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## Is a Random Number Actually Random?

We live by "random" numbers: pulling numbered slips out of a hat...thinking of a number...Draft Status draws...lottery ball draws...being assigned a protected password...using the RND function on a calculator.

But, are these numbers actually random? In a 1994 AAAS talk, mathematician/magician Persi Diaconis says probably not....labeling it a "minor scandal."

We have numerical algorithms that claim to spew out random numbers. Yet, when Diaconis applied a series of tests to determine "true" randomness (based on work by George Marsaglia in the 1980s), he discovered that every existing generator failed at least one of the tests for randomness.

For example, an algorithm may start with a “seed” number (e.g. 5), multiply it by a prime number (e.g. 11), divide by another prime number (e.g. 7), and then take the remainder. This process generates a sequence of remainders (e.g. 5,6,3,…). Mathematically, this sequence must repeat in a cycle because the number of possible remainders is finite {0-7}. Though the process is improved by computing with very large numbers or using trigonometric or logarithmic functions, the process always will repeat itself.

To overcome the weaknesses of a numerical algorithm, scientists use natural events or measurements to produce “random” seeds. Simple examples include a user’s motion of their mouse or static noise from a radio tuned between two stations. More complex examples are physical devices that produce “random” numbers using quantum physics, such as Geiger counters timing radioactive decays of Cobalt-60 atoms or photons of light beamed at semitransparent mirrors.

In his talk, Diaconis suggested an unusual method based on a seed of 55 odd numbers. Then, new "random" numbers are calculated by the formula xn = xn-24*xn-55 mod(232). He claims that his approach passes all of the standard tests for randomness...but warns that "no one knows how well it really works."

Comforting, right!

Source: Adapted from B. Cipra's article in SIAM News, August 1994.