The Importance of Data

An interesting switch has occurred in my thinking about the world. It’s difficult to determine whether this switch was caused by my work that is the subject of this blog, or whether the influence was the other way around, or whether the timing is just coincidental. Over the last few years I have made the switch from a person that thinks about things exclusively in the abstract to a person that considers all such thinking as a “model”, to be verified or refuted by “data”. I am using these words in a very fuzzy sense. Any ideology of any kind can be considered a model, though I grant that these “models” can also affect the real world through human behavior. Nevertheless, there is a certain simplification of the world inherent in any ideology, and this leads me to the claim that any ideology will fail to be sufficient for the sum of all human needs and experiences. All ideas should be held up to “data”, and constantly checked and tested against all experience. This isn’t a new claim, and is reminiscent of “logical positivism”, whatever that means. Philosophers will rail against the inconsistency inherent in this claim, since it isn’t really self-supporting, but I don’t care. For me this is the most pragmatic way to live.

Returning to the theme of the blog, I’m coming to the conclusion that this might be a possible division between “pure” and “applied” mathematics. Logical constructs can be, in and of themselves, elegant and beautiful. But logic for its own sake doesn’t really interest me, because there’s no “data” to hold it up to. It’s a model of itself, and nothing else. It doesn’t deal with questions about things observable, and so is in some sense a “game”. I don’t in any way suggest that these problems lack value. For many mathematicians, they are the most interesting. I am only trying to define my own interests and motivations. There’s no judgement inherent in my discussion. I value things that are tangible, testable, observable. Others value things that are beyond the tangible. The world is large enough for both groups, surely.