## Stupid Monkey

If a creature can only add, say, integers less than nine, do they really grasp what addition is? Whatever faults generalized conceptual holism might have, isn’t it still pretty plausible for the concept of addition?

Tad Zawidzki emailed the following link to a video of a mathematical monkey (Thanks, Tad!):

www.duke.edu/web/mind/level2/faculty/liz/addition.htm

The following link describes the relevant research:

http://www.duke.edu/web/mind/level2/faculty/liz/macaque_research.htm

Not unrelated is Tanasije Gjorgoski’s recent post on whether babies intuit that 1+1=2:

http://broodsphilosophy.wordpress.com/2006/12/02/is-112-intuited/

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Hey Pete -

Thanks for posting this. I can’t get the video to work, but maybe it’s because my office computer doesn’t have the apple application.

It occurred to me: what if you could train the monkeys in some function more difficult than addition - division or multiplication say, or squaring or square root, or even some ‘nonsense function’ variant of Kripke’s ‘quus’? If there was no significant difference in the time it takes to train the animal, then I think this would show that it’s merely learning some kind of perceptual association rather than true addition, in the original task. After all, surely monkeys can’t find square roots! I should have a look at the actual paper to see if they consider this.

I would guess that if they can train monkeys addition on one set of numbers (e.g. below 4), and then the monkeys show ability to do addition on novel cases (addition of numbers bigger than 4), it can’t be case of perceptual association.

But the link to the page describing the research isn’t clear on this.

Â¿ Is arithmetic intuited as well?. Stanislas Dehaene, says that arithmetic is more than a cultural invention based on brain evolution, that is, when people or even animals substract quantities in numerosities they do the way they do because it is something necessary and possibly unique given our convergent genetic endowment. Arithmetic has clear traces of evolutionary precursors in non-human animals. In other words, we all are born with arithmetic capabilities. Pete, is possible that someday researchers argue for inborn beliefs?

Tad and Tanasije,

What do you guys take “perceptual association” to mean? When you deny perceptual association, are you guys denying that it’s perceptual or that it’s association?

Anibal,

I certainly wouldn’t deny that such a thing is

possible.I’m not sure what I mean exactly. I mean some kind of ability to correlate perceptually represented stimuli, I suppose. I think Tanasije is right that a lot depends on whether the capacity is at all generative. It’s unclear from the blurb whether this is the case in this research. In any case, how much generativity could there be, given that monkeys can only recognize numerosities smaller than 9 (I think). How many sums does that make possible? 81 if I’m counting right. Now if they were trained on a small subset of these, and afterwards, with no further training, able to do the rest, then I guess there’s no doubt that they add, though of course this isn’t the same as having our concept of addition which applies to an infinity of numbers.

TZ.

BTW,

I still get an error page when I try to link to the video from the blog, even using my mac.

TZ.

One more thing -

I just had a look at the video to me. As I first responded to the person who sent me the link - the monkey’s reactions strike me as too fast to indicate true addition. It’s coming up with the answers faster than I can. It strikes me that the monkey is just a really good estimator of group size, based on how groups look. When it sees the two groups it’s supposed to add, it can picture, roughly, what the union of the two groups will look like, and then select the answer that comes closest. There’s no way that monkey is counting! And can you truly add w/o counting?

Tad,

I think you and I have similar reactions on this.

BTW, I finally fixed the link. I think.

Hi Pete,

By perceptual association I was thinking something like training the monkey by showing two groups of dots, and then showing required result.. and the monkey associating the first two groups with the second, or something like that.

So that after the training when you show the starting two groups, it simply remembers the associated sum-group, without having any idea of what it does (except “if I do what I remembered I will get a banana” I guess).

That’s why I said that if it is trained on one set of numbers, and then does “addition” on novel cases, it can’t be case of such association.

So…in that case I would deny that it is association in general.

Hello All,

I haven’t looked at the video, but I wanted to extend Anibal’s first comment here. I was recently reading a commentary on Dennett by Andy (Clark) where he discusses Dehaene’s work on numerical cognition. According to Andy’s gloss, we humans have a basic “biological competence at low grade arithmetic: a simple number sense, shared by infants and other animals and involving the rough appreciation of changes in quantity, of relative quantities, and of a couple of precise quantities such as oneness, twoness, and threeness” and additionally, “a culturally acquired capacity to think about exact quantities (other than 1,2,3) courtesy of verbal and language-specific representations of numbers” (in Clapin, ed. PHILOSOPHY OF MENTAL REPRESENTATION, 2002, OfxordUP, p. 86). Andy wants to show that we adults use an interesting combination of both.

Do these categories help here?

JRT

I forgot to add that the more basic competence is supposed to be something like the estimator Tad mentioned, and is unable to do the more precise calculations made available with the cultural stuff. So, the estimator can tell the difference between, say, 10 and 20, or 10 and 30, but can’t discriminate between 50 and 53, I think.

Robert -

I like the proposal. I think there’s a paper by Bloom on generativity that suggests that the ability to understand that counting can go on for ever (discrete infinity) is acquired as the result of a recursive system of number naming. So even a language-first guy like Bloom sees sophisticated numerosity as a linguistic artifact.

This raises the usual bootstrapping puzzle - how could we invent a recursive system of number naming without first being able to mentally represent numbers that way? Obviously Bloom must countenance some kind of bootstrapping solution to this. It’s curious that he doesn’t favor such language-thought bootstrapping in other domains. E.g., he thinks recursion in language and verbal expressions of social relations derives from prior recursive mental representations.

Back to the monkeys - surely the experiments controlled for all this. All you need is to see whether the monkey will distinguish correct from incorrect sums when both options are large and similar (differing by only 1 or 2 dots).

So are we stupid monkeys? I don’t do very well adding numbers over, say, a few digits long. Of course with pencil and paper and time I can go a big farther. Does possible addition count? Or is it a matter of knowing rules that would, given enough paper pencil time, probably lead to the right result. Or do I have to be able to cite the Peano axioms to “grasp” addition? Or be able to prove theorems about addition? Or what? Here’s something about addition that we don’t “grasp” — every even number is the sum of two primes. Or not. And, obviously, angels are to us as we are to monkeys. So probably the angels doubt that we “grasp” addition.

Eric,

I’d be much happier saying that most humans don’t know what addition is than that any monkeys do.