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...

### 3/14/16

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".