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How can you not be intrigued by the subject matter of this talk? Ok, I can see why some may not be, as even the mention of math sends many running for the aisles. But, I find it very intriguing. I mean, this is one of our uniquely human* characteristics that encompasses consciousness, logic, reason and a set of rules that appears be applicable to the entire physical (and perhaps metaphysical) world! So where the hell does one begin to study such a phenomenon as mathematical reasoning???
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In infants, of course. And in monkeys, pigeons, mice and the lowly lab rat. This may seem counterintuitive at first glance, studying high-level human processes in beings with limited cognitive abilities. But Spelke makes a good argument for conducting such studies - and their applicability to higher-level reasoning - by investigating mechanisms found across cultures and species, and which may serve as the foundation of mathematical reasoning. As a quick example from the talk, studies have shown that human infants (along with nonhuman animals) are able to discriminate gross values. E.g., an infant will spend a longer time looking at a visual display of dots if the quantity of dots is changed (vs. if the contrast, color, or general size of dots is changed) from a previous display. So, it appears there exists an innate mechanism for crudely evaluating sets of objects. And this “nonsymbolic” numerical ability correlates well with symbolic abilities later in life (that is, mathematical abilities such as addition – the process of combining symbols (numbers)). Thus, if we can locate where this nonsymbolic numerical evaluation resides in the brain, we have a good start point of where our abstract abilities might reside. And this is being done. Admittedly, it’s a large jump from nonsymbolic numerical abilities to abstract mathematical reasoning, but it’s a start. And considering all the mystic phenomena involved in abstraction, I think it’s about all we can expect at this point in time. And once we understand these foundational processes, maybe we can tweak downstream (or would that be upstream?) connections to see which additional structures may contribute to this complex process. Obviously is a very intricate question, one that I certainly can't do justice. But it is exciting to see the scope of questions we are beginning to actually crack with scientific inquiry.
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Oct 18 2009 8:18 pm
Good stuff!