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From: gsmith@brahms.BERKELEY.EDU (Gene Ward Smith)
Newsgroups: net.origins,net.bio
Subject: Re: Review of Michael Denton, _Evolution: a Theory in Crisis_
Message-ID: <13305@ucbvax.BERKELEY.EDU>
Date: Sun, 20-Apr-86 06:58:08 EST
Article-I.D.: ucbvax.13305
Posted: Sun Apr 20 06:58:08 1986
Date-Received: Wed, 23-Apr-86 20:54:58 EST
References: <760@petsd.UUCP> <13299@ucbvax.BERKELEY.EDU>
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Reply-To: gsmith@brahms.UUCP (Gene Ward Smith)
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Xref: watmath net.origins:3025 net.bio:393

In article <13299@ucbvax.BERKELEY.EDU> weemba@brahms.UUCP (Matthew P. Wiener) writes:
>In article <760@petsd.UUCP> cjh@petsd.UUCP (Chris Henrich) writes:
>>     Now, why should this be so?  Why is the space of
>>organisms ultrametric?  I conjecture that the answer will be
>>generally illuminating for biology.

>I'd like some mathematical illumination first.  I am familiar with
>the p-adics and ultrametrics in general etc. but I failed to see
>what your analogy was.

   I think it is worth mentioning that a tree each of whose nodes 
branchs n times has a natural ultrametric topology on it; this is 
one way of getting this for the p-adics. (The p-adic integers are
an inverse limit and the topology and metric is easily derived from
a tree branching p times at each node). Does evolution result in
trees? Trees with regular branching properties? If the answer is
yes, ultrametric norms are no surprise.

ucbvax!brahms!gsmith    Gene Ward Smith/UCB Math Dept/Berkeley CA 94720
ucbvax!weyl!gsmith       "DUMB problem!! DUMB!!!" -- Robert L. Forward