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 <[email protected]> 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:[email protected] > <[email protected]>] *On Behalf Of *Steven A Smith > *Sent:* Saturday, March 09, 2019 4:17 PM > *To:* The Friday Morning Applied Complexity Coffee Group > <[email protected]> <[email protected]> > *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. > > > > ============================================================ > 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
