[FRIAM] Manifold Enthusiasts

Sat Mar 9 18:01:18 EST 2019

Steve is in excruciating pain too?

-----------------------------------
Frank Wimberly

My memoir:
https://www.amazon.com/author/frankwimberly

My scientific publications:
https://www.researchgate.net/profile/Frank_Wimberly2

Phone (505) 670-9918

On Sat, Mar 9, 2019, 3:07 PM Nick Thompson <nickthompson at earthlink.net>
wrote:

> 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/
>
>
>
> *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>
> 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] On Behalf Of
> lrudolph at meganet.net
> Sent: Saturday, March 09, 2019 5:10 AM
> To: The Friday Morning Applied Complexity Coffee Group <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
>
>
>
> ============================================================
>
> 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/20190309/35ea4b44/attachment.html>