[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index][Subject Index][Author Index]

*To*: dinosaur@usc.edu*Subject*: Re: WAS-- Re: Hanson 2006, Mortimer, Baeker response*From*: Graydon <graydon@epiphyte.net>*Date*: Sun, 25 Jun 2006 13:00:03 -0400*In-reply-to*: <20060625.091938.-1045461.0.bigelowp@juno.com>*References*: <20060625.091938.-1045461.0.bigelowp@juno.com>*Reply-to*: oak@uniserve.com*Sender*: owner-DINOSAUR@usc.edu

On Sun, Jun 25, 2006 at 09:04:49AM +0000, Phil Bigelow scripsit: > "Andreas Johansson" <andreasj@gmail.com> writes: > > > The axioms, themselves, are based on earlier real-world > > > observations. > > > Not necessarily. > > I noticed that you didn't say "never". You have this wonderful > ability to under-elaborate on your responses. ;-) Give us an example > of an axiom that is based on earlier real-world observations. "The sum of the interior angles of a triangle is 180 degrees." Since you may well have meant *not* based on early real-world observations, consider "the sum of the interior angles of a triangle is less than 180 degrees"; that'd apply to concave-plane geometry, of which we don't have a real-world example. ("Greater than" gets you into convex plane and spherical trig used for navigation.) Advanced math -- eg., Riemann spaces with all the bizarre, n-dimensional stuff involved in manifolds and tensor transforms -- frequently hasn't got any specific connection to *anything* tangible. Practical applications of math, including statistics, represent either isomorphic (point-to-point) or homomorphic (math sense; "A transformation of one set into another that preserves in the second set the operations between the members of the first set." So "descended from" in the model is the same as "descended from" in evolution, sort of thing) models, and *of course* those relate to real-world things in some relatively clear way. Most of math isn't like that. I mean, come on, if you're talking about measuring properties of arbitrary curvature in arbitrary dimension, you don't have anything of arbitrary dimension to point to, do you? The thing about the models is interesting for dinosaur stuff because there's absolutely no way we can have an isomorphic model -- no soft tissue characters, no genes -- and we *probably* can't have a homomorphic model based solely on osteological characters, but proving that one way or the other would be astonishingly challenging. So one of the potential challenges for phylogenetic systematics would be to find a way to quantify how bad the model is. -- Graydon

**References**:**Re: WAS-- Re: Hanson 2006, Mortimer, Baeker response***From:*Phil Bigelow <bigelowp@juno.com>

- Prev by Date:
**Re: Hanson 2006, Mortimer, Baeker response** - Next by Date:
**Re: Hanson 2006, Mortimer, Baeker response** - Previous by thread:
**Re: WAS-- Re: Hanson 2006, Mortimer, Baeker response** - Next by thread:
**Dead: Harriet, Tortoise, age 175** - Indexes: