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 <[email protected]> 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:[email protected]] *On Behalf Of *Steven A > Smith > *Sent:* Saturday, March 09, 2019 2:42 PM > *To:* [email protected] > *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 <[email protected]> > 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:[email protected]] On Behalf Of > [email protected] > Sent: Saturday, March 09, 2019 5:10 AM > To: The Friday Morning Applied Complexity Coffee Group <[email protected]> > 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 >
============================================================ 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
