Re: K the Master Set (+ partial answer to Tom's Diagonalization)

From: Bruno Marchal <marchal.domain.name.hidden>
Date: Thu, 20 Jul 2006 14:22:59 +0200

John,


Le 19-juil.-06, à 18:01, John M a écrit :

> Bruno,
>  
> George wrote an admirably wise note and you picked positively on the
> roadmap with the fruitful mind of a logician.
> It looks like you both start out from "not agreeing because of
> non-understanding math sufficiently" - which may be true, but not
> necessarily the "real" root.
>  
> I think many of us have the wrong information about 'math' in
> question. You called "numbers" the series of '1,2,3...many' and "we"
> think 'math' is a manipulation of such, even if many substitute and
> functional symbols are used.


All right.



>  
> My question (and I asked it several times here and on diverse other
> lists and got no satisfactory answer) - still prevails:
> What are (in the new meaning) NUMBERS - how can we handle the
> non-number concepts by numbers - (whatever they are)? Rephrased: What
> is the 'new' meaning of "math" and how can non-math concepts be
> handled by math?


OK, OK, but this is a difficult question, John. Let me give you a
standard answer, which should be simple, and then add a comp nuance,
which is probably a little bit more subtle.
First I don't think there is new meaning of math. Just new branch of
math like mathematical logics, philosophical logics, metamathematics,
computer science, etc.
Since Euler I think mathematician are more and more aware that the
numbers are mysterious, and since Godel we have results which somehow
explain why numbers are necessarily mysterious. Such limitation results
are made *general* (machine or formalism independent) with Church
thesis. And then with comp above, those results will bear on the
limitation of *humans*: in that sense we can say that we begin to
understand why the numbers are mysterious, why we cannot find unifying
theory for the numbers, etc.

Now for the question "How can non-math concept be handled by math?"
The standard answer goes trough the label "applied mathematics". You
just need to make a correspondence between some term of the theory and
some element of the "reality" you want to modelize with the math
theory. This is what physicists do all the time, and this what
theologians have done during one millenia (before "religion" has been
used as a political power (say)(*))
It just applied mathematics.
Unfortunately with comp there is a big nuance here.
Indeed, when you are using some theory (model in the physicist sense)
to predict the whether (say), it is clear that the "model" is a
thorough simplification of "reality". In the case of whether
prediction, we have no "exact equations", and worst, the few equation
we have are not analytically soluble, so that a computer simulation is
in need. Similarly you can *apply* math to simulate neural networks and
(perhaps) learn something about the brain.
OK, but now, when you are willing to say "yes" to a doctor when he
proposes to you an artificial digital brain body things are
fundamentally different. The artificial brain is no more supposed to
*modelize* you brain, like in the whether case, but to save your
"soul". In this case the "model" is supposed to be the reality. That
is obviously quite a jump, but it is made reasonable through the
computer scientist distinction between "emulation" and "simulation". It
is known that universal machine can not only simulate many things, but
can also emulate exactly all digital processes (thanks to Church
thesis). Eventually this can be explained through diagonalization and
"semantical fixed points", but I don't want to be technical here. So
with comp (= mainly "yes doctor") you apply math to a part of pure
math, like in metamathematics or theoretical computer science, which,
through comp, describe the living realm we are inhabiting.



(*) See perhaps the following PDF on "Mathematics and Theology" Note
that I disagree with the main conclusion.
http://www2.hmc.edu/www_common/hmnj/davis2brieflook1and2.pdf


>  
> Norman touched it, 1Z goes around it, David Bohm even went that far as
> to state: numbers (and so math) are human inventions, probably based
> on Plato, who made the biggest (philosophical) argument - as the
> product  of HIS mind.


Bohm is even more coherent with respect to the comp consequence than
Chalmers in the sense that he explictly postulate non-comp (in its
"intricate order" book).



> Words are loaded with different meanings and people tend to use their
> favorite - mostly from the mother tongue.  I admire George's open mind
> accepting the diverse positions and I am also no missionary who wants
> to convert people, but even if I think differently, I like to follow
> the mental ways of others. It may add usefully to my own thinking.


Note, and this is a key point, I am not defending any position at all.
I try not to insist too much because it could look pretentious, but I
do think even just the UDA (including the Movie-Graph) does not leave
any choice in the matter. In a nutshell I believe the UDA shows that IF
comp is taken sufficiently seriously (as to say purposefully yes to a
doctor for example) then Plato's conception of reality is correct and
Aristotle's one is incorrect.


>  
> So I propose a 'starting' point to the 'roadmap':
> How may one consider the new version(s) of number and math instead of
> the arithmetic-based and binary computer founded conventional
> ignorance? (It is not a 101 course what this list should be above, it
> may draw in 'more-sided' opinions into the discussion - which is now
> pretty much on the math - physics base only. Extending to other planes
> of 'everything'.)
>  
> Then we may proceed in understanding the 'stuffy' matter (as e.g.. a
> photon - ha ha) and the physicists' concepts mostly based on some
> mathematical application, including the most esoteric 'everything'
> topics.
> After all that I may try to speak about my ways how I am not in
> controversy with all that - only regarding it as a partial view of the
> totality (which is hard to talk about). Not for converting you or
> others, just for proving to myself some (Levy-type) sanity.
>  
> So how should I include the validity of a legal opinion into the
> numbers?


Here I am not sure I follow you. When I talk about (natural) numbers I
am really talking about those (non definable) entities that every
schoolchild learn about through table of addition, multiplication, etc.
They are the same as Euclid's one in the sense that all what Euclid
proved about them is still valid today.




> How should I 'comp'(?) the feeling of love?


In principle there will no be problem for that, although I still cannot
explain this without explaining more about the G-G* gap. Later perhaps.
Note that such a question is more difficult for a physicalist who
believes only in atoms or strings (or quantum gravity loops ...)
because they don't have (yet) the equivalent of the G-G* gap (akin to
the explanation gap of the philosopher of mind). Try to explain why you
like potatoes using only terms from string theory, for example.
But comp provides an explanation why anything describable in a
seemingly third person way, will automatically be extended into a math
structure divided in two parts: a 3-communicable part (deriving from
G), and a non-3-communicable part (deriving from the corona G* minus
G).
I recall that G is a mathematical theory describing completely the
(skeleton) of what a correct machine can prove about itself, and G*
describes the (skeleton) of all the truth---including the non provable
one---concerning what a machine can (and cannot) prove about itself.

For those who have read a bit on the difference between programmable
function Fi and the total computable function fi could perhaps already
smell the mathematical justification of that "explanatory" gap.


> How should I 'materialize' (physically?) the beauty of a sunset?
> (all without flattening those qualia into a quantitative plane)?


It is exactly here that it is hard for me non going technical because I
find it is worth. Indeed it can be proved that when a universal machine
M1 introspects herself, she will discover both sharable (provable)
quantitative truth and non sharable qualitative (non quantitative, nor
even 3-describable) truth. Actually any much stronger (in term of its
set of beliefs) universal machine, M2 say, will be able to show that
those non quantitative truth are really disguised form of quantitative
truth, but M2 can understand why, from the many points of view of M1
itself (including both the 1 and 3 povs), although quantitative, those
truth cannot *appear* to be quantitative. M1 can grasp those personal
truth only in a qualitative way. This will explain qualia, but also why
in some sense a universal machine cannot know she is a machine, nor
even any 3-entity.

Later I will come back on the "arithmetical notion of persons" we
encounter through the self-reference theories (G and G*) in computer
science. I call them "hypostases" so that people who read Plotinus can
see how close we are, with comp, to Plato, and even to Plotinus'
critics of Aristotle "misunderstanding" of Plato.

But that is probably on the last point of the roadmap, so I stop,
momentarily here. If I have already been too technical just tell me or
ask questions. Hope this helps a bit,

Bruno


>  
> Eager to learn
>  
> John Mikes
>> ----- Original Message -----
>> From: Bruno Marchal
>> To: everything-list.domain.name.hidden
>> Sent: Wednesday, July 19, 2006 10:39 AM
>> Subject: Re: K the Master Set (+ partial answer to Tom's
>> Diagonalization)
>>
>> Hi George,
>>
>>
>> A roadmap could be a very good idea. I will think about it. <snip>


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


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Received on Thu Jul 20 2006 - 08:24:12 PDT

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