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There are many studies of language learning abilities of primates (mostly chimpanzee, bonobo) and studies of tool use, knowledge transmission and number sense.

Are there studies or documented cases of drawing, any form of abstract graphical representation, use of concrete objects as representatives, symbols for other things not present, hints of ideal shapes such as circles or lines, uses of markings or pebbles for counting, etc ?

The less influenced by trainers and observers, the better.

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This seems like a question for BiologyOverflow. –  Steven Gubkin May 9 '10 at 13:18
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Hm. I smell another closure debate coming on. I too think the question is interesting, but I also think it's too far out beyond the fringes of what research mathematicians do to be suitable for MO. Anyone who strongly disagrees, please open a new thread on meta to discuss the issue. (There are two votes to close so far.) –  Harald Hanche-Olsen May 9 '10 at 14:14
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I agree that most users of MathOverflow are not likely to be knowledgeable in this area and that a site devoted to questions about biology, or cognition or both might be a better choice, if it exists. -- I hope that if anyone here has further suggestion on where to look about this subject, he or she might leave a short comment here. Thanks. –  ogerard May 9 '10 at 16:49
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I voted to reopen this question, since I would be interested to see a knowledgeable answer. The fact that the "average" MO user (as mentioned in the meta-discussion) or that "most MO users" are not likely to be knowledgeable about it does not seem relevant---such an objection after all would apply to most all of our questions---the right question, instead, is whether any MO user knows biology, and I would rather wait and see. The situation is similar to the more philosophical questions that are often closed here, even when there are MO users who can answer knowledgeably and mathematically. –  Joel David Hamkins May 10 '10 at 2:59
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@Joel: thanks for the explanation. I've copied your comment to the meta thread (tea.mathoverflow.net/discussion/397/…) and responded to it there. –  Anton Geraschenko May 10 '10 at 3:47
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closed as off topic by Harry Gindi, Felipe Voloch, Reid Barton, Andrew Stacey, Qiaochu Yuan May 11 '10 at 14:49

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2 Answers

The following is an informal response written by Professor Laurie R. Santos of Yale University.

This is a tricky one, as there's lots of controversy on the specifics related to these questions in the field of primate cognition. On the one hand, there is evidence that some primates (chimpanzees and capuchin monkeys) can use some kinds of symbolic representations in some situations. For example, both chimpanzees and capuchins can be trained to use tokens to represent different numerosities. Once trained, they can do all kinds of smart things with these new symbols-- including adding and subtracting them, and so on. There's also evidence that chimpanzees can understand some spatial symbols, such as using a scale model of a room to figure out where a piece of food in a real room is hidden. I think this use of a scale geometric model is actually the best evidence for symbol use that's really geometric in nature. That said, it's pretty limited and does appear to require at least some training to get going. To my knowledge, there are not real cases of other spontaneous kinds of symbols. There's nothing like representational drawing in primates (lots of very abstract painting, but nothing that would suggest graphical representations) or anything like spontaneous use of marking/pebbles for counting. So I guess the upshot is that primates can use symbols sometimes, but in very restricted, very scaffolded, and often very limited ways.

Here are also two references that might be of use...

chimpanzee use of scale models: http://www.infantcognitiongroup.com/Portals/0/PapersPosters/KuhlmeierEtAl(1999).pdf

capuchin use of symbols: http://www.sciencedaily.com/releases/2008/06/080610212404.htm

(ed -- note that the comments below were written about a previous revision of this answer, which was just a promise to ask Prof. Santos! Since the question is currently closed, Pete's only option was to edit this answer.)

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Thanks very much Pete for your intermediation in this matter. –  ogerard May 11 '10 at 5:51
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I'm voting this down for the simple reason that it isn't an answer! It may well be a very helpful comment, and probably the best possible from MO, but nonetheless, it is not an answer. –  Andrew Stacey May 11 '10 at 10:50
    
Let's say it is a temporary placeholder for the answers Pete L. Clark contact may provide. –  ogerard May 11 '10 at 11:14
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Placeholders are completely unnecessary. If Pete gets any answers from his contact, he could simply edit the original question to include a link to them. Something along the lines of "As this question did not fit MO, anyone interested in finding out more is encouraged to follow this link.". –  Andrew Stacey May 11 '10 at 12:50
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@Andrew: I think you're getting a little carried away. Whether it fits MO is the matter in contention, but what is beyond contention is (i) some people here are interested in the question and (ii) the question does not have a natural home on any other current Stack Exchange site. So if I happen to get an answer from an expert, it seems natural to post it here. I fail to see the harm. –  Pete L. Clark May 11 '10 at 14:44
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By following links provided by contributors to the meta-discussion, I have found these two resources of interest:

The Comparative Cognition Society

and the book Animal Spatial Cognition

Reading the rather strait-jacketed Wikipedia article on Animal Cognition, the idea of Cephalopodic Mathematics comes to mind as another pursuit.

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