This paper hit the popular news media. "We are all natural bookmakers," said New Scientist. And the senior author, Vittorio Girotto, said,
"We wanted to show that this sense of chance exists, that it is universal, and that you do not need to be trained to evaluate uncertainty," says Girotto. "We have good evidence now that the human mind does possess this ability."Researchers have also reported that infants have a sense of "intuitive physics," seemingly being born with the ability to understand gravity (that is, by 2 months of age, they expect an object to fall -- really, who understands gravity?), and to expect that an object doesn't cease to exist when hidden from view.
And, studies (e.g., here and here) suggest that by 5 or 6 months, infants have a sense of numbers. But then, so, apparently, do non-human primates, such as tamarins. When two objects were hidden behind a screen, tamarins expected to see two objects when the screen was lifted; when there were three, the animals looked at the objects longer than when they were presented with the expected number, suggesting surprise or confusion. But then, dogs are good at playing Frisbee because they understand physics, too -- what does up there, comes down here.
And, even crows understand water displacement, knowing that if they raise the water level in a small beaker, they'll be able to pluck out a piece of floating food.
And look at how bats, and even dragonflies track their in-flight prey.
There seem to be several things going on when things like the probability study in unschooled Mayans make the news. To those of us who are schooled, probability, mathematics, physics -- or even grammar -- can seem like rather esoteric subjects that take years of training to master, or to even vaguely understand (though really, who understands probability?). Traditional schooling has divided the world we know into disciplines that have names and bodies of knowledge that must be mastered.
But, in large part, formal education is giving names to things we already knew. We have already internalized grammar as infants, we have a grasp of essential physical or mathematical principles, and it seems some basic understanding of chance as well. Essentially we're formalizing our description of the world we know from experience, but clearly we -- and dogs and tamarins, and crows and dragonflies and many other animals -- know that world before we know words or equations or models or principles that describe it. And indeed, most animals never get to that stage. I think we all can do this not because we have an innate sense of physics, or grammar, but because our brains have evolved to be able to recognize some kind of order, and to make generalizations from what we experience. It's apparently important to survival, because so many organisms have evolved the same ability.
In this context, we should keep in mind that mathematics is just an elegant way of describing relationships and really exists only because over the millennia humans did in fact realize that relationships had regularity. The long-known fact to western science, for example, that the Mayans had very sophisticated calendars shows that the recent news story is no surprise at all -- indeed, it would be very surprising were it not so. How things work in the brain is, however, a different order of question.
Holly elegantly suggests it simply comes down to pattern recognition. Frisbees follow predictable arcs, objects don't disappear inexplicably, if there are 5 yellow tokens and only 1 red, the chance of choosing a yellow one is higher than the chance of choosing a red one. I'm happy with that.