Tuesday, June 29, 2010

The First Published Random Walk?

According to Alex Bellos in his new book "Here's Looking at Euclid", this is the world's first graph of a random walk, published by John Venn in his book "The Logic of Chance" in 1888. Venn produces this path using the digits from 0 to 7 from the first 707 digits of π. Venn writes,
"Of these, after omitting 8 and 9, there remain 568; the diagram represents the course traced out by following the direction of these as the clue to our path. Many of the steps have of course been taken in opposite directions twice or oftener. The result seems to me to furnish a very fair graphical indication of randomness. I have compared it with corresponding paths furnished by rows of figures taken from logarithmic tables, and in other ways, and find the results to be much the same."
Here are the directions Venn uses and the results from the first ten decimal digits.

1 comment:

Mark said...

Is it possible that Venn had some incorrect digits for pi? I tried to replicate his image using Mathematica but my picture differs from his...