Sunday, November 01, 2015

Holiday's read - DFW - Everything and more

I am ambivalent towards David Foster Wallace. He can write the most creative sentences and make innocuous subjects very interesting. At the same time, i never finished his book Infinite Jest, partly because the characters names are too awkward for me so that i never exactly remember who is who, but also because the story itself is a bit too crazy.
I knew however that a non fiction book on the subject of infinity written by him would make for a very interesting read. And I have not been disappointed. It's in between maths and philosophy going back to the Greeks up to Gödel through a lot of Cantor following more or less the historical chronology.
Most of it is easy to read and follow, except the last part around sets and transfinite numbers. This last part is actually quite significant as it tries to explain why we still have no satisfying theory around the problems raised by infinity especially in the context of a Sets theory. I did not expect to learn much around the subject, I was disappointed. The book showed me how naive I was and how tricky the concept of infinity can be.
While I found the different explanations around Zeno's paradox of the arrow very clever, there is one other view possible: the arrow really does not move at each instant (you could think of those as a snapshot) but an interval of time is just not a simple succession of instants. This is not so far of Aristotle attack, but the key here is around what is an interval really. DFW suggests slightly this interpretation as well p144 but it's not very explicit.
I had not heard about Kronecker's conception that only integers were mathematically real (against decimals, irrationals, infinite sets). I find it very appropriate in the frame of computer science. Everything ends up as finite integers (a binary representation) and we are always confronted to the process of transforming the continuous, that despite all its conceptual issues is often simpler to reason in to solve concrete problems, to the finite discrete.

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