Lakoff and Nuñez might have some relevant data. --- Frank C. Wimberly 140 Calle Ojo Feliz, Santa Fe, NM 87505
505 670-9918 Santa Fe, NM On Wed, Nov 10, 2021, 7:35 AM uǝlƃ ☤>$ <[email protected]> wrote: > The conclusion that the deepest math structures are innate and the "finer" > structures are acquired is interesting and suspect. Do we have source > material for that? I didn't see any in the knots book. > > Intuitively, following my post about how some tonic behaviors are more > easily expressed with some biological/anatomical structures than others, > I'd guess proprioception would be more self-oriented and operational > (swimming through the milieu), whereas visual perception would be more > other-oriented ("watching" objects swim through a stationary frame). I > think a properly controlled trial would expect proprioception to be a > confounder. So you would have to include both visually and proprioceptively > disabled subjects < > https://link.springer.com/article/10.1007/s00221-021-06037-4> to compare > with the control subjects. > > Your "koan" is spot-on for riddling that out, I suppose. Were I not > already canalized by my answer to Dave's question about Jungian archetypes. > For lack of a better (or more ironic, since Euler went blind) dichotomy > lever, the operational conception might be called Lagrangian and the latter > Eulerian. From a Lagrangian perspective any point in an open ball is > infinitely far from the outer bound as long as our operations are functions > of that outer bound. But from an Eulerian perspective, it's trivial to see > the boundary is just fuzzy and all we need do is take constant steps to > leave the ball. That renders the koan a simple fallacy of ambiguity, hinged > on the conception of "center". > > > > On 11/10/21 12:37 AM, Jon Zingale wrote: > > """ > > The fact that such distance (euclidean as well as non-euclidean as well > > as network) is a heuristic for "otherness" seems very much implicit in > > life itself, most familiarly among visual creatures, less so for audio, > > and even less so for chemical (smell/taste) and least for tactile (if I > > am not touching it, it doesn't exist?). > > """ > > > > I wonder about the price paid for privileging sight. Trivedi recounts > > an observation of Sossinsky[☍]: > > > > “It is not surprising at all that almost all blind mathematicians are > > geometers. The spatial intuition that sighted people have is based on > > the image of the world that is projected on their retinas; thus it is a > > two (and not three) dimensional image that is analysed in the brain of > > a sighted person. A blind person’s spatial intuition, on the other hand, > > is primarily the result of tile and operational experience. It is also > > deeper – in the literal as well as the metaphorical sense. > > > > recent biomathematical studies have shown that the deepest mathematical > > structures, such as topological structures, are innate, whereas finer > > structures, such as linear structures are acquired. Thus, at first, the > > blind person who regains his sight does not distinguish a square from a > > circle: He only sees their topological equivalence. In contrast, he > > immediately sees that a torus is not a sphere” > > > > Which dovetails nicely with my mathematical goal of the day to think > > about p-adic metrics, a subject where *visual* habits seem to get in my > > way or otherwise lead my intuitions astray[p, p²]. P-adic considerations > > lead to formal koans like: > > > > "Every point in an open ball is a centre of the ball." > > > > [☍] https://onionesquereality.wordpress.com/2011/07/31/blind-geometers/ > <https://onionesquereality.wordpress.com/2011/07/31/blind-geometers/> > > [p] > https://math.stackexchange.com/questions/2225905/interpretation-of-open-balls-with-the-p-adic-metric > < > https://math.stackexchange.com/questions/2225905/interpretation-of-open-balls-with-the-p-adic-metric > > > > [p²] https://www.math.uh.edu/~haynes/files/topgps5.pdf < > https://www.math.uh.edu/~haynes/files/topgps5.pdf> > > -- > "Better to be slapped with the truth than kissed with a lie." > ☤>$ uǝlƃ > > > .-- .- -. - / .- -.-. - .. --- -. ..--.. / -.-. --- -. .--- ..- --. .- - . > FRIAM Applied Complexity Group listserv > Zoom Fridays 9:30a-12p Mtn UTC-6 bit.ly/virtualfriam > un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com > FRIAM-COMIC http://friam-comic.blogspot.com/ > archives: > 5/2017 thru present https://redfish.com/pipermail/friam_redfish.com/ > 1/2003 thru 6/2021 http://friam.383.s1.nabble.com/ >
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