I appreciate your efforts to 'enlighten' me (and
maybe others as well). my case there is more ignorance interfering with the
explanations and I will re-re-read your post before I come to a
As I tried to tell, when you "matter-of-factly"
handle concepts of your 'daily bread' I have to search after for some meaning I
can assign as a key to 'read on'.
Even the cardinal points in your theory are not
functional parts of my mi nd-content (UD, YesDr, even 'comp') but I get lost
with G and G', even I have to translate for my own vocabulary the 1- and 3-
features or expressions from 'logics'. All these are raining down in your
sentences and I cannot ask you not to use them: I use MY 'words' just the same
and others ask back many times using for themselves in other meanings.
There are very few math\ematically gifted minds
among us and it does not help what a post yesterday stated that "everybody can
learn math (thinking) if diligent". You as math teacher may know pupils
who "just CANNOT get it.
The fraction of humanity cursed with mathematical
imparement (ha ha) looks down to the rest of us, a natural defence of the
A special case the 'applied math' you
Mostly physicists (and other scientists as well) -
thinking in limited models - learned math and aooky itg equationally to a
quantized system of their model-view. It elevates
the model content to 'total' and the imperfections from neglectimg the 'rest of
the world - beyond the model's boundaries' lead to paradoxes and orher
misconceptions over millennia.
I have some understanding in the math0thinking, my
problem is that I did not 'learn' and 'continue' enough math after that
rudimentary conventional domain necessary for the Ph,D exam as 'elective'.
In my practical polymer R&D including numerous implementations and
consulting I did not need 'math' and so it faded over all those decades. I never
lear\ned theo. logics.
I think I am not the worst candidate for what I
proposed, yet it may be more than the burden you might take on.
Sorry if I wasted your time and
----- Original Message -----
Sent: Thursday, July 20, 2006 8:22
Subject: Re: K the Master Set (+ partial
answer to Tom's Diagonalization)
Le 19-juil.-06, à 18:01, John M a écrit
wrote an admirably wise note and you picked positively on the roadmap with
the fruitful mind of a logician./fontfamily>
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"
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
My question (and I asked it
several times here and on diverse other lists and got no satisfactory
answer) - still
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
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.
don't think there is new meaning of math. Just new branch of math like
mathematical logics, philosophical logics, metamathematics, computer science,
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?"
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)(*))
Unfortunately with comp there is a big nuance
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
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
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
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./fontfamily>
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.
I propose a 'starting' point to the 'roadmap':/fontfamily>
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'.)/fontfamily>
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'
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
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
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.
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
How should I 'materialize'
(physically?) the beauty of a sunset?/fontfamily>
(all without flattening
those qualia into a quantitative
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
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
Wednesday, July 19, 2006 10:39 AM/x-tad-bigger>/fontfamily>
Re: K the Master Set (+ partial answer to Tom's Diagonalization)/x-tad-bigger>/fontfamily>
A roadmap could be a very good idea. I will think about
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