[FRIAM] The danger of a single story

[Frank Wimberly]

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 ☤>$ <gepropella at gmail.com> 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
>
>
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