Next they’ll train monkeys to remember where you put your car keys
December 5th, 2007 by WaltI had a pet theory that a large part of what made some people good at mathematics was simply memory. A large part of mathematical practice is remembering bits of trivia: standard counterexamples, definitions, little technical tricks. BBC News is reporting on a discovery that makes that seem less plausible: chimpanzees may have better memories than people do. Scientists compared the performance of chimpanzees and their closest relatives, university students, when tested on their ability to remember a random pattern of numbers on a screen. The BBC story comes with two videos of the chimps in action that are worth watching.
December 5th, 2007 at 9:38 pm
I think this is expected. Shouldn’t their mind be at a fresh state more often than humans since then don’t have to think on a daily basis as much as we do. I don’t think this comparison makes sense unless you force a monkey to lead the complex life of a human subject, or get the human subject to live like a monkey for a while.
December 6th, 2007 at 1:56 am
I seem to remember Poincaré ironically proposed your theory in order to best refute it later (arguing that in fact a mathematician rediscovers a proof each time he does it, and does not in fact memorize many things).
Anon, they trained student for one year and still they couldn’t compete against the chimps. And frankly, having seen the videos, I believe it, most of the time I don’t see the numbers at all.
By the way, the article I read contained the following sentence (my translation) “a team of students was pitted against a team of chimps who had been previously taught to count”. I thought it is the rare occurrence for a journalist to write that.
Z
PS: Walt, would it be conceivable that you change your spam block? I don’t comment 50% of the time because I can’t read the words.
December 6th, 2007 at 2:06 pm
Well, duh. Technologically, humans had the purely accidental advantage of inhabiting the south asian alluvial plains, thereby needing civilised collection points for finding tool quality stones.
December 6th, 2007 at 10:34 pm
> I had a pet theory that a large part of what made some people good at mathematics was simply memory.
It is, but you got the relationship the wrong way around. I always felt a bit sorry for people learning other subjects having to cram their brains with arbitrary facts. Nothing in mathematics is arbitrary. If you can’t remember it, you derive it from scratch. And once you understand the subject, the derivation often seems obvious. I could never understand the all-night cramming sessions people doing other subjects would do before exams. Mathematics is the subject for people with sieves for brains.
December 7th, 2007 at 3:12 pm
How does chimpanzees’ superior(*) performance make it less plausible that being good at mathematics requires a good memory? It can’t be because chimpanzees aren’t doing mathematics as memory is not the only thing math requires.
Even though you can trace every theorem all the way back to axioms (or whichever lemma you do remember), it is computationally expensive. In order to make progress you need to memorize them anyway (and with impressive precision).
Having a good memory may not automatically make you good at math, but I don’t think I’ve ever met anyone who was good at math but seemed to have an ordinary memory.
(*) I haven’t analyzed the study carefully, but I doubt it’s easy to devise a contest which puts chimps and humans at equal footing. The chimps are at a very early stage of studying anything at all while the university students have gone through years of swimming through seas of symbols and memorizing combinations of them. Children versus chimps could be more interesting.
December 13th, 2007 at 3:41 am
From the video clip I saw, the numbers flashed so rapidly, and the chimps responded likewise, that the memory in use was shorter than I would usually call short-term (the where-did-I-put-my-keys kind). It seemed that the location-response system they were using was more akin to the kind of skill one would use to fight off multiple attackers, or that soldiers use to identify multiple targets.
Perhaps the chimp, which lives in large family groups that could be attacked territorially by other groups has retained this out of evolutionary necessity. I’m not sure that it demonstrates any mathematical ability - surely the same test could be done with any sequential symbols? If the numbers had been the first ten letters of the alphabet, would we have ascribed to them a talent for written language?
Mathematics, like language, is, it seems to me, a much greater thing than the symbolic code it uses. As far as memory is concerned, I know people who remember all the trig formulae, and others who don’t, but derive them anew from Euler’s relation each time they need them. It seems that this latter group is demonstrating more mathematical ability than the former, whilst remembering - long-term - only one relation.
What has always intrigued me, however, is that when I was at university, there were a couple of blind mathematics students. Now, when I was solving a long mathematics problem, I could maybe retain the last line and last-but-one in my head, just enough to turn the page without making a mistake, but would not be able to retain the whole thing in my head. I always had pen and paper to hand, and always needed it. How does a blind student achieve the same thing? Sure, there are braille aids and transcribers available some of the time, but not all the time. It occurred to me that blind students must be retaining in their head a great deal more than I can, i.e. they must have a very large working memory.
December 13th, 2007 at 8:56 pm
I don’t think that an excellent memory is a necessary condition for doing mathematics, but functional short term memory definitely is. I discovered this the hard way as a long undiagnosed antibody deficiency became a big problem as an adult and the years of chronic infection and incompetent immune activation took its toll on my brain, severely compromising my short term memory. I was in the kind of state where one would lose the car keys and finally stumble across them in the freezer. Word finding was greatly degraded and I had a great deal of trouble reading my old math research notes because I just could not load everything that I needed into short term memory, which is really our scratch pad. Finally, after years, I got a proper diagnosis, and with periodic immune globulin my brain has returned to normal and I can do math again, which, of course, is wonderful!
December 22nd, 2007 at 11:08 pm
Monkeys Can Perform Mental Addition
http://www.sciencedaily.com/releases/2007/12/071218101240.htm
ScienceDaily (Dec. 20, 2007) — Researchers at Duke University have demonstrated that monkeys have the ability to perform mental addition.
In fact, monkeys performed about as well as college students given the same test.
The findings shed light on the shared evolutionary origins of arithmetic ability in humans and non-human animals, according to Assistant Professor Elizabeth Brannon, Ph.D. and Jessica Cantlon, Ph.D., of the Duke Center for Cognitive Neuroscience.
Current evidence has shown that both humans and animals have the ability to mentally represent and compare numbers. For instance, animals, infants and adults can discriminate between four objects and eight objects. However, until now it was unclear whether animals could perform mental arithmetic.
“We know that animals can recognize quantities, but there is less evidence for their ability to carry out explicit mathematical tasks, such as addition,” said graduate student Jessica Cantlon. “Our study
shows that they can.”
Cantlon and Brannon set up an experiment in which macaque monkeys were placed in front of a computer touch screen displaying a variable number of dots. Those dots were then removed and a new screen appeared with a different number of dots. A third screen then appeared displaying two boxes; one containing the sum of the first two sets of dots and one containing a different number. The monkeys were rewarded for touching the box containing the correct sum of the sets.
The same test was presented to college students, who were asked to choose the correct sum without counting the individual dots. While the
college students were correct 94 percent the time and the monkeys 76 percent, the average response time for both monkeys and humans was about one second.
Interestingly, both the monkeys’ and the college students’ performance worsened when the two choice boxes were close in number.
“If the correct sum was 11 and the box with the incorrect number held 12 dots, both monkeys and the college students took longer to answer and had more errors. We call this the ratio effect,” explained
Cantlon. “What’s remarkable is that both species suffered from the ratio effect at virtually the same rate.”
That monkeys and humans share the ability to add suggests that basic arithmetic may be part of our shared evolutionary past.
Humans have added language and writing to their repertoire, which undoubtedly changes the way we represent numbers. “Much of adult humans’ mathematical capacity lies in their ability to represent numerical concepts using symbolic language. A monkey can’t tell the difference between 2000 and 2001 objects, for instance. However, our work has shown that both humans and monkeys can mentally manipulate representations of number to generate approximate sums of individual objects,” says Brannon.
Citation: Cantlon JF, Brannon EM (2007) Basic math in monkeys and college students. PLoS Biol 5(12): e328.
doi:10.1371/journal.pbio.0050328
Adapted from materials provided by Duke University Medical Center.
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