Steve- There is a rigorous definition of curvature that doesn't depend on the manifold's being embedded in Euclidean space. Right, Jon?
By the way, I was a private pilot during the 70s. Hywel was a more experienced and more cautious pilot. I think there are others in Friam. Frank --- Frank C. Wimberly 140 Calle Ojo Feliz, Santa Fe, NM 87505 505 670-9918 Santa Fe, NM On Thu, May 28, 2020, 10:17 PM Steve Smith <[email protected]> wrote: > > On 5/28/20 9:32 PM, Frank Wimberly wrote: > > Steve, > > > > After thinking about them I think curved manifolds are real just as > > right triangles. Perhaps my introspection deludes me. > I think manifolds "just are", to call them "curved" is to place them in > the reference frame of Euclidean. To a creature who lives on the > surface of a sphere or a torus, a euclidean straight line or > poly-gon/hedron would be "just wrong". Euclidean straight lines are now > curved and vice-versa. The problem is that *we* are mostly > experienced/habituated to thinking in Euclidean Straight lines (what > light (nearly)travels along at the scale of gravitational flux we live > in). In another post I appeal to global scale navigation for an > alternative, and in my orbital mechanics dreams I claim that I > *experience* a (pseudo) complex manifold *directly* (following the > isoclines of "least action" in Guerin's terminology?) or > conserved/budgeted Delta-V. > > I think you agree with me about thinking without language. > > Sometimes. In the morning I don't think, "Now I am going to open this > > cabinet to get a bowl..." > > I think I agree that on a good day this happens (otherwise I'd not have > coffee and my avocado-toasted-bagel until later in the day). > > I had a friend/tenant living in my house for couple of years (2016-2018) > who had a brain injury 30 years ago which was treated with a variety of > physical and talk therapy, psychotropics, ECTs, and other "mind bending" > things like EMDR and bilateral-something-or other. He had a horrible > problem with "sequencing". Once he DID formulate something in language > he would be stuck with that formulation... and if interrupted while > executing or if someone tried to inject into or reorder his formulation > , he would get stalled and all but have to "start over" and talk himself > through his formulated steps until he got to the point where he had been > derailed. Things he had done habitually in his life (driving, cooking > his favorite chile, etc. were mostly immune to this...) > > I will agree that there are many familiar/practiced sequences of > impulses and actions that we atomize to the point that it takes > virtually no conscious attention to execute them. For example, not long > after I learned to type, my ability to translate language into pixels > (ink, ???) is entirely subconscious. If I *think* too much about what > my fingers are doing, I get fumbly and have to do a lot of backing up > and starting again. My orbital dreams felt like I was training myself > to "gesture in 3D delta-V phase space"... I don't claim that anything > I've done in my dreams is particularly registered to real orbital > mechanics (though it resembles it in some ways as best I can tell), only > that it is (was) becoming subliminal/subconscious/embodied. > > I believe you are also a tennis player (you current, me long-since > deprecated skill) so you know the huge "lexicon" of > motions/trajectories/gestures your body knows how to execute in phase > space... from your serve to a "rush to the net" or an "overhead slam" or > a variety of top, side, back-spin ways to stroke the ball. I can > *still* without a racquet in my hand for decades or a foot on a court > "feel" these things in my body... which allows me to watch Tennis on TV > (mirror neurons) in a way I will (and have) never been able to watch any > other sport... even though I've thrown a few spiral passes, kicked a few > soccer balls, hit a few home runs (or pop flys), and sunk a few > freethrows/3pointers/layups in my life, they never really got fully > encoded the way a decade or more of (weakly) competitive tennis did. > > I *think* this is the level of "sensorial grounding out" that > Lakoff/Nunez appeal to at the bottom of their own "metaphors all the way > down" conception. In deference to my trying to allow some of the > layers to be analogies, models and mappings, I suppose I might say "it > is mappings all the way down" until it hits the hardware (wetware) where > I contend there are still "mappings" but rather different than the ones > we think of in the "mappings" from metaphorical target to source > domains. The grounding under the ground are the kinds of ion-channels > described recently in his Touch/Pressure/Temperature/Proprioception > paper link. I hope Glen will agree with me (not so that I feel I am > *right* only because I *think* this captures/resolves a lot of what we > have argued here and offline?) somewhat on this alternative of "maps" > all the way down? > > I think your sense that space-time is "bent" or "curved" is an example > of where the metaphor (mapping) has been atomized. To your conception > (I suggest) absolute space is Cartesian and the *real* topology of space > is "curved" in that frame of reference. I say this because I think > until I started working with global-scale navigation and more recently > dreaming in orbital mechanics, I pretty much felt the way you describe > the "shape of space". > > I think it is similar to the duality I've described here before between > *believing* or *understanding* or *knowing* that the moon orbits the > earth while the earth-moon system orbits the sun whilst *experiencing* > it as "the sun and moon, each on their own schedule, rise in the east > and set in the west. Every day!". The earth doesn't spin at all (the > sky does!). > > Mumble, > > - Steve > > > > > -- --- .-. . .-.. --- -.-. -.- ... -..-. .- .-. . -..-. - .... . -..-. . > ... ... . -. - .. .- .-.. -..-. .-- --- .-. -.- . .-. ... > FRIAM Applied Complexity Group listserv > Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam > un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com > archives: http://friam.471366.n2.nabble.com/ > FRIAM-COMIC <http://friam.471366.n2.nabble.com/FRIAM-COMIC> > http://friam-comic.blogspot.com/ >
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