Fate Of Schrodinger's Cat, The: Using Math And Computers To Explore The Counterintuitive by Stein James D;

Author:Stein, James D;
Language: eng
Format: epub
Publisher: World Scientific Publishing Company
Published: 2020-02-15T00:00:00+00:00

Computers could not be made to deal cards or roll dice — at least, not back in the 1960s. In order to test his ideas, Thorp used a random number generator, a type of mathematical algorithm, to supply the random numbers which mimicked the dealing of cards.

7.1 Random Number Generators

It’s important to have a really good random number generator. Many random number generators work with a seed, which we’ll call r0. The random number generator is a function we’ll just call R, and it generates random numbers simply by applying R to the last random number, so rn+1 =R(rn). It’s actually not a true random number generator, because all practical random number generators used by computers are periodic — sooner or later, the sequence of generated numbers repeats.

The current favorite random number generator is known as the Mersenne Twister. It has a period of 219937 − 1, so you, or anyone of your descendants, or anyone in the Universe, is not going to have to worry about the Mersenne Twister repeating. Ever. I like to do simple computations; so suppose that you have a computer that can generate a sextillion (1021) sequential random numbers per second. The Universe is about 1017 seconds old, so if you had such a computer and started running it with the Mersenne Twister at the time of the Big Bang, it would have generated approximately 1038 = 2126 random numbers. So, as I said, you’re not going to have to worry about the Mersenne Twister repeating.

And the good news is that, if you use Excel, C++, Maple, or MatLab to write your simulators, the Mersenne Twister is the beating heart of your random number generator. But I use JustBasic, and I had a really bad feeling about its random number generator. I had written a number of simulators with it, and had gotten some results that looked a little strange. So how do you tell if you’ve got a good random number generator?

Well, you can’t just let it run until it repeats. So I decided to check out a chi-square test on it.

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