Re: Gödel's Miracle and Why Conventionalism makes no sense in Computer Science

2020-05-31 Thread 'Brent Meeker' via Everything List 



On 5/31/2020 4:32 PM, Bruce Kellett wrote:
On Mon, Jun 1, 2020 at 9:05 AM 'Brent Meeker' via Everything List 
> wrote:


On 5/31/2020 3:49 PM, Bruce Kellett wrote:

On Mon, Jun 1, 2020 at 8:31 AM 'Brent Meeker' via Everything List
mailto:everything-list@googlegroups.com>> wrote:

On 5/31/2020 3:23 PM, Bruce Kellett wrote:

On Mon, Jun 1, 2020 at 3:12 AM 'Brent Meeker' via Everything
List mailto:everything-list@googlegroups.com>> wrote:

On 5/30/2020 10:44 PM, Bruce Kellett wrote:

On Sun, May 31, 2020 at 2:26 AM Bruno Marchal
mailto:marc...@ulb.ac.be>> wrote:


Let us write f_n for the function from N to N
computed by nth expression.

Now, the function g defined by g(n) = f_n(n) + 1 is
computable, and is defined on all N. So it is a
computable function from N to N. It is computable
because it each f_n is computable, “+ 1” is
computable, and, vy our hypothesis it get all and
only all computable functions from N to N.

But then, g has have itself an expression in that
universal language, of course. There there is a
number k such that g = f_k. OK?

But then we get that g_k, applied to k has to give
f_k(k), as g = f_k, and f_k(k) + 1, by definition
of g.



That is a fairly elementary blunder. g_k applied to k,
g_k(k) = f_n(k)+1, by definition of g_k. You do not get
to change the function from f_n to f_k in the
expression. It is only the argument that changes: in
other words, f_n(n) becomes f_n(k). So you are talking
nonsense.


No, I think that's OK.  It's a straight substitution
n->k.  The trick is that g(n) is not some well defined
specific function because n has infinite range.  So none
of this works in a finite world.  But it's not
surprising that there is incompleteness in an infinite
theory.



Yes, I had misunderstood what g(n) was supposed to be -- it
is simply a representation of the diagonal elements of the
array, plus 1. But Bruno's attempt to use the diagonal
argument here fails, because  he has to show that f_n(n)+1
is not contained in the infinite list. He has failed to do this.


All computable functions are in the list ex hypothesi.



That is what the diagonal argument is all about: you hypothesize
that all bit strings (for example) are in your infinite list.
Then you flip the diagonal bit of each string and form a new
string from all the diagonal elements. And lo, that new string is
not in the initial list. Therefore your hypothesis that all bit
strings are in the list is disproven.

Bruno has attempted toride to glory on this argument, and has
failed miserably!


That's a general problem with reductio arguments.  When you get to
end you don't know which premise was wrong. Bruno, isn't changing
the hypothetical list though, so he's saying the premise that you
can order the total functions is wrong.  You can order the
functions (say lexigraphically) but you can't know which are total.

ISTM the result, that there's an incompleteness theorem for the
set of all functions, is quite intuitive.  But Bruno seems to be
saying this is all finitist because he doesn't assum and axiom of
infinity.  Yet the "diagonalization" doesn't work in a finite world.



Take all bit strings of length N (finite) and apply the diagonal 
argument. The string resulting from putting all the flipped diagonal 
bits together is not in the original list, contradicting the 
assumption that the list is complete.


If N is finite then there are only 2^N possible bit strings and the list 
will include all of them.  So when you flip a bit in each one you get 
the same list, just reordered.


Brent

Of course, the list of all strings of length N contains more than N 
elements, so the diagonal argument does not apply. The set of all 
strings of infinite length is certainly infinite, so one might work 
the diagonal argument there -- if one doesn't worry too much about 
cardinality issues..


I think Bruno should rephrase his argument -- it might be sensible, 
but as presented it was clearly invalid.


Bruce
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Re: Gödel's Miracle and Why Conventionalism makes no sense in Computer Science

2020-05-31 Thread Bruce Kellett 
On Mon, Jun 1, 2020 at 9:05 AM 'Brent Meeker' via Everything List <
everything-list@googlegroups.com> wrote:

> On 5/31/2020 3:49 PM, Bruce Kellett wrote:
>
> On Mon, Jun 1, 2020 at 8:31 AM 'Brent Meeker' via Everything List <
> everything-list@googlegroups.com> wrote:
>
>> On 5/31/2020 3:23 PM, Bruce Kellett wrote:
>>
>> On Mon, Jun 1, 2020 at 3:12 AM 'Brent Meeker' via Everything List <
>> everything-list@googlegroups.com> wrote:
>>
>>> On 5/30/2020 10:44 PM, Bruce Kellett wrote:
>>>
>>> On Sun, May 31, 2020 at 2:26 AM Bruno Marchal  wrote:
>>>

 Let us write f_n for the function from N to N computed by nth
 expression.

 Now, the function g defined by g(n) = f_n(n) + 1 is computable, and is
 defined on all N. So it is a computable function from N to N. It is
 computable because it each f_n is computable, “+ 1” is computable, and, vy
 our hypothesis it get all and only all computable functions from N to N.

 But then, g has have itself an expression in that universal language,
 of course. There there is a number k such that g = f_k. OK?

 But then we get that g_k, applied to k has to give f_k(k), as g = f_k,
 and f_k(k) + 1, by definition of g.

>>>
>>>
>>> That is a fairly elementary blunder. g_k applied to k, g_k(k) =
>>> f_n(k)+1, by definition of g_k. You do not get to change the function from
>>> f_n to f_k in the expression. It is only the argument that changes: in
>>> other words, f_n(n) becomes f_n(k). So you are talking nonsense.
>>>
>>>
>>> No, I think that's OK.  It's a straight substitution n->k.  The trick is
>>> that g(n) is not some well defined specific function because n has infinite
>>> range.  So none of this works in a finite world.  But it's not surprising
>>> that there is incompleteness in an infinite theory.
>>>
>>
>>
>> Yes, I had misunderstood what g(n) was supposed to be -- it is simply a
>> representation of the diagonal elements of the array, plus 1. But Bruno's
>> attempt to use the diagonal argument here fails, because  he has to show
>> that f_n(n)+1 is not contained in the infinite list. He has failed to do
>> this.
>>
>>
>> All computable functions are in the list ex hypothesi.
>>
>
>
> That is what the diagonal argument is all about: you hypothesize that all
> bit strings (for example) are in your infinite list. Then you flip the
> diagonal bit of each string and form a new string from all the diagonal
> elements. And lo, that new string is not in the initial list. Therefore
> your hypothesis that all bit strings are in the list is disproven.
>
> Bruno has attempted toride to glory on this argument, and has failed
> miserably!
>
>
> That's a general problem with reductio arguments.  When you get to end you
> don't know which premise was wrong.  Bruno, isn't changing the hypothetical
> list though, so he's saying the premise that you can order the total
> functions is wrong.  You can order the functions (say lexigraphically) but
> you can't know which are total.
>
> ISTM the result, that there's an incompleteness theorem for the set of all
> functions, is quite intuitive.  But Bruno seems to be saying this is all
> finitist because he doesn't assum and axiom of infinity.  Yet the
> "diagonalization" doesn't work in a finite world.
>


Take all bit strings of length N (finite) and apply the diagonal argument.
The string resulting from putting all the flipped diagonal bits together is
not in the original list, contradicting the assumption that the list is
complete. Of course, the list of all strings of length N contains more than
N elements, so the diagonal argument does not apply. The set of all strings
of infinite length is certainly infinite, so one might work the diagonal
argument there -- if one doesn't worry too much about cardinality
issues..

I think Bruno should rephrase his argument -- it might be sensible, but as
presented it was clearly invalid.

Bruce

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Re: Gödel's Miracle and Why Conventionalism makes no sense in Computer Science

2020-05-31 Thread 'Brent Meeker' via Everything List 



On 5/31/2020 3:49 PM, Bruce Kellett wrote:
On Mon, Jun 1, 2020 at 8:31 AM 'Brent Meeker' via Everything List 
> wrote:


On 5/31/2020 3:23 PM, Bruce Kellett wrote:

On Mon, Jun 1, 2020 at 3:12 AM 'Brent Meeker' via Everything List
mailto:everything-list@googlegroups.com>> wrote:

On 5/30/2020 10:44 PM, Bruce Kellett wrote:

On Sun, May 31, 2020 at 2:26 AM Bruno Marchal
mailto:marc...@ulb.ac.be>> wrote:


Let us write f_n for the function from N to N computed
by nth expression.

Now, the function g defined by g(n) = f_n(n) + 1 is
computable, and is defined on all N. So it is a
computable function from N to N. It is computable
because it each f_n is computable, “+ 1” is computable,
and, vy our hypothesis it get all and only all
computable functions from N to N.

But then, g has have itself an expression in that
universal language, of course. There there is a number k
such that g = f_k. OK?

But then we get that g_k, applied to k has to give
f_k(k), as g = f_k, and f_k(k) + 1, by definition of g.



That is a fairly elementary blunder. g_k applied to k,
g_k(k) = f_n(k)+1, by definition of g_k. You do not get to
change the function from f_n to f_k in the expression. It is
only the argument that changes: in other words, f_n(n)
becomes f_n(k). So you are talking nonsense.


No, I think that's OK.  It's a straight substitution n->k. 
The trick is that g(n) is not some well defined specific
function because n has infinite range.  So none of this works
in a finite world.  But it's not surprising that there is
incompleteness in an infinite theory.



Yes, I had misunderstood what g(n) was supposed to be -- it is
simply a representation of the diagonal elements of the array,
plus 1. But Bruno's attempt to use the diagonal argument here
fails, because  he has to show that f_n(n)+1 is not contained in
the infinite list. He has failed to do this.


All computable functions are in the list ex hypothesi.



That is what the diagonal argument is all about: you hypothesize that 
all bit strings (for example) are in your infinite list. Then you flip 
the diagonal bit of each string and form a new string from all the 
diagonal elements. And lo, that new string is not in the initial list. 
Therefore your hypothesis that all bit strings are in the list is 
disproven.


Bruno has attempted toride to glory on this argument, and has failed 
miserably!


That's a general problem with reductio arguments.  When you get to end 
you don't know which premise was wrong.  Bruno, isn't changing the 
hypothetical list though, so he's saying the premise that you can order 
the total functions is wrong.  You can order the functions (say 
lexigraphically) but you can't know which are total.


ISTM the result, that there's an incompleteness theorem for the set of 
all functions, is quite intuitive.  But Bruno seems to be saying this is 
all finitist because he doesn't assum and axiom of infinity.  Yet the 
"diagonalization" doesn't work in a finite world.


Brent



Bruce
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Re: Maxwell's Equations and Black Body radiation

2020-05-31 Thread Alan Grayson 


On Saturday, May 30, 2020 at 6:41:35 PM UTC-6, Alan Grayson wrote:
>
>
>
> On Friday, May 29, 2020 at 9:31:19 AM UTC-6, Alan Grayson wrote:
>>
>>
>>
>> On Friday, May 29, 2020 at 9:07:12 AM UTC-6, John Clark wrote:
>>>
>>> On Fri, May 29, 2020 at 10:46 AM Alan Grayson  
>>> wrote:
>>>
>>> *> Clark, since you claim implicitly to having a serious understanding 
 of E&M, can you give a proof of Planck's BB radiation law? AG *

>>>
>>> Of course I can't! Mathematicians prove things, physicists don't. 
>>> Physicists propose theories and if it turns out the theory is compatible 
>>> with empirically derived results then it is generally accepted by the 
>>> scientific community, at least within a certain range of applicability. No 
>>> physicist gives a hoot in hell for a theory that is contradicted by 
>>> experimental results regardless of how closely it follows somebody's 
>>> "postulates". 
>>>
>>> John K Clark
>>>
>>
>> You're just displaying your ignorance, shamelessly as suggested by your 
>> emotional insistence. Physics starts with postulates about how nature 
>> behaves. It's basically guesswork as Feynman asserts. I gave you some 
>> examples. And one can prove specific results from postulates, as Einstein 
>> did in his 1905 paper on SR in* DERIVING* the LT. Postulates are 
>> accepted if they give good predictions. No one doubts that, so you're 
>> affirming something no one disputes. Similarly, Planck didn't pull his BB 
>> radiation formula out of his hat. He must have started with some 
>> postulates, from which he derived his formula, and we accept the formula as 
>> "true" since it accurately predicts what is measured. If you can't say 
>> anything about Planck's formula, except obvious superficial comments such 
>> as the fact that he quantizes of the frequency modes, you know nothing more 
>> about this subject compared to someone like me who admits his courses in 
>> E&M were "crappy". AG
>>
>
> Clark; take the noble path. Acknowledge that what I wrote above is 
> correct. TY, AG
>

Some other examples: using Newton's law of gravitation, one can 
mathematically DERIVE the result that planet trajectories are conic 
sections; using mathematics one can show that Newton's equations of motion, 
Hamilton's equations of motions, and Lagrange's equations of motion are 
equivalent; using mathematics one can show that the HUP is implied by the 
principles or postulates of QM (although the principle was established by 
Heisenberg independent of the postulates of QM). Are you ready to take the 
noble path and acknowledge that I am correct about the relationship of 
mathematics to the principles or postulates of physics? AG

>  
>

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Re: Gödel's Miracle and Why Conventionalism makes no sense in Computer Science

2020-05-31 Thread Bruce Kellett 
On Mon, Jun 1, 2020 at 8:31 AM 'Brent Meeker' via Everything List <
everything-list@googlegroups.com> wrote:

> On 5/31/2020 3:23 PM, Bruce Kellett wrote:
>
> On Mon, Jun 1, 2020 at 3:12 AM 'Brent Meeker' via Everything List <
> everything-list@googlegroups.com> wrote:
>
>> On 5/30/2020 10:44 PM, Bruce Kellett wrote:
>>
>> On Sun, May 31, 2020 at 2:26 AM Bruno Marchal  wrote:
>>
>>>
>>> Let us write f_n for the function from N to N computed by nth
>>> expression.
>>>
>>> Now, the function g defined by g(n) = f_n(n) + 1 is computable, and is
>>> defined on all N. So it is a computable function from N to N. It is
>>> computable because it each f_n is computable, “+ 1” is computable, and, vy
>>> our hypothesis it get all and only all computable functions from N to N.
>>>
>>> But then, g has have itself an expression in that universal language, of
>>> course. There there is a number k such that g = f_k. OK?
>>>
>>> But then we get that g_k, applied to k has to give f_k(k), as g = f_k,
>>> and f_k(k) + 1, by definition of g.
>>>
>>
>>
>> That is a fairly elementary blunder. g_k applied to k, g_k(k) = f_n(k)+1,
>> by definition of g_k. You do not get to change the function from f_n to f_k
>> in the expression. It is only the argument that changes: in other words,
>> f_n(n) becomes f_n(k). So you are talking nonsense.
>>
>>
>> No, I think that's OK.  It's a straight substitution n->k.  The trick is
>> that g(n) is not some well defined specific function because n has infinite
>> range.  So none of this works in a finite world.  But it's not surprising
>> that there is incompleteness in an infinite theory.
>>
>
>
> Yes, I had misunderstood what g(n) was supposed to be -- it is simply a
> representation of the diagonal elements of the array, plus 1. But Bruno's
> attempt to use the diagonal argument here fails, because  he has to show
> that f_n(n)+1 is not contained in the infinite list. He has failed to do
> this.
>
>
> All computable functions are in the list ex hypothesi.
>


That is what the diagonal argument is all about: you hypothesize that all
bit strings (for example) are in your infinite list. Then you flip the
diagonal bit of each string and form a new string from all the diagonal
elements. And lo, that new string is not in the initial list. Therefore
your hypothesis that all bit strings are in the list is disproven.

Bruno has attempted toride to glory on this argument, and has failed
miserably!

Bruce

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Re: Gödel's Miracle and Why Conventionalism makes no sense in Computer Science

2020-05-31 Thread 'Brent Meeker' via Everything List 



On 5/31/2020 3:23 PM, Bruce Kellett wrote:
On Mon, Jun 1, 2020 at 3:12 AM 'Brent Meeker' via Everything List 
> wrote:


On 5/30/2020 10:44 PM, Bruce Kellett wrote:

On Sun, May 31, 2020 at 2:26 AM Bruno Marchal mailto:marc...@ulb.ac.be>> wrote:


Let us write f_n for the function from N to N computed by nth
expression.

Now, the function g defined by g(n) = f_n(n) + 1 is
computable, and is defined on all N. So it is a computable
function from N to N. It is computable because it each f_n is
computable, “+ 1” is computable, and, vy our hypothesis it
get all and only all computable functions from N to N.

But then, g has have itself an expression in that universal
language, of course. There there is a number k such that g =
f_k. OK?

But then we get that g_k, applied to k has to give f_k(k), as
g = f_k, and f_k(k) + 1, by definition of g.



That is a fairly elementary blunder. g_k applied to k, g_k(k) =
f_n(k)+1, by definition of g_k. You do not get to change the
function from f_n to f_k in the expression. It is only the
argument that changes: in other words, f_n(n) becomes f_n(k). So
you are talking nonsense.


No, I think that's OK.  It's a straight substitution n->k.  The
trick is that g(n) is not some well defined specific function
because n has infinite range.  So none of this works in a finite
world.  But it's not surprising that there is incompleteness in an
infinite theory.



Yes, I had misunderstood what g(n) was supposed to be -- it is simply 
a representation of the diagonal elements of the array, plus 1. But 
Bruno's attempt to use the diagonal argument here fails, because  he 
has to show that f_n(n)+1 is not contained in the infinite list. He 
has failed to do this.


All computable functions are in the list ex hypothesi.

Brent



Bruce
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Re: Gödel's Miracle and Why Conventionalism makes no sense in Computer Science

2020-05-31 Thread Bruce Kellett 
On Mon, Jun 1, 2020 at 3:12 AM 'Brent Meeker' via Everything List <
everything-list@googlegroups.com> wrote:

> On 5/30/2020 10:44 PM, Bruce Kellett wrote:
>
> On Sun, May 31, 2020 at 2:26 AM Bruno Marchal  wrote:
>
>>
>> Let us write f_n for the function from N to N computed by nth expression.
>>
>> Now, the function g defined by g(n) = f_n(n) + 1 is computable, and is
>> defined on all N. So it is a computable function from N to N. It is
>> computable because it each f_n is computable, “+ 1” is computable, and, vy
>> our hypothesis it get all and only all computable functions from N to N.
>>
>> But then, g has have itself an expression in that universal language, of
>> course. There there is a number k such that g = f_k. OK?
>>
>> But then we get that g_k, applied to k has to give f_k(k), as g = f_k,
>> and f_k(k) + 1, by definition of g.
>>
>
>
> That is a fairly elementary blunder. g_k applied to k, g_k(k) = f_n(k)+1,
> by definition of g_k. You do not get to change the function from f_n to f_k
> in the expression. It is only the argument that changes: in other words,
> f_n(n) becomes f_n(k). So you are talking nonsense.
>
>
> No, I think that's OK.  It's a straight substitution n->k.  The trick is
> that g(n) is not some well defined specific function because n has infinite
> range.  So none of this works in a finite world.  But it's not surprising
> that there is incompleteness in an infinite theory.
>


Yes, I had misunderstood what g(n) was supposed to be -- it is simply a
representation of the diagonal elements of the array, plus 1. But Bruno's
attempt to use the diagonal argument here fails, because  he has to show
that f_n(n)+1 is not contained in the infinite list. He has failed to do
this.

Bruce

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Re: Gödel's Miracle and Why Conventionalism makes no sense in Computer Science

2020-05-31 Thread 'Brent Meeker' via Everything List 



On 5/30/2020 10:44 PM, Bruce Kellett wrote:
On Sun, May 31, 2020 at 2:26 AM Bruno Marchal > wrote:



Let us write f_n for the function from N to N computed by nth
expression.

Now, the function g defined by g(n) = f_n(n) + 1 is computable,
and is defined on all N. So it is a computable function from N to
N. It is computable because it each f_n is computable, “+ 1” is
computable, and, vy our hypothesis it get all and only all
computable functions from N to N.

But then, g has have itself an expression in that universal
language, of course. There there is a number k such that g = f_k. OK?

But then we get that g_k, applied to k has to give f_k(k), as g =
f_k, and f_k(k) + 1, by definition of g.



That is a fairly elementary blunder. g_k applied to k, g_k(k) = 
f_n(k)+1, by definition of g_k. You do not get to change the function 
from f_n to f_k in the expression. It is only the argument that 
changes: in other words, f_n(n) becomes f_n(k). So you are talking 
nonsense.


No, I think that's OK.  It's a straight substitution n->k.  The trick is 
that g(n) is not some well defined specific function because n has 
infinite range.  So none of this works in a finite world.  But it's not 
surprising that there is incompleteness in an infinite theory.


Brent



Bruce

So f_k(k) = f_k(k) +1.

And f_k(k) has to be number, given that we were enumerating
functions from N to N. So we can subtract f_k(k) on both sides,
and we get 0 = 1. CQFD.

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Francesca Vidotto on quantum gravity

2020-05-31 Thread Philip Thrift 


and her new book with Carlo Rovelli:

https://daily.jstor.org/francesca-vidotto-the-quantum-properties-of-space-time/


"My philosophical background was also informed by the feminist philosophy of 
sciences. Feminist philosophers have been debating how you can have a notion of 
objectivity while there are so many different standpoints. From each 
standpoint, you have access to a bit of truth, but if you want to have a full 
description of reality, somehow again you have to accept this plurality of 
standpoints and eventually find a way to put them together. I believe this 
gives you a powerful key to interpret the world in which we live.'

@philipthrift 

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Re: The size of the universe

2020-05-31 Thread Bruno Marchal 


> On 31 May 2020, at 09:50, Russell Standish  wrote:
> 
> On Sun, May 24, 2020 at 01:21:38PM +0200, Bruno Marchal wrote:
>> 
>>> On 24 May 2020, at 01:37, Russell Standish  wrote:
>>> 
>>> However, I would think that ultrafinitism would change COMP's
>>> predictions, and in a sense be incompatibe with it. Some programs will
>>> not exist, because one would need to wait too long
>> 
>> “Too long” is still finite.
>> 
>> The biggest natural number is of course “infinite”, but the ultrafinitist 
>> cannot know that.
>> 
>> That is why a “real ultrafinitiste” will never say that he is ultrafinitist. 
>> He has no means to explains why ultra-finitism means. Only a finitists can 
>> prove that ultra-finitsime is consistent (indeed PA can prove that RA is 
>> consistent).
>> 
>> 
>> 
>>> for them to be
>>> executed by the UD. In fact, the choice of reference universal machine
>>> would be significant in ultrafinitism, IIUC.
>> 
>> Why? As long as the theory is Turing complete, all programs are run (in all 
>> interpretation of the theory), including all finite segment of the 
>> executions of all  non terminating programs, and this with the usual 
>> redundancy.
>> 
> 
> For an ultrafinitist, there is a biggest number (perhaps unknowable),
> and consequently computer programs that don't get run (because they
> take more steps than that biggest number.

The biggest number is a non-standard number, meaning that a genuine 
ultra-finest machine will be, in the eye of a non ultra-finitist, be a “non 
standard machine”, making a non-standard computations (quite out of the one 
defined by CT)


> 
> The CT thesis is strictly false in such a case,

Indeed.


> but could possibly
> apply in an approximate sense.


That remains to be made more precise, but will require non finitism, … It is 
the general problem of the ultrafinitist, which is that they cannot define 
“ultrafinitist”. An ultrafinitst cannot say “I am an ultrafinitist” !

Bruno



> 
> 
>> Bruno
>> 
>> 
>> 
>>> 
>>> 
>>> -- 
>>> 
>>> 
>>> Dr Russell StandishPhone 0425 253119 (mobile)
>>> Principal, High Performance Coders hpco...@hpcoders.com.au
>>> http://www.hpcoders.com.au
>>> 
>>> 
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>  http://www.hpcoders.com.au
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Re: Gödel's Miracle and Why Conventionalism makes no sense in Computer Science

2020-05-31 Thread Bruce Kellett 
On Sun, May 31, 2020 at 8:56 PM Bruno Marchal  wrote:

>
> On 31 May 2020, at 10:08, Bruce Kellett  wrote:
>
> That is your notation: "But then we get that g_k, applied to k has to give
> f_k(k),”
>
>
> That was a typo error. You need to read “g applied to k”. Sorry. But you
> should have just ask “what is g_k?”.
> I mean it is not a blunder, but a typo error (probably among many). The
> typo error is detectable from just the few words which go after.
>

I am not a mind reader. I try to understand what you write, but I can't
always differentiate between typos and straight blunders.

Your attempted diagonalization argument just does not work here.

f_n(n)+1 has not been shown not to be among the other enumerated functions.
f_n(n) is just a number, as is f_n(n)+1, so it is clearly among the
functions that map N to N, it is just not f_n. Remember that N is not
finite.

Bruce

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Re: Gödel's Miracle and Why Conventionalism makes no sense in Computer Science

2020-05-31 Thread Bruno Marchal 

> On 31 May 2020, at 10:08, Bruce Kellett  wrote:
> 
> On Sun, May 31, 2020 at 5:21 PM Bruno Marchal  > wrote:
> On 31 May 2020, at 07:44, Bruce Kellett  > wrote:
>> On Sun, May 31, 2020 at 2:26 AM Bruno Marchal > > wrote:
>> 
>> Let us write f_n for the function from N to N computed by nth expression. 
>> 
>> Now, the function g defined by g(n) = f_n(n) + 1 is computable, and is 
>> defined on all N. So it is a computable function from N to N. It is 
>> computable because it each f_n is computable, “+ 1” is computable, and, vy 
>> our hypothesis it get all and only all computable functions from N to N.
>> 
>> But then, g has have itself an expression in that universal language, of 
>> course. There there is a number k such that g = f_k. OK?
>> 
>> But then we get that g_k, applied to k has to give f_k(k), as g = f_k, and 
>> f_k(k) + 1, by definition of g. 
>> 
>> 
>> That is a fairly elementary blunder. g_k
> 
> What is g_k?
> 
> That is your notation: "But then we get that g_k, applied to k has to give 
> f_k(k),”

That was a typo error. You need to read “g applied to k”. Sorry. But you should 
have just ask “what is g_k?”. 
I mean it is not a blunder, but a typo error (probably among many). The typo 
error is detectable from just the few words which go after. 


> 
> 
> The only enumeration here is the f_k, then we have define a precise, single, 
> function g such that
> 
> g(n) = f_n(n) + 1.  (f_n(n) is the diagonal term, you can see this by making 
> the table (the infinite matrice) with the number in the top row, and the f_i 
> in a column):
> 
>   0   1   2   3   ...
> f_0   f_0(0)  f_0(1)  f_0(2)  f_0(3)
> f_1   f_1(0)  f_1(1)  f_1(2)  f_1(3)
> f_2   f_2(0)  f_2(1)  f_2(2)  f_2(3)
> …
> Here the underlining means “+1”.
> 
> 
> 
>> applied to k, g_k(k) = f_n(k)+1,
> 
> There are no g_k.
> 
> 
> You defined g_k!!  g_k applied to k is f_k(k), and that is your error.

“g_k" just has no meaning at all. Nowhere is a sequence g_k defined. 



> 
> g is the function defined by diagonalisation. g(x) = f_x(x) + 1, that g(0) = 
> f_0(0) + 1, g(1) = f_1(1) + 1, g(2) = f_2(2) + 1, ...
> 
> But that is not what you said before.

It is. Read again, avoid the typo error when I apply g on its code k. 



> 
>  
>> by definition of g_k.
> 
> The only enumeration was the enumeration of the functions f_k
> 
>> You do not get to change the function from f_n to f_k in the expression.
> We do. 
>> It is only the argument that changes: in other words, f_n(n) becomes f_n(k).
> 
> This makes no sense. What is g(2) ? f_n(2) + 1 ? What is n then? 
> 
> 
> n is the number of the function in the ordered list of all functions from N 
> to N. Adding 1 to f_n(n) gives a different function. Diagonalization does not 
> help you here.


It defines g. 

g(n) = f_n(n) + 1

To compute g, enumerate the f_i up to f_n, and compute f_n on n, and add one. 
Of course this will lead to a contradiction, which shows that the bijection n 
—> f_n is not computable. (But that does not destroy CT, it only make the f_n 
mixed with partial (defined on a subset of N) computable function, and that 
mowing has to be non computable (if not we can filter out the partial and get a 
computable enumeration of the f_n, and get again the contradiction).



> 
> So g(n) = f_n(n)+1 is a different function.

Different from what? If it is different from all f_n, the language is no more 
universal. It means that if the language is universal, g is not computable, and 
what is not computable is not the f_n, nor “+ 1”, so it can only be the 
enumeration f_n itself. That is the point against conventionalism: computable 
entails the existence of non computable well defined entities.



> It is NOT f_n() with some different argument. So your attempt to make them 
> the same function is invalid.


?

Are you saying that you believe that we can enumerate computably the computable 
functions from N to N? If that is the case, you have missed the argument.

Apology for the typo error. But now that it is has been corrected, you might 
read more cautiously the argument; I just do not understand you last remark. I 
will re-explain, if necessary. This post is the minimal think to proceed. It 
ex^lmains also why the universal dovetailer has to … dovetail, necessarily.


Bruno






> 
> Bruce
> 
>> So you are talking nonsense.
> 
> You miss the diagonal. Read again.
> 
> Bruno
> 
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Re: Witten proposes planet 9 is small black hole

2020-05-31 Thread Lawrence Crowell 
On Saturday, May 30, 2020 at 1:49:23 PM UTC-5, ronaldheld wrote:
>
> Not certain those flyby micro craft will determine whether it exists.
>  Ronald
>

It requires some prior information on possible location. It is a radar or 
laser ranging process. It occurred to me that maybe a better approach would 
be to direct radar microwaves into the Kuiper belt. Return signals would 
come from reflecting off of Kuiper belt objects. This could establish a 
geodetic map out there. Also if there is an invisible gravitating body out 
there the small timing difference could be measured.

The problem I do see with actually sending spacecrafts out there is this 
involves a lot of spatial volume. If one's initial estimate on where this 
gravitating body is wrong by a few steradian angle measure you can easily 
miss it.

LC
 

>
> On Friday, May 29, 2020 at 7:48:58 PM UTC-4, Lawrence Crowell wrote:
>>
>> This is entertaining. He also coauthored a paper below on using photon 
>> sails to perform this probing.
>>
>> LC
>>
>> https://arxiv.org/abs/2004.14192  
>> Searching for a Black Hole in the Outer Solar System
>> Edward Witten 
>> 
>>
>> There are hints of a novel object ("Planet 9") with a mass 5−10 M⊕ in 
>> the outer Solar System, at a distance of order 500 AU. If it is a 
>> relatively conventional planet, it can be found in telescopic searches. 
>> Alternatively, it has been suggested that this body might be a primordial 
>> black hole (PBH). In that case, conventional searches will fail. A possible 
>> alternative is to probe the gravitational field of this object using small, 
>> laser-launched spacecraft, like the ones envisioned in the Breakthrough 
>> Starshot project. With a velocity of order .001 c, such spacecraft can 
>> reach Planet 9 roughly a decade after launch and can discover it if they 
>> can report timing measurements accurate to 10−5 seconds back to Earth.
>>
>> Comments: 4 pp, additional references
>> Subjects: Earth and Planetary Astrophysics (astro-ph.EP); High Energy 
>> Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th)
>> Cite as: arXiv:2004.14192 
>>  [astro-ph.EP]
>>   (or arXiv:2004.14192v2 
>>  [astro-ph.EP] for this version)
>>
>>
>> https://arxiv.org/abs/2005.12336  
>>
>> Exploration of the outer solar system with fast and small sailcraft
>> Slava G. Turyshev 
>> 
>> , Peter Klupar 
>> , 
>> Abraham 
>> Loeb 
>> , 
>> Zachary 
>> Manchester 
>> 
>> , Kevin Parkin 
>> , 
>> Edward 
>> Witten 
>> , S. 
>> Pete Worden 
>> 
>>
>> Two new interplanetary technologies have advanced in the past decade to 
>> the point where they may enable exciting, affordable missions that reach 
>> further and faster deep into the outer regions of our solar system: (i) 
>> small and capable interplanetary spacecraft and (ii) light-driven sails. 
>> Combination of these two technologies could drastically reduce travel times 
>> within the solar system. We discuss a new paradigm that involves small and 
>> fast moving sailcraft that could enable exploration of distant regions of 
>> the solar system much sooner and faster than previously considered. We 
>> present some of the exciting science objectives for these miniaturized 
>> intelligent space systems that could lead to transformational advancements 
>> in the space sciences.
>>
>> Comments: A White Paper to the National Academy of Sciences Planetary 
>> Science and Astrobiology Decadal Survey 2023-2032. 13 pages, 5 figures and 
>> 2 tables
>> Subjects: Instrumentation and Methods for Astrophysics (astro-ph.IM); 
>> Earth and Planetary Astrophysics (astro-ph.EP); Solar and Stellar 
>> Astrophysics (astro-ph.SR); General Relativity and Quantum Cosmology (gr-qc)
>> Cite as: arXiv:2005.12336 
>>  [astro-ph.IM]
>>   (or arXiv:2005.12336v1 
>>  [astro-ph.IM] for this version)
>>
>

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Re: Gödel's Miracle and Why Conventionalism makes no sense in Computer Science

2020-05-31 Thread Bruce Kellett 
On Sun, May 31, 2020 at 5:21 PM Bruno Marchal  wrote:

> On 31 May 2020, at 07:44, Bruce Kellett  wrote:
>
> On Sun, May 31, 2020 at 2:26 AM Bruno Marchal  wrote:
>
>>
>> Let us write f_n for the function from N to N computed by nth expression.
>>
>> Now, the function g defined by g(n) = f_n(n) + 1 is computable, and is
>> defined on all N. So it is a computable function from N to N. It is
>> computable because it each f_n is computable, “+ 1” is computable, and, vy
>> our hypothesis it get all and only all computable functions from N to N.
>>
>> But then, g has have itself an expression in that universal language, of
>> course. There there is a number k such that g = f_k. OK?
>>
>> But then we get that g_k, applied to k has to give f_k(k), as g = f_k,
>> and f_k(k) + 1, by definition of g.
>>
>
>
> That is a fairly elementary blunder. g_k
>
>
> What is g_k?
>

That is your notation: "But then we get that g_k, applied to k has to give
f_k(k),"


The only enumeration here is the f_k, then we have define a precise,
> single, function g such that
>
> g(n) = f_n(n) + 1.  (f_n(n) is the diagonal term, you can see this by
> making the table (the infinite matrice) with the number in the top row, and
> the f_i in a column):
>
> 0 1 2 3 ...
> f_0  *f_0(0)* f_0(1) f_0(2) f_0(3)
> f_1 f_1(0) *f_1(1)* f_1(2) f_1(3)
> f_2 f_2(0) f_2(1) *f_2(2)* f_2(3)
> …
> Here the underlining means “+1”.
>
>
>
> applied to k, g_k(k) = f_n(k)+1,
>
>
> There are no g_k.
>


You defined g_k!!  g_k applied to k is f_k(k), and that is your error.

g is the function defined by diagonalisation. g(x) = f_x(x) + 1, that g(0)
> = f_0(0) + 1, g(1) = f_1(1) + 1, g(2) = f_2(2) + 1, ...
>

But that is not what you said before.



> by definition of g_k.
>
>
> The only enumeration was the enumeration of the functions f_k
>
> You do not get to change the function from f_n to f_k in the expression.
>
> We do.
>
> It is only the argument that changes: in other words, f_n(n) becomes
> f_n(k).
>
>
> This makes no sense. What is g(2) ? f_n(2) + 1 ? What is n then?
>


n is the number of the function in the ordered list of all functions from N
to N. Adding 1 to f_n(n) gives a different function. Diagonalization does
not help you here.

So g(n) = f_n(n)+1 is a different function. It is NOT f_n() with some
different argument. So your attempt to make them the same function is
invalid.

Bruce

So you are talking nonsense.
>
>
> You miss the diagonal. Read again.
>
> Bruno
>

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Re: The size of the universe

2020-05-31 Thread Russell Standish 
On Sun, May 24, 2020 at 01:21:38PM +0200, Bruno Marchal wrote:
> 
> > On 24 May 2020, at 01:37, Russell Standish  wrote:
> > 
> > However, I would think that ultrafinitism would change COMP's
> > predictions, and in a sense be incompatibe with it. Some programs will
> > not exist, because one would need to wait too long
> 
> “Too long” is still finite.
> 
> The biggest natural number is of course “infinite”, but the ultrafinitist 
> cannot know that.
> 
> That is why a “real ultrafinitiste” will never say that he is ultrafinitist. 
> He has no means to explains why ultra-finitism means. Only a finitists can 
> prove that ultra-finitsime is consistent (indeed PA can prove that RA is 
> consistent).
> 
> 
> 
> > for them to be
> > executed by the UD. In fact, the choice of reference universal machine
> > would be significant in ultrafinitism, IIUC.
> 
> Why? As long as the theory is Turing complete, all programs are run (in all 
> interpretation of the theory), including all finite segment of the executions 
> of all  non terminating programs, and this with the usual redundancy.
> 

For an ultrafinitist, there is a biggest number (perhaps unknowable),
and consequently computer programs that don't get run (because they
take more steps than that biggest number.

The CT thesis is strictly false in such a case, but could possibly
apply in an approximate sense.


> Bruno
> 
> 
> 
> > 
> > 
> > -- 
> > 
> > 
> > Dr Russell StandishPhone 0425 253119 (mobile)
> > Principal, High Performance Coders hpco...@hpcoders.com.au
> >  http://www.hpcoders.com.au
> > 
> > 
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Re: Max Tegmark: AI discovers physics

2020-05-31 Thread Bruno Marchal 

> On 30 May 2020, at 21:51, ronaldheld  wrote:
> 
> Is the AI discovering some Physics or just fitting data which produces 
> equations that look like physical laws?

The question is if the equation obtained makes the good predictions, on any, or 
at least “many” different data. 

It is easy to make a machine predicting an earthquake the day before an 
earthquake, by making it predicting everyday that there will be an earthquake …

My point is that such AI research avoid the metaphysical problem: even us 
cannot use physics to predict an eclipse, in a way coherent with mechanism. 
Physical laws works only if they solve the measure problem, which is typically 
not the case today, except QM is promising, as we can see from the study of 
self-reference. The problem is in making negligible the measure of the aberrant 
histories (which are executed in arithmetic).

Bruno




>  Ronald
> On Thursday, May 28, 2020 at 12:20:49 PM UTC-4, Philip Thrift wrote:
> 
> https://www.facebook.com/461616050561921/posts/3107668729289960/ 
> 
> 
> We just posted a new AI paper on how to automatically discover laws of 
> physics from raw video with machine learning. For example, we feed in the 
> video below of a rocket moving in a circles in a magnetic field, seen through 
> a distorting lens, and our code automatically discovers the Lorentz Force 
> Law. It took Silviu and me about a year to get this working, by using ideas 
> inspired by general relativity and the the theory of knots in 5-dimensional 
> space, so we're excited to be done!  https://arxiv.org/abs/2005.11212 
> 
> @philipthrift
> 
> 
> 
> 
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Re: Max Tegmark: AI discovers physics

2020-05-31 Thread Bruno Marchal 

> On 30 May 2020, at 19:24, Lawrence Crowell  
> wrote:
> 
> I wrote a paper recently for publication on how the unital set of QM is a 
> Cantor/fractal set that is fundamentally incomputable.

I use the Cantor (triadic) set, or the Baire space. But it is more the measure 
on the possible local input puts. 

I am not sure what you mean by a set (or real) being “fundamentally 
incomputable”.

The Church thesis is on function defined on natural numbers.  On the reals, 
there are as much definition of computability than there are mathematicians. 
But to get the measure, it makes sense to study the subset of the real line 
structured by some degrees of complexity, and some results related this to the 
arithmetical and analytical hierarchy in recursion theory (and their has some 
importance for the extraction of physics (the self-referential measure on 
possible inputs) from “the head of the universal machine” ).




> This is a measure of nonlinearity a quantum system is forced into, say with 
> gravitation or with einselection into classicality. To compute it requires a 
> single algorithmic system for computing all p-adic sets, where the theorem by 
> Matyiaesovich is a form of Gödel's theorem that illustrates this does not 
> exist.

What is the relation between p-adic sets and Matiyasevitch theorem? (I see the 
relation with Gödel, but only with dioplnatine polynomial (with integers). I 
don’t see the relation between non linearity and non computability. You need to 
elaborate perhaps, or give a link to some draft of your paper.



> It corresponds to the unobservability of hidden variables, or that they are 
> nonlocal, and establishes entanglement symmetries as topological indices or 
> obstructions. This might mean we are saved by the Bell, here Bell's theorem 
> in a sense, from the invasion of the robots.

You need to clarify this.



> It will be some time I think before AI systems can work through 
> self-referential inference. 

That is weird. Have you read my paper on "amoeba, planaria and dreaming 
machine”. Self-reference is just not avoidable. Once a universal machine can 
believe in the induction, like PA, ZF, any of their consistent extension, they 
are already as self-referential than you and me. They obey to the theology G* 
(with the same physics as us (Z1*, X1* and S4Grz1).

Bruno



> 
> LC
> 
> On Saturday, May 30, 2020 at 2:00:16 AM UTC-5, Philip Thrift wrote:
> 
> 
> Of course nature's "theory" could be beyond a human's comprehension.
> 
> It is assumed that there all that's needed can be reduced to human 
> (mathematical) language that can be expressed in a few lines of LaTeX Math.
> 
> @philipthrift
> 
> On Friday, May 29, 2020 at 7:45:58 PM UTC-5, Lawrence Crowell wrote:
> On Thursday, May 28, 2020 at 11:20:49 AM UTC-5, Philip Thrift wrote:
> 
> https://www.facebook.com/461616050561921/posts/3107668729289960/ 
> 
> 
> We just posted a new AI paper on how to automatically discover laws of 
> physics from raw video with machine learning. For example, we feed in the 
> video below of a rocket moving in a circles in a magnetic field, seen through 
> a distorting lens, and our code automatically discovers the Lorentz Force 
> Law. It took Silviu and me about a year to get this working, by using ideas 
> inspired by general relativity and the the theory of knots in 5-dimensional 
> space, so we're excited to be done!  https://arxiv.org/abs/2005.11212 
> 
> @philipthrift
> 
> 
> 
> The preprint address is below. I would like to think the big question on 
> quantum gravitation is resolved by basic human thought. Maybe AI systems can 
> verify the theoretical result(s) and give some support.
> 
> LC
>  
> https://arxiv.org/abs/2005.11212 
> 
> Symbolic Pregression: Discovering Physical Laws from Raw Distorted Video
> 
> Silviu-Marian Udrescu 
>  (MIT), Max 
> Tegmark  
> (MIT)
> We present a method for unsupervised learning of equations of motion for 
> objects in raw and optionally distorted unlabeled video. We first train an 
> autoencoder that maps each video frame into a low-dimensional latent space 
> where the laws of motion are as simple as possible, by minimizing a 
> combination of non-linearity, acceleration and prediction error. Differential 
> equations describing the motion are then discovered using Pareto-optimal 
> symbolic regression. We find that our pre-regression ("pregression") step is 
> able to rediscover Cartesian coordinates of unlabeled moving objects even 
> when the video is distorted by a generalized lens. Using intuition from 
> multidimensional knot-theory, we find that the pregression step is 
> facilitated by first adding extra latent space dimensions to avoid 
> topological problems during traini

Re: Gödel's Miracle and Why Conventionalism makes no sense in Computer Science

2020-05-31 Thread Bruno Marchal 

> On 31 May 2020, at 07:44, Bruce Kellett  wrote:
> 
> On Sun, May 31, 2020 at 2:26 AM Bruno Marchal  > wrote:
> 
> Let us write f_n for the function from N to N computed by nth expression. 
> 
> Now, the function g defined by g(n) = f_n(n) + 1 is computable, and is 
> defined on all N. So it is a computable function from N to N. It is 
> computable because it each f_n is computable, “+ 1” is computable, and, vy 
> our hypothesis it get all and only all computable functions from N to N.
> 
> But then, g has have itself an expression in that universal language, of 
> course. There there is a number k such that g = f_k. OK?
> 
> But then we get that g_k, applied to k has to give f_k(k), as g = f_k, and 
> f_k(k) + 1, by definition of g. 
> 
> 
> That is a fairly elementary blunder. g_k

What is g_k? The only enumeration here is the f_k, then we have define a 
precise, single, function g such that

g(n) = f_n(n) + 1.  (f_n(n) is the diagonal term, you can see this by making 
the table (the infinite matrice) with the number in the top row, and the f_i in 
a column):

0   1   2   3   ...
f_0 f_0(0)  f_0(1)  f_0(2)  f_0(3)
f_1 f_1(0)  f_1(1)  f_1(2)  f_1(3)
f_2 f_2(0)  f_2(1)  f_2(2)  f_2(3)
…
Here the underlining means “+1”.



> applied to k, g_k(k) = f_n(k)+1,

There are no g_k. 
g is the function defined by diagonalisation. g(x) = f_x(x) + 1, that g(0) = 
f_0(0) + 1, g(1) = f_1(1) + 1, g(2) = f_2(2) + 1, ...


> by definition of g_k.

The only enumeration was the enumeration of the functions f_k


> You do not get to change the function from f_n to f_k in the expression.

We do. 



> It is only the argument that changes: in other words, f_n(n) becomes f_n(k).

This makes no sense. What is g(2) ? f_n(2) + 1 ? What is n then? 



> So you are talking nonsense.

You miss the diagonal. Read again.

Bruno


> 
> Bruce
> 
> So f_k(k) = f_k(k) +1.
> 
> And f_k(k) has to be number, given that we were enumerating functions from N 
> to N. So we can subtract f_k(k) on both sides, and we get 0 = 1. CQFD.
> 
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