[FRIAM] Manifold Enthusiasts

Sat Mar 9 18:46:30 EST 2019

My pain was unbearable until I saw my neurologist who prescribed Gabapentin
and then my primary care physician added Cymbalta.  Both relieve nerve
pain.  My left arm is partially paralyzed.  I can't raise it above my
chest. All of this is because of an impingement of a nerve on C6, left
side.  It was amazing how the neurologist diagnosed that.  It involved tiny
needles and mild shocks.

-----------------------------------
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, 4:28 PM Steven A Smith <sasmyth at swcp.com> wrote:

> Nick -
>
> I do know that reading my missives *can be* excruciatingly painful but I
> do trust those without such masochistic tendencies to use their <delete> or
> <next> buttons freely.
>
> Frank -
>
> Sorry I can't commiserate better with your physical pain... but in an
> ironic reversal of roles, my pain is entirely abstract (existential angst)
> while yours sounds to be entirely embodied!
>
> - Steve
> On 3/9/19 4:23 PM, Nick Thompson wrote:
>
> Sorry, everybody,
>
>
>
> I am experiencing phantom pain in Steve’s body.
>
>
>
> Gotta read these threads  more carefully.
>
>
>
> 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
> <friam-bounces at redfish.com>] *On Behalf Of *Steven A Smith
> *Sent:* Saturday, March 09, 2019 4:17 PM
> *To:* The Friday Morning Applied Complexity Coffee Group
> <friam at redfish.com> <friam at redfish.com>
> *Subject:* Re: [FRIAM] Manifold Enthusiasts
>
>
>
> Nick -
>
> All I can say is, for a man in excruciating pain, you sure write good.
> Your response was just what I needed.
>
> Something got crossed in the e-mails.   *I'*m not in excruciating pain...
> that would be (only/mainly/specifically) Frank, I think.  But thanks for
> the thought!
>
> Any excruciating pain I might be in would be more like existential angst
> or something... but even that I have dulled with a Saturday afternoon
> Spring sunshine, an a cocktail of loud rock music, cynicism, anecdotal
> nostalgia, and over-intellectualism.  Oh and the paint fumes (latex only)
> I've been huffing while doing some touch-up/finish work in my sunroom on a
> sunny day is also a good dulling agent.
>
> 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.
>
> Hmm... I don't know if I can answer this fully/properly but as usual, I'll
> give it a go:
>
> I think the Baez paper Carl linked to has some help for this in that.  I
> just tripped over an elaboration of a topological boundary/graph duality
> which might have been in that paper.    But to be as direct as I can for
> you, I think the two properties of *shroud* that *are* relevant is
> *continuity* with a surplus but not always irrelevant meaning of *smooth*.
> In another (sub?)thread about *Convex Hulls*, we encounter inferring a
> continuous surface *from* a finite point-set.   A physical analogy for
> algorithmically building that *Convex Hull* from a point set would be to
> create a physical model of the points and then drape or pull or shrink a
> continuous surface (shroud) over it.    Manifolds needn't be smooth
> (differentiable) at every point, but the ones we usually think of generally
> are.
>
>  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.
>
> In the abstract, I think that coastline (projected onto a plane) IS a 1d
> fractal surface (line).  To become a manifold, it needs to be *closed*
> which would imply continuing on around the entire mainland of the western
> hemisphere (unless we artificially use the non-ocean political boundaries
> of Maine to "close" it).
>
>  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?
>
> I think the "smoothing" caused by rendering the coastline in ink the width
> of the nib on your pen (or the 300dpi printer you are using?) yields a
> continuous (1d) surface (line) which is also smooth (differentiable at all
> points)... if you *close* it (say, take the coastline of an island or the
> entire continental western hemisphere (ignoring the penetration of the
> panama canal and excluding all of the other canals between bodies of water,
> etc. then you DO have a 1D (and smooth!) manifold.
>
> If you zoom out and take the surface of the earth (crust, bodies of liquid
> water, etc), then you have another manifold which is topologically a
> "sphere" until you include any and all natural bridges, arches, caves with
> multiple openings.  If you "shrink wrap" it  (cuz I know you want to) it
> becomes smooth down to the dimension of say "a neutrino".   To a neutrino,
> however, the earth is just a dense "vapor" that it can pass right through
> with very little chance of intersection... though a "neutrino proof" shroud
> (made of neutrino-onium?) would not allow it I suppose.
>
> This may be one of the many places Frank (and Plato) and I (and Aristotle)
> might diverge...   while I enjoy thinking about manifolds in the abstract,
> I don't think they have any "reality" beyond being a useful
> archetype/abstraction for the myriad physically instantiated objects I can
> interact with.  Of course, the earth is too large for me to apprehend
> directly except maybe by standing way back and seeing how it reflects the
> sunlight or maybe dropping into such a deep and perceptive meditative state
> that I can experience directly the gravitational pull on every one of the
> molecules in my body by every molecule in the earth (though that is
> probably not only absurd, but also physically out of scale... meaning that
> body-as-collection-of-atoms might not represent my own body and that of the
> earth and I think the Schroedinger equation for the system circumscribing
> my body and the earth is a tad too complex to begin to solve any other way
> than just "exisiting" as I do at this location at this time on this earth.)
>
> If you haven't fallen far enough down a (fractal dimensioned?) rabbit hole
> then I offer you:
>
>
> https://math.stackexchange.com/questions/1340973/can-a-fractal-be-a-manifold-if-so-will-its-boundary-if-exists-be-strictly-on
>
> Which to my reading does not answer the question, but kicks the
> (imperfectly formed, partially corroded, etc.) can on down the  (not quite
> perfectly straight/smooth) road, but DOES provide some more arcane verbage
> to decorate any attempt to explain it more deeply?
>
> - Steve
>
> PS.  To Frank or anyone else here with a more acutely mathematical
> mind/practice, I may have fumbled some details here...  feel free to
> correct them if it helps.
>
>
>
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> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9a-11:30 at cafe at St. John's College
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