jason,

this also captures every instance of random numbers as well.

It is not clear to me what "random" means in arithmetical truth.

Randomness can appear from the perspectives of observers, but I
don't see how it can arise in arithmetic.

It appears in all numbers written in any base. Most numbers are
already random (even incompressible).
I guess you know that. In the phi_i(j) in the UD, randomness can
appear in the many j used as input, as we usually dovetail on the
function of one variable. (but such input can easily be internalized
in 0-variable programs).

For a long time I got opponent saying that we cannot generate
computationally a random number, and that is right, if we want
generate only that numbers. but a simple counting algorithm generating
all numbers, 0, 1, 2, 6999500235148668, ... generates all random
finite incompressible strings, and even all the infinite one (for the
1p view, notably).

In that (trivial) sense, arithmetic contains a lot of 3p randomness,
even perhaps too much. Then 1p randomeness appears too, by the 1p
indeterminacy (and that one is in the eyes of the machine).

Chaitin's results can also explain why we cannot filter out that 3p
randomness from arithmetic.

Bruno

What method is deployed to ensure that a program is not just a
"regular" random number and not some random number prefixed on a
"real" halting program?

It don't see how it makes a difference.

Truth is not a measure zero set, or is it?

I don't understand this question.. Could you clarify?

Jason

On Fri, Dec 27, 2013 at 10:09 PM, Jason Resch
wrote:

On Fri, Dec 27, 2013 at 9:31 PM, Stephen Paul King > wrote:

Hi Jason,

Could you discuss the "trace of the UD" that LizR mentioned? How
is it computed? Could you write an explicit example? I have never
been able to grok it.

Bruno has written an actual UD in the LISP programming language. I
will write a simple one in pseudo-code below:

List listOfPrograms = new List[]; # Empty list
int i = 0;
while (true)
{
# Create a program corresponding to the binary expansion of the
integer i

Program P = createProgramFromInteger(i);

# Add the program to a list of programs we have generated so far
listOfPrograms.add(P);

# For each program we have generated that has not halted, execute
one instruction of it

for each (Program p in listOfPrograms)
{
if (p.hasHalted() == false)
{
executeOneInstruction(p);
}
}

# Finally, increment i so a new program is generated the next
time through

i = i + 1;
}

Any program, and whether or not it ever terminates can be translated
to a statement concerning numbers in arithmetic. Thus mathematical
truth captures the facts concerning whether or not any program
executes forever, and what all of its intermediate states are. If
these statements are true independently of you and me, then the
executions of these programs are embedded in arithmetical truth and
have a platonic existence. The first, second, 10th, 1,000,000th,
and 10^100th, and 10^100^100th state of the UD's execution are
mathematical facts which have definite values, and all the conscious
beings that are instantiated and evolve and write books on
consciousness, and talk about the UD on their Internet, etc. as part
of the execution of the UD are there, in the math.

Jason

--
Kindest Regards,

Stephen Paul King

Senior Researcher
Mobile: (864) 567-3099

stephe...@provensecure.com

http://www.provensecure.us/

“This message (including any attachments) is intended only for the
use of the individual or entity to which it is addressed, and may
contain information that is non-public, proprietary, privileged,
confidential and exempt from disclosure under applicable law or may
be constituted as attorney work product. If you are not the intended
recipient, you are hereby notified that any use, dissemination,
distribution, or copying of this communication is strictly
prohibited. If you have

Re: Bruno's mathematical reality

On 28 Dec 2013, at 04:52, Jason Resch wrote:

On Fri, Dec 27, 2013 at 10:39 PM, Stephen Paul King > wrote:

Dear Jason,

ISTM that the line " For each program we have generated that has
not halted, execute one instruction of it for each (Program p in
listOfPrograms)" is buggy.

It assumes that the space of "programs that do not halt" is
accessible. How?

We never know a prior if a program will halts or not. However, once
a program has reached a halted stated it is immediately apparent.
If the function name was "willThisProgramHalt()", then I agree it
would be a buggy program. :-)

The UD as I wrote it executes all programs, whether they will halt
or not, but it never wastes time trying to run another instruction
of a program that has halted. This is only an optimization, and I
added it only to reduce the ambiguity of "running another
instruction of a program that has halted".

OK. The LISP UD is even more optimized, and the small UD I just gave
is not optimal at all. Of course, to optimize a UD is a bit like pure
coquetry :) (it should not change anything in the measure conflicts,
a priori).

Bruno

Jason

On Fri, Dec 27, 2013 at 10:09 PM, Jason Resch
wrote:

On Fri, Dec 27, 2013 at 9:31 PM, Stephen Paul King > wrote:

Hi Jason,

Could you discuss the "trace of the UD" that LizR mentioned? How
is it computed? Could you write an explicit example? I have never
been able to grok it.

Bruno has written an actual UD in the LISP programming language. I
will write a simple one in pseudo-code below:

List listOfPrograms = new List[]; # Empty list
int i = 0;
while (true)
{
# Create a program corresponding to the binary expansion of the
integer i

Program P = createProgramFromInteger(i);

# Add the program to a list of programs we have generated so far
listOfPrograms.add(P);

# For each program we have generated that has not halted, execute
one instruction of it

for each (Program p in listOfPrograms)
{
if (p.hasHalted() == false)
{
executeOneInstruction(p);
}
}

# Finally, increment i so a new program is generated the next
time through

i = i + 1;
}

Any program, and whether or not it ever terminates can be translated
to a statement concerning numbers in arithmetic. Thus mathematical
truth captures the facts concerning whether or not any program
executes forever, and what all of its intermediate states are. If
these statements are true independently of you and me, then the
executions of these programs are embedded in arithmetical truth and
have a platonic existence. The first, second, 10th, 1,000,000th,
and 10^100th, and 10^100^100th state of the UD's execution are
mathematical facts which have definite values, and all the conscious
beings that are instantiated and evolve and write books on
consciousness, and talk about the UD on their Internet, etc. as part
of the execution of the UD are there, in the math.

Jason

--
Kindest Regards,

Stephen Paul King

Senior Researcher
Mobile: (864) 567-3099

stephe...@provensecure.com

http://www.provensecure.us/

“This message (including any attachments) is intended only for the
use of the individual or entity to which it is addressed, and may
contain information that is non-public, proprietary, privileged,
confidential and exempt from disclosure under applicable law or may
be constituted as attorney work product. If you are not the intended
recipient, you are hereby notified that any use, dissemination,
distribution, or copying of this communication is strictly
prohibited. If you have received this message in error, notify
sender immediately and delete this message immediately.”

To post to t

Re: Bruno's mathematical reality

On 28 Dec 2013, at 04:44, Stephen Paul King wrote:

Hi Jason,

"The first, second, 10th, 1,000,000th, and 10^100th, and
10^100^100th state of the UD's execution are mathematical facts ..."
Umm, how? Godel and Matiyasevich would disagree!

No logicians at all would ever disagree on this. They are the one who
proved this.

If there does not exist a program that can evaluate whether or not a
UD substring is a faithful representation of a "true theorem", then
how is it "a fact"?

It does not need to be a fact. *you* recognize you are conscious, even
if no one can prove it by looking at your code and state, and that is
enough to proceed in the reasoning.

bruno

On Fri, Dec 27, 2013 at 10:09 PM, Jason Resch
wrote:

On Fri, Dec 27, 2013 at 9:31 PM, Stephen Paul King > wrote:

Hi Jason,

Could you discuss the "trace of the UD" that LizR mentioned? How
is it computed? Could you write an explicit example? I have never
been able to grok it.

Bruno has written an actual UD in the LISP programming language. I
will write a simple one in pseudo-code below:

List listOfPrograms = new List[]; # Empty list
int i = 0;
while (true)
{
# Create a program corresponding to the binary expansion of the
integer i

Program P = createProgramFromInteger(i);

# Add the program to a list of programs we have generated so far
listOfPrograms.add(P);

# For each program we have generated that has not halted, execute
one instruction of it

for each (Program p in listOfPrograms)
{
if (p.hasHalted() == false)
{
executeOneInstruction(p);
}
}

# Finally, increment i so a new program is generated the next
time through

i = i + 1;
}

Any program, and whether or not it ever terminates can be translated
to a statement concerning numbers in arithmetic. Thus mathematical
truth captures the facts concerning whether or not any program
executes forever, and what all of its intermediate states are. If
these statements are true independently of you and me, then the
executions of these programs are embedded in arithmetical truth and
have a platonic existence. The first, second, 10th, 1,000,000th,
and 10^100th, and 10^100^100th state of the UD's execution are
mathematical facts which have definite values, and all the conscious
beings that are instantiated and evolve and write books on
consciousness, and talk about the UD on their Internet, etc. as part
of the execution of the UD are there, in the math.

Jason

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Re: Bruno's mathematical reality

On 28 Dec 2013, at 04:39, Stephen Paul King wrote:

Dear Jason,

ISTM that the line " For each program we have generated that has
not halted, execute one instruction of it for each (Program p in
listOfPrograms)" is buggy.

It assumes that the space of "programs that do not halt" is
accessible. How?

The space of all programs that do not halt is not Turing accessible.
The space of all programs that do halt is not Turing accessible.

The space of all programs (that do halt of do not halt) *is* accessible.

All what happen is that we have no general systematic, computational,
means to distinguish the programs that halt from the programs that
does not halt (on their inputs), and that is why the universal
dovetailer must *dovetail* on the executions of all programs.

Bruno

On Fri, Dec 27, 2013 at 10:09 PM, Jason Resch
wrote:

On Fri, Dec 27, 2013 at 9:31 PM, Stephen Paul King > wrote:

Hi Jason,

Could you discuss the "trace of the UD" that LizR mentioned? How
is it computed? Could you write an explicit example? I have never
been able to grok it.

Bruno has written an actual UD in the LISP programming language. I
will write a simple one in pseudo-code below:

List listOfPrograms = new List[]; # Empty list
int i = 0;
while (true)
{
# Create a program corresponding to the binary expansion of the
integer i

Program P = createProgramFromInteger(i);

# Add the program to a list of programs we have generated so far
listOfPrograms.add(P);

# For each program we have generated that has not halted, execute
one instruction of it

for each (Program p in listOfPrograms)
{
if (p.hasHalted() == false)
{
executeOneInstruction(p);
}
}

# Finally, increment i so a new program is generated the next
time through

i = i + 1;
}

Any program, and whether or not it ever terminates can be translated
to a statement concerning numbers in arithmetic. Thus mathematical
truth captures the facts concerning whether or not any program
executes forever, and what all of its intermediate states are. If
these statements are true independently of you and me, then the
executions of these programs are embedded in arithmetical truth and
have a platonic existence. The first, second, 10th, 1,000,000th,
and 10^100th, and 10^100^100th state of the UD's execution are
mathematical facts which have definite values, and all the conscious
beings that are instantiated and evolve and write books on
consciousness, and talk about the UD on their Internet, etc. as part
of the execution of the UD are there, in the math.

Jason

--
Kindest Regards,

Stephen Paul King

Senior Researcher
Mobile: (864) 567-3099

stephe...@provensecure.com

http://www.provensecure.us/

“This message (including any attachments) is intended only for the
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Re: Bruno's mathematical reality



On 28 Dec 2013, at 04:41, Jason Resch wrote:





On Fri, Dec 27, 2013 at 10:20 PM, LizR  wrote:
There is one point to add which I think you've missed, Jason  
(apologies if I've misunderstood). The UD generates the first  
instruction of the first programme, then the first instruction of  
the second programme, and so on. Once it has generated the first  
instruction of every possible programme, it then adds the second  
instruction of the first programme, the second instruction of the  
second programme, and so on.


If it did work like this, it would never get to run the second  
instruction of any program, since there is a countable infinity of  
possible programs.


 This is why it's called a dovetailer, I believe, and stops it  
running into problems with non-halting programmes, or programmes  
that would crash, or various other contingencies...


This is addressed by not trying to run any one program to its  
completion, instead it gives each program it has generated up to  
that point some time on the CPU.



This isn't intrinsic to the UD, which could in principle write the  
first programme before it moves on to the next one - but it allows  
it to avoid certain problems caused by having a programme that  
writes other programmes.


There is no program with the UD encountering programs that  
themselves instantiate other programs.


I guess you mean "there is no problem with the UD encountering  
programs ...", and you are right.





 Indeed, the UD encounters itself, infinitely often.



...I think. I'm sure Bruno will let me know if that's wrong.

:)




Jason did it. Liz, Stephen, Are you OK with the UD and UD*. Both the  
list of all programs AND their execution are done little bit by little  
bit.


Thanks to Jason for a code. With the phi_i, you can code the UD by

For all i, j, k,
execute k steps of phi_i(j)



Bruno





PS I like the "while (true)" statement. What would Pontius Pilate  
have made of that? :-)


:-)  Good question, I haven't the faintest idea.  I could have used  
"while (i == i)" but then if someday Brent's paralogic takes over,  
it might fail.


Jason

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Re: Bruno's mathematical reality



On 28 Dec 2013, at 04:36, Stephen Paul King wrote:





I loath Kronecker's claim! It is synonymous to "Man is the measure  
of all things".



What is his claim?  I am not familiar with it.

God created the Integers, all else is the invention of man.



"man is a measure of all things" is a quote from a french philosopher  
(I just forget right now his name) itself taken from a greek general,  
which cut the feet or head of all soldier having not the right size  
(!).  (Sorry for those vague memories, learn this in highschool)


Now, of course, comp saves Kronecker from anthropomorphism, as with  
comp we can say that:

"God created the integers, all else is the invention of ... integers".

Of course it made comp number-centered, but this we knew at the start  
with comp, and ... with christianism, in which it is important to  
realize our finiteness.


Bruno

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Re: Bruno's mathematical reality



On 28 Dec 2013, at 03:29, LizR wrote:

What I think Jason is saying is that the TRACE of the UD (knowns as  
UD* - I made the same mistake!)


Good :)




will eventually contain your mind.



Perhaps; but only for nano second. you real mind overlap on sequence  
of states, with the right probabilities, and for this you need the  
complete run of the UD, because your next "moment" is determioned by  
the FPI on all computations. Here the invariance of first person  
experience for the "UD time delays" is capital. But I see your point.


Bruno





See my previous post for an elaboration.









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Re: Bruno's mathematical reality



On 28 Dec 2013, at 02:04, LizR wrote:


On 28 December 2013 13:56, Jason Resch  wrote:

The UDA is a comparatively short program, and provably contains the  
program that is identical to your mind.


To be more precise (I hope) - assuming that thoughts, experiences  
etc are a form of computation at some level, the output (or trace)  
of the UDA, which I seem to recall is designated UDA*, will  
eventually generate those thoughts, experiences etc. Though if run  
on a PC it would probably take a few googol years to do so (and  
require many hubble volumes of storage space too, I imagine).


However, arithmetical realism assumes that the trace of the UDA  
already exists timelessly.



Of the UD. UD is the program doing the universal dovetailing.

UDA is for the 8 step argument showing that if we are machine, physics  
is a brnach of machine's theology, itself a branch of arithmetic or  
computer science.


Bruno




 Similarly, all of the known laws of physics could fit on a couple  
sheets of paper.  QM seems to suggest that all possible solutions to  
certain equations exist, and so there is no need to specify the  
initial conditions of the universe (which would require much more  
information to describe than your brain).


This sounds like the "Theory of Nothing" again.?

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Re: Bruno's mathematical reality



On 28 Dec 2013, at 02:03, Edgar L. Owen wrote:


Jason,

You state "The UD is a comparatively short program, and provably  
contains the program that is identical to your mind."


You can't be serious! As stated that's the most ridiculous statement  
I've heard here today in all manner of respects!



If you believe this, you cannot believe in computationalism.  If your  
brain work  is Turing emulable, that emulation is provably in  
arithmetic, which emulates all (it is a theorem in arithmetic) all  
computations. It is long to prove, but not so much difficult if you  
add some axioms like the exponentiation axioms. It is a hell of a  
difficulty to eliminate that exponentiation axioms, but that has been  
done, even in some strong way (eliminating universal quantifiers  
altogether) by Matiyasevitch, and that is well known (by logicians).


That the UD itself exist is a consequence of Church thesis, and is  
obvious to many for wrong reason. If you know Cnator diagonalization,  
then at first sight, it looks we can diagonalized against the UD  
existence, but it happens that the UD and arithmetic is close for the  
diagonalization procedure, making the UD, or equivalently the sigma_1  
part of arithmetic, complete for the computational reality (of course  
not complete for truth: that never happens by incompleteness à-la  
Gödel).


Bruno





Edgar



On Friday, December 27, 2013 7:56:44 PM UTC-5, Jason wrote:



On Fri, Dec 27, 2013 at 6:33 PM, Stephen Paul King  
 wrote:

Dear Jason,

Interleaving below.


On Fri, Dec 27, 2013 at 6:20 PM, Jason Resch   
wrote:




On Fri, Dec 27, 2013 at 6:03 PM, LizR  wrote:
On 28 December 2013 11:55, Stephen Paul King  
 wrote:

Hi LizR,

   That is what is not explicitly explained! I could see how one  
might make an argument based on Godel numbers and a choice of a  
numbering scheme could show the existence of a string of numbers  
that, if run on some computer, would generate a description of the  
interaction of several actors. But this ignores the problems of  
concurrency and "point of view". The best one might be able to do,  
AFAIK, is cook up a description of the interactions of many  
"observers" -each one is an intersection of infinitely many  
computations, but such a description would itself be the content of  
some observer's point of view that assumes a choice of Godel  
numbering scheme.

  Something doesn't seem right about this!

It seems to suggest "multi-solipsism" or something along those lines  
- which doesn't make it wrong, of course.


I await Bruno's answer with interest. I think he has already said  
something about this, but I don't recall it being satisfactory, at  
least to my limited understanding.


I am also interested to hear what Bruno has to say.  My perspective  
is that most of the computations that support you and I are not  
isolated and short-lived "computational Boltzmann brains" but much  
larger, long-running computations such as those that correspond to a  
universe in which life adapts and evolves.


I agree. I have never been happy with the Boltzman brain argument  
because it seems to assume that the probability distribution of  
"spontaneous" BBs is independent of the complexity of the content of  
the minds associated with those brains. I have been studying this  
relationship between complexity or "expressiveness" of a B.B. My  
first guesstimation is that there is something like a Zift's Law in  
the distribution: the more expressive a BB the less chance it has to  
exist and evolve at least one "cycle" of its computation. (After  
all, computers have to be able to run one clock cycle to be said  
that they actually "compute" some program...)



 The starting conditions for these is much less constrained, and  
therefore it is far more probable to result in conscious  
computations such as ours than the case where the computation  
supporting your brain experiencing this moment is some initial  
condition of a very specific program. Certainly, those programs  
exist too, but they are much rarer.


RIght, but how fast do they get rarer?

It's hard to say. We would have to develop some model for estimating  
the Kolmogorov complexity (and maybe also incorporate frequency) of  
different programs and their relation to a given mind.





They appear in the UD much less frequently than say the program  
corresponding to the approximate laws of physics of this universe.


 It takes far more data to describe your brain than it does to  
describe the physical system on which it is based.



How do you estimate this?

The UDA is a comparatively short program, and provably contains the  
program that is identical to your mind.  Similarly, all of the known  
laws of physics could fit on a couple sheets of paper.  QM seems to  
suggest that all possible solutions to certain equations exist, and  
so there is no need to specify the initial conditions of the  
universe (which would require much more information to describe t

Re: Bruno's mathematical reality



On 28 Dec 2013, at 01:56, Jason Resch wrote:








Somewhat. I think how frequently a program is referenced /  
instantiated by other non-halting programs may play a role.


Yes. It has to be like that. Stopping programs should contribute to 0,  
in the "measure conflict".









So we are (mostly) still "in the same universe", and so we can  
interact with and affect the consciousness of other people.



From my reasoning, the appearance that we are "in the same universe"  
is a by product of bisimilarities in the infinity of computations  
that are each of us. In other words, there  are many computations  
that are running Stephen that are identical to and thus are the same  
computation to many of the computations that are running Jason.


Yes. We would be programs instantiated within a (possibly but not  
necessarily) shared, larger program.


  This gives an overlap between our worlds and thus the appearance  
of a common world for some collection of "observers".


Right.

The cool thing is that this implies that there are underlaps;  
computations that are not shared or bisimilar between all of us.


Yes, I agree.  In some branches of the MW, perhaps you were born but  
I was not, or I was, and you weren't.


COuld those be the ones that we identify as "ourselves"?



Personal identity can become a very difficult subject, since there  
may be paths through which my program evolves to become you, and  
vice versa.


Yes, indeed.

Bruno





Jason

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Re: Bruno's mathematical reality



On 28 Dec 2013, at 00:20, Jason Resch wrote:





On Fri, Dec 27, 2013 at 6:03 PM, LizR  wrote:
On 28 December 2013 11:55, Stephen Paul King > wrote:

Hi LizR,

   That is what is not explicitly explained! I could see how one  
might make an argument based on Godel numbers and a choice of a  
numbering scheme could show the existence of a string of numbers  
that, if run on some computer, would generate a description of the  
interaction of several actors. But this ignores the problems of  
concurrency and "point of view". The best one might be able to do,  
AFAIK, is cook up a description of the interactions of many  
"observers" -each one is an intersection of infinitely many  
computations, but such a description would itself be the content of  
some observer's point of view that assumes a choice of Godel  
numbering scheme.

  Something doesn't seem right about this!

It seems to suggest "multi-solipsism" or something along those lines  
- which doesn't make it wrong, of course.


I await Bruno's answer with interest. I think he has already said  
something about this, but I don't recall it being satisfactory, at  
least to my limited understanding.


I am also interested to hear what Bruno has to say.


I should have read this before answering. Hope you are not too much  
disappointed :)



My perspective is that most of the computations that support you and  
I are not isolated and short-lived "computational Boltzmann brains"  
but much larger, long-running computations such as those that  
correspond to a universe in which life adapts and evolves.


Yes. I suspect both deep (in Bennett sense) computations, + the  
physical symmetrical and linear core. This would makes us both  
relatively very numerous in our type of reality, and relatively very  
rare at some other level. I suspect also the FPI relative random  
oracles to play some role in the "continuous" self-multiplication. But  
this is speculation, and should be derived from self-reference alone,  
to keep intact the exploitation of the G* minus G difference, on the  
intensional variants, to have the qualia and their non communicable  
feature.





The starting conditions for these is much less constrained, and  
therefore it is far more probable to result in conscious  
computations such as ours than the case where the computation  
supporting your brain experiencing this moment is some initial  
condition of a very specific program. Certainly, those programs  
exist too, but they are much rarer. They appear in the UD much less  
frequently than say the program corresponding to the approximate  
laws of physics of this universe.  It takes far more data to  
describe your brain than it does to describe the physical system on  
which it is based.


That is right. I think it is the correct intuition, but unfortunately,  
we cannot use it per se, we have to derive it from the math to be able  
to exploit the whole "theology" of the numbers. Universal system like  
the braids group, or the unitary group, might solve this, but we  
cannot use them directly, we have to derived them from the comp mind- 
body constraints.






So we are (mostly) still "in the same universe", and so we can  
interact with and affect the consciousness of other people.


Hopefully. The existence of 3 different sort of physical realities  
seems to give sense to a pretension of salvia (i), which is that a  
form of plural first person reality might still exists "near and after  
clinical death". this is not obvious. A priori, with comp, we might  
surivive in solipsist state, but apparently, there are entities with  
which we can communicate. In fact our own consciousness here and now,  
seems to involve many internal dialog and interaction.
Note that no Boltzman brain can ever implement a UD, nor even  
arbitrary part of UD*, which involves very long and stable  
computations. Eventually the "simple" but global and complete  
arithmetical reality is a very highly structured reality.


Bruno




Jason


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Re: Bruno's mathematical reality



On 27 Dec 2013, at 23:50, LizR wrote:

On 28 December 2013 05:51, Stephen Paul King > wrote:


It has always seemed to me that UDA cannot solve the mind-body  
problem strictly because it cannot comprehend the existence of  
"other minds".


Actually, I have wondered about this. How do all these "threads of  
computation" which are assumed to exist in arithmetic actually  
manage to communicate with each other?



Some universal system (in arithmetic, thus), can emulate interacting  
universal systems. Indeed the UD simulates even all possible  
interactions between universal systems. The only problem which remains  
is in the search of why such universal systems (allowing interactions)  
win the "measure battle", but for this we have to extract the measure  
first, and then the interaction from them. If we add interaction,  
without extracting it from comp, we are doing traditional physics, and  
we lost the qualia and all the non communicable stuff, and we put  
again the mind under the rug.


Stephen critics seems to miss the point that UDA *formulates* the  
constraints we have to follow in solving the mind body problem. he  
could as well say that UDA miss the gravitation law, Maxwell's  
equation, the H bosons, and actually even space and time. We are only  
at the beginning here.  All what comp already say, is that the  
possible answer are closer to Plato's theology than Aristotle  
theology, which means that comp forces us to backtrack on 1500 years  
on "theology", to get the comp-correct physics.


Bruno


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Re: Bruno's mathematical reality



On 27 Dec 2013, at 17:51, Stephen Paul King wrote:


Dear Bruno,


On Fri, Dec 27, 2013 at 11:11 AM, Bruno Marchal   
wrote:


On 25 Dec 2013, at 18:40, spudboy...@aol.com wrote:

Are we not presuming, structure, or a-priori, existence of  
something, doing this processing, this work?



In the UDA we assume a "Turing universal", or "sigma_1-complete"  
physical reality, in some local sense.



Could this "Turing universal/sigma_1-complete in a local sense" be  
the exact criteria required to define the observations 3-experiences  
of individuals or is it the 1-experiences of individuals (observers)  
in keeping with the definition of an observer as the intersection of  
infinitely many computations?


I think the UDA answers this question. You need Turing universality,  
but also the FPI, which in some sense comes from mechanism, but not  
necessarily "universality", which has, here, only an indirect  
relevance in the definition of what is a computation in arithmetic.









We need this to just explain what is a computer, alias, universal  
machine, alias universal number (implemented or not in a physical  
reality).
Note that we do not assume a *primitive physical reality*. In comp,  
we are a priori agnostic on this. The UDA, still will explains that  
such "primitiveness" cannot solve the mind-body problem when made  
into a dogma/assumption-of-primitiveness.


It has always seemed to me that UDA cannot solve the mind-body  
problem strictly because it cannot comprehend the existence of  
"other minds".


UDA formulates the problem, and show how big the mind-body problem is,  
even before tackling the "other minds" problem. But something is said.  
In fact it is easy to derive from the UDA the following assertions:


comp + explicit non-solipsism entails sharable many words or a core  
linear physical reality.


But comp in fact has to justify the non-solipsism, and this is begun  
through the nuance Bp & p versus Bp & Dt. Normally the linearity  
should allow the first person plural in the "& Dt" nuance case.


Keep in mind that UDA does not solve the problem, but formulate it.  
AUDA go more deep in a solution, and the shape of that solution (like  
UDA actually) provides already information contradicting the  
Aristotelian theology (used by atheists and the main part of  
institutionalized abramanic religion).


Bruno






Then in AUDA, keeping comp at the meta-level, I eliminate all  
assumptions above very elementary arithmetic (Robinson Arithmetic).


The little and big bangs, including the taxes, and why it hurts is  
derived from basically just


Kxy = x
Sxyz = xz(yz)

or just

x + 0 = x
x + s(y) = s(x + y)

 x *0 = 0
 x*s(y) = x*y + x





http://iridia.ulb.ac.be/~marchal/



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Re: Bruno's mathematical reality

Hi Brent,

  How "long do we have to wait" of the "generations" to "run" when time
isn't an allowed concept? In Platonia there is no time, therefore no
arguments that imply the necessary existence of time are allowed.

On Sat, Dec 28, 2013 at 1:40 AM, meekerdb  wrote:

>  On 12/27/2013 8:37 PM, Stephen Paul King wrote:
>
>  Why do "real world" computers use noise oracles, or their equivalent?
>
>
> Because for some problems it is quick and easy to check a proposed
> solution, but difficult to calculate one.  So you generate proposed
> solutions at random until one of them checks out as correct; and this may
> be more efficient.
>
> Brent
>
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Re: Bruno's mathematical reality

On Sat, Dec 28, 2013 at 12:23 AM, Stephen Paul King <
stephe...@provensecure.com> wrote:

> Hi Jason,
>
>
> On Sat, Dec 28, 2013 at 12:14 AM, Jason Resch wrote:
>
>>
>>
>>
>> On Sat, Dec 28, 2013 at 12:03 AM, Stephen Paul King <
>> stephe...@provensecure.com> wrote:
>>
>>> Hi Jason,
>>>
>>>   I would like to know the definition of "reality" that you are using
>>> here.
>>>
>>
>> Reality I normally define as "that which exists".
>>
>
> How is it that you can have knowledge of "what which exists"?
>

I don't. I don't know what reality is, but if something exists it is an
element of reality.

> Is your mind somehow a map of "all that exists"? Even if it was, the set
> of computations that is your mind is some measure zero subset. So how is it
> that your claim stands? That which exists cannot be contingent, just as the
> primeness of 17 is not contingent. Right?
>

This is ambiguous. You might say 17's primality is contingent on the fact
that it has no positive integer factors besides 1 and 17, but I would not
say it is contingent on a mathematician knowing that, or a computer
verifying it.

>
>
>
>>
>>
>>> Here is mine: *That which is incontrovertible for some collection of
>>> observers that can communicate*.
>>>
>>
>> So if there was a lone being in a universe would that being not have a
>> reality?  Is there no reality for deaf, illiterate, mutes?
>>
>
> A lone being in a universe has, by definition, no one to communicate with
> thus has no constraints on its state of being.
>

It still has a brain of its own, and perhaps physical laws that constrain
it.

What about the two hemispheres of its brain, can they be considered two
communicating observers?

> What is it? Everything. By definition. My definition does not have this
> problem.
>
>
>
>>
>>
>>> This definition requires interactions and thus requires some form of
>>> primitive becoming. Platonia does not change. Explain why there is an
>>> appearance of change that does not involve some reference to the natural
>>> ordering of the integers. Please.
>>>
>>
>> It's not the natural ordering of the integers, but the natural ordering
>> of each step in the states of a computation.  Though, even this does not
>> necessarily guarantee a "time-like" experience.  To experience time as we
>> do requires some memory and comparison between different states, and
>> perhaps some ignorance of future states.
>>
>
>
> What? What is the difference?
>

There is the ordering of the integers: 1, 2, 3, ...

But there is a different ordering of states (numbers) which may will differ
for different programs.

> How many ways are there to obtain a natural ordering of " each step in the
> states of a computation"?
>

There is a different one for each program.

> What is doing the mapping from that particular computation to the
> Integers?
>

The mathematical relation defining the UD, or some other program.

> Is it the integers? How? This is not an answer to my question. What
> determines the measure of change if change does not exist?
>

The presence of information and knowledge existing in a brain concerning
the difference between two or more successive states.

> If everything is "in Platonia" there is no change at all, and neither is
> any measure of what does not exist. Platonia has a Problem, Huston.
>

See the arguments with Edgar concerning presentism / eternalism in other
threads.  There is no need for change at the ultimate levels of reality, to
give rise to the experience of change within us.  Note, there is no
physical correlation of the color "pink" anywhere in our universe, it is
something that our brains manufacture.

>
>>
>>>
>>>
>>> Once we allow for Godel numbers, how can we still claim to use the
>>> natural order of the integers?
>>>
>>
>> I wasn't using this.
>>
>
> So what distinguishes one program from another?
>
>
It has its own memory space in the UD, its own history, and its own
counterfactuals.

>
>
>>
>>
>>>  We have already shown that a random sequence of numbers is a
>>> computation.
>>>
>>
>> When?
>>
>
> When we considered that the string that 'is' a computation can be
> encrypted by a one time pad or a randomly chosen godel numbering scheme.
> There is no unique universal Godel numbering!
>

A string is not a computation.  You may be making a similar confusion as
thinking the ASCII string "1 + 1 = 2" is identical with the computation 1 +
1 = 2. There is only one way a given Turing machine can/will interpret its
own tape, regardless of whether or not a differently configured Turing
machine could/would interpret the same tape in a different way.

>
>
>
>>
>>
>>>  Where do we find a "random sequence" in the naturally ordered string of
>>> Integers?
>>>
>>
>> It is not clear to me what you are asking.
>>
>>
> Does there exist a random string in the sequence of integers?
>

I don't think so. (at least not in any normal sense of the word random that
I would use)

Jason

>
>
>
>> Jason
>>
>>
>>>
>>>
>>>
>>> On Fri, Dec 27, 2013 at 11:58 PM,

Re: Bruno's mathematical reality


On 12/27/2013 8:37 PM, Stephen Paul King wrote:

Why do "real world" computers use noise oracles, or their equivalent?


Because for some problems it is quick and easy to check a proposed solution, but difficult 
to calculate one.  So you generate proposed solutions at random until one of them checks 
out as correct; and this may be more efficient.


Brent

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Re: Bruno's mathematical reality

On 28 December 2013 19:34, meekerdb  wrote:

>  On 12/27/2013 8:32 PM, LizR wrote:
>
>  On 28 December 2013 17:27, Jason Resch  wrote:
>
>>   On Fri, Dec 27, 2013 at 11:13 PM, Stephen Paul King <
>> stephe...@provensecure.com> wrote:
>>
>>>  If it is Markov, the BB problem automatically follows.
>>>
>>>"BB = Boltzmann Brains" ?
>>
>
>  Yes.
>
>>
>>  What is the problem?  BB's exist in the UD, as we discussed above, but
>> they seem like they would have a low measure compared to brains that arise
>> from less specific initial conditions.
>>
>
>  Very very low measure, apparently. I've never met one.
>
>
> You mean you don't remember meeting one. :-)
>
> I've never met the Silence from Dr Who either...

[insert slightly worried looking emoticon]

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Re: Bruno's mathematical reality


On 12/27/2013 8:32 PM, LizR wrote:
On 28 December 2013 17:27, Jason Resch > wrote:


On Fri, Dec 27, 2013 at 11:13 PM, Stephen Paul King 
mailto:stephe...@provensecure.com>> wrote:

If it is Markov, the BB problem automatically follows.

"BB = Boltzmann Brains" ?


Yes.


What is the problem?  BB's exist in the UD, as we discussed above, but they 
seem
like they would have a low measure compared to brains that arise from less 
specific
initial conditions.


Very very low measure, apparently. I've never met one.


You mean you don't remember meeting one. :-)

Brent

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Re: Bruno's mathematical reality

Right. That is why the word "incontrovertible" is included. One's opinions
and desires, etc. con't matter a hill of beans to what is necessarily true
for come collection of (multiple!) observers. I also assume a version of
the anthropic principle: An observer can only experience a "reality" that
is not contradictory to its existence.

On Sat, Dec 28, 2013 at 1:32 AM, LizR  wrote:

> On 28 December 2013 18:03, Stephen Paul King 
> wrote:
>
>> Hi Jason,
>>
>>   I would like to know the definition of "reality" that you are using
>> here.
>>
>
> I quite like "whatever doesn't go away when you stop believing in it."
>
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Re: Bruno's mathematical reality

On 28 December 2013 19:31, Stephen Paul King wrote:

> Computed how? By what?
>

I know the answer to this one! To quote Brent -- "He proposes to dispense
with any physical computation and have the UD exist via arithmetical
realism as an abstract, immaterial computation."

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Re: Bruno's mathematical reality

On 28 December 2013 18:03, Stephen Paul King wrote:

> Hi Jason,
>
>   I would like to know the definition of "reality" that you are using here.
>

I quite like "whatever doesn't go away when you stop believing in it."

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Re: Bruno's mathematical reality


On 12/27/2013 8:24 PM, Stephen Paul King wrote:

Hi Edgar,

  But here is the thing. If we assume timelessness, Bruno is CORRECT! THe question then 
becomes: What is "time"?


It's a computed partial ordering relation between events.

Brent

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Re: Bruno's mathematical reality

Computed how? By what?

On Sat, Dec 28, 2013 at 1:30 AM, meekerdb  wrote:

>  On 12/27/2013 8:24 PM, Stephen Paul King wrote:
>
>  Hi Edgar,
>
>But here is the thing. If we assume timelessness, Bruno is CORRECT!
> THe question then becomes: What is "time"?
>
>
> It's a computed partial ordering relation between events.
>
> Brent
>
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Re: Bruno's mathematical reality

On 12/27/2013 8:08 PM, Edgar L. Owen wrote:

Jason,

Let me point out one fatal problem with Bruno's theory as you present it.

According to you there is some single processor that runs all this UD stuff, but the
truth is that in actual computational reality every logical element

What is a "logical element"? a NAND gate?

functions as a processor so all computations proceed at once in every cycle of
time.

So this computation is embedded in time, but not in space. In the UD model time and space
are both computed relations.

This is the only way everything in the universe could possibly get computed. A
computation here can't possibly wait for one on the other side of the universe!

If time is a computed relation it doesn't matter how many steps it takes to compute it -
the duration is whatever it is computed to be. It's just like most simulations I know; it
runs a lot slower than "real" time.

If Bruno's UD requires a single processor of reality it simply cannot describe actual
computational reality.

He proposes to dispense with any physical computation and have the UD exist via
arithmetical realism as an abstract, immaterial computation.

Brent

Re: Bruno's mathematical reality

Hi Brent,

What is "executing" it?


On Sat, Dec 28, 2013 at 1:13 AM, meekerdb  wrote:

>  On 12/27/2013 7:54 PM, LizR wrote:
>
>  On 28 December 2013 16:44, Stephen Paul King 
> wrote:
>
>>  Hi Jason,
>>
>>  "The first, second, 10th, 1,000,000th, and 10^100th, and 10^100^100th
>> state of the UD's execution are mathematical facts ..." Umm, how? Godel
>> and Matiyasevich would disagree! If there does not exist a program that can
>> evaluate whether or not a UD substring is a faithful representation of a
>> "true theorem", then how is it "a fact"?
>>
>
> The UD is deterministic.  Part of Bruno's point is to explain apparent
> randomness without having to assume any.  Any computational state reached
> by the UD is a "true theorem" of whichever program it is executing.
>
> Brent
>
>
>>  That depends on whether the UD is deterministic or not. If it is, then,
> its Nth state is a fact. (It doesn't need to be run or evaluated, and the
> Nth state may be a fact that nobody knows, like the googolth digit of pi,
> assuming no one's worked that out.)
>
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Re: Bruno's mathematical reality


On 12/27/2013 7:54 PM, LizR wrote:
On 28 December 2013 16:44, Stephen Paul King > wrote:


Hi Jason,

"The first, second, 10th, 1,000,000th, and 10^100th, and 10^100^100th state 
of the
UD's execution are mathematical facts ..." Umm, how? Godel and Matiyasevich 
would
disagree! If there does not exist a program that can evaluate whether or 
not a UD
substring is a faithful representation of a "true theorem", then how is it "a 
fact"?



The UD is deterministic.  Part of Bruno's point is to explain apparent randomness without 
having to assume any.  Any computational state reached by the UD is a "true theorem" of 
whichever program it is executing.


Brent



That depends on whether the UD is deterministic or not. If it is, then, its Nth state is 
a fact. (It doesn't need to be run or evaluated, and the Nth state may be a fact that 
nobody knows, like the googolth digit of pi, assuming no one's worked that out.)


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Re: Bruno's mathematical reality

Hi Jason,

On Sat, Dec 28, 2013 at 12:14 AM, Jason Resch  wrote:

>
>
>
> On Sat, Dec 28, 2013 at 12:03 AM, Stephen Paul King <
> stephe...@provensecure.com> wrote:
>
>> Hi Jason,
>>
>>   I would like to know the definition of "reality" that you are using
>> here.
>>
>
> Reality I normally define as "that which exists".
>

How is it that you can have knowledge of "what which exists"? Is your mind
somehow a map of "all that exists"? Even if it was, the set of
computations that is your mind is some measure zero subset. So how is it
that your claim stands? That which exists cannot be contingent, just as the
primeness of 17 is not contingent. Right?

>
>
>> Here is mine: *That which is incontrovertible for some collection of
>> observers that can communicate*.
>>
>
> So if there was a lone being in a universe would that being not have a
> reality?  Is there no reality for deaf, illiterate, mutes?
>

A lone being in a universe has, by definition, no one to communicate with
thus has no constraints on its state of being. What is it? Everything. By
definition. My definition does not have this problem.

>
>
>> This definition requires interactions and thus requires some form of
>> primitive becoming. Platonia does not change. Explain why there is an
>> appearance of change that does not involve some reference to the natural
>> ordering of the integers. Please.
>>
>
> It's not the natural ordering of the integers, but the natural ordering of
> each step in the states of a computation.  Though, even this does not
> necessarily guarantee a "time-like" experience.  To experience time as we
> do requires some memory and comparison between different states, and
> perhaps some ignorance of future states.
>

What? What is the difference? How many ways are there to obtain a natural
ordering of " each step in the states of a computation"? What is doing the
mapping from that particular computation to the Integers? Is it the
integers? How? This is not an answer to my question. What determines the
measure of change if change does not exist? If everything is "in
Platonia" there is no change at all, and neither is any measure of what
does not exist. Platonia has a Problem, Huston.

>
>
>>
>>
>> Once we allow for Godel numbers, how can we still claim to use the
>> natural order of the integers?
>>
>
> I wasn't using this.
>

So what distinguishes one program from another?

>
>
>> We have already shown that a random sequence of numbers is a computation.
>>
>
> When?
>

When we considered that the string that 'is' a computation can be
encrypted by a one time pad or a randomly chosen godel numbering scheme.
There is no unique universal Godel numbering!

>
>
>>  Where do we find a "random sequence" in the naturally ordered string of
>> Integers?
>>
>
> It is not clear to me what you are asking.
>
>
Does there exist a random string in the sequence of integers?

> Jason
>
>
>>
>>
>>
>> On Fri, Dec 27, 2013 at 11:58 PM, Jason Resch wrote:
>>
>>>
>>>
>>>
>>> On Fri, Dec 27, 2013 at 11:53 PM, Stephen Paul King <
>>> stephe...@provensecure.com> wrote:
>>>
 Hi LizR,

   This is fun! :-) We must remember that we are defining People as
 intersections of infinitely many computations. Right? Their perceptions of
 themselves as physical being having some particular set of configuration,
 for example bilateral symmetry, etc. is not really relevant to UDA. So, if
 there is a change in accessibility to data, facts, etc. Where is that
 "change" coming from".

   This is my problem: We are presented with an argument that works in
 Platonia and we have no explanation as to the relation it has with the
 "real world" where things change and degrade and evolve, etc. What is
 measuring that change?

>>>
>>> If the argument is correct there is no other reality but Platonia. The
>>> "real world" is a product of the computations in platonia.
>>>
>>> Jason
>>>
>>>

 On Fri, Dec 27, 2013 at 11:49 PM, LizR  wrote:

> On 28 December 2013 17:46, Stephen Paul King <
> stephe...@provensecure.com> wrote:
>
>> Ah, but they do degrade. Consider your ability to access a '80s
>> floppy drive's data.
>>
>> Well, that's because people haven't worked out how to do it
> perfectly. I agree digital archaeology is a real problem, but so would
> analogue be without the relevant machines to play it back (admittedly it's
> easier to decode analogue from first principles). But that is a different
> form of degrading. If you have a system capable of copying the data it
> should be more or less 100% accurate.
>
>>
>> On Fri, Dec 27, 2013 at 11:44 PM, LizR  wrote:
>>
>>>  On 28 December 2013 17:41, Jason Resch wrote:
>>>
 On Fri, Dec 27, 2013 at 11:27 PM, Stephen Paul King <
 stephe...@provensecure.com> wrote:

> Hi LizR and Jason,
>
>   Responding to both of you. I don't understand

Re: Bruno's mathematical reality

On Sat, Dec 28, 2013 at 12:03 AM, Stephen Paul King <
stephe...@provensecure.com> wrote:

> Hi Jason,
>
>   I would like to know the definition of "reality" that you are using
> here.
>

Reality I normally define as "that which exists".


> Here is mine: *That which is incontrovertible for some collection of
> observers that can communicate*.
>

So if there was a lone being in a universe would that being not have a
reality?  Is there no reality for deaf, illiterate, mutes?


> This definition requires interactions and thus requires some form of
> primitive becoming. Platonia does not change. Explain why there is an
> appearance of change that does not involve some reference to the natural
> ordering of the integers. Please.
>

It's not the natural ordering of the integers, but the natural ordering of
each step in the states of a computation.  Though, even this does not
necessarily guarantee a "time-like" experience.  To experience time as we
do requires some memory and comparison between different states, and
perhaps some ignorance of future states.


>
>
> Once we allow for Godel numbers, how can we still claim to use the natural
> order of the integers?
>

I wasn't using this.


> We have already shown that a random sequence of numbers is a computation.
>

When?


> Where do we find a "random sequence" in the naturally ordered string of
> Integers?
>

It is not clear to me what you are asking.

Jason


>
>
>
> On Fri, Dec 27, 2013 at 11:58 PM, Jason Resch wrote:
>
>>
>>
>>
>> On Fri, Dec 27, 2013 at 11:53 PM, Stephen Paul King <
>> stephe...@provensecure.com> wrote:
>>
>>> Hi LizR,
>>>
>>>   This is fun! :-) We must remember that we are defining People as
>>> intersections of infinitely many computations. Right? Their perceptions of
>>> themselves as physical being having some particular set of configuration,
>>> for example bilateral symmetry, etc. is not really relevant to UDA. So, if
>>> there is a change in accessibility to data, facts, etc. Where is that
>>> "change" coming from".
>>>
>>>   This is my problem: We are presented with an argument that works in
>>> Platonia and we have no explanation as to the relation it has with the
>>> "real world" where things change and degrade and evolve, etc. What is
>>> measuring that change?
>>>
>>
>> If the argument is correct there is no other reality but Platonia. The
>> "real world" is a product of the computations in platonia.
>>
>> Jason
>>
>>
>>>
>>>
>>> On Fri, Dec 27, 2013 at 11:49 PM, LizR  wrote:
>>>
 On 28 December 2013 17:46, Stephen Paul King <
 stephe...@provensecure.com> wrote:

> Ah, but they do degrade. Consider your ability to access a '80s floppy
> drive's data.
>
> Well, that's because people haven't worked out how to do it perfectly.
 I agree digital archaeology is a real problem, but so would analogue be
 without the relevant machines to play it back (admittedly it's easier to
 decode analogue from first principles). But that is a different form of
 degrading. If you have a system capable of copying the data it should be
 more or less 100% accurate.

>
> On Fri, Dec 27, 2013 at 11:44 PM, LizR  wrote:
>
>>  On 28 December 2013 17:41, Jason Resch  wrote:
>>
>>> On Fri, Dec 27, 2013 at 11:27 PM, Stephen Paul King <
>>> stephe...@provensecure.com> wrote:
>>>
 Hi LizR and Jason,

   Responding to both of you. I don't understand the claim of
 determinism is "random noise" is necessary for the computations. Turing
 machines require exact pre-specifiability. Adding noise oracles is 
 cheating!


>>> I think you misunderstand.  Computers are deterministic, but they
>>> often need randomness to implement things such as cryptography or
>>> monte-carlo simulations, etc.  Due to this need for true 
>>> unpredictability,
>>> our computers must harness environmental noise if they are to have any 
>>> hope
>>> of being unpredictable.  This is because computers cannot generate
>>> unpredictability on their own.
>>>
>>> They are engineered not to! This is why digital recordings don't
>> degrade, etc.
>>
>> --
>> You received this message because you are subscribed to a topic in
>> the Google Groups "Everything List" group.
>> To unsubscribe from this topic, visit
>> https://groups.google.com/d/topic/everything-list/sqWzozazMg0/unsubscribe
>> .
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>>
>
>
>
> --
>
> Kindest Regards,
>
> Stephen Paul King
>
> Senior Researcher
>
> Mobile: (

Re: Bruno's mathematical reality

Hi Jason,

  I would like to know the definition of "reality" that you are using here.
Here is mine: *That which is incontrovertible for some collection of
observers that can communicate*. This definition requires interactions and
thus requires some form of primitive becoming. Platonia does not change.
Explain why there is an appearance of change that does not involve some
reference to the natural ordering of the integers. Please.

Once we allow for Godel numbers, how can we still claim to use the natural
order of the integers? We have already shown that a random sequence of
numbers is a computation. Where do we find a "random sequence" in the
naturally ordered string of Integers?



On Fri, Dec 27, 2013 at 11:58 PM, Jason Resch  wrote:

>
>
>
> On Fri, Dec 27, 2013 at 11:53 PM, Stephen Paul King <
> stephe...@provensecure.com> wrote:
>
>> Hi LizR,
>>
>>   This is fun! :-) We must remember that we are defining People as
>> intersections of infinitely many computations. Right? Their perceptions of
>> themselves as physical being having some particular set of configuration,
>> for example bilateral symmetry, etc. is not really relevant to UDA. So, if
>> there is a change in accessibility to data, facts, etc. Where is that
>> "change" coming from".
>>
>>   This is my problem: We are presented with an argument that works in
>> Platonia and we have no explanation as to the relation it has with the
>> "real world" where things change and degrade and evolve, etc. What is
>> measuring that change?
>>
>
> If the argument is correct there is no other reality but Platonia. The
> "real world" is a product of the computations in platonia.
>
> Jason
>
>
>>
>>
>> On Fri, Dec 27, 2013 at 11:49 PM, LizR  wrote:
>>
>>> On 28 December 2013 17:46, Stephen Paul King >> > wrote:
>>>
 Ah, but they do degrade. Consider your ability to access a '80s floppy
 drive's data.

 Well, that's because people haven't worked out how to do it perfectly.
>>> I agree digital archaeology is a real problem, but so would analogue be
>>> without the relevant machines to play it back (admittedly it's easier to
>>> decode analogue from first principles). But that is a different form of
>>> degrading. If you have a system capable of copying the data it should be
>>> more or less 100% accurate.
>>>

 On Fri, Dec 27, 2013 at 11:44 PM, LizR  wrote:

>  On 28 December 2013 17:41, Jason Resch  wrote:
>
>> On Fri, Dec 27, 2013 at 11:27 PM, Stephen Paul King <
>> stephe...@provensecure.com> wrote:
>>
>>> Hi LizR and Jason,
>>>
>>>   Responding to both of you. I don't understand the claim of
>>> determinism is "random noise" is necessary for the computations. Turing
>>> machines require exact pre-specifiability. Adding noise oracles is 
>>> cheating!
>>>
>>>
>> I think you misunderstand.  Computers are deterministic, but they
>> often need randomness to implement things such as cryptography or
>> monte-carlo simulations, etc.  Due to this need for true 
>> unpredictability,
>> our computers must harness environmental noise if they are to have any 
>> hope
>> of being unpredictable.  This is because computers cannot generate
>> unpredictability on their own.
>>
>> They are engineered not to! This is why digital recordings don't
> degrade, etc.
>
> --
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 --

 Kindest Regards,

 Stephen Paul King

 Senior Researcher

 Mobile: (864) 567-3099

 stephe...@provensecure.com

  http://www.provensecure.us/


 “This message (including any attachments) is intended only for the use
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Re: Bruno's mathematical reality

On Fri, Dec 27, 2013 at 11:53 PM, Stephen Paul King <
stephe...@provensecure.com> wrote:

> Hi LizR,
>
>   This is fun! :-) We must remember that we are defining People as
> intersections of infinitely many computations. Right? Their perceptions of
> themselves as physical being having some particular set of configuration,
> for example bilateral symmetry, etc. is not really relevant to UDA. So, if
> there is a change in accessibility to data, facts, etc. Where is that
> "change" coming from".
>
>   This is my problem: We are presented with an argument that works in
> Platonia and we have no explanation as to the relation it has with the
> "real world" where things change and degrade and evolve, etc. What is
> measuring that change?
>

If the argument is correct there is no other reality but Platonia. The
"real world" is a product of the computations in platonia.

Jason


>
>
> On Fri, Dec 27, 2013 at 11:49 PM, LizR  wrote:
>
>> On 28 December 2013 17:46, Stephen Paul King 
>> wrote:
>>
>>> Ah, but they do degrade. Consider your ability to access a '80s floppy
>>> drive's data.
>>>
>>> Well, that's because people haven't worked out how to do it perfectly. I
>> agree digital archaeology is a real problem, but so would analogue be
>> without the relevant machines to play it back (admittedly it's easier to
>> decode analogue from first principles). But that is a different form of
>> degrading. If you have a system capable of copying the data it should be
>> more or less 100% accurate.
>>
>>>
>>> On Fri, Dec 27, 2013 at 11:44 PM, LizR  wrote:
>>>
  On 28 December 2013 17:41, Jason Resch  wrote:

> On Fri, Dec 27, 2013 at 11:27 PM, Stephen Paul King <
> stephe...@provensecure.com> wrote:
>
>> Hi LizR and Jason,
>>
>>   Responding to both of you. I don't understand the claim of
>> determinism is "random noise" is necessary for the computations. Turing
>> machines require exact pre-specifiability. Adding noise oracles is 
>> cheating!
>>
>>
> I think you misunderstand.  Computers are deterministic, but they
> often need randomness to implement things such as cryptography or
> monte-carlo simulations, etc.  Due to this need for true unpredictability,
> our computers must harness environmental noise if they are to have any 
> hope
> of being unpredictable.  This is because computers cannot generate
> unpredictability on their own.
>
> They are engineered not to! This is why digital recordings don't
 degrade, etc.

 --
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>>>
>>>
>>>
>>> --
>>>
>>> Kindest Regards,
>>>
>>> Stephen Paul King
>>>
>>> Senior Researcher
>>>
>>> Mobile: (864) 567-3099
>>>
>>> stephe...@provensecure.com
>>>
>>>  http://www.provensecure.us/
>>>
>>>
>>> “This message (including any attachments) is intended only for the use
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>>> hereby notified that any use, dissemination, distribution, or copying of
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Re: Bruno's mathematical reality

http://kauffman2013.wordpress.com/

:-)

On Fri, Dec 27, 2013 at 11:51 PM, LizR  wrote:

> On 28 December 2013 17:47, Stephen Paul King 
> wrote:
>
>> Loops are sometimes allowed as outputs of computations. :-)
>>
>
> I think we came out one turn higher on the spiral staircase.
>
> --
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stephe...@provensecure.com

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Re: Bruno's mathematical reality

Hi LizR,

  This is fun! :-) We must remember that we are defining People as
intersections of infinitely many computations. Right? Their perceptions of
themselves as physical being having some particular set of configuration,
for example bilateral symmetry, etc. is not really relevant to UDA. So, if
there is a change in accessibility to data, facts, etc. Where is that
"change" coming from".

  This is my problem: We are presented with an argument that works in
Platonia and we have no explanation as to the relation it has with the
"real world" where things change and degrade and evolve, etc. What is
measuring that change?


On Fri, Dec 27, 2013 at 11:49 PM, LizR  wrote:

> On 28 December 2013 17:46, Stephen Paul King 
> wrote:
>
>> Ah, but they do degrade. Consider your ability to access a '80s floppy
>> drive's data.
>>
>> Well, that's because people haven't worked out how to do it perfectly. I
> agree digital archaeology is a real problem, but so would analogue be
> without the relevant machines to play it back (admittedly it's easier to
> decode analogue from first principles). But that is a different form of
> degrading. If you have a system capable of copying the data it should be
> more or less 100% accurate.
>
>>
>> On Fri, Dec 27, 2013 at 11:44 PM, LizR  wrote:
>>
>>>  On 28 December 2013 17:41, Jason Resch  wrote:
>>>
 On Fri, Dec 27, 2013 at 11:27 PM, Stephen Paul King <
 stephe...@provensecure.com> wrote:

> Hi LizR and Jason,
>
>   Responding to both of you. I don't understand the claim of
> determinism is "random noise" is necessary for the computations. Turing
> machines require exact pre-specifiability. Adding noise oracles is 
> cheating!
>
>
 I think you misunderstand.  Computers are deterministic, but they often
 need randomness to implement things such as cryptography or monte-carlo
 simulations, etc.  Due to this need for true unpredictability, our
 computers must harness environmental noise if they are to have any hope of
 being unpredictable.  This is because computers cannot generate
 unpredictability on their own.

 They are engineered not to! This is why digital recordings don't
>>> degrade, etc.
>>>
>>> --
>>> You received this message because you are subscribed to a topic in the
>>> Google Groups "Everything List" group.
>>> To unsubscribe from this topic, visit
>>> https://groups.google.com/d/topic/everything-list/sqWzozazMg0/unsubscribe
>>> .
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>>> For more options, visit https://groups.google.com/groups/opt_out.
>>>
>>
>>
>>
>> --
>>
>> Kindest Regards,
>>
>> Stephen Paul King
>>
>> Senior Researcher
>>
>> Mobile: (864) 567-3099
>>
>> stephe...@provensecure.com
>>
>>  http://www.provensecure.us/
>>
>>
>> “This message (including any attachments) is intended only for the use of
>> the individual or entity to which it is addressed, and may contain
>> information that is non-public, proprietary, privileged, confidential and
>> exempt from disclosure under applicable law or may be constituted as
>> attorney work product. If you are not the intended recipient, you are
>> hereby notified that any use, dissemination, distribution, or copying of
>> this communication is strictly prohibited. If you have received this
>> message in error, notify sender immediately and delete this message
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Senior Researcher

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stephe...@provensecure.com

 http://www.provensecure.us/


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Re: Bruno's mathematical reality

On Fri, Dec 27, 2013 at 11:31 PM, Stephen Paul King <
stephe...@provensecure.com> wrote:

> Hi Jason,
>
>
> On Fri, Dec 27, 2013 at 11:23 PM, Jason Resch wrote:
>
>>
>>
>>
>> On Fri, Dec 27, 2013 at 11:09 PM, Stephen Paul King <
>> stephe...@provensecure.com> wrote:
>>
>>> Hi Jason,
>>>
>>>   "It is not a question of whether or not that binary string refers to
>>> anything that is true or not, only what its particular value happens to
>>> be." No no no! We can not make statements without showing how their
>>> proof are accessible!
>>>
>>>
>> The proof is straight forward. Run the UD and see what the state is.
>>
>
> Run it, on what hardware? ??
>
>
Bruno ran the UD on his computer a few years ago.  I don't know how many
programs and instructions it got through running though.

In any case, the there is a proof that there is a proof that the Nth state
of the UD has a particular definite value.


>
>
>>
>> Are you objecting that it does not have a definite value because you or I
>> are not capable of computing it?
>>
>> Did the 100th digit of Pi not exist until the first human computed it?
>>
>
> Pfft, that is a red herring and you know it! Why even mention humans? If
> numbers exist, then that existence has nothing at all to do with humans or
> aliens of black clouds.
>

That's my point.  It doesn't matter if anyone computes it or not, its
computation exists already in mathematical truth.


> It is merely the necessary possibility that the numbers are not
> inconsistent. If they were inconsistent, then all that would exist is
> noise. And we are back to my question. What decodes the noise into
> "meaningful" strings?
>

The conscious programs make sense of their own environments in which they
arise.


>
>
>
>>
>>
>>>  Consider the i-th through j_th values of pi's expansion in binary. If
>>> it is a finite string, how do we know that it is a Turing machine program?
>>>
>>>
>> All integers can be mapped directly to Turing machine programs.  Consider
>> Java: it uses a byte-code where every byte is an instruction for the Java
>> virtual machine.  Every string of bytes can therefore be considered as a
>> sequence of instructions for the Java virtual machine to execute.
>>
>
> SO it is OK to include the java code that generates noise.
>

There is isn't quite noise, it is more analogous to counting.


> There are your oracles! Pick one. Whoops, how is the selection made?
>
>
The anthropic principle chooses universes where conscious life can arise.
 The same is true of the UD. Programs and environments in which
consciousness can arise is selected by those conscious entities.

Jason


>
>
>>
>> Jason
>>
>>
>>>
>>>
>>> On Fri, Dec 27, 2013 at 11:06 PM, Jason Resch wrote:
>>>



 On Fri, Dec 27, 2013 at 10:44 PM, Stephen Paul King <
 stephe...@provensecure.com> wrote:

> Hi Jason,
>
> "The first, second, 10th, 1,000,000th, and 10^100th, and 10^100^100th
> state of the UD's execution are mathematical facts ..." Umm, how?
> Godel and Matiyasevich would disagree! If there does not exist a program
> that can evaluate whether or not a UD substring is a faithful
> representation of a "true theorem", then how is it "a fact"?
>
>
 The mathematical fact to which I am referring is only a basic and
 straight-forward statement like "the binary representation of the state of
 UD after executing 100..00th steps is '101010010...0010". It is not a
 question of whether or not that binary string refers to anything that is
 true or not, only what its particular value happens to be.

 Jason


>
> On Fri, Dec 27, 2013 at 10:09 PM, Jason Resch wrote:
>
>>
>>
>>
>> On Fri, Dec 27, 2013 at 9:31 PM, Stephen Paul King <
>> stephe...@provensecure.com> wrote:
>>
>>> Hi Jason,
>>>
>>>   Could you discuss the "trace of the UD" that LizR mentioned? How
>>> is it computed? Could you write an explicit example? I have never been 
>>> able
>>> to grok it.
>>>
>>>
>> Bruno has written an actual UD in the LISP programming language.  I
>> will write a simple one in pseudo-code below:
>>
>> List listOfPrograms = new List[]; # Empty list
>> int i = 0;
>> while (true)
>> {
>># Create a program corresponding to the binary expansion of the
>> integer i
>>Program P = createProgramFromInteger(i);
>>
>># Add the program to a list of programs we have generated so far
>>listOfPrograms.add(P);
>>
>># For each program we have generated that has not halted, execute
>> one instruction of it
>>for each (Program p in listOfPrograms)
>>{
>>  if (p.hasHalted() == false)
>>  {
>> executeOneInstruction(p);
>>  }
>>}
>>
>># Finally, increment i so a new program is generated the next time
>> through
>>i = i + 1;
>> }
>>
>>
>> Any

Re: Bruno's mathematical reality

On 28 December 2013 17:47, Stephen Paul King wrote:

> Loops are sometimes allowed as outputs of computations. :-)
>

I think we came out one turn higher on the spiral staircase.

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Re: Bruno's mathematical reality

On 28 December 2013 17:47, Stephen Paul King wrote:

> Yeah, it is! Its about how one computer's noise is another computer's
> signal!
>

It throws SETI into a loop too. How can we detect encrypted signals from
the stars? They'll look like noise!

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Re: Bruno's mathematical reality

On 28 December 2013 17:46, Stephen Paul King wrote:

> Ah, but they do degrade. Consider your ability to access a '80s floppy
> drive's data.
>
> Well, that's because people haven't worked out how to do it perfectly. I
agree digital archaeology is a real problem, but so would analogue be
without the relevant machines to play it back (admittedly it's easier to
decode analogue from first principles). But that is a different form of
degrading. If you have a system capable of copying the data it should be
more or less 100% accurate.

>
> On Fri, Dec 27, 2013 at 11:44 PM, LizR  wrote:
>
>> On 28 December 2013 17:41, Jason Resch  wrote:
>>
>>> On Fri, Dec 27, 2013 at 11:27 PM, Stephen Paul King <
>>> stephe...@provensecure.com> wrote:
>>>
 Hi LizR and Jason,

   Responding to both of you. I don't understand the claim of
 determinism is "random noise" is necessary for the computations. Turing
 machines require exact pre-specifiability. Adding noise oracles is 
 cheating!


>>> I think you misunderstand.  Computers are deterministic, but they often
>>> need randomness to implement things such as cryptography or monte-carlo
>>> simulations, etc.  Due to this need for true unpredictability, our
>>> computers must harness environmental noise if they are to have any hope of
>>> being unpredictable.  This is because computers cannot generate
>>> unpredictability on their own.
>>>
>>> They are engineered not to! This is why digital recordings don't
>> degrade, etc.
>>
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Re: Bruno's mathematical reality

Loops are sometimes allowed as outputs of computations. :-)


On Fri, Dec 27, 2013 at 11:46 PM, LizR  wrote:

> On 28 December 2013 17:45, Stephen Paul King 
> wrote:
>
>> That is the question, isn't it!
>>
>> I think this thread just disappeared into its own Ouroboros...
>
>>
>> On Fri, Dec 27, 2013 at 11:42 PM, LizR  wrote:
>>
>>> On 28 December 2013 17:38, Stephen Paul King >> > wrote:
>>>
 "Anything that emulates a Turing machine to sufficient accuracy (i.e.
 can expand its tape as necessary)." How is this determined without actually
 running the computation on a physical machine?

>>>
>>> How is what determined?
>>>
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>>
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>>
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Re: Bruno's mathematical reality

On 28 December 2013 17:45, Stephen Paul King wrote:

> That is the question, isn't it!
>
> I think this thread just disappeared into its own Ouroboros...

>
> On Fri, Dec 27, 2013 at 11:42 PM, LizR  wrote:
>
>> On 28 December 2013 17:38, Stephen Paul King 
>> wrote:
>>
>>> "Anything that emulates a Turing machine to sufficient accuracy (i.e.
>>> can expand its tape as necessary)." How is this determined without actually
>>> running the computation on a physical machine?
>>>
>>
>> How is what determined?
>>
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Re: Bruno's mathematical reality

Yeah, it is! Its about how one computer's noise is another computer's
signal!

On Fri, Dec 27, 2013 at 11:45 PM, LizR  wrote:

> On 28 December 2013 17:44, Stephen Paul King 
> wrote:
>
>> I have studied encryptions. My mind is still recovering from reading the
>> Stay and Vicary paper! (It shows an equivalence in principle between one
>> time pad encryptions and quantum teleportation protocols...)
>>
>
> I read up on encryption once. It's pretty mind boggling stuff, isn't it!
>
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Re: Bruno's mathematical reality