I am curious. What is wrong with the axiom of choice? Do you not choose when deciding what action to take from the output of your models? What are the implications of choices made? How can you study such things without the AOC?

once mathematicians flocked into physics, we got super-strings theory... it's better to keep them away from any field

QuoteOriginally posted by: MCarreiraQuoteOriginally posted by: NFake mathematics such as 'stochastic calculus' is not only taught but is required for degrees like the MSFE. The students get hit from several angles - first the math is useless in quantitative finance (someone please argue with me on this assertion)Shouldn't the burden of proof lie with you on that assertion ?If we define quantitative finance as what is practiced today, shouldn't your assertion be: "... the math should be useless in what should constitute proper quantitative finance" ?Stochastic 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).

QuoteOriginally posted by: crowlogicI am curious. What is wrong with the axiom of choice? Do you not choose when deciding what action to take from the output of your models? What are the implications of choices made? How can you study such things without the AOC?Assuming AOC is the worst type of wrong for a mathematician. AOC ignores the fact that reals comprise different types of field extensions (think Galos theory).

QuoteOriginally posted by: jawabeanonce mathematicians flocked into physics, we got super-strings theory... it's better to keep them away from any field The funny thing is that string theory is the only thing going for physicists. Read Penrose - QM is a real bust; either the math is wrong or the physics is wrong or both are wrong. The math is never right when the physics is right! Now what type of manifold will produce this apparent inconsistency - you got it, those associated with superstrings...

QuoteOriginally posted by: NThe funny thing is that string theory is the only thing going for physicists.it's not physics at all, imho. it's acrobatics. physics has to do with understanding nature, not with equal opportunities to unemployed math structures.

The next question... If there is no such thing as brownian motion (or more exactly, no such thing as stochastic flows), then is there no such thing as 'random'?States can be orthogonal, independent, etc., but their values aren't random. Timeseries can never have elements that are random. Random doesn't exist. On this forum, random number generators are discussed, but do you realize that all those generators are just solutions to difference equations, which are in no way random.The bottom line is that it is so hard to be random that it's actually impossible! (This a well know, but hard to believer result of KAM theory)Anyone disagree or isn't ready to throw out their copy of Hamilton's' Time Series Analysis'.

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Random is a synonym for ignorance which implies that the state of the supposedly random system is not coupled to the state of the observer until it interacts. I suppose you could argue that randomness only occurs under an inconsistent definition of the system boundaries -- that the "random" entity is both outside (=unknown) and inside (=interacting) with the system of interest.

QuoteOriginally posted by: NThe bottom line is that it is so hard to be random that it's actually impossible! (This a well know, but hard to believer result of KAM theory)Anyone disagree or isn't ready to throw out their copy of Hamilton's' Time Series Analysis'.in quantum physics random's everywhere. the state of the system is defined in terms of probabilities. and it's done with an amazing precision. pls, dont even go into "flows" and "manifolds", restrain your math reflexi

QuoteOriginally posted by: jawabeanQuoteOriginally posted by: NThe bottom line is that it is so hard to be random that it's actually impossible! (This a well know, but hard to believer result of KAM theory)Anyone disagree or isn't ready to throw out their copy of Hamilton's' Time Series Analysis'.in quantum physics random's everywhere. the state of the system is defined in terms of probabilities. and it's done with an amazing precision. pls, dont even go into "flows" and "manifolds", restrain your math reflexi Actually the accuracy of QFT is quite poor unless you average and average and average and average and average some more. Quantum physics is useless at very short time scales (see Penrose).

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QuoteOriginally posted by: NQuantum physics is useless at very short time scales (see Penrose).as long as it helps make bombs and reactors, nobody cares... i keep hearing about Penrose, never read anything of his. Theor Phys is very fragmented, in my field whatever he does didnt have any effect. then when u talk about time scales, u have to define what u mean. characteristic times of scatterings and reactions were "short" by any means, imho.

QuoteOriginally posted by: NThe next question... If there is no such thing as brownian motion (or more exactly, no such thing as stochastic flows), then is there no such thing as 'random'?States can be orthogonal, independent, etc., but their values aren't random. Timeseries can never have elements that are random. Random doesn't exist. On this forum, random number generators are discussed, but do you realize that all those generators are just solutions to difference equations, which are in no way random.The bottom line is that it is so hard to be random that it's actually impossible! (This a well know, but hard to believer result of KAM theory)Anyone disagree or isn't ready to throw out their copy of Hamilton's' Time Series Analysis'.Random exists in Nature. Special Theory of Relativity and the existence of Entangled Quantum states implies that Quantum Measurements are truely random. To assert that there is no randomness is equivalent to rejecting either STR or Entanglement or both! So which theory do you reject?

QuoteOriginally posted by: vixenRandom exists in Nature. Special Theory of Relativity and the existence of Entangled Quantum states implies that Quantum Measurements are truely random. To assert that there is no randomness is equivalent to rejecting either STR or Entanglement or both! So which theory do you reject?Which? STR and Entangled states are the same mathematically. They both involve SUSY transforms to a particular group velocity. And as with all canonical transforms, the system is fully deterministic.Now I've gotta admit that entangled state transforms look very random, but apply the inverse scattering xfm and bingo - the original orthogonal states reappear.Random, no way. Magic, possibly.

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You can only say that the system is deterministic if you exclude Measurements from the system. For example, the time evolution of wave functions ( whatever variable is in your system ) is deterministic but this system does not in any way model the outcome of measurements.

QuoteOriginally posted by: vixenYou can only say that the system is deterministic if you exclude Measurements from the system. For example, the time evolution of wave functions ( whatever variable is in your system ) is deterministic but this system does not in any way model the outcome of measurements.You're spouting quantum mechanics nonsense. Entangled states are ideal for use in high-performance digital communication - there's nothing unknown in those systems except perhaps chirality (but who actually cares about rotation direction of polarization - everything's symmetric).

Last edited by N on May 3rd, 2007, 10:00 pm, edited 1 time in total.

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