Fooled by Randomness, The Hidden Role of Chance in Life and in the Markets

The stereotype of a pure mathematician presents an anemic man with a shaggy beard and grimy and uncut fingernails silently laboring on a Spartan but disorganized desk. With thin shoulders and a pot belly, he sits in a grubby office, totally absorbed in his work, oblivious to the grunginess of his surroundings. He grew up in a communist regime and speaks English with an astringent and throaty Eastern European accent. When he eats, crumbs of food accumulate in his beard. With time he becomes more and more absorbed in his subject matter of pure theorems, reaching levels of ever increasing abstraction. The American public was recently exposed to one of these characters with the unabomber, the bearded and recluse mathematician who lived in a hut and took to murdering people who promoted modern technology. No journalist was capable of even coming close to describing the subject matter of his thesis, Complex Boundaries, as it has no intelligible equivalent ± a complex number being an entirely abstract and imaginary number, the square root of minus one, an object that has no analog outside of the world of mathematics.

The name Monte Carlo conjures up the image of a suntanned urbane man of the Europlayboy variety entering a casino under a whiff of the Mediterranean breeze. He is an apt skier and tennis player, but also can hold his own in chess and bridge. He drives a gray sports car, dresses in a well ironed Italian handmade suit, and speaks carefully and smoothly about mundane, but real, matters, those a journalist can easily describe to the public in compact sentences. Inside the casino he astutely counts the cards, mastering the odds, and bets in a studied manner, his mind producing precise calculations of his optimal betting size. He could be James Bond’s smarter lost brother.

Now when I think of Monte Carlo mathematics, I think of a happy combination of the two: the Monte Carlo man’s realism without the shallowness combined with the mathematician’s intuitions without the excessive abstraction. For indeed this branch of mathematics is of immense practical use ± it does not present the same dryness commonly associated with mathematics. I became addicted to it the minute I became a trader. It shaped my thinking in most matters related to randomness. Most of the examples used in the book were created with my Monte Carlo generator, which I introduce in this chapter. Yet, it is far more a way of thinking than a computational method. Mathematics is principally a tool to meditate, rather than to compute.

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If I make everything is predictable, human beings will no have motive to do anything since the future is totally determined. If I make everything is unpredictable, human beings will no have motive to do anything as there is no rational basis for any decision. I must therefore create a mixture of two.

This explanation is a good approach to understand what probability is.

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The Riemann Zeta function is an important complex function whose behavior has implication for the prime numbers among the natural numbers, which is the simplest of Dirichlet series. This series only converge when the real part of *s *is greater then one, outside the area of the complex relevant to the distribution of the primes.

In the year 2000, the Clay Mathematics Institute offered a $1 million prize for proof of the Riemann hypothesis. The proof can not be done by computerization (read: disproof) to earn the prize, e.g. by using computer to actually find a zero off the critical line. It is going interesting, since this hypothesis was showing up in television crime drama “Prime Suspect” (2005) in Season 1, the math genius Charlie Eppes has been kidnapped because he is close to solving the Riemann hypothesis, which allegadly would allow the perpetrators to break essentially all internet security.

The Riemann hypothesis, what a genius conjecture!

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1. “God does not care about our mathematical difficulties, He integrates empirically”, Albert Einstein.

2. “An education isn’t how much you have committed to memory, or even how much you know. It’s being able to differentiate between what you know and what you don’t”, Malcolm Forbes.

3. “I am a thing that thinks, that is to say, a thing that doubts, affrims, denies, understands a few things, is ignorant of many things, wills, refrains from willing, and also imagines and senses”, Rene Descartes.

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