So that’s super-fun. The Optical Acceleration is a constant of the joint motions. Is there then a Lagrangian for which, in suitable coordinates, the OA disappears as a kinetic argument, and becomes manifestly a conserved quantity, as in Hamilton-Jacobi theory?
Obviously, the answer to my query is for me to go sit with paper and look at this, but today that is forbidden to me. Eric > On Nov 9, 2025, at 1:25, Stephen Guerin <[email protected]> wrote: > > attn: Nick and Eric C > > Glen writes: >> But we've been here before, right? What does it mean to "do math"? Is the >> outfielder "doing math" when she catches a fly ball? I mean, we know missile >> interceptors are "doing math" ... maybe. Is a Kalman filter executing in the >> on board computer a "mental image". Can one understand quantum mechanics >> without doing the math? Etc. > > Mike McBeath, one of my cogsci professors, wrote this 1995 short Science > ecological psych article on how fielders catch fly balls. > https://redfish.com/papers/McBeath-BaseballCatch.pdf > <https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fredfish.com%2fpapers%2fMcBeath-BaseballCatch.pdf&c=E,1,Z1f81H9_SvCwA7rDW2PG6vjeQqvRKyF8ZywILNgH3086P6cQ3MJdNR7VQzALV5B5jU_kPc4wWNYTxSc0EAUGkef91_qcmeME_AsR1IdUMw9uJSZp0FE,&typo=1> > > In Gibsonian and Turvey ecological language: the fielder does not calculate > trajectories or predict where the ball will land; instead, they visually > couple their locomotion to optical information that specifies the event of > interception. By continuously adjusting their movement to maintain a constant > optical acceleration pattern (the Optical Acceleration Cancellation > strategy), they exploit invariants in the optic flow—the affordance of > catching emerges directly from perceiving how the optical variables change, > not from internal computation or prediction.: > > > _________________________________________________________________ > Stephen Guerin > CEO, Founder > https://simtable.com > <https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fsimtable.com&c=E,1,2crdSwIfa87nIRtrhHXjWoUtJvjN3l7SY6VKjbFctcgBoQvIYmOcGUr6HiP7n-sKqyZ5m_65Sa1WVBsUvYB9Q6GFXADTFeoiqtJVHvx6GAj7sw,,&typo=1> > [email protected] <mailto:[email protected]> > > [email protected] <mailto:[email protected]> > Harvard Visualization Research and Teaching Lab > <https://hwpi.harvard.edu/eps-visualization-research-laboratory/home> > > mobile: (505)577-5828 > > > On Fri, Nov 7, 2025 at 10:43 AM glen <[email protected] > <mailto:[email protected]>> wrote: >> I haven't read the New Yorker article. But the category seems hopelessly >> fraught. Even the 2 "objective" measures I'm aware of (pupil response and >> binocular rivalry) are intertwined with the body. I'm reminded of "motor >> imagery", where imagining some physical action causes similar patterns to >> performing that action, and so-called mirror neuron[al activation]. >> >> But we've been here before, right? What does it mean to "do math"? Is the >> outfielder "doing math" when she catches a fly ball? I mean, we know missile >> interceptors are "doing math" ... maybe. Is a Kalman filter executing in the >> on board computer a "mental image". Can one understand quantum mechanics >> without doing the math? Etc. >> >> But I'm attracted to the invocation of analysis. My prof, which I managed to >> retain during all 3 of Anal I, II, & III, was a fan of priming. He'd *draw* >> graduate level concepts on the chalkboard before class, then really quickly >> run through all the jargon as if we understood whatever he was yappin' >> about. Then he'd callously erase the art and get on with what we were >> "supposed" to be learning. Dude was an artist. Full stop. >> >> >> On 11/6/25 3:24 PM, Santafe wrote: >> > I see; thanks Nick, >> > >> > I am happy the expected categories fell apart. But there have been >> > occasions when I went looking for categories something like these on my >> > own too. >> > >> > In college (which I hit about like a bird flying into a window), as >> > sophomores we were taught algebra by Mike Aschbacher, one of the great >> > algebraists of the just-past generation. A man who never brought notes, >> > wrote every proof spontaneously, and could write on a chalkboard at the >> > same speed as he talked. >> > >> > A friend and I — both of us just getting pounded into the ground — decided >> > that there were geometric thinkers, who exapted visual thinking, and >> > algebraic thinkers, who exapted syntactic thinking. Aschbacher being the >> > most syntactically superhuman being we had ever encountered. And we >> > decided we were both “algebraically impaired”. >> > >> > In contrast, analysis was straightforward, and always seemed to me to have >> > a somewhat visual angle to it, and algebraic topology and differential >> > geometry were even better. Although I never tried anything hard in those >> > fields, like proving things about more than 3 dimensions. So not sure how >> > much visual/geometric skill I have beyond the baseline for primates. >> > >> > I have continued to wonder where one should go to characterize >> > “elementary” or “primitive” modalities of cognition, and how to take them >> > to assemble into the kinds of synthetic things we call “skills”. Marc >> > Hauser once gave some very compelling talks along these lines for >> > mathematical reasoning. But since he was found fabricating data some >> > years later, I don’t know how much of the earlier stuff I should continue >> > to find compelling. It might not have been tainted at all; but I am not >> > in the field. >> > >> > It’s a nice topic. >> > >> > Eric >> > >> > >> > >> > >> > >> >> On Nov 6, 2025, at 15:59, Nicholas Thompson <[email protected] >> >> <mailto:[email protected]>> wrote: >> >> >> >> I’m sorry for the misprint. The correct term is aphantasia. >> >> >> >> It took 15 minutes with a handful of people at thuam for the categories >> >> to break down horribly. My prediction was based on no great insite. I had >> >> divided the world up into picture people and word people assume that our >> >> word. I claimed no wisdom here, only prejudices I seem to be a.-side >> >> myself >> >> Sent from my Dumb Phone >> >> >> >> On Nov 6, 2025, at 1:02 PM, Prof David West <[email protected] >> >> <mailto:[email protected]>> wrote: >> >> >> >> Yes, please, what Eric asked. >> >> >> >> I would expect most people on this list to tend towards the "hyper," not >> >> the "apha." >> >> >> >> davew >> >> >> >> >> >> On Thu, Nov 6, 2025, at 10:38 AM, Santafe wrote: >> >>> That’s interesting, Nick (on limited time here, but just for a while) >> >>> >> >>>> On Nov 6, 2025, at 11:19, Nicholas Thompson <[email protected] >> >>>> <mailto:[email protected]>> wrote: >> >>>> >> >>>> Given the work that many of you do, many of you are candidates for >> >>>> "aphatasia" >> >>> >> >>> Can you say more about why you expect a correlation? 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