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.
 
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?
 
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.

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.
 
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? How should I 'comp'(?) the feeling of love? How should I 'materialize' (physically?) the beauty of a sunset?
(all without flattening those qualia into a quantitative plane)?
 
Eager to learn
 
John Mikes
----- Original Message -----
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.
I will keep on your level notions:

-kids
-grandmother
-colleagues

(But not in any normative sense: I know kids who are better in math than colleagues, and I know a family where the computer and the net has been installed by the grand-grandmother! So here each one should judge by him/herself on which level they to feel to be.

But a roadmap, some summaries ... are in need, sure. Not so easy of course. Just let me think about it.
Note also that if I explain in plain english, what I say could appear as a little weird, that is why I tend to be technical. And also, I don't know much people who can swallow both Godel/Church... and Everett/Deutsch ... Quantum information science can help, but this is a bit tricky by itself when you want to be enough precise, and still a long way from Godel-lobian notions.

In any case thanks for letting me know when I get too much technical. Thanks to Norman who tries sometimes to convey a similar message, and thanks to Tom for enjoying apparently the more technical posts ...., and thanks to 1Z for playing the role of the skeptical one, and thanks to all of you, especially Wei Dai, for the kind patience.

I will think about some roadmap, but also about some books which could provide helps.

Feel free to say more on your "relativity"-information theory. Everyone can talk I certainly don't want to monopolize the threads (but then I got a result and I like to share with motivated people ...)...

Now I will leave my office before I liquefy completely ....

Bruno




Le 19-juil.-06, à 00:32, George Levy a écrit :

Hi Bruno

Each one of us like to do what we do best and we apply our preferred techniques to the problem at hand. Thus a mechanic may solve the pollution problem by building electric cars, and the cook may solve the same problem by preparing vegetarian meals.

As a mathematician you are trying to compose a theory of everything using mathematics, this is understandable, and you came up with COMP which is strongly rooted in mathematics and logic.

I came up independently with my own concept involving a generalization of relativity to information theory ( my background is engineering/physics) and somehow we seem to agree on many points. Unfortunately I do not have the background and the time to give my ideas a formal background. It is just an engineering product and it feels right.

I believe that what you are saying is right,  however I am having some trouble following you, just like Norman Samish said. It would help if you outlined a roadmap. Then we would be able to follow the roadmap without having to stop and admire the mathematical scenery at every turn even though it is very beautiful to the initiated, I am sure. For example you could use several levels of explanation: a first level would be as if your were talking to your grandmother; a second level, talking to your kids (if they listen); a last level, talking to your colleagues.

George




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



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