I have always wondered how your brain works so well in situations where you are in motion. Consider this:
you are driving down the road in your car, and you wish to make a left turn at a street ahead. You see an oncoming car-your decision to wait for the car to pass, or to turn in fron of it is dictated by the following :
-you must be able to estimate the speed of the oncoming car, and the approximate distance from your car
-you must be able to estimate the time at which you would be turning…you must know your speed and the distance to the turn
-To solve a problem like this on paper, you need to solve two simultaneous algebraic equations, and make some accurate estimates. yet, your brain does all of this for you without thinking a lot about it.
So, does the brain actually solve this problem for you (as you would on paper)?
If there is evidence it does, then why do most of us struggle with mathematics? It ought to be second nature to us!
WAG: Your brain does it with ‘fuzzy logic;’ that is, it doesn’t take accurate measurements and perform complex calculations. Rather, it draws on experience and develops rule ‘patches’ - if something is similar enough (fuzzy concept) to a previously seen situation, the rule applied should be the same.
How close is ‘close enough’? Close enough so that you haven’t seen any contradictory examples in the recent past. All situations that were this much alike ended the same way, or required the same action.
IANA physiologist, but I doubt it, if what you’re asking is whther there is some kind unconscious center selecting formulas and doing math to come up with a go no-go decision.
To me, a decision like this is rarely “automatic” anyway. I think about traffic visually. I can “see” about where there other car will be by visually projecting it forward in time. I don’t think mathematics is necessary to achieve this.
Of course, at base level, your question is similar to a very fundamental one about mathematics. Is it a purely human construct, or does it have some independent existence in the universe outside of our brains?
I’m on the “purely human construct” side, which is why I don’t think math is necessary in the situation you desribe. IMO the physiology involved in making these decisions uses “other means” to make them.
I saw on a science program once (sorry to be vague, and no cite) that when a basketball player shoots a basket, he is mentally solving a cubic equation.
D’oh :smack: it’s actually a quadratic equation - since a thrown object describes a parabola - how silly of me. Obligatory link
At my prime I can do LOGs to 2 decimal places in my head in under 3 seconds and solve systems of linear equastions with two unknowns.
If I am really on top of it I can to systems of linear equastions with three unknowns or systems or non-linear equations with two unknowns with an integer degree equal to or less then 2.
But those moments come VERY rarely, but they do feel ooooh so sweet when they do come. 
Any animal that has to interact with its environment, by moving about or directing forces (like throwing missiles, catching prey, etc.) needs to be able to effectively do things that can be described by mathematical equations of motion…So, yes, these organisms do “solve” such equations in a certain sense. For those organisms with developed nervous systems, we can say that their “brains” do the math. Yet some organisms without much in the way of nervous systems (like paramecia) perform relatively complex “math.”
Natural Selection and evolution can create these computers. Those organisms that can’t perform the “calculations” just lose out to those that can. Doesn’t mean that they can “do the math” like Newton, however…
we solve such problems heuristically, not algebraically.
Agree. By the way, consider that when you listen to an orchestra, the only inputs to your ears are one-dimensional variations in pressure on your eardrums. And yet, your brain can pick out violins, trumpets, etc. So in some sense, your brain is doing a Fourrier Transform!!
I always thought it was pretty nifty that you can throw a ball in the air and look away, but your brain can still stick our your arm and catch the ball. Always amazed me, but I’m pretty easy to amaze.
I’m going with what Shalmanese said. There is NO way you (or a dog or a cat or whatever) is actually doing math in their heads of this caliber. Consider an outfielder trying to catch a pop-fly. Not only would they have to calculate the entire trajectory of the ball they have to do it in realtime to allow for changing parameters (say a strong wind gust blows it off course or they stumble meaning they have to speed-up to still catch the ball). Additionally, your judgement of speed and distance is nowhere near good enough to plug into an equation such that your answer will be accurate enough to be standing under the ball when it lands. You’d be much more likely to be a few feet off in one direction or the other at best.
Certainly there have been some people who can do amazing math in their heads. I read about a guy who kept his check ledger in hex and wrote it as normally as you would with ‘normal’ numbers.
Perhaps the best I’ve ever heard of in this realm is Srinivasa Ramanujan. The guy was unbelieveable. The quote below is from Michio Kaku’s book Hyperspace. The quote however is how I remember it and not directly from the book since I don’t have it in front of me but I think the upshot of the whole thing is maintained.
Anyone who can do that off the cuff gets my vote for amazing mathematician.
[sub]–> 111 + 121212 and 999 + 1010*10 [/sub]
Well, there may not be an explicit formula, but there’s certainly computation taking place.
It’s probably not a good idea to rely on introspection to figure out what your brain is doing in any particular situation. There’s a tremendous amount of processing that takes place way below the conscious level.
I think the closest answer you can give to the OP is that the brain is probably not formulating the problem as an explicit set of linear equations/algebraic/differential equations, or whatever. However there probably are a lot of analog computations taking place that could be modeled using these equations.
In other words, the brain does a lot of the processing at the hardware/firmware level (if we can be allowed a brain/computer analogy). This pretty much answers the “Why are we so bad at math” question of the OP – rather than a general purpose calculator, the brain has the equivalent of dedicated hardware to do specific tasks. This may also explain why some people are so good at math and problem solving – they have learned to take advantage of the brain’s specialized “hardware” to solve tasks. The classic example of this is posing a hard problem in such a way that it can be visualized. Vision is a very, very computation intensive process and the brain has lots of “hardware” to help out (sort of analogous to the super high-powered graphics card on your PC).
Although feedback plays a very important role, I doubt all our abilities in judging motion are based on continuous feedback. We have a good idea of when to start braking at a stop light or when to start running to swing at a tennis ball. Even if this is done via precompiled rules, we still have to have some accurate estimate of speed, distance, and acceleration as input into these rules.
I thought that the ears had various fibers that were tuned to various frequencies. So the input to your brain is already the frequency components. So your bran does not do anything remotely like a Fourrier Transform.
A cite
If you set the problems up on an analog computer the solution is inherent to the underlying structure rather than the result of any formal calculation. Lotso good links here.
I checked your cite, and yeah, it looks I had it wrong. For what it’s worth, I got that fact out of a textbook a class in medical imaging. Thanks for correcting me.
I checked your cite, and yeah, it looks I had it wrong. For what it’s worth, I got that fact out of a textbook a class in medical imaging. Thanks for correcting me.
As far as the traffic related question is concerned, I think it has a lot to do with experience.
Sit in the passenger seat with a newbie driver at the wheel facing the same situation of making a left turn with oncoming traffic to deal with.
Chances are, assuming you’re an experienced driver, that you will become exasperated at the drivers reluctance to make a move when an opportunity to do so presents itself.
You know from experience that the vehicle heading your way could not possibly reach you before you’ve completed the turn.
The new driver however, has not faced this situation often enough to trust his/her judgment, even though they most likely suspect that they would have had plenty of time.
Obviously you are not solving the equations very consciously, but possibly more un/semi-consciously? Perhaps the exceptional faculty of intuition in top sports-persons is due to a number-crunching subconscious?
Gross exaggeration: You are solving equations about as much as a falling piano knows Newton’s laws of gravitation, or Mercury understands Einstein.
Less exaggeration: Acting under the laws of physics does not require knowing them. To fall off a cliff, just fall, you don’t have to calculate anything.
Even less: You don’t need to understand parabolic motion to throw a ball. You just need to throw it a bunch of times, and learn by trial and error which ways work and which don’t. 5 year olds don’t learn to throw a ball by learning algebra, they learn it by trying it hundreds and thousands of times.
85% of the teenagers in the world couldn’t solve 2 simultaneous equations if it meant dinner with Brittney Spears. Yet, the species perseveres. Remarkable really. 