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advanced math has, for the past few decades, been used Possibly not as intensely and religiously as conventionally believed, but used nonetheless The nancial markets of May 2007 were faithful adherents to that three-decades-old legacy The nancial order prevalent just as the horrendous credit crisis began to rear its ugly head was one where theoretical models and quantitatively charged dictums enjoyed a privileged existence Far from being widely shunned, many of them were adoringly abided by and wholeheartedly accepted as backbones of the system A few skeptical outsiders had been crying wolf for a while, but those who matter (the practitioners, the rating agencies, the regulators) had overwhelmingly decided not to entirely ban the math from the premises The nancial Titanic that hit the iceberg in the summer of 2007 and then began a painfully lengthy descent into total darkness was, in modern fashion, inescapably inhabited by quantitative machinations.

As we shall see, such machinations not only failed to forewarn of the iceberg in advance, or may have actually directed the ship towards it They helped create the iceberg themselves There is reason to believe that May 2007 could represent the highwater mark for the application of quantitative tools in nance A backlash against theoretical devices seems to be in the works Simply stated, the crisis has highlighted too many failings at the same time Models did not work, guiding measures failed horribly, sacred assumptions broke down The math did not forewarn, afforded excess complacency and misguided con dence, and justi ed lethal business practices Above all, the mayhem has helped con rm what many had always known or at least suspected: Markets are not quantitatively tamable, and efforts in that direction can destroy us.

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The properties of the 2-D Fourier transform are generalizations of the 1-D Fourier transform. We will need the de nitions of even and odd signals in 2-D. A signal u x; y is even (symmetric) if u x; y u x; y u x; y is odd (antisymmetric) if u x; y u x; y (2.5-2) (2.5-1)

The development of information theory was very important It enabled us to see how a physical event, an electrical impulse, could become a mental event, a message But there was a fundamental problem in the original formulation The amount of information in a message or, more generally, in any stimulus was entirely determined by that stimulus This way of de ning information is all very well, but it can lead to paradoxical results Remember that a letter in a message carries more information when it is more surprising So the letter Q usually carries a lot of information, while the U that comes after it carries none We can apply the same argument to a picture A picture is not made up of letters, but of picture elements (or pixels), which can be of different colors Consider a simple picture of a black square on a white background.

It is dif cult to see how something that is not really necessary for the evolution of nance, whose success is quite improbable, and which can contribute to generating untold pain, could continue to play a prominent role in the markets It is one thing for academics and maybe a few insiders to spend their time thinking big mathematical nance thoughts (not much downside, maybe some signi cant upside if someone does come up with valuable insights), but quite another to allow such ideas to un lteredly affect practice Perhaps it is time to turn back the clock 30 years and return to a world in which theoretical certainties were not an ingrained part of the nancial industry..

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Which elements of this picture will be most informative When we move our eye across an area of constant color there is no surprise, because there is no change When our eye meets an edge, there is an abrupt change of color and we are surprised So, according to information theory, it is the edges in the picture that are most informative This agrees with our intuition If we replace an object by its outline, in other words leaving only the informative edges, then we can still recognize the object But this formulation leads to a paradox By this de nition, the most informative picture is one in which we can never predict what is going to happen next as we move our eye across it This a picture entirely composed of random dots.

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