Lauri Kettunen
Well-known member
Do you think some extraterrestrial intelligent lifeform doesn't discover the same mathematics as we do?
If I had to speculate I would say, probably yes. But still, this just means if there were somebody in Mars pointing his finger to the sun, his and our fingers just pointed to the same star.
Perhaps I should confess that I've spent forty years of my life studying like mad mathematical physics, especially electromagnetic theory and modern mathematics. So, this question is precisely something I've also discussed with some of the very best people in the world.
It's very difficult to say which one comes first mathematics or physics. My own explanation is, physics relies on the observation that there are phenomena which appear always the same way under the same conditions. That is, these phenomena appear in a logical manner. Mathematics, in turn, condense this logic into a framework --or language, if you like-- which does not rely in any instances. In other words, mathematics is free of examples. Say, take two stones or RED cameras and bring in another three to get five stones or RED cameras, respectively. In mathematics one says this by stating 2+3=5 without a reference to any instance. But, what we call number two, three or five, i.e., the natural numbers, is still a man made construction from the notion of set, empty set, and successor set. This boils down to the so called Peano Axioms. (If you want to know more, suggest to read Halmos: Naive Set Theory, Springer-Verlag or see a quick explanation at http://mathworld.wolfram.com/PeanosAxioms.html.) My guess is some "extraterrestrial intelligent lifeform" would phrase natural numbers pretty much the same way.
Getting back to Shawn's question a thought came into mind. When I saw the first episods of BBC Planet Earth series I found them totally amazing and was hit by the beauty of the images. But then, after seeing four or fives episods did not anymore find the rest as beautiful, for they repeated the same structure and pattern as the earlier ones. However, technically the last episods are as wonderful as the first ones. So, at least in my case, when I get the impression of beauty, there is a flavour or aspect of novelity. There's probably a lot of beautiful things around us we just do not realize as we are so used to them that we are no longer able to feel the beauty.
In fact, I'm rather grateful to Shawn raising the question. For, once I'll get my RED camera, will start to work with a new three year wildlife document project. The more I've processed on Shawn's question the more clear it has become that we have to seek very seriously for a new view surprising the audience.