[FRIAM] Manifold Enthusiasts

[Steven A Smith]

Carl -

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.

Nick -

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".  

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).   

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.

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?).

 - Ettiene SHRDLU

> Nick, 
>
> This may help with manifold analogies.   Or should I phrase that
> differently....
> http://math.ucr.edu/home/baez/rosetta.pdf . See esp table 1, though
> most of the paper is probably more than you want.
>
> Carl
>
>
> On Sat, Mar 9, 2019 at 10:20 AM Nick Thompson
> <nickthompson at earthlink.net <mailto:nickthompson at earthlink.net>> wrote:
>
>     Ok, so:  consider a corpse.  Is the skin of a corpse a manifold? 
>     Now. Drop
>     a shroud over that corpse, is the shroud a manifold?  Now, shrink
>     wrap the
>     corpse and carefully seal the edges.  Is it now a closed manifold? 
>
>     No, huh?  Well, ok. 
>
>     Nick
>
>     Nicholas S. Thompson
>     Emeritus Professor of Psychology and Biology
>     Clark University
>     http://home.earthlink.net/~nickthompson/naturaldesigns/
>
>
>     -----Original Message-----
>     From: Friam [mailto:friam-bounces at redfish.com
>     <mailto:friam-bounces at redfish.com>] On Behalf Of
>     lrudolph at meganet.net <mailto:lrudolph at meganet.net>
>     Sent: Saturday, March 09, 2019 5:10 AM
>     To: The Friday Morning Applied Complexity Coffee Group
>     <friam at redfish.com <mailto:friam at redfish.com>>
>     Subject: Re: [FRIAM] excess meaning alert? (was, Re: are we how we
>     behave?)
>
>     Nick et al., "surplus meaning" was the term I was misremembering.
>
>     Further replies to Nick's further questions later.
>
>
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