Monday, March 14, 2016

The date is the title...

J. Venn - Logic of Chance

Turtle Graphics?

The above, looks suspiciously like a printout from my first session with Apple Logo (the language, not the branding), before I figured the command for "pen up"...

A few months back, I was reading a few books and found the above in one of them. It is titled "Logic of Chance", by John Venn (mostly known for the Venn diagram). The year? 1866.

So, where were we? Ah yes...


Yes, that famous sequence of number. What was the story with John Venn and pi, here? Whereas I used digits 0-9 in "the 10 colors of pi", John used digits 0-7, discarding all 8s and 9s. Since back then there were no computers, he picked his numbers from a book (by R. Shank) which had 707 digits of pi, leaving him with 568 digits between 0 and 7. He mapped 0 to 7 to directions (10 directions might have felt a bit odd, at 36 degrees, versus nice 45 degree lines):

Although he doesn't specify the mapping, it is easy to infer from the graph. The first digit after the decimal is 1, then 4 and we can see the path as NE, then S, so:

0 N
1 NE
2 E
3 SE
4 S
5 SW
6 W
7 NW

The random walk

He would then move by 1 unit in the direction of each digit / direction mapping. NE, S, NE, SW, skip 9, E, so on and so forth. (NB: This is easy to reproduce in python with the turtle module. A quick search of my blog will get you started on this, from a pi generator to import turtle.)

His conclusion stated: 
"The result seems to me to furnish a very fair graphical indication of randomness". 

Francois Dion

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