Late to the table, I know, but it just occurred to me that humans have an innate and intuitive understanding of projectile motion, which is why we can accurately throw and catch objects. Juggling, as an example, has been around for thousands of years, and it’s a uniquely human activity (other apes can’t be taught to juggle, and it’s an incredibly difficult task to teach a machine).
Even if medieval theoreticians had never come across parabolic curves before, there was some gooey parabola-like shape somewhere in their brain.
some gooey parabola-like shape somewhere in their brain
This does not seem obvious to me. The ability to make a rock go roughly where you want does not translate to the ability to accurately draw its trajectory on paper. Granting that there is clearly some part of the brain that does calculations (which may not involve parabolas because of the air resistance, as noted in earlier comments) you have no introspective access to those calculations. Besides which, they might well be wrong for cannonballs; humans do not throw half-ton weights at a good fraction of the speed of sound.
Yeah, I’ve re-addressed that line of reasoning. I became briefly fascinated by how a human brain could plot a quadratic shape, until I discovered the Gaze Heuristic.
I’m still convinced there’s some sort of parabola heuristic though, simply through my own experience of juggling, which doesn’t seem to conform to the gaze heuristic. I also cite the popularity of Angry Birds as weak but hilarious evidence.
Scratch that. I’ve put a bit more thought into it.
Primates can throw but not catch. More to the point, they can accurately hit things with projectiles, but they are considerably worse at anticipating the trajectory of an incoming projectile, (c.f. “chimps can’t juggle”).
Being a quadratic shape, calculating an intercept of a projectile’s parabolic trajectory would require a square root operation. Our brains can’t natively do that, so they need to cheat.
In order to anticipate where a parabolic projectile is going to land, you need to see it in motion a fraction of a second before or after the apex of its curve. (Disclosure: I’ve read this fact somewhere I trust but for the life of me can’t remember where). Then you can just treat it as a falling object with a constant horizontal velocity, and no square root is required. Since the parabola’s symmetrical about its apex, you can plot its entire path provided you know where its apex is, what gravity’s like, and how fast it’s going horizontally.
That explains catching, but how the hell does throwing work? That requires a complete projection of the parabola, which is presumably some sort of spandrel from the catching heuristic, so how come chimps can throw but not catch?
Late to the table, I know, but it just occurred to me that humans have an innate and intuitive understanding of projectile motion, which is why we can accurately throw and catch objects. Juggling, as an example, has been around for thousands of years, and it’s a uniquely human activity (other apes can’t be taught to juggle, and it’s an incredibly difficult task to teach a machine).
Even if medieval theoreticians had never come across parabolic curves before, there was some gooey parabola-like shape somewhere in their brain.
Even later in replying, but oh well.
This does not seem obvious to me. The ability to make a rock go roughly where you want does not translate to the ability to accurately draw its trajectory on paper. Granting that there is clearly some part of the brain that does calculations (which may not involve parabolas because of the air resistance, as noted in earlier comments) you have no introspective access to those calculations. Besides which, they might well be wrong for cannonballs; humans do not throw half-ton weights at a good fraction of the speed of sound.
Yeah, I’ve re-addressed that line of reasoning. I became briefly fascinated by how a human brain could plot a quadratic shape, until I discovered the Gaze Heuristic.
I’m still convinced there’s some sort of parabola heuristic though, simply through my own experience of juggling, which doesn’t seem to conform to the gaze heuristic. I also cite the popularity of Angry Birds as weak but hilarious evidence.
Scratch that. I’ve put a bit more thought into it.
Primates can throw but not catch. More to the point, they can accurately hit things with projectiles, but they are considerably worse at anticipating the trajectory of an incoming projectile, (c.f. “chimps can’t juggle”).
Being a quadratic shape, calculating an intercept of a projectile’s parabolic trajectory would require a square root operation. Our brains can’t natively do that, so they need to cheat.
In order to anticipate where a parabolic projectile is going to land, you need to see it in motion a fraction of a second before or after the apex of its curve. (Disclosure: I’ve read this fact somewhere I trust but for the life of me can’t remember where). Then you can just treat it as a falling object with a constant horizontal velocity, and no square root is required. Since the parabola’s symmetrical about its apex, you can plot its entire path provided you know where its apex is, what gravity’s like, and how fast it’s going horizontally.
That explains catching, but how the hell does throwing work? That requires a complete projection of the parabola, which is presumably some sort of spandrel from the catching heuristic, so how come chimps can throw but not catch?