[FRIAM] The danger of a single story

[uǝlƃ ☤>$]

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