It’s an interesting time to a member of the Fairview High School class of ’99 right now. Actually, to be more precise, it’s an interesting time to be a member of the aforementioned class who also played baseball in high school. Two of my former teammates have been making headlines recently; one is in the final 12 of American Idol (haven’t watched the show myself, but apparently he’s a little grating, which, admittedly, isn’t a total surprise), while the other was just eliminated from the World Baseball Classic (playing for Canada, oddly enough, even though he’s also played for Team USA).

This, needless to say, is one of the reasons high school reunions are bad news.

Sorry, I just can’t resist things like this tidbit from a summary of an article in the Süddeutsche Zeitung:

Gustav Seibt attended a speech in Berlin by Jean-Noël Jeanneney, president of the Bibliotheque nationale in Paris, who hopes to reinforce all of Europe like a Gaulish village against Google Book Search, to break the back of Anglo-Saxon dominance in the world wide web. “Monsieur Jeanneney gave a harrowing example of what it could lead to if an Anglo-Saxon world-view came to dominate: the French Revolution could widely be seen as a period ‘of guillotine and terror,’ whereas ‘we on the continent’ see it as a time of humanity and progress. Parbleu! Terror in the grand revolution? That is new!”

That there is what one might euphemistically call a hyperbolic soccer ball. It’s a model of the hyperbolic plane that I made using this template. For those that aren’t up on their non-euclidean geometry, the hyperbolic plane is a 2-dimensional space of constant curvature -1 (for comparison, the sphere has curvature +1 and a regular plane has zero curvature); it was the first example of a consistent geometry in which Euclid’s parallel postulate doesn’t hold.

The above model is based on the standard soccer ball pattern, which has black pentagons surrounded by white hexagons. That pattern works nicely on a sphere, but you can’t flatten it out; to flatten it, you have to exchange the pentagons for hexagons and then you get a tiling of the regular flat plane. Going one step further gives you the above picture: black heptagons surrounded by white hexagons, which, as with the regular soccer ball, can’t be flattened out without ripping the paper.

See the bigger version for a closer look, where you can more easily discern the obscene geoboard, platonic solids and other geometrical miscellanea cluttered in the background (all extensively documented in the notes to the Flickr version). There’s also another view, which gives a better sense of how the hyperbolic plane is sort of a bunch of saddle shapes all nested together. The best visual model might be the crochet model made by Daina Taimina. Of course, all of these models are incomplete: the actual hyperbolic plane extends out forever but gets totally curled up on itself when you try to embed it into regular 3-dimensional space.

And yes, before you ask, I do get paid for this.

Steven Pinker here suggests a development that was all but inevitable at the nexus between cognitive science and evolutionary biology, that is the erosion of the distinction between “intentional” and “non-intentional” processes in organisms. Intentionality is usually attributed solely to the conscious operations of the human mind, or perhaps to a few other animals with large brains. Hence, emotions and intents are usually taken to be attributes solely of minds like that, and phrases like “the selfish gene” to be strictly metaphorical. But Pinker suggests that, since what we know scientifically of the mind suggests that it is merely a particularly elaborate mechanism of biological properties, there is no reason in principle to suppose that there is some fundamental division between the way that, for example, genetic coding works and the way that neurons in the brain function, and hence that one might be able to apply at least the concepts of intentionality and intelligence to the one in the same way (if not to the same degree) that we can to the other.

Obviously, we don’t know nearly enough about how the mind works to know whether it really is just a physical biological system like any other, or if there really is some distinctive “spiritual” property that gives it intentionality and intelligence that other organic systems do not possess. And it must be said that in a sense in order to study it scientists have to assume that it is essentially a physical system like any other, since that is what science studies. But it does represent a refreshing turn away from philosophers like Mary Midgley who announce a priori that “genes cannot be selfish or unselfish, any more than atoms can be jealous, elephants abstract or biscuits teleological” as if it were a simple category mistake. Those people are extremely irritating, because instead of questioning whether intelligence and intentionality are exclusive to human minds or whether they can manifest themselves in other forms they simply presuppose them to exclusively human mental qualities as part of the definition. Cognitive scientists like Pinker are at least questioning these boundaries. And although it is often assumed that intentionality can only arise from the mind as a whole, the idea that it might exist in individual components of an organism’s physiology receives indirect support from the recent work of the great Robert Trivers, who suggests that the genome does not always work as a harmonious whole, that genetic elements sometimes aggrandize themselves and increase their chances of reproduction at the expense of others. In other words, orgnanisms are perhaps not unitary and indivisible from an evolutionary perspective, so perhaps intelligence likewise does not arise from a a single cohesive source. Perhaps particular intentions arise from one of the many possibly conflicting biological sub-systems. In any case, it is pretty evident that elements even at the molecular rules conform to rational rules of behavior and accomplish rational goals, so whether or not we wish to attribute “mentalistic” attributes to them there seems to be a continuity in objective output between microscopic and macroscopic systems in organisms.