[FRIAM] Manifold Enthusiasts

Sat Mar 9 17:07:41 EST 2019

Steve, 

All I can say is, for a man in excruciating pain, you sure write good.  Your response was just what I needed.  

Now, when I think of a manifold, my leetle former-english-major brain thinks shroud, and the major thing about a shroud is that it covers something.  Now I suspect that this is an example of irrelevant surplus meaning to a mathematician, right?  A mathematician doesn’t give a fig for the corpse, only for the properties of the shroud.  But is there a mathematics of the relation between the shroud and the corpse?  And what is THAT called.  

So, imagine the coast of Maine with all its bays, rivers and fjords.  Imagine now a map of infinite resolution of that coastline, etched in ink.  I assume that this is a manifold of sorts.   Now gradually back off the resolution of the map until you get the kind of coastline map you would get if you stopped at the Maine Turnpike booth on your way into the state and picked a tourist brochure.  Now that also is a manifold of sorts, right?  In my example, both are representations of the coastline, but I take it that in the mathematical conception the potential representational function of a “manifold” is not of interest? 

Nick 

Nicholas S. Thompson

Emeritus Professor of Psychology and Biology

Clark University

 <http://home.earthlink.net/~nickthompson/naturaldesigns/> http://home.earthlink.net/~nickthompson/naturaldesigns/

From: Friam [mailto:friam-bounces at redfish.com] On Behalf Of Steven A Smith
Sent: Saturday, March 09, 2019 2:42 PM
To: friam at redfish.com
Subject: Re: [FRIAM] Manifold Enthusiasts

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.

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe
http://redfish.com/mailman/listinfo/friam_redfish.com
archives back to 2003: http://friam.471366.n2.nabble.com/
FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com
archives back to 2003: http://friam.471366.n2.nabble.com/
FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://redfish.com/pipermail/friam_redfish.com/attachments/20190309/f2fc4d39/attachment.html>