Is it possible that we know math already?

[1MileCrash]

Is it possible that we "know" math already?

You've all heard of Stan Lee, I presume? He's able to multiply, divide, add and subtract, cube, give the root, etc. of numbers within seconds and with calculator accuracy.

I was watching a special on him recently. A brain scan revealed that Stan Lee's brain shows activity in a different area when doing math than a normal person's. Stan's math skills are based in the movement/muscle control area of the brain.

So I thought about it. How much math does our brain do for even our simplest motions through our muscles? Vast amounts. You know how your limbs are oriented in space without looking at them, so the brain must calculate the angles of joints, perhaps based on the tensity of the attached muscles, just one example.

Is it possible that our brain use functions such as those of trigonometry, perhaps even vectors and calculus already, subconsciously, as part of just performing tasks?

Math is a way man describes the world and predicts things. I think that it's an even deeper part of us, and the math we are able to write down and number crunch is merely scratching the surface of what our brains truly do, mathematically. And, maybe those calculations we do on pen and paper is just what we are able to pull from our subconscious and think about.

Your heart rate changes based on your fitness. A stronger heart can pump blood more effectively, resulting in a lowered resting heart rate. How does your brain know how to adjust the heart rate?

You are able to exert the exact amount of effort required to bend your arm to a 90* angle. Does your brain already know that F = ma?

 

[zoobyshoe]

You are able to exert the exact amount of effort required to bend your arm to a 90* angle. Does your brain already know that F = ma?

It took you years to master that skill (moving your arm where you actually wanted it to go) in your early childhood, you just don't remember it. It isn't hardwired, but learned, and you will still make mistakes under some circumstances. The brain doesn't move muscles by doing math calculations, it simply remembers the cumulative lesson of thousands of attempts.

Whatever Stan Lee's motor strip might be contributing to his calculating ability it is probably not calculation. He may have developed an idiosyncratic muscular mnemonic he can't explain, for example, because he doesn't realize everyone doesn't do it that way.

 

[BobG]

It took you years to master that skill (moving your arm where you actually wanted it to go) in your early childhood, you just don't remember it. It isn't hardwired, but learned, and you will still make mistakes under some circumstances. The brain doesn't move muscles by doing math calculations, it simply remembers the cumulative lesson of thousands of attempts.

As opposed to doing math calculations, which took the cumulative lesson of how many attempts?

Just like humans are born with an inherent capability to learn language, they're also born with an inherent ability to learn math. Humans can recognize the number of objects there are, without having to count them, up to at least 4 and probably 5 objects. For larger numbers, humans may not know which pile is bigger if one has 8 objects and the other 9 unless they sit down and actually count them, but they can tell which is bigger if one pile has twice as many objects (or about twice as many). In other words, their ability to compare works on more of a logarithmic scale than a linear scale.

Given that limitation, yes, a person can "weigh" an object in his hand, figure out roughly how far a basket is by visual triangulation (plus other clues), and at least toss the object somewhere close to the basket. In other words, it isn't a purely random trial and error process for each new situation.

Besides, every time I see a woman walking across a parking lot in high heels on a windy day, it brings me pleasure to think how good she must be at calculus, solving those triple integrals for torque in her head in mere fractions of a second.

 

[AlephZero]

Your heart rate changes based on your fitness. A stronger heart can pump blood more effectively, resulting in a lowered resting heart rate. How does your brain know how to adjust the heart rate?

You are able to exert the exact amount of effort required to bend your arm to a 90* angle. Does your brain already know that F = ma?

You don't need any sort of "brain" to perform either of those tasks. It doesn't even need any sort of "memory". You just need a system with a feedback loop in it.

It is more than 200 years since James Watt invented a mechanical "governor" so that a steam engine "knew" how to adjust the throttle to maintain constant speed. That was long before anybody had any detailed knowledge of how the brain works.

 

[rhody]

Besides, every time I see a woman walking across a parking lot in high heels on a windy day, it brings me pleasure to think how good she must be at calculus, solving those triple integrals for torque in her head in mere fractions of a second.

:rofl:

Rhody...

 

[KingNothing]

Besides, every time I see a woman walking across a parking lot in high heels on a windy day, it brings me pleasure to think how good she must be at calculus, solving those triple integrals for torque in her head in mere fractions of a second.

Oh wow...that is FUNNY!

 

[BobG]

You've all heard of Stan Lee, I presume? He's able to multiply, divide, add and subtract, cube, give the root, etc. of numbers within seconds and with calculator accuracy.

Actually, I think you must be talking about Scott Flansburg, who appeared on the first episode of Stan Lee's "Superhumans".

 

[GregJ]

He's able to multiply, divide, add and subtract, cube, give the root, etc. of numbers within seconds and with calculator accuracy.

Just from memory, there was a book that was supposed to be able to teach you to do exactly this. I never read it however, but the book was called Mathemagics. I forget the author's name though.

So maybe it is something that could actually be learned? Maybe it is possible to "train" certain areas of your brain to help with mathematical processing?

***Edit: And now I am thinking of high heels***

 

[zoobyshoe]

As opposed to doing math calculations, which took the cumulative lesson of how many attempts?

Just like humans are born with an inherent capability to learn language, they're also born with an inherent ability to learn math. Humans can recognize the number of objects there are, without having to count them, up to at least 4 and probably 5 objects. For larger numbers, humans may not know which pile is bigger if one has 8 objects and the other 9 unless they sit down and actually count them, but they can tell which is bigger if one pile has twice as many objects (or about twice as many). In other words, their ability to compare works on more of a logarithmic scale than a linear scale.

Given that limitation, yes, a person can "weigh" an object in his hand, figure out roughly how far a basket is by visual triangulation (plus other clues), and at least toss the object somewhere close to the basket. In other words, it isn't a purely random trial and error process for each new situation.

Besides, every time I see a woman walking across a parking lot in high heels on a windy day, it brings me pleasure to think how good she must be at calculus, solving those triple integrals for torque in her head in mere fractions of a second.

It is true that we're born with populations of neurons that will adopt the performance of dedicated functions if those functions are taught to us. Teaching those neurons to do that takes years. Consider the four year old who, when asked how old he is, might resort to clumsily holding up fingers and saying "This many!", indicating he is still grappling with the basic concept of numerals and relative amounts, not to mention language and muscular coordination, and several dozen (at least) other more subtle processes, despite four years of daily exposure to all of them. We are only hardwired for anything in the sense we are born with neurons that can handle that thing if they are subjected to daily drill in that thing for years. We are not brought home from the hospital with Windows 7 or OS 10.5 installed and in operation in an occult partition of the hard drive as the OP wonders.

Judging relative weights and amounts and distances is all learned. The concept of enumeration, itself, has to be taught, as does the concept of weight, amount, and distance, etc.

The OP is wondering if the neurons that initiate, carry out, and sense, muscle movements are doing so by literally calculating according to formulas we would recognize. What's actually happening is vastly simpler: neurons remember and repeat what worked best in the past. We don't arrive in the world with the axioms of physics unconsciously in place.

 

[zoobyshoe]

Besides, every time I see a woman walking across a parking lot in high heels on a windy day, it brings me pleasure to think how good she must be at calculus, solving those triple integrals for torque in her head in mere fractions of a second.

As an extension of your premise (that a thing knows the physics by which it moves) the Cern situation can be explained by understanding that neutrinos are "crackpot particles" whose behavior is the result of a refusal to accept what mainstream physics asserts as truth.

That's probably pretty much what's going on.

 

[BobG]

It is true that we're born with populations of neurons that will adopt the performance of dedicated functions if those functions are taught to us. Teaching those neurons to do that takes years. Consider the four year old who, when asked how old he is, might resort to clumsily holding up fingers and saying "This many!", indicating he is still grappling with the basic concept of numerals and relative amounts, not to mention language and muscular coordination, and several dozen (at least) other more subtle processes, despite four years of daily exposure to all of them. We are only hardwired for anything in the sense we are born with neurons that can handle that thing if they are subjected to daily drill in that thing for years. We are not brought home from the hospital with Windows 7 or OS 10.5 installed and in operation in an occult partition of the hard drive as the OP wonders.

Judging relative weights and amounts and distances is all learned. The concept of enumeration, itself, has to be taught, as does the concept of weight, amount, and distance, etc.

The OP is wondering if the neurons that initiate, carry out, and sense, muscle movements are doing so by literally calculating according to formulas we would recognize. What's actually happening is vastly simpler: neurons remember and repeat what worked best in the past. We don't arrive in the world with the axioms of physics unconsciously in place.

A bird can remember the location of its favorite birdfeeders, but can't learn to stop crashing into the same window over and over? Usually during mating season - it's believed that it's trying to chase off its own reflection (magpies are the only bird that can associate its reflection with its own identity). Yet, a bird can build a mud nest on the side of a building/bridge on the first try? And a bird can tell the difference between one person and two or three people.

Your example of the four-year-old is flawed. You're measuring more than simple enumeration. You're measuring the four-year-old's ability to correlate 'four things' with the word, "four", and measuring his ability to extend that concept to non-physical things (what the heck is a year?) Some bird species and primates are the only animals that can actually associate some number of objects with a symbol. Associating the amount with a symbol requires learning, but recognizing amounts is innate.


Give an 18-month-old three nice, smooth, small, attractive stones. Cover them up and remove one of the them. See how upset the 18-month-old gets at having one of his stones stolen. Or, give him three stones, cover them up, leaving a fourth stone. See how surprised and happy he is when he now has an extra stone in the group. Then try it with other amounts of stones and you can figure out how high he can recognize. It may be learned, but it's learned pretty darn early - long before you start teaching them how to count.

http://gse.buffalo.edu/fas/clements/files/Subitizing.pdf
http://www.pigeon.psy.tufts.edu/avc/emmerton/

 

[D H]

Give an 18-month-old three nice, smooth, small, attractive stones. Cover them up and remove one of the them. See how upset the 18-month-old gets at having one of his stones stolen. Or, give him three stones, cover them up, leaving a fourth stone. See how surprised and happy he is when he now has an extra stone in the group. Then try it with other amounts of stones and you can figure out how high he can enumerate. It may be learned, but it's learned pretty darn early - long before you start teaching them how to count.

This is not learned behavior. It apparently is innate. It is not unique to humans. Crows have it. So do monkeys, and so do lots of other animals. This innate ability is limited; try showing your 18 month old twelve pretty stones and then cover them up. The reaction won't be nearly as strong when you remove the cover and show eleven or thirteen pretty stones compared to the situation with three stones.

We apparently also have an innate logarithmic number sense. A farmer who has a thirty cows will not immediately see anything amiss if there are only twenty nine in the pasture. He has to count; counting herd was perhaps the first use of counting. He most certainly will immediately see something amiss if there are only three in the field. No counting needed.

http://www.clarku.edu/faculty/nthom...-1974/Counting_and_communication_in_crows.pdf
http://web.mit.edu/newsoffice/2002/monkeys-0911.html
http://www.scientificamerican.com/article.cfm?id=a-natural-log

 

[zoobyshoe]

A bird can remember the location of its favorite birdfeeders, but can't learn to stop crashing into the same window over and over? Usually during mating season - it's believed that it's trying to chase off its own reflection (magpies are the only bird that can associate its reflection with its own identity). Yet, a bird can build a mud nest on the side of a building/bridge on the first try? And a bird can tell the difference between one person and two or three people.

We don't know how birds learn but, interestingly enough, thanks to Temple Grandin, we know how autistic people learn, and that is: in one big gulp of memorization. Grandin told Oliver Sacks she can replay the memory of anything she has experienced over and over in her mind, literally like a movie, and examine the movie in minute detail to find whatever element of the memory she happens to be looking for. In this manner she learned drafting by simply sitting and watching a draftsman at work once. When she tried it herself she got it all correct on the very first try, with pauses to review the "movie" when needed. An onlooker would not have been aware she had never drafted anything before or that she'd never taken a course in drafting. Sack mentions this spooky ability to learn things apparently all at once is fairly common in high functioning autistic people.

This may well explain animal's apparent "innate" abilities: they actually do learn it, but learning it only requires them to have seen it done ONCE. Simply having grown up in a nest and having seen the parents make occasional adjustments to it, might be all a bird needs to know how to make a nest when the time comes.

Your example of the four-year-old is flawed. You're measuring more than simple enumeration. You're measuring the four-year-old's ability to correlate 'four things' with the word, "four", and measuring his ability to extend that concept to non-physical things (what the heck is a year?)

I pretty much said that:

he is still grappling with the basic concept of numerals and relative amounts, not to mention language and muscular coordination, and several dozen (at least) other more subtle processes, despite four years of daily exposure to all of them.

Some bird species and primates are the only animals that can actually associate some number of objects with a symbol. Associating the amount with a symbol requires learning, but recognizing amounts is innate.

Simply making sense of what's in your visual field requires learning to do so. In the same book as the Temple Grandin story, An Anthropologist on Mars Sacks tells the story of a man blind since early childhood who is given an operation and can see again. When that happens he is utterly confused. It takes him quite a long time to sort out that a certain visual event is to be understood as what it means to "see" a human face. After that, it takes him much longer to understand that certain sorts of changes to the human face represent "the look on ones face", i.e. that these alterations are taken to represent people's moods. He has to learn all this from scratch. The fact of shadows, for instance, is another thing that utterly confuses him for quite a while. Most of us have no recollection of ever having had to sort all this out, and therefore consider it "innate". You are born with all the neurons for the job, but they all have to be taught.

It may be learned, but it's learned pretty darn early - long before you start teaching them how to count.

That's all I'm saying: it has to be learned, and that's what's happening to babies all day long: they are having experiences that are teaching them to sort basic things like this out.

I have no objection to the idea neurons might have a penchant for algorithms. I think that's quite different than saying we unconsciously already "know" math.