From Orthodoxy by G. K. Chesterton:
The real trouble with this world of ours is not that is an unreasonable world, nor even that is a reasonable one. The commonest kind of trouble is that is nearly reasonable, but not quite. Life is not an illogicality; yet it is a trap for logicians. It looks just a little more mathematical and regular than it is; its exactitude is obvious, but its inexactitude is hidden; its wildness lies in wait.
7 thoughts on “The world looks more mathematical than it is”
As Douglas Adams wrote in “The Restaurant at the End of the Universe”:
There is a theory which states that if ever anybody discovers exactly what the Universe is for and why it is here, it will instantly disappear and be replaced by something even more bizarre and inexplicable. There is another theory which states that this has already happened.
Chesterton’s quote goes a long way in explaining our tendency to underestimate “black swan” events. (>>but its inexactitude is hidden)
It is also adds reason to look skeptically on knowledge obtained through “simulation”, or at least to review the methodology of the simulation in very great detail.
I agree with Gene: Simulation is a great tool for checking that a method does what it is designed to do, but doesn’t tell us much about the world we are simulating.
Oh, I dunno. Maybe I’m actually an unabashed Platonist. I know what I’m not. I’m not a mathematical Maoist, nor a formalist, nor a constructivist. I use these terms as described in Davis and Hersh, The Mathematical Experience.Maybe someday I’ll write a blog entry titled “The world is more mathematical than it looks.”
ekzept: Your comment about math philosophy reminds me of a line that was said of Malcolm Muggeridge: “He knew what he disbelieved long before he knew what he believed.”
This seems more like a problem of using either too small a chalkboard (need 10^?? equations in 10^?? dimensions to model the economy of a small town), the wrong kind of computer (brain which is better at intuition than computations), or too specific of mathematics.
Just as a for-instance, say I want to figure out how opening various combinations of windows will aereate my house. This is indisputably mathematical but fluid computations would be impractical.
I don’t know enough to say exactly, but I bet some abstract math like http://www.johndcook.com/blog/2010/09/13/applied-topology-and-dante-an-interview-with-robert-ghrist/ could help sort it out in a practical time frame