Monday, January 30, 2012

Is Math in the Universe?

Is Math in the Universe? Or just in humankind’s minds?
Why is mathematics so effective in physics and engineering? Is math really “in the world”, in some sense, or is it just some peculiarly human way of interpreting things? It seems that physicists in particular are divided on this issue. Stephen Hawking has asked the celebrated question, “What is it that breathes the fire into the equations?”, which would seem to imply that he believes that “the universe knows about math”.
The great physicist Eugene Wigner wrote an oft cited essay, "The Unreasonable effectiveness of Mathematics in the Natural Sciences” , which, if not explicitly suggesting that the universe is built on our math, at least suggests that there may be some deep connection between the two.
A great many of my science colleagues, though, have maintained the opposite--namely, that the math models of the world are purely human inventions, and the equations really just represent the way our minds work, and that nature knows nothing about these equations.
I realize the very question I am asking may be naive, and it is difficult to even frame the issue in a rigorous manner. But I have to confess that I like the idea that the equations do have some real connection with the way the world is, and that they are more than just some human-centered version of reality. For one thing, such entities as electrons, quarks, and so forth are so deeply nested in the mathematical constructs of physics, and these constructs seem to be so highly consistent, and work so well in explaining and predicting events on the micro scale, that it just seems like nature must “know” something about them.