The Middle Square Method (Generating Random Sequences VIII)

Von Neumann proposed the middle square method of generating pseudo-random numbers in 1949, in a paper published a bit later. The method is simple: you take a seed, say 4 digits long, you square it, and extract the middle 4 digits, which become the next seed. For example:

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While it seems random enough, is it?

Suggested Reading: Computing with Quantum Cats

John Gribbin — Computing with Quantum
Cats: from Colossus to Qubits — Prometheus Books, 2014,
295 pp. ISBN 978-1-61614-921-5

(Buy at Amazon)

The book presents the genesis of the various ideas that may lead, one day, to a practical quantum computer. Gribbin takes a well-documented historico-biographical approach to the topic, while avoiding getting too deep into the science part of the story. On great many occasions, he cuts short an interesting avenue with a “but that’s another story”, which I find most frustrating. Those are the good parts I want to know about!

Despite all this, the book is still worth reading. It will expose you clearly (albeit summarily) the various ideas behind quantum computing, and is a good starting point if you’re interested in quantum computing, as the book also ends with a bibliography on the topic.

The quantum cats of the title refers, of course, to the famous Schrödinger cat gedankenexperiment, but the term also to macroscopic objects exhibiting quantum behavior.

Unfair Coin Tossing

Suppose you want a fair coin, one that yields heads and tails with equal probability, but only have a bizarre coin that yields a side more often than the other. Can we remove the bias?

John von Neumann gave us a surprisingly simple procedure to remove bias from a coin and yield a fair toss.