I have a puzzle from c. 1970. Back then, it was science fiction, but now it looks less farfetched. Suppose we have a big computer with everyone's genome data. [Looking less farfetched every day, in fact.] What can we deduce about the genomes of our ancestors? Could we reconstruct an estimated genome of Fermat, Buddha, or Caesar? There's some information loss from generation to generation: Parents with N children will (on average) omit 2^-N of their genes from (the set of) their children. Some of that lost information could be deduced from knowing genomes of cousins (-> aunts & uncles -> grandparents), so it's hard to see exactly how much is erased. If we throw in present-day location information, we can probably figure our who moved where, when, and perhaps deduce population movements from long ago. Rich -----Original Message----- From: math-fun-bounces+rschroe=sandia.gov@mailman.xmission.com on behalf of James Propp Sent: Thu 6/29/2006 10:29 AM To: math-fun@mailman.xmission.com Subject: [math-fun] Re: genetics-fun question
So figuring out who's mother and who's daughter is as easy as labelling their genomes a,b and c,d and noticing which of them has the property that, eg, ccccccccccccc is the same as aaaabbbaabbbb.
Neat! (And not even all that subtle; if I'd thought a bit harder about what I supposedly learned in high school, I could've figured it out.) This fact about the asymmetry of the parent-child relationship suggests a more general question: How much can you deduce about the precise way in which two blood-relatives are related simply from looking at their genes? This can be a real-world issue ("And is it your sworn testimony before this court, as an expert in the field of genetics, that this man cannot possibly be the nephew of Howard Hughes?"), but I could imagine it also giving rise to some mathematically amusing albeit unrealistic puzzles ("Assume an infinite genome..."). Michael? Jim _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun