For The Genealogy Crowd…

One of my sisters works on our family genealogy, and since there are sometimes interesting results, I've always noted that if you just go back far enough we are ALL related to one another.

John Brockman's latest Edge book is out, "This Explains Everything," with responses from 150 science-y sorts. I've been perusing the more mathematically-related replies and thus far my favorite is from Jon Kleinberg who uses the "pigeon-hole principle" to demonstrate that somewhere well within the previous 4000 years anybody's mother AND father will have a common ancestor:

http://www.edge.org/response-detail/11067

When Sol Lederman interviewed me for his podcast series, at one point I remarked, tongue-in-cheek, that perhaps somewhere in my distant past I shared some genes with Bernhard Riemann, the great German mathematician who's namesake I use here, and who lived in the same area of the world as my father's ancestors. Nice to apply some mathematics to that thought.

You can view all the responses to the 2012 Edge annual question here:

http://www.edge.org/contributors/what-is-your-favorite-deep-elegant-or-beautiful-explanation

The Pigeon-hole Principle

I've mentioned the "pigeon-hole principle" briefly before, and it crossed my radar again when James Tanton put up a video on it here:

http://www.jamestanton.com/?p=810

It is one of those intuitive mathematical concepts that seems so obvious upon first glance that one wonders why it must even be stated, or how it could possibly be of any use... and yet that is the essence and beauty of mathematics: that basic, seemingly obvious ideas can be massaged by logic to produce significant and less obvious outcomes and ramifications.

If you're familiar with the pigeon-hole principle (it is especially used in combinatorics) you understand what I mean; if you're not familiar with it, then I won't even state it lest you think it too boring to bother with, but direct you instead to another link further elucidating it:

http://mindyourdecisions.com/blog/2008/11/25/16-fun-applications-of-the-pigeonhole-principle/