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<p>Carl -</p>
<p>This may be a bit more than Nick is prepared for, but it IS an
interesting/useful paper and table... and perhaps somewhat
relevant to the discussion around embodiment and mathematics and
whether understanding through analogy/metaphor grounds out in
sensorial experience or in something more platonic like Frank's
"Right Triangles" and such.</p>
<p>Nick -</p>
<p>Like all good answers, mine to your shroud/manifold starts with
"it depends". You are capturing *part* of the essence of a
Manifold with your "shroud" and yet another with your "shrink
wrap". <br>
</p>
<p>If the "corpse is complete with skin/tissues/etc. and we don't
imagine stuffing the shroud or shrink-wrap material through the
gastrointestinal track, then the shroud you drape over it provides
a continuous surface, but of course it is not closed. When you
come to the edge (hemmed or not) you would need to flip over and
walk "the other side" or *fall off*. Your "shrink wrap" goes one
further and *closes* the shroud. which then makes it a simple
manifold topologically equivalent to a sphere (as the decomposing
body emits gas, the shrink wrap may inflate to a roughly spherical
shape). <br>
</p>
<p>There are a number of examples of how your shrink-wrap manifold
might have a more complex topology. The aforementioned GI tract
represents a hole-through which if shrink-wrapped
fully/properly/vigorously (perish the image!) yields a torus
(donut). IF your corpse was "shot or stabbed through with holes"
(or decomposed to the point of only consisting of bones and
minimal connective tissue) it becomes "yet more complex" with "yet
more holes". I can't think of a physically possible way said body
could become a more complex topology through in principle, one
might graft arms and legs (or other appendages) to one another in
such a manner as to make a trefoil or more complex knot, but that
verges on "just silly". If you read Science Fiction, even someone
as respectable as Kurt Vonnegut (often treated more as mainstream
literature in spite of his very fanciful assumptions) then you
might have encountered an alternative example of such a
shrink-wrap-cum-knot that is topologically equivalent to a klein
bottle (or yet more interesting/complex) but the narrative leading
there would probably seem gratuitously silly.</p>
<p>As for manifolds as used for internal combustion engines, I won't
try to reproduce my painful description/speculation about the
relation between those and *mathematical manifolds*. Let it
suffice to say that the purpose of an intake or exhaust manifold
is to route a volume of fuel-air mixture from the carbuerator
(possibly more than one in some engines) to the intake ports of
each of several cylinders in a smooth and continuous fashion.
These are NOT closed surfaces since they are open on the
carburator end as well as each of the intake port ends, but their
geometric complexity is reminiscent/suggestive of mathematical
manifolds. The exhaust manifold(s) on an internal combustion
engine do just the opposite, collecting hot exhaust gasses from
several cylinders and combining them into a single output to run
through things like catalytic converters and mufflers before
releasing into the atmosphere to choke pedestrians, the city, and
the globe (can you tell I've become an EV snob?).</p>
<p> - Ettiene SHRDLU<br>
</p>
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cite="mid:CAFi2r0jRk-vZ+kMkJ7hD7FcHORWumreG0bSfX__=_dwzVp=HYg@mail.gmail.com">
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<div dir="ltr">
<div dir="ltr">Nick, </div>
<div dir="ltr"><br>
</div>
<div dir="ltr">This may help with manifold analogies. Or
should I phrase that differently....
<div><a href="http://math.ucr.edu/home/baez/rosetta.pdf"
moz-do-not-send="true">http://math.ucr.edu/home/baez/rosetta.pdf</a>
. See esp table 1, though most of the paper is probably more
than you want.<br>
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<div>Carl</div>
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<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Sat, Mar 9, 2019 at 10:20
AM Nick Thompson <<a
href="mailto:nickthompson@earthlink.net"
moz-do-not-send="true">nickthompson@earthlink.net</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote" style="margin:0px 0px 0px
0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">Ok,
so: consider a corpse. Is the skin of a corpse a manifold?
Now. Drop<br>
a shroud over that corpse, is the shroud a manifold? Now,
shrink wrap the<br>
corpse and carefully seal the edges. Is it now a closed
manifold? <br>
<br>
No, huh? Well, ok. <br>
<br>
Nick <br>
<br>
Nicholas S. Thompson<br>
Emeritus Professor of Psychology and Biology<br>
Clark University<br>
<a
href="http://home.earthlink.net/~nickthompson/naturaldesigns/"
rel="noreferrer" target="_blank" moz-do-not-send="true">http://home.earthlink.net/~nickthompson/naturaldesigns/</a><br>
<br>
<br>
-----Original Message-----<br>
From: Friam [mailto:<a href="mailto:friam-bounces@redfish.com"
target="_blank" moz-do-not-send="true">friam-bounces@redfish.com</a>]
On Behalf Of<br>
<a href="mailto:lrudolph@meganet.net" target="_blank"
moz-do-not-send="true">lrudolph@meganet.net</a><br>
Sent: Saturday, March 09, 2019 5:10 AM<br>
To: The Friday Morning Applied Complexity Coffee Group <<a
href="mailto:friam@redfish.com" target="_blank"
moz-do-not-send="true">friam@redfish.com</a>><br>
Subject: Re: [FRIAM] excess meaning alert? (was, Re: are we
how we behave?)<br>
<br>
Nick et al., "surplus meaning" was the term I was
misremembering.<br>
<br>
Further replies to Nick's further questions later.<br>
<br>
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