The fourth installment in the series The Power of Thought on the topic The Philosophy of Mathematics (the show is hosted by my colleague at Roskilde U. Vincent F. Hendricks) begins for me, per se, with the ending – with Hendricks’s announcement of the next week’s topic: on aesthetics. At that point I was already half way to heaven swooning over the beauty of all those ideas that have to do with notions such as infinity, the geometry of circles and spheres, and sensible skepticism that situates itself between reality and fiction.

Depending on the dominant discourse of each age marked by some sort of enlightenment, one tends to go with the swing of the pendulum either towards the one or the other side. This was emphasized equally beautifully by my other colleague at Roskilde U, Stig Andur Pedersen, called in to initiate us in some of these matters. He did a good job. His talk and examples of different worlds and dimensions – and how it’s difficult for us to stick our heads out of the dimension and world we find ourselves in, and perhaps test parallel worlds by observing them from our own vantage point – trigger the part of the imagination that has to do with pure beauty. While I intend to watch the next week’s installment, I can, however, already declare that on the question of aesthetics I’ve already gotten what I want.

Along this line, yet on a more concrete level, towards the end of the show I couldn’t help making the analogy between infinity and Vincent’s interminably long legs, all dressed in black. Good choice. Step into the black to paint infinity on cloth. This latter observation, it occurs to me, stems from the fact that what I imagine about math comes from an angle that is definitely not the manifestation of any formal training. For me, numbers that run off to form complex equations are pictures of juxtaposing different numerical textures that we find particularly in Judaic philosophy. The Kabbalists, for instance, were known to invent one baloney idea after the other about the uncertainty of numbers in relation to infinity by making recourse to fabrics. When Andur mentions the interesting dilemma regarding the container/contained dichotomy, his illustration of two sacks, one containing an infinite number of objects, the other empty but ready to be filled with some of these objects, I think, silk sack or linen sack? – that is, before I think of the problem that arises if we want to do a ‘complete’ job, alas, only to discover that we can never finish either emptying or filling the containers. On another plane, I think there is something reassuring about Andur’s potential reaction to my associations, had I been one of his pupils: ‘ignorance, my dear, is bliss.’ Especially when it’s well dressed.

What I liked about this particular show is the fact it threw the uninitiated in the philosophy of mathematics right into the core of what is most interesting: the question of uncertainty. Hendricks started with his specialty: a quote regarding the relation of philosophy to mathematics: in philosophy we have aims that don’t have rules; in mathematics we have rules that don’t have aims. So we shoot aimlessly but think about the act in formal terms. Grammars of creation. The philosophy of mathematics is thus the philosophy of the impossible in the possible, and the possible in the impossible.

For those in need of scenarios, choreographies, and costumes, the good news about imagining abstract situations is that they always relate to some concrete reality. We make analogies between dreams and numbers. Take my meeting the other day with my bank manager. While he was trying to explain to me alternatives for a major loan for the beautiful apartment I’ve just bought outside the university – so I can be closer to the universe, obviously – all I could think and dream about was the probability of winning the lottery and hence pay with cash for my extravaganza. I said to myself that that event is probably as likely as my figuring out Riemann’s hypothesis. Now, there was an analogy. Since its inception by Bernard Riemann in 1859, mathematicians have been working to find a proof for it. Riemann’s hypothesis seeks to explain where every single prime number to infinity will occur. Karl Sabbagh’s book Dr Riemann’s Zeros (2003) explains also by anecdote how the ‘simplicity’ of a number such as zero has made it into a prize. An American foundation offers 1 million US dollars to the first person to demonstrate that the hypothesis is correct, so the joke is that many mathematicians are now 'stalking' Riemann’s conjecture by trying out different disguises. (See also Dan Rockmore’s Stalking the Riemann Hypothesis (2005)).

I’ll take my cue from Hendricks: keep wearing black, escape down the spiral, and come out on top from the other side, ready to hijack the geometry of money.


Camelia said…
I've just got a mail from Karl Sabbagh praising my cross interdisciplinarity. Nice. It goes to show that there's more to 'stalking' mathematicians. In the blogosphere zeroes must assume the value of odd numbers. Cheers, Karl.
Bent said…
I usually find it very hard to stick my head out of a torus-shaped object, such as a doughnut, esp. if I am in the process of eating it...

I did do it once, however, and heard a similar comparison to the one the programme was making between mathematicians and philosophers:

Why do Dept. Heads love these two types of scholars so much? Well, with the mathematicians it is very easy to fulfil their research needs - you just give them lots of pens and paper, and a wastebasket... With the philosophers it is also very easy - you just give them lots of pens and paper...

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