Of Mathematics and Radical Change: Alain Badiou’s Set-Theoretical Ontology by Glenn Gomes

Dear Edward and Glenn,

You are invited see the result of radical thinking in mathematics in the essay on Five Dimensions of universe .

You will see,w e question validity of arithmatic numbers to express quantity and reach a subset of transfinite numbers that can express the quantity.

Look forward to your evaluation on departure from conventional approach to mathematics.

thanks & Regards,

Vijay Gupta

Dear Glenn Gomes,

Law of sines for tetrahedral, may be applicable to describe the string dynamics of the infinite universe for quantizing in finite conditions, in that its consistency in continuum is expressional.

With best wishes,

Jayakar

Hello Glenn,

Very interesting and unusual essay for the contest. It makes us look for new ways to solve old problems in the foundations of physics and mathematics. I constantly read and ponder in this regard the paper by Zenkin «Scientific Counter-Revolution in Mathematics» and contemplate his idea: "the truth should be drawn and should be presented to" an unlimited circle "of spectators".

Sincerely, Vladimir Rogozhin

Well now, if this isn't precisely the point.

We are loathe to question the characteristics of our own shadow -- let alone even enumerate them in the first place -- because we're just too busy forcing the rest of the universe to conform to our strict beliefs.

Bravo!

A very good essay. In my opinion, the essay fits the topic perfectly.

P.S. That comment was aimed at Ekart, not Glenn.

Glenn

I noted your attitude to non- euclidean geometry

In the last essay competition my essay

http://www.fqxi.org/community/forum/topic/946

dedicated ANALOGY BETWEEN PHYSICS AND MATH.

Can you comment?

If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is [math]R_1 [/math] and [math]N_1 [/math] was the quantity of people which gave you ratings. Then you have [math]S_1=R_1 N_1 [/math] of points. After it anyone give you [math]dS [/math] of points so you have [math]S_2=S_1+ dS [/math] of points and [math]N_2=N_1+1 [/math] is the common quantity of the people which gave you ratings. At the same time you will have [math]S_2=R_2 N_2 [/math] of points. From here, if you want to be R2 > R1 there must be: [math]S_2/ N_2>S_1/ N_1 [/math] or [math] (S_1+ dS) / (N_1+1) >S_1/ N_1 [/math] or [math] dS >S_1/ N_1 =R_1[/math] In other words if you want to increase rating of anyone you must give him more points [math]dS [/math] then the participant`s rating [math]R_1 [/math] was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process. I hope the FQXI community will change the rating process.

Sergey Fedosin

Dear Glenn,

Thanks for your important contribution! After reading your essay, I looked at your bio expecting to find you an eminent mathematician in one of the world's great research institutions and was surprised to see that you are on another path entirely! Regarding your essay, some thoughts come to mind:

1. Nice discussion of Cantor, set theory, and ordinals. In my own efforts to understand quantum gravity, I have found it necessary to deal with something similar, though somewhat more general (which I call a "semiordinal;" the object in footnote 14 of my essay is an example of one). All this arises from the most naive physical ideas of cause and effect and reasonable local conditions!

2. I've run into the continuum hypothesis in thinking about physics too! It's funny how most people regard these things (and other "purely mathematical issues" like undecidability and the uncountable axiom of choice) as physically irrelevant when they are anything but.

3. Regarding ZFC, Russell's paradox, etc... as you know the ordinals form a proper class, not a set. Hence, again these issues become physically relevant from the most primitive physical considerations.

4. Regarding Godel's work and model theory... Torsten Asselmeyer-Maluga, Jerzy Krol, and Michael Goodband all have excellent essays here that would interest you.

5. Regarding geometry, as an aspiring algebraic geometer, I strongly suspect that the geometry of smooth manifolds may ultimately prove "too good to be true" in regard to spacetime structure. But it's been fantastically useful and astonishingly accurate so far.

6. Excellent endnotes!

Thanks again for the interesting read! Your work rates very highly in my opinion. Take care,

Ben Dribus