Once in a long while, I have the good fortune of coming across a message that resonates profoundly within me, and yet manages to turns just about everything that I know into pieces.

I’m feeling this way now, after taking a break from my prep work for my candidacy exam., and having coming back from listening to Douglas Hofstadter’s talk on analogies as the core of cognition. Hofstadter is the author of the prize-winning book Gödel, Escher, Bach: An Eternal Golden Braid, which I love very much.

There were some claims thrown out that fly in the face of common sense, but are actually very meaningful. The primary one Hofstadter focused on was that the process of forming analogies should not be restricted to the IQ-puzzle sense ( ___ : hand :: shoe : foot, for example), but should really be thought of rather a much more general process of connecting a concrete event with a mental abstraction such as a recollection of a past memory or classifying the event into a category. Which actually makes a lot of sense, since a “low-level analogy” such as seeing something happen and recalling a similar event in your own past is in a fundamantal sense is also connecting the dots in your own mental landscape. Hofstadter is careful, though, to point out that such connections are highly contextual, in the sense of fortune favoring the prepared mind. It is very hard to draw analogies between (say) groups and matrix representations of groups unless one is already pretty familiar with group theory and the concept of a group representation. But yet things happen that trigger memories from the deep cellars of the mind. It’s odd, how the mind works.

Hofstadter also points out that a lot of cognition can interpreted as the act of classifying things, i.e. to assign categories to specific memories and assemble specific instances to form classes of objects. Another point I thought was highly counterintuitive: that in informal contexts (i.e. excluding the rigorous, formal modes of mathematical and scientific thought), there is no essential distinction between a category and a member of that category. In a logical sense, it’s like saying that tags and objects with those tags are in the same equivalence class. Which neatly explains how abstract concepts like number and color can exist despite the immense logical difficulties in explaining them. Anyone who has taken abstract algebra will know how hard it is to prove that 1 + 1 = 2, because first one has to define what is meant by ‘1′, and then what is meant by addition, and then what is meant by equality, and then the product of performing the binary operation of addition on two unit numbers, etc. It seems hopeless then to prove that the number four exists, yet even young children (though not infants) are able to appreciate how four dogs is the same as four books is the same as four telephone calls. Color is a similar exercise in formal futility. I can say this rose is red, and you can say this rose is red, but it is really, really hard to get a (completely) color-blind person to understand what it means for a rose to be red. And even then, there is no certainty that your concept of redness is the same as my concept of redness. And so on and so forth.

There was also a point about the inherent coarse-graining of information that happens in the brain as time goes on. It’s like how learning how to ride a bike was in the beginning all about the mechanics of moving faster than you can fall, and trying (usually unsuccessfully) it out many times, and then all of a sudden there’s that epiphanic moment of actually moving the way the bicycle was designed to, and then falling again; and then eventually one gets the hang of it and it becomes second nature, and for all eternity into the future riding a bicycle is something that happens subconsciously without conscious effort thinking about the mechanics of how to move and pedal and brake and all that. I like this idea very much. This kind of internalization explains beautifully why teaching is such a difficult activity to pull off: when you know so much more, it’s hard to remember what it was like to be learning things for the first time, and pitching the idea to students without the undertone of dumbing it down to their level.

At some point during the lecture, I paused to think about how odd the job of a cognitive psychologist has to be. Most of us scientists investigate phenomena that, for the most part have nothing to do with ourselves. We then luxuriate in the role of the clinically detached observer, watching atoms jump through hoops and rats fornicate and all sorts of weird shit like that. (There are of course undeniable ontological issues such as the paradox of Schrödinger’s cat, but I digress.) But the cognitive psychologist investigates how people think, and the act of studying something like that is inevitably introspective and highly participatory. It’s like trying to imagine a play where the audience are acting as they watch, and the actors are watching as they act. And yet in some sense Hofstadter still preserves the semblance of an observer immersed in his own mental river of thought, fishing out cognitive oddities such as jumbled-together words (”I took a capsi to work every morning”) even as he says them, and then catches himself saying them. It’s fascinating to hear about.

I don’t know how cognitive psychologists don’t eventually end up with analysis paralysis; thinking thoughts, and then thinking about their thoughts, and then thinking about how they think thoughts, then thinking about how they think about thinking thoughts, and so on. If they were computers, people would have to drop by once in a while and reboot them to get them out of the infinite loops of thinking about thinking.

There’s something ineffable about the process of thinking. It’s mind-boggling how thinking about it makes the concept of thinking recede from clarity.

But I’m sure about one thing: after this talk, I’ll never think the same way about thinking about things again.