I'll sidestep that fray momentarily, but it does cause my mind to drift elsewhere:
One of the most incredible human feats I’ve ever heard about is human echolocation (using mouth clicks and subsequent echoes to recognize, or “see” your environment, when blind), made famous with Daniel Kish’s TED talk here:
When I first heard of it I thought it might be some sort of hoax, so implausible did it seem… the sightless maneuvering around the world by means of echolocating the size, shape, and position of objects… but, it is not.
Another pioneer of this phenomenal skill was Ben Underwood a young California blind man who sadly died at age 16 from the same cancer that took his eyesight. A longer, wonderful documentary on him here:
“Visioneers” is the non-profit organization that seeks to teach blind people the echolocation techniques that Kish and others promote.
I have no idea how many people are capable of learning the technique (or maybe everyone is if they start young enough)?
Perhaps, not surprisingly, echolocation has probably been studied most in bats, though certainly sonar (principally underwater echolocation) has been widely studied as well.
There’s no doubt some interesting math going on in human echolocation, though I’m not bringing it up for that aspect, but solely for the inspiration I find in this odd attunement of a modality rarely activated in people! If you do want to scan some more technical and mathematical research on it check out this interesting 2017 piece:
…and here’s a simpler layman version of the above study:
At any rate, people popularly say that we only use 10% of our brain (or some such) and this sort of capability almost make it seem true!
Before his untimely death in a car accident, I encountered Marty Ravellette multiple times. Marty was born without arms but learned early on to use his legs as most of us employ our arms (others have done the same). It was remarkable to view him living a relatively normal life, sipping coffee and smoking a cigarette (with his feet) in a restaurant, driving a vehicle, and even running his own one-man business, believe-it-or-not called “Hands-On Landscaping” (yeah, he had a sense of humor too). He gained national news attention once when he saved a lady from a burning car on a highway, and won various awards throughout his life. If you didn’t witness it with your own eyes it would be hard to imagine how well he managed in life without arms.
Just another inspirational figure; making do, quite successfully, with what he had. What abilities do the rest of us have that we never develop because we're never pushed to?
Even the adroit and rapid manipulation of abstract symbols, both in mathematics and language, is an incredible talent, we take for granted, that, in a Wignerian sense, is largely inexplicable -- linguists and psycholinguists have tried for decades to account for the phenomena (of language learning and speech processing-and-production), with little real progress methinks! At a very young age we learn to both voice and decipher high-speed phonemic sounds (such that, to this day, I really have no good idea how I write/compose these blog posts, nor read those of others!). The human animal is marvelous... so too others:
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There's much that humans seem to commonly share in the way of capabilities... but surely not everything. I often encounter individuals questioning the notion of 'innate' talents — but I honestly don’t understand how anyone, given our knowledge of genetics and twin studies and the like, keep putting forth blank slate arguments and doubting innate differences in skill levels. We all enter this world with a range of talents, but those ranges clearly differ from individual to individual (despite overlap), just as we all have a range of height we will reach — one person may grow to somewhere between say 5’2” and 5’10” depending on their environment, and another somewhere between perhaps 5’4” and 6’2”… and no one, no matter how rich the environment, will reach 18’7” (genes won’t permit it). Individual skills operate within ranges as well.
People espousing the more open-ended view fear that young people will be harmed if it’s implied that they lack certain innate skills or aptitudes… I’m GLAD to attribute my weaknesses to a lack of innate skills; the alternative is to believe I just didn’t have the discipline, the work ethic, the perseverance to master certain fields. Essentially, telling kids who don’t do well in math that they did have the necessary talent all along, but didn't cultivate it, is to tell them they are lazy… and that to me is more harmful. We can't all be good writers, spellers, mathematicians, musicians, or even finger-painters (and, moreover, we ought be exalting in our skill differences, instead of stressing our sameness -- if anything, I'm more interested in our 'sameness' to other primates, mammals, and vertebrates, than our sameness to other people).
Dr. Jo Boaler takes a somewhat different view of matters in this article (and her general work at YouCubed) on advances in neuroscience:
https://blogs.ams.org/matheducation/2019/02/01/everyone-can-learn-mathematics-to-high-levels-the-evidence-from-neuroscience-that-should-change-our-teaching/
I agree with the basic view that specific neuro skills are not "fixed" from birth, but still believe that skill-ranges (as well as many other aspects of psychology and personality) are fixed and vary widely from person-to-person, which is a subtly different point. Nonetheless, her multifold approach to math-teaching may well produce the most good for the most (not all) students until the day comes when truly individualized teaching is possible.
Anyway, I'm fascinated by the minds of towering mathematicians…
Thomas Lin’s (editor) “The Prime Number Conspiracy” is a darn near riveting compendium of essays from Quanta Magazine. Section 4, “How Do the Best Mathematical Minds Work,” is one of my favorites, wherein each of 8 essays profiles a different modern premier mathematician. These are people whose brains are definitely wired differently from mine, or most people’s. Anyone who tries to tell me that, no, these individuals simply concentrated more, practiced more, focused more, in certain areas than did I and others, I hardly have patience to respond to. All human brains are different going right back to the womb, as are their fingerprints, but the kinds of minds outlined in section 7 of Lin's volume see the world, and the patterns of the world, and the patterns of the patterns of the world, and... so on, differently than do I. You may as well tell me that I and Pablo Picasso and Evel Knievel and Ted Bundy were the same at birth, as tell me that I share much with these penetrating mathematical minds. And I don't care if we call them "geniuses," or "savants," or "prodigies," or "gifted," or whatever. These are just short-hand labels we use for convenience; terms that need not be over-stressed or dwelled upon, but nor should they be abandoned for fear of harming others who are set apart from them.
Meanwhile, excuse me now while I attempt to go and echolocate my car keys.
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Meanwhile, excuse me now while I attempt to go and echolocate my car keys.
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