Re: Dreams and Machines

[Rex Allen]

Brent,

So my first draft addressed many of the points you made, but it that
email got too big and sprawling I thought.

So I've focused on what seems to me like the key passage from your
post.  If you think there was some other point that I should have
addressed, let me know.

So, key passage:

> Do these mathematical objects "really" exist?  I'd say they have
> logico-mathematical existence, not the same existence as tables and
> chairs, or quarks and electrons.

So which kind of existence do you believe is more fundamental?  Which
is primary?  Logico-mathematical existence, or quark existence?  Or
are they separate but equal kinds of existence?

In what way, exactly, does logico-mathematical existence differ from
quark existence?  Is logico-mathematical existence a lesser kind of
existence?  Is logico-mathematical existence derivative of and
dependant on quark existence?

Further, do tables and chairs even have the same kind of existence as
quarks and electrons?  A table is something that we perceive visually,
but we intellectually take "tables" to be ultimately and fully
reducible to "quarks and electrons".   So chairs and quarks certainly
exist at different levels.  Quarks would seem to be more fundamental
than chairs.  But obviously we don't actually perceive quarks or
electrons...instead we infer their existence from our actual
perceptions of various types of experimental equipment and from there
associate them back with tables.

As for our experience of logico-mathematical objects, we certainly can
translate them into more "chair-like" perceptions by visualization via
computer programs, right?  This would put them very much on similar
footing with our experience of quarks and electrons at least, which we
also only visualize via computer reconstructions.

And, presumably it is possible for a human with exceptional
visualization abilities to experience logico mathematical objects in a
way that is even more "chair-like" than that.  For instance, there are
people with Synesthesia (http://en.wikipedia.org/wiki/Synesthesia),
for whom some letters or numbers are perceived as inherently colored,
or for whom numbers, months of the year, and/or days of the week
elicit precise locations in space (for example, 1980 may be "farther
away" than 1990).

But what if this type of synesthesia had some use that strongly aided
in human survival and reproduction?  Then (speaking in materialist
terms) as we evolved synesthesia would have become a standard feature
for humans and would now be considered just part of our normal sensory
apparatus.  We would be able to "sense" numbers in a way similar to
how we sense chairs.  In this case we would almost certainly consider
numbers to be unquestionably objectively real and existing.  Though
maybe we would ponder their peculiar qualities, in the same way we now
puzzle over the strangeness of quantum mechanics.

A further example:

"Autistic savant Daniel Tammet shot to fame when he set a European
record for the number of digits of pi he recited from memory (22,514).
 For afters, he learned Icelandic in a week. But unlike many savants,
he's able to tell us how he does it.

Q.  But how do you visualise a number? In the same way that I
visualise a giraffe?

A.  Every number has a texture. If it is a "lumpy" number, then
immediately my mind will relate it to other numbers which are lumpy -
the lumpiness will tell me there is a relationship, there is a common
divisor, or a pattern between the digits.

Q. Can you give an example of a "lumpy" number?

A.  For me, the ideal lumpy number is 37. It's like porridge. So 111,
a very pretty number, which is 3 times 37, is lumpy but it is also
round. It takes on the properties of both 37 and 3, which is round.
It's an intuitive and visual way of doing maths and thinking about
numbers.  For me, the ideal lumpy number is 37. It's like porridge."

I think we can say (again, speaking in materialist/physicalist terms)
that it's purely an accident of evolution that numbers don't seem as
intuitively real to us as chairs, or colors, or love, or free will
(ha!).

Speaking in platonist terms, it's an accident of our particular
mental/symbolic structure that numbers don't seem as intuitively real
to us as chairs, or colors, or love, or free will (ha!).

Speaking in computationalist terms, it's an accident of our
causal/representational/algorithmic structure that numbers don't seem
as intuitively real to us as chairs, or colors, or love, or free will
(ha!).

But, no matter what terms you use, it's conceivable, and we have
significant evidence that points to the possibility, that our
conscious perceptions could be modified in a way such that numbers and
other abstractions would seem much more substantial and real than they
do currently, even as substantial and real as chairs and tables.  And
this wouldn't require any change in what actually exists or "how"
these things exists (logico-mathematical or otherwise).

So based on all of the above, returning to

Re: The seven step series

[Brent Meeker]

Take all strings of length 2
 00 01   10   11
Make two copies of each
 00  00  01  01  10  10  11  11
Add a 0 to the first and a 1 to the second
000001  010   011  100   101   110  111
and you have all strings of length 3.

Brent

m.a. wrote:
> *Thanks Brent,*
> *   Could you supply some illustrative examples?*
> * 
> marty a.*
> ** 
>  
> - Original Message -
> From: "Brent Meeker"  >
> To:  >
> Sent: Tuesday, July 21, 2009 3:57 PM
> Subject: Re: The seven step series
>
> >
> > Each binary string of length n has two possible continuations of  
> length
> > n+1, one of them by appending a 0 and one of them by appending a 1.  So
> > to get all binary strings of length n+1 take each string of length n,
> > make two copies, to one copy append a 0 and to the other copy append 
> a 1.
> >
> > Brent
> >
> > m.a. wrote:
> >> Hi Bruno,
> >>I'm not clear on the sentence in bold below,
> >> especially the word "correspondingly". The example of Mister X only
> >> confuses me more. Could you please give some simple examples? Thanks,
> >>
> >>
> >>
> >>
> >> marty a.
> >> 
> >> 
> >>
> >>  >>
> >> >
> >
> >
> >
> >


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Re: The seven step series

[m.a.]

Thanks Brent,
   Could you supply some illustrative examples?

 marty a.


- Original Message - 
From: "Brent Meeker" 
To: 
Sent: Tuesday, July 21, 2009 3:57 PM
Subject: Re: The seven step series


> 
> Each binary string of length n has two possible continuations of  length 
> n+1, one of them by appending a 0 and one of them by appending a 1.  So 
> to get all binary strings of length n+1 take each string of length n, 
> make two copies, to one copy append a 0 and to the other copy append a 1.
> 
> Brent
> 
> m.a. wrote:
>> Hi Bruno,
>>I'm not clear on the sentence in bold below, 
>> especially the word "correspondingly". The example of Mister X only 
>> confuses me more. Could you please give some simple examples? Thanks,
>> 
>> 
>> 
>> 
>> marty a.
>>  
>>  
>>
>>  >>
>> >
> 
> 
> >
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Re: The seven step series

[Brent Meeker]

Each binary string of length n has two possible continuations of  length 
n+1, one of them by appending a 0 and one of them by appending a 1.  So 
to get all binary strings of length n+1 take each string of length n, 
make two copies, to one copy append a 0 and to the other copy append a 1.

Brent

m.a. wrote:
> Hi Bruno,
>I'm not clear on the sentence in bold below, 
> especially the word "correspondingly". The example of Mister X only 
> confuses me more. Could you please give some simple examples? Thanks,
> 
> 
> 
> 
> marty a.
>  
>  
>
> - Original Message -
> *From:* Bruno Marchal 
> *To:* everything-list@googlegroups.com
> 
> *Sent:* Monday, July 20, 2009 3:17 PM
> *Subject:* Re: The seven step series
>
>
> On 20 Jul 2009, at 15:34, m.a. wrote:
>
>> And then we have seen that such cardinal was given by 2^n. 
> You can see this directly by seeing that adding an element in a
> set, double the number of subset, due to the dichotomic choice in
> creating a subset "placing or not placing" the new element in the
> subset.
>  
> *Likewise with the strings. If you have already all strings of
> length n, you get all the strings of length n+1, by doubling them
> and adding zero or one correspondingly.*
>  
> This is also illustrated by the iterated self-duplication W, M.
> Mister X is cut and paste in two rooms containing each a box, in
> which there is a paper with zero on it, in room W, and 1 on it in
> room M. After the experience, the 'Mister X' coming out from room
> W wrote 0 in his diary, and the 'Mister X' coming out from room M
> wrote 1 in his diary. And then they redo each, the experiment. The
> Mister-X with-0-in-his-diary redoes it, and gives a Mister-X
> with-0-in-his-diary coming out from room W, and adding 0 in its
> diary and a  Mister-X with-0-in-his-diary coming out from room M,
> adding 1 in its diary: they have the stories 
>
>  
> Bruno
>
>
>
> http://iridia.ulb.ac.be/~marchal/
> 
>
>
>
>
>
> >


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Re: The seven step series

[m.a.]

Hi Bruno,
   I'm not clear on the sentence in bold below, especially the 
word "correspondingly". The example of Mister X only confuses me more. Could 
you please give some simple examples? Thanks,



marty a.


  - Original Message - 
  From: Bruno Marchal 
  To: everything-list@googlegroups.com 
  Sent: Monday, July 20, 2009 3:17 PM
  Subject: Re: The seven step series




  On 20 Jul 2009, at 15:34, m.a. wrote:


And then we have seen that such cardinal was given by 2^n. 
  You can see this directly by seeing that adding an element in a set, double 
the number of subset, due to the dichotomic choice in creating a subset 
"placing or not placing" the new element in the subset.

  Likewise with the strings. If you have already all strings of length n, you 
get all the strings of length n+1, by doubling them and adding zero or one 
correspondingly.

  This is also illustrated by the iterated self-duplication W, M. Mister X is 
cut and paste in two rooms containing each a box, in which there is a paper 
with zero on it, in room W, and 1 on it in room M. After the experience, the 
'Mister X' coming out from room W wrote 0 in his diary, and the 'Mister X' 
coming out from room M wrote 1 in his diary. And then they redo each, the 
experiment. The Mister-X with-0-in-his-diary redoes it, and gives a Mister-X 
with-0-in-his-diary coming out from room W, and adding 0 in its diary and a  
Mister-X with-0-in-his-diary coming out from room M, adding 1 in its diary: 
they have the stories 



  Bruno






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






  

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Re: Dreams and Machines

[Bruno Marchal]

On 21 Jul 2009, at 07:22, Rex Allen wrote:

>
> Brent, I intend to reply more directly to your post soon, as I think
> there's a lot to be said in response.

I agree! I let you comment first.


>
>
> But in the meantime:
>
> So I just finished reading David Deutsch's "The Fabric of Reality",
> and I'm curious what you (Brent, Bruno, and anyone else) make of the
> following passage at the end of chapter 10, The Nature of Mathematics.
> The first paragraph is at least partly applicable to Brent's recent
> post, and the second seems relevant to Bruno's last response.  It
> makes one wonder what other darkly esoteric abstractions may stalk the
> abyssal depths of Platonia???
>
> The passage:
>
> "Mathematical entities are part of the fabric of reality because they
> are complex and autonomous.  The sort of reality they form is in some
> ways like the realm of abstractions envisaged by Plato or Penrose:
> although they are by definition intangible, they exist objectively and
> have properties that are independent of the laws of physics.

OK. Note that assuming comp, the laws of physics are dependent of the  
math.




> However,
> it is physics that allows us to gain knowledge of this realm.

This is a physicalist assumption.




> And it
> imposes stringent constraints.

Assuming comp, those constraints are themselves a mathematical origin.




> Whereas everything in the physical
> reality is comprehensible,

Everything? This is an assumption (and is probably wrong in the comp  
frame).



> the comprehensible mathematical truths are
> precisely the infinitesimal minority which happen to correspond
> exactly to some physical truth - like the fact that if certain symbols
> made of ink on paper are manipulated in certain ways, certain other
> symbols appear.  That is, they are the truths that can be rendered in
> virtual reality.

This follows from comp.



> We have no choice but to assume that the
> incomprehensible mathematical entities are real too, because they
> appear inextricably in our explanations of the comprehensible ones.

They appear in the mind or dreams of the universal machine. Here the  
comp hyp. makes possible to distinguish ontological mathematics (no  
need to take more than a tiny part of arithmetic), and the  
epistemological mathematics, which has no mathematically definable  
bound.



>
>
> There are physical objects - such as fingers, computers and brains -
> whose behaviour can model that of certain abstract objects.  In this
> way the fabric of physical reality provides us with a window on the
> world of abstractions.

Physicalist assumption. With comp the physical world emerges itself  
from a statistical sum on infinitely many computations.



> It is a very narrow window and gives us only a
> limited range of perspectives.  Some of the structures that we see out
> there, such as the natural numbers or the rules of inference of
> classical logic, seem to be important or 'fundamental' to the abstract
> world, in the same way as deep laws of nature are fundamental to the
> physical world.

Yes. Comp explains this, and exploits this.



> But that could be a misleading appearance.  For what
> we are really seeing is only that some abstract structures are
> fundamental to our understanding of abstractions.  We have no reason
> to suppose that those structures are objectively significant in the
> abstract world.

Comp does make them significant.


>  It is merely that some abstract entities are nearer
> and more easily visible from our window than others."

Comp explains this.

I appreciate very much the FOR book, but Deutsch does not take into  
account the fact that if we are digitalizable machines, our  
predictions have to rely eventually on the infinitely many relations  
between numbers. From the first person point of view, those relations  
rely themselves on many infinities which goes beyond elementary  
arithmetic.

With the comp assumption, we have a simple theory of everything:  
elementary arithmetic (without the induction axioms). In that theory  
we can prove the existence of universal machine, and their (finite)  
pieces of dreams, and why those machines will, from their own point of  
view infer the "induction axioms" and glue their dreams in projecting  
physical universe. Comp makes a tiny part of arithmetic a virtual  
"matrix" or "video game", which viewed from inside, will seem as a  
locally concrete reality. Problem: there could be too much "white  
rabbits", and other non computable manifestations predictable in our  
neighborhood. It could be no more than the 'quantum indeterminacy',  
but this remain to be completely proved (a part of this has been  
verified though).

Note that the epistemology is far richer than the ontology. The 'first  
person plenitude' (cf George Levy) is MUCH bigger than the minimal  
third person reality we need to explain the origin of the appearances.

Bruno

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




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