Finance, Mathematics, Software

My wife and I spent a glorious day with our friends on July 4th. It was a potluck with the theme of typical American food, but almost everyone was born somewhere else. My potato salad didn’t go over so well, mustard was a must in my upbringing in the South, but my baked beans with bbq pork was a hit with the meatatarians.

Usually we watch the fireworks from our deck in Brooklyn if they are being exploded somewhere around the Brooklyn bridge, but this year Macy’s shot the works over the Hudson instead of the East River. The last time they did that was 400 years ago, or something like that.

Our friends live next to Battery Park which juts out a bit into the Hudson, but the local papers claimed it would be closed. Fortunately it was not. It was a perfect spot to view the fireworks with old friends and young kids on a global warming defying day. My friend’s wife is an artist that suggested, after we retired post fireworks, and a few gin gimlets, that mathematics could explain the world.

Silly artists. Actually, she’s not silly at all. She has a PhD in philosophy and is a very talented artist. One of her paintings showed up on the cover of Best American Short Stories 2008. Somehow. But that is a different story.

Her claim was far from the truth, and only mathematics can make a real claim at describing truth. I was at a loss at where to start. I suggested mathematics does not really have much to say about a statement like “‘I have a Love I love too well; Where Dunkery frowns on Exon Moor.”

One funny thing about math is that even though it deals with absolute truth, it is very difficult not to lie when describing mathematics in short sentences. I’m going to do that now. Mathematics deals only with sentences that are either true or false. These are called propositions. The good/bad thing about this is that only a handful of words that we all use in the real world are needed: ‘not’, ‘and’, ‘or’, ‘implies’ to make new propostions. And even these are redundant. One of my hobbies is Category Theory. One branch of it attempts to provide a new foundation for mathematics. 

My friend was on to something, though. One goal of mathematics is to increase the scope of what human beings can think rigourously about. Category Theory seems to be the latest attempt silly humans are making at that. How can Horner’s Rule for reducing the number of multiplications in evaluating a polynomial expression be an intial object in a category? According to Richard Bird and Oege de Moor in ‘Algebra of Programming’, it is.

My current subway reading is ‘First-Order Logic” by Raymond Smullyan. His tableau method beats the heck out of the axioms combined with modus ponens proofs I had to do in my first course in mathematical logic. I must have learned this at one point, but I forgot that Godel proved first order logic is both complete and consistent.

Maybe that makes it even more amazing he derailed David Hilbert’s program by showing how if you add enough axioms to do simple arithmetic that you can no longer prove those rules are consistent.