QuoteOriginally posted by: crowlogicQuoteOriginally posted by: NQuoteOriginally posted by: dongtaQuoteOriginally posted by: NThey no value in nontrivial mathematics and physics.Terence Tao once said that mastering Fourier Transform can get you a Fields medal. (I cannot remember exactly where and when he said so). But anyway, it's true in some sense as most of Terry's business (Combinatorics, PDE, Additive Number Theory) nowadays have roots in Harmonic Analysis, his main field.Tao is a junior grade mathematician at best since he has only mastered real and complex analysis. He has no clue about harmonic analysis on two and three manifolds. I'm sorry to say it just don't see anything of value in his work (He's yet another example of university mathematics inbreeding).You are not a fan of analytic number theory N?I'm a very big fan of analytic number theory! The key to mathematics is knowning which mathematician is correct and which one is not. Tao isn't qualified to clean Victor Kac's or John Baez's toilet!

QuoteOriginally posted by: NQuoteOriginally posted by: crowlogicQuoteOriginally posted by: NQuoteOriginally posted by: dongtaQuoteOriginally posted by: NThey no value in nontrivial mathematics and physics.Terence Tao once said that mastering Fourier Transform can get you a Fields medal. (I cannot remember exactly where and when he said so). But anyway, it's true in some sense as most of Terry's business (Combinatorics, PDE, Additive Number Theory) nowadays have roots in Harmonic Analysis, his main field.Tao is a junior grade mathematician at best since he has only mastered real and complex analysis. He has no clue about harmonic analysis on two and three manifolds. I'm sorry to say it just don't see anything of value in his work (He's yet another example of university mathematics inbreeding).You are not a fan of analytic number theory N?I'm a very big fan of analytic number theory! The key to mathematics is knowning which mathematician is correct and which one is not. Tao isn't qualified to clean Victor Kac's or John Baez's toilet!Ok, I'm with ya there, John Baez's stuff is very good. To be honest, I like Tao's prime number stuff but haven't found much use for it really..

Then N is one of the very few that are qualified mathematicians. This list of course doesn't have Charles Fefferman, Elias Stein, Jean Bourgain, etc. It probably doesn't have Peter Lax, Nirenberg, Carleson, P-L Lions, Varadhan, Caffarelli, etc. as well since they don't study the right mathematics (i.e. Noncommutative Geometry, Quantum Field Theory, Super-String Theory...). If I could, I'd nominate N for a 2010 Fields medal.But then, why are you around this forum?

Last edited by dongta on May 6th, 2007, 10:00 pm, edited 1 time in total.

N, is it your opinion that the use of the AOC leads to the very serious difficulties and apparent paradoxes? Essentially, it appears any use of the AOC or the Hahn-Banach theorem (existence of maximal ideals) leads to answers that depend on the methods used in that they are "sensitive to direction". This can be very disconcerting if your trying to figure out if your solution is the "best". In a book by M.M. Rao he treats both viewpoints, one the "idealistic" based on the AOC and the other a constructivist approach and shows how apparant paradoxes arise. The existence of these 'paradoxes' is probably the strongest reason I can see for not using the axiom. See Large Excursions of Gaussian ProcessesMark Kac, David SlepianThe Annals of Mathematical Statistics, Vol. 30, No. 4 (Dec., 1959), pp. 1215-1228where they find uncountably infinite many different answers to the same question. Weird.

N, is it your opinion that the use of the AOC leads to the very serious difficultiesCrow, there are other issues but AOC is definitely an immediate show-stopper.dongta, Fefferman added zippo to the theory of PDEs and harmonic functions. His work is pretty sad. And Elias Stein is in the same boat. Is there a reason you only mention "academic inbreds"?How do I know? I'm not interested in creating mathematics, but rather, I'm into creating technology that determines which existing mathematics is correct. I certainly wouldn't even qualify for a Boy Scout's medal.

Last edited by N on May 6th, 2007, 10:00 pm, edited 1 time in total.

QuoteOriginally posted by: Ndongta, Fefferman added zippo to the theory of PDEs and harmonic functions. His work is pretty sad. And Elias Stein is in the same boat. Is there a reason you only mention "academic inbreds"?Since I knew that you would reject those celebrated analysts as mathematicians. I have 2 friends (both are geometers) who are just like you.(Btw, I don't scorn Geometry since I see them as important, if not more than, as Analysis.)QuoteHow do I know? I'm not interested in creating mathematics, but rather, I'm into creating technology that determines which existing mathematics is correct. I certainly wouldn't even qualify for a Boy Scout's medal.Trust me, if you understand all of their work and publish a paper that classifies which mathematics is correct, you're more than qualified to win a the medal (if not Ig Fields medal).

Last edited by dongta on May 6th, 2007, 10:00 pm, edited 1 time in total.

the name john baez came up and wouldn't you know he gave us the crackpot index:A -5 point starting credit. 1 point for every statement that is widely agreed on to be false. 2 points for every statement that is clearly vacuous. 3 points for every statement that is logically inconsistent. 5 points for each such statement that is adhered to despite careful correction. 5 points for using a thought experiment that contradicts the results of a widely accepted real experiment. 5 points for each word in all capital letters (except for those with defective keyboards). 5 points for each mention of "Einstien", "Hawkins" or "Feynmann". just throw'n it out there ps the typo in the last point is deliberate, see http://math.ucr.edu/home/baez/crackpot.html

z,Tony Smith (baez's sidekick in theoretical physics) is viewed by the Cornell Physics dept as a total crackpot, but smith doesn't score any points on baez's crackpot scale. Do ya think that this may say something about the quality of Cornell physics?n

QuoteOriginally posted by: NStochastic processes require infinite energy (that's a slam-dunk since a stochastic process must have infinite bandwidth). Any second year EE knows that. The stock market has energy, but not infinite energy!In the real world, no one in finance uses stochastic calculus for any length of time. If you don't make money you're out! In fact, Black Scholes is never used either (another math orgasm).I think that one thing we can (or should) agree on is:-No one will ever have a model that describes financial markets, no matter how good the underlying mathematics isGiven that, it seems that sometimes one is forced to choose between good math and bad tractability or "bad" math and good tractability.Now, I assume that when you say "in the real world no one uses stochastic calculus for any length of time" you are prepared to back up such a strong affirmative (given that one successful user is enough to prove you wrong). Are you ?

QuoteOriginally posted by: MCarreiraQuoteOriginally posted by: NStochastic processes require infinite energy (that's a slam-dunk since a stochastic process must have infinite bandwidth). Any second year EE knows that. The stock market has energy, but not infinite energy!In the real world, no one in finance uses stochastic calculus for any length of time. If you don't make money you're out! In fact, Black Scholes is never used either (another math orgasm).I think that one thing we can (or should) agree on is:-No one will ever have a model that describes financial markets, no matter how good the underlying mathematics isGiven that, it seems that sometimes one is forced to choose between good math and bad tractability or "bad" math and good tractability.Now, I assume that when you say "in the real world no one uses stochastic calculus for any length of time" you are prepared to back up such a strong affirmative (given that one successful user is enough to prove you wrong). Are you ?"-No one will ever have a model that describes financial markets, no matter how good the underlying mathematics is", We do not agree.Regarding affirmation - Absolutely...And the definition of stochatic calculus is? Pick any text.

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N,If you think that the problem of modelling something (financial markets) that is influenced by the models that try to describe it is going to be solved by "better" maths, then discussing whether stochastic calculus is good or bad is irrelevant to the main argument.My view - for whatever it 's worth - is that models, imperfect though, drive markets and are driven by those market in return (not much of an original view - it seems "An Engine, Not a Camera" has the same argument, haven't had the time to read it yet).Are there better ways of describing financial markets (like Mandelbrot's modelling of it) than the standard textbook ? Yes.Would they be classified as "good" math in your way of thinking ?Would the financial markets and the products be the same if you had published "The Pricing of Options and Corporate Liabilities" ?

QuoteOriginally posted by: MCarreiraN,If you think that the problem of modelling something (financial markets) that is influenced by the models that try to describe it is going to be solved by "better" maths, then discussing whether stochastic calculus is good or bad is irrelevant to the main argument.My view - for whatever it 's worth - is that models, imperfect though, drive markets and are driven by those market in return (not much of an original view - it seems "An Engine, Not a Camera" has the same argument, haven't had the time to read it yet).Are there better ways of describing financial markets (like Mandelbrot's modelling of it) than the standard textbook ? Yes.Would they be classified as "good" math in your way of thinking ?Would the financial markets and the products be the same if you had published "The Pricing of Options and Corporate Liabilities" ?The problem with stochastic calculus is that it's based on combining properties of zero and one manifolds. That's just impossible. Mandelbrot's observations are instrumental in understanding market dynamics, but he has no background in mathematics so his observations are all that there is.

Is there a way to express your assertions in a way I could follow or at least a book/paper I could read ? It's really hard (at least for me) to agree or disagree with a phrase like "The problem with stochastic calculus is that it's based on combining properties of zero and one manifolds. That's just impossible.".I cannot find a way to follow a line of thought and either:-agree with the conclusion because every step is true and they all follow each other in a logical way or-disagree because one step is false or there's no logical chainIf you could refer me to something I could read that would help me in understanding your points I would be very pleased.

QuoteOriginally posted by: MCarreiraIs there a way to express your assertions in a way I could follow or at least a book/paper I could read ?I'm not a particularly strong mathematician, but from what I do understand from the multitude of N's posts, his abhorrence of stochastic calculus seems to stem from the fact that it uses a continuous process to represent a system that is inherently discrete. (Successive observations necessarily have a finite time difference.)If this is, as I suspect, the core of his case, then I wish he would state it as simply as this and stop the endless distractions with hyperbolae, obscurantism and tirades against other mathematicians and physicists. By using simple English like this, instead of trying to quell rational thought by bombing us with mathematical jargon, he might give myself (and, I suspect, others) a better chance of both understanding and joining in a reasoned discussion.

QuoteOriginally posted by: FermionQuoteOriginally posted by: MCarreiraIs there a way to express your assertions in a way I could follow or at least a book/paper I could read ?I'm not a particularly strong mathematician, but from what I do understand from the multitude of N's posts, his abhorrence of stochastic calculus seems to stem from the fact that it uses a continuous process to represent a system that is inherently discrete. (Successive observations necessarily have a finite time difference.)True, it is inherently discrete, but could it not be said that the stochastic process is that which is between the discrete observations? A hybrid continuous-discrete setup.

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