typodupeerror

## Brains Hard-Wired for Math246

Posted by samzenpus
from the easy-as-1-2-3 dept.
mcgrew writes "New Scientist is reporting that "non-human primates really can understand the meaning of numerals." The small study of two rhesus monkeys reveals that cells in their brains respond selectively to specific number values — regardless of whether the amount is represented by dots on a screen or an Arabic numeral. For example, a given brain cell in the monkey will respond to the number three, but not the number one. The results suggest that individual cells in human brains might also have a fine-tuned preference for specific numerical values." The report itself is online at PLoS Biology, Semantic Associations between Signs and Numerical Categories in the Prefrontal Cortex."
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## Brains Hard-Wired for Math

• #### First post (Score:5, Funny)

on Thursday November 01, 2007 @12:23AM (#21193179) Homepage Journal
My brain has a fine-tuned preference for the number 'one'.
• #### Ethics (Score:2, Funny)

Readers be at ease. No cute furry animals were used in the research: They shaved the monkeys and dressed them up to look like [inser favourite politician] first.
• #### Re: (Score:2)

They shaved the monkeys and dressed them up to look like [inser favourite politician] first.
I would prefer them dressed up as my least favourite politician.
• #### Re: (Score:2, Insightful)

What a marvelous first post referencing a first post while being understated. :)

~S
• #### One is boring. Try two. (Score:3, Funny)

My brain has a fine-tuned preference for the number 'one'.

Strange... I've always favoured two. Preferably twins ;)
• #### Re: (Score:2)

Huh. With me, it's more of a preference for the number 'beer'.
• #### and there you see! (Score:4, Funny)

by Anonymous Coward on Thursday November 01, 2007 @12:27AM (#21193197)

• #### Re: (Score:3, Funny)

We already knew that, however we need to take their brains out to see if we can find parts of the question in there.
• #### Re: (Score:2)

It is if you believe in UNIX (which uses AD 1970 as the calendar's base) and the Mayan calendar (which ends this instance of creation in 2012).
• #### Numbers or numerals? (Score:5, Insightful)

by Anonymous Coward on Thursday November 01, 2007 @12:29AM (#21193203)
Isn't it more likely that the brain responds to numbers, and is also able to learn an association between numerals and numbers?

To say that nonhuman primates respond to numerals makes it sound like they evolved to benefit from written language, which would be kinda weird, ya know.
• #### Re: (Score:2)

That they can associated numerals with numbers IS to say that they find numerals meaningful. It's to say that they're capable of that level of abstraction, when it comes to numerical values.
• #### Re: (Score:3, Insightful)

That they can associated numerals with numbers IS to say that they find numerals meaningful. It's to say that they're capable of that level of abstraction, when it comes to numerical values.

Oh, come on.

Unless they're proposing that Arab numerals are directly, non-symbolically related to the numerical concepts they represent, the only thing they've proved is that yay, primates are capable of learning some symbols.

If the same neurons react to quantity(3) and to symbol(3) with no previous training, then this discovery will revolutionize our schooling systems, not to mention cognitive science, semiotics and linguistics.
If, on the other hand, this included some training beforehand, then I fail

• #### Re: (Score:2)

Well the arab numerals for 3 involve 3 symbols anyway.. III. The big deal is that some animals are smarter than some people would expect. Even a human wouldn't be able to recognise a symbol without training, duh.. they're just saying that monkeys can learn numbers the same as us, which is semi interesting.
• #### Re: (Score:2)

'III' is roman (they also had no zero).

The summary is implying they had some inherited recognition of the character '3' that just doesn't make sense.. it's more likely that they just recognised it as a symbol they'd seen before.
• #### Re: (Score:2)

Oh yeah oops, arab is 3, roman is III, got a bit muddled there.
• #### I = E, information = energy (Score:2)

"Isn't it more likely that the brain responds to numbers, and is also able to learn an association between numerals and numbers?"

Actually the brain is geared to understand visual (and other) frequencies and "numbers" are nothing more then deduced descriptions of our visual geometric world. Math was built into the universe, and our systems of math are nothing more really then mutations of basic math embedded in nature. In fact we might say mathematics is lower down on the chain then visual geometry. Sinc
• #### Re:Numbers or numerals? (Score:5, Interesting)

on Thursday November 01, 2007 @05:12AM (#21194307)
It isn't surprising that monkeys can understand an abstraction like 'numbers' - a brain is a neural network, and neural nets are 'abstraction engines' by definition. Consider the nature of abstractions: an abstract concept is one that describes a set of properties that are common to a class of objects. A number, for example, is the property that is common to all sets that are isomorphic in the category of sets (to spell it out: what is common to 'five apples', 'five oranges', 'five cows', ...? The number 5, of course). And what is it a neural net does? It learns to recognise patterns that are shared by all the 'objects' it 'sees' (if you will excuse the metaphor) - in other words, it creates an abstraction.

The numbers 1 and 0, although fundamental to our numerical notation, are not really 'interesting' in nature - 0 is simply 'nothing' and 1 is 'anything', they sort of fade into the background. Being able to recognise other, small numbers can be useful, however. Two fruits is one for me and one for you; if you have four children, but can only see three, then you should go looking for the last one, etc etc.

This is the way evolution works - nothing evolves with any purpose; things evolve because there are new traits that turn out to be beneficial in the given environment. And then, down the line, it sometimes also turns out that a trait that evolved at some point in the past allows the organism to do something entirely new in a new environment. So the monkeys didn't evolve to benefit from written language, it turned out that this is one of the things their brains can learn. The real question here is: Why did brains evolve - and that all starts with biofilms ;-)
• #### Re: (Score:3, Insightful)

A number, for example, is the property that is common to all sets that are isomorphic in the category of sets (to spell it out: what is common to 'five apples', 'five oranges', 'five cows', ...? The number 5, of course).

True, but that's not the impressive thing. The article points out:

The small study of two rhesus monkeys reveals that cells in their brains respond selectively to specific number values - regardless of whether the amount is represented by dots on a screen or an Arabic numeral.

The "numeral" a

• #### Re: (Score:2)

I remember reading a long time ago about some study done on primitive people (well I should say pristine aka uncorrupted by modern concepts). They had symbols for 1-4 but anything above was "lots". The conclusion was that we can see "4", but need to count "5" (or match it to a pattern).

As a side note, I wonder if this is because patterns for 4 or less are few and obvious while there are "5" patterns that are hard to catch. I also wonder if dynamic patterns formed by fast moving objects would make it impossi
• #### Re: (Score:2)

That's the only piece of trivia that survived the ages, if someone else has more to share that would be interesting.

I don't know if it's the case you're thinking of, but the Pirahã [wikipedia.org] people don't have any counting words besides 'one', 'two' and 'many' (and there's some doubt that even 'one' and 'two' exist in their language.)

also check out the wiki article on the Pirahã language [wikipedia.org]

Interesting stuff...
• #### Re: (Score:2)

Erm, plenty of things ended up evolved for no reason, as they may have no bearing on the reproductability or survival of the species in question.
• #### Re: (Score:2)

It isn't surprising that monkeys can understand an abstraction like 'numbers' - a brain is a neural network, and neural nets are 'abstraction engines' by definition.

Well, then the question arises is how do monkeys evolve understanding of 'number' in the abstract, while other organisms with similar or larger brains show no such ability? How do we measure the power or ability of a neural network and compare that to the power and structure of an organic brain? If ape brains are powerful enough to understand number, why haven't they developed some sort of sign language?

For me, I don't buy the theory that an organic brain or mind is anything like a computer or a neural n

• #### Re: (Score:2)

Interested parties should check out The Math Instinct [amazon.com] by Keith Devlin, who points out that many higher mammals have a kind of number sense (lions seem to be able to tell by the number of roars whether another pride has more or fewer members than their own). Gorillas and chimps can be taught to do single-digit arithmetic, although it takes much longer than it does with humans. And infant humans can definitely recognize, for instance, that one-ball plus one-ball should equal two-balls and that something's wro
• #### Not just math (Score:4, Interesting)

on Thursday November 01, 2007 @12:30AM (#21193207) Homepage
Bottom of the friendly article: The results are not the first to suggest there may be specific brain cells tied to individual concepts. In 2005 researchers discovered that individual neurons become activated by images of specific celebrities such as Jennifer Aniston and Halle Berry.

So I guess it is up to individuals to decide how best to utilize limited brain cells. I'm pretty sure that those monkeys can tied a couple of their brain cells to other concepts given enough training.
• #### Obvious (Score:5, Interesting)

on Thursday November 01, 2007 @12:38AM (#21193249)
In other news, reality is hardwired for math.

Seriously, why wouldn't a brain, which exists to process data in one form or another, respond to math positively at some level? Geometry is math, and that is hardwired in our brains to a high level. Any brain that has to process spacial information in any way must be predisposed to math.
• #### Re: (Score:2)

Spatial reasoning is separate from mathematical/logical reasoning. Plus maths is not required for practical geometry or navigation.
• #### Re: (Score:2)

In other news, reality is hardwired for math.

1.618? [wikipedia.org]

• #### Re: (Score:2)

Sure, but:
1) Why one brain cell per number?
2) What's the max number before the primate stops allocating a brain cell to numbers? Does that vary a lot on a per individual basis? Does that vary significantly on a per species basis? Is there a correlation with the perceived intelligence of the individual?

• #### Re:Obvious (Score:5, Interesting)

on Thursday November 01, 2007 @03:26AM (#21193923) Homepage
I agree...

I can't stand the over-use of the expression "hard-wired" when the data only indicates something that is universal. It implies that the structures responsible would develop in that function no matter what, without the experience in the world of, for example, things in sets-of-three, etc.

The data really supports dynamical systems models of cognitive development [indiana.edu] more than pure innatist ones. Just look at what the brain of someone blind from birth develops into, absent visual input.

I highly recommend the books of Andy Clark, particularly his "Being There," as an introduction that starts to explain just how flawed the seemingly harmless phrase "hard-wired" is.

• #### Hardwired? (Score:2)

Was it the same cell or group of cells in all of the monkeys, or was it different cells or groups of cells in different monkeys that registered the numbers.

Hardwired implies that it is specific cells that should be the same in all of the monkeys.

If you selectively destroyed all the cells that respond to a digit, say 5. Is the monkey then no longer able to respond to 5 as a stimulus, or would other cells "relearn" the meaning of 5? Is such "relearning" possible if the knowledge was truly hardwired?
• #### Re: (Score:2)

Seriously, why wouldn't a brain, which exists to process data in one form or another, respond to math positively at some level?

Because it's not, from an evolutionary perspective, necessary -- not beyond something like "I'm hungry, he has more berries than I do, therefore I should drop my food and take all of his."

Try something sometime: see how many randomy-arranged objects you can count in a split-second glance. Most people do well up to five. After that it gets tricky, unless, for example, six objects are
• #### title wrong (Score:5, Funny)

on Thursday November 01, 2007 @12:45AM (#21193289)
I've co-taught an undergraduate mathematics course. Based on this experience and many others, I assure you the human mind is not hard-wired for math.
• #### Re:title wrong (Score:4, Insightful)

on Thursday November 01, 2007 @12:56AM (#21193353)
Good point. While brains may be wired for numbers, I highly doubt that any brain is hardwired for differential equations.
• #### I really like seven... (Score:5, Funny)

on Thursday November 01, 2007 @12:54AM (#21193337) Homepage
For some reason I get aroused when I hear the number seven. Especially when it's followed by "of nine".
• #### music and singing (Score:4, Interesting)

on Thursday November 01, 2007 @12:57AM (#21193357)
A colleague of mine once pointed out that the ability of most humans to sing (speak for yourself!), play music, and even distinguish different tunes implies an intrinsic hard-wired affinity for numbers since music depends on very specific ratios of frequencies to be gauged and produced accurately real time. You are in effect doing a Fourier transform of the music, finding the strongest peaks, and reproducing them and/or scaling them by fairly exact amounts (in spite of a broad spectrum of other frequencies present creating timbre). On top of that, one is usually doing this accurately in the context of much, much lower frequencies (i.e. rhythms/tempos on the scale of Hertz rather than "tones" on the scale of 100s of Hertz) as well. Of course, not all music is western, 12 tone, tuned the same, etc., etc. etc. But I think there may still be a (fairly well understood??) psycho-acoustic music-math connection in there.
• #### Re: (Score:2, Insightful)

A colleague of mine once pointed out that the ability of most humans to sing (speak for yourself!), play music, and even distinguish different tunes implies an intrinsic hard-wired affinity for numbers since music depends on very specific ratios of frequencies to be gauged and produced accurately real time. You are in effect doing a Fourier transform of the music, finding the strongest peaks, and reproducing them and/or scaling them by fairly exact amounts (in spite of a broad spectrum of other frequencies present creating timbre).

The Fourier transform is done in hardware. That's just how hearing works. Specific intervals are pleasing largely because of the way their overtones line up; that's why pretty much every music system has a third, a fifth and an octave. I'd bet that producing music is done based on memory and calibration, the same way many other actions are done; no math involved.

On top of that, one is usually doing this accurately in the context of much, much lower frequencies (i.e. rhythms/tempos on the scale of Hertz rather than "tones" on the scale of 100s of Hertz) as well.

People are good at things involving periodic events on the order of a second. Not sure that math enters into it. I'd guess that the math/mus

• #### Re: (Score:3, Interesting)

Specific intervals are pleasing largely because of the way their overtones line up; that's why pretty much every music system has a third, a fifth and an octave. I'd bet that producing music is done based on memory and calibration, the same way many other actions are done; no math involved.

Point well taken. As you probably know, that what is considered a pleasing tone is very culturally dependent. Most of the world's music involves what to "western ears" sounds microtonal -- but perhaps 3rds, 5ths, and octaves are universal, I'm not sure. IF this were true, it would signal to me that there IS a hardware component to at least detecting (and reproducing) certain mathematical ratios. On the other hand, most of western music is mean tempered and only approximates perfect 3rds, and 5ths. Nev

• #### Re: (Score:2)

music depends on very specific ratios of frequencies to be gauged and produced accurately real time. You are in effect doing a Fourier transform of the music, finding the strongest peaks, and reproducing them and/or scaling them by fairly exact amounts

Respectfully disagree. Matching a sound you can hear is simply a matter of listening closely to the "beats" that occur when the frequencies don't quite match up in tune.

Similarly, chords and harmonies sound pleasant because the frequency ratios [yorku.ca] are small. The
• #### This just in! (Score:2)

Perceptrons hardwired for mathematics!

In a far reaching experiment, a generic group of second year CS students trained a neural network classifier on pairs of images consisting of a number of dots, and a corresponding arabic symbol. The students trained their perceptron [wikipedia.org] on four pairs of images representing the numbers 1 through 4. The successfully trained AI was then shown pairs of dots and numerals and identified incorrect pairings. An interesting feature of the experiment is that some of the neural net

• #### Personal Experience (Score:3, Insightful)

on Thursday November 01, 2007 @01:17AM (#21193449)
Based on my experiences teaching science classes, not ALL brains are hard-wired for math.
• #### What about the Pirahã? (Score:5, Interesting)

on Thursday November 01, 2007 @01:38AM (#21193537)
The notion that primates are genetically predisposed to have mathematical ability is tenuous. Why should we believe there is some neural circuitry designed explicitly for math? First of all, all studies teaching non-human primates to count involve extensive training of the primates; it doesn't just "click" for them. This would suggest that it is a struggle for them to learn the concept of counting and mathematics. (Of course it doesn't help that TFA is extremely light on the gory details of the methodology and results of the study.)

Secondly, the Pirahã people [wikipedia.org] of Amazonia do not have numbers or counting. Professor Everett, despite months of instruction, was unable to make any progress in teaching them how to count. The Pirahã themselves were highly motivated learners, as they didn't want to be ripped off in trade by visiting merchants, but nevertheless, they had no success in learning the most basic concepts of math. Indeed the Pirahã language has no numerals, and is claimed to have no quantifiers, either.

Everett, D.L. (2005). Cultural constraints on grammar and cognition in Pirahã. Current Anthropology, 46, 621-646.
Hauser, M.D., Chomsky, N. and Fitch, W.T. (2002) The faculty of language: what is it, who has it, and how did it evolve? Science, 298, 1569-1579.
Pinker, S. & Jackendoff, R. (in press). The components of language: What's specific to language, and What's specific to humans? In M.H. Christiansen, C. Collins & S. Edelman (Eds.), Language universals. New York: Oxford University Press.
• #### Re:What about the Pirahã? (Score:5, Funny)

on Thursday November 01, 2007 @02:00AM (#21193635) Homepage Journal
Did you just add footnotes to actually back up your claim on a slashdot discussion? *rubs eyes* You're going to destroy this site's reputation.
• #### Re:What about the Pirahã? (Score:5, Funny)

on Thursday November 01, 2007 @04:00AM (#21194021)
these were non-numbered footnotes so they don't count.
• #### Re: (Score:2)

*Phew*! That was a close one!

-Mike

• #### Obviously (Score:2)

Well of course the PRNGs in their little monkey brains are seeded differently. Otherwise, an infinite number of them sat at typewriters would all type exactly the same gibberish, and we wouldn't have any Shakespeare.
• #### Close Enough for Hand Grenades (Score:2)

They're not wired for exact sums, they're wired for approximation. Once you can convince people of their ignorance of math they'll fly off into all kinds of logically-predicted directions of randomness. BINGO! People do not understand math! Simple.
• #### Refer to previous article (Score:2)

"non-human primates really can understand the meaning of numerals."

Good! Let's fire Diebold and hire them to count the ballots instead.

• #### monkey professor (Score:4, Funny)

on Thursday November 01, 2007 @02:11AM (#21193679)
I wish they'd teach me math then; considering my college math grades, I'm worse off than these monkeys.
• #### Well there are (Score:2)

There already are cells for numbers, namely the follicles in the ear that are used to detect pitch IIRC each cell picks up a specific frequency.
• #### Infinity (Score:4, Funny)

on Thursday November 01, 2007 @05:56AM (#21194499)
So, don't think of infinity. Your skull will explode...
• #### That's why ... (Score:2)

... they're still monkeys and we're running the show -- they have no concept of Numero Uno.
• #### Wired? (Score:2)

So some neurons are be tied to the concept of "three" which is an abstraction. Primates can abstract up to that level and more. So the relation to math seems not so direct, I'd not call it being wired. There might be much math and fuzzy logic goes on in the brain, at a lower level, but it doesn't traslate to powerful math ability at conscience level.
• #### The number 3 (Score:2)

I can think of at least 2 reasons why monkeys may prefer the number 3, and it has nothing to do with numbers.

o3- (boobs)

o-3 (butts)

• #### Man! (Score:2)

This is why I get those uncontrollable urges to speak in Algebraic terms! You X^2+Y^2= f(x) !!!
• #### Basics only (Score:2)

That people can close their eyes and catch a ball suggests that we can do at least basic algeobra/calculus.

estimates of the volumes of diffrent containers suggests something similar.

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