Ability to do calculus in head, origins?

For instance, you are driving down the road doing 80 Km/hr and a stupid school bus is ahead about 200 meters doing 30 Klicks. You know you can save a bit of energy not hitting your brakes but letting the engine slow you down and you find yourself able to judge the decel rate well enough to usually avoid hitting the bus, that is to say, making your relative velocity = 0 at some safe distance, all without hitting the brakes. It seems to me a correct math solution would involve calculus but we are able to do that kind of thing instinctively.
Or a basketball player shooting a 3 shot from such a long distance, mentally visualizing the whole parabola and getting it right a good deal of the time.
What is the origin of such ability?
I was thinking about people who never drove, say an Inuit way up north in Canada, coming or emigrating to a city and being forced to learn to drive, would he also have that skill from the start, with the bus example?

I think people can do that pretty poorly, actually. It's infuriating how many people accelerate into a red light just to hit the brakes a few seconds later (especially if someone tries to cross the street!).

But there is an intuitive understanding that applying more force can lead to acceleration of objects and stopping to apply leads to an inertial deceleration. I think these two basic things can provide the basis for a quick understanding of those two things.

Heh, this is a subject I've wondered about as well.

My thoughts are that there is no mathematics going on at all in doing such things. Rather, we recall on past experiences and recognize patterns here and there, something our brains are relatively good at. No idea if thats true or not, just my two cents.

Originally posted by amolv06
Heh, this is a subject I've wondered about as well.

My thoughts are that there is no mathematics going on at all in doing such things. Rather, we recall on past experiences and recognize patterns here and there, something our brains are relatively good at. No idea if thats true or not, just my two cents.

But can't learned experiences/behaviors be based on mathematical calculations even if we
don't know we're doing it?

Example: a 3-yr old learning to shoot basketballs into a hoop. Surely the toddler doesn't know
calculus, but aren't the patterns and actions he is doing over and over based on some sort of
"advanced" calculations? Even if it is just from trial and error, he knows that he needs to
produce X amount of force at an arch at an angle of Z (etc.) to make it arrive at the correct
destination. (Maybe there's a name for this already, like intuitive biomathematics or something.)

Are dogs conducting similarly advanced calculations when they chase down a thrown frisbee
and catch it in mid-air? Or can it not be considered mathematical unless it's spoken in the
language of labels and definitions and X's and Y's? It seems like the laws of mathematics exist
even without the ability to articulate it in writing or on graphs.

Very interesting thread.

Originally posted by Palynka
I think people can do that pretty poorly, actually. It's infuriating how many people accelerate into a red light just to hit the brakes a few seconds later (especially if someone tries to cross the street!).

But there is an intuitive understanding that applying more force can lead to acceleration of objects and stopping to apply leads to an inertial dece ...[text shortened]... ink these two basic things can provide the basis for a quick understanding of those two things.

I think we do math all the time, but crude, and not based on nombers.

Like, if I accellerate a bit, I can come before the other car to the crossing, or if I turn my wheel too much I lose the friction of the road in the coming corner.

Or money, if I buy 3 boxes of cherries for a fiver I save a little instead of bying two for 1€70 and another one tomorrow, or if I save some for my retirement fond I can live good for a while when I quit my job.

Sometimes you calculate wrong, like probabilities in a poker game, or how much you save if you buy your gas cheaper in a station two miles away.

Originally posted by FabianFnas
[b]I think we do math all the time, but crude, and not based on nombers.

Like, if I accellerate a bit, I can come before the other car to the crossing, or if I turn my wheel too much I lose the friction of the road in the coming corner.

Or money, if I buy 3 boxes of cherries for a fiver I save a little instead of bying two for 1€70 and another one tomo ust comes from my natural curiosity, not sure anyone else consciously attempts that while driving.

Do you remember my poser of that last, how far is the max distance you can drive to save gas at a cheaper station X distance away? Someone made up a very long formula for that, reminded me of the drake equation a bit🙂
But I digress. Interesting point about dogs catching a frizbee though. That puts to mind the ability of insects to land, the changes they have to go through even though there may be difficulties like gusts of wind, moving target like a flower attracting a honeybee in a windstorm but the bee still lands.
So even insects with a very limited neuron system solves calculus type problems!

The slow car with fast car approaching is a kind of study of mine, I consciously try to get the minimum energy approach to get to zero relative velocity without hopefully, not actually hitting the slower one🙂 Don't know if anyone else consciously tries that kind of thing.
Another mind game I play is when in a high traffic area I try to minimize my braking when everyone else slams on their brakes at the slightest hint of trouble ahead. I found that keeping a nice gap ahead and behind, to ride the middle of a pack, allows me to get a difference in my braking to as much as ten to one, in other words, I brake once by modulating my gap and just letting up on the gas to sometimes as much as ten braking episodes by the driver in front.

http://www.wired.com/magazine/2009/12/st_alphageek_mahadevan/
Bland article but I've always thought so

Originally posted by ua41
http://www.wired.com/magazine/2009/12/st_alphageek_mahadevan/
Bland article but I've always thought so

A sign of real intelligence, his last statement, Mahadvan says winning the MacArthur Genius award: Now I can fail in even MORE spectacular ways🙂

Originally posted by sonhouse
For instance, you are driving down the road doing 80 Km/hr and a stupid school bus is ahead about 200 meters doing 30 Klicks. You know you can save a bit of energy not hitting your brakes but letting the engine slow you down and you find yourself able to judge the decel rate well enough to usually avoid hitting the bus, that is to say, making your relative ...[text shortened]... g forced to learn to drive, would he also have that skill from the start, with the bus example?

Trial and error, and lots of dead people who can't judge these things to weed them out of the breeding pool.

Originally posted by AThousandYoung
Trial and error, and lots of dead people who can't judge these things to weed them out of the breeding pool.

Ah yes, the old Darwin award theory🙂

http://www.maa.org/features/elvisdog.pdf

The answer is induction. People don't really understand how acceleration, friction, gravity, etc. work but they get a feel of the effects due to experience.

For example, a darts player does not improve by more accurately taking into account the friction of the dart arrow, but by practising so that his brain is more accustomed to estimating the trajectory of the arrow by induction.

Originally posted by KazetNagorra
The answer is induction. People don't really understand how acceleration, friction, gravity, etc. work but they get a feel of the effects due to experience.

For example, a darts player does not improve by more accurately taking into account the friction of the dart arrow, but by practising so that his brain is more accustomed to estimating the trajectory of the arrow by induction.

Consuming vast quantities of beer and crisps aids a dart-player's induction considerably.

Originally posted by Traveling Again
But can't learned experiences/behaviors be based on mathematical calculations even if we
don't know we're doing it?

Example: a 3-yr old learning to shoot basketballs into a hoop. Surely the toddler doesn't know
calculus, but aren't the patterns and actions he is doing over and over based on some sort of
"advanced" calculations? Even if i ...[text shortened]... out the ability to articulate it in writing or on graphs.

Very interesting thread.

Math describes the dog, but the dog is not performing mathematical calculations. Is a raindrop doing math in order to maintain as close to a perfect sphere as it possibly can?

Originally posted by AThousandYoung
Math describes the dog, but the dog is not performing mathematical calculations. Is a raindrop doing math in order to maintain as close to a perfect sphere as it possibly can?

The raindrop fairy is, of course.