Quote of the Week: The utterly unspeakable is utterly irrelevant

[gusl]

from http://www.livejournal.com/users/fare/40458.html?#cutid1

The utterly unspeakable is utterly irrelevant. But to be fair, it seems that DCD is unable to articulate it either, though he doesn't contradict it. Determinism is irrelevant to the nature of the universe, because it is a feature of models of our universe that isn't intrinsic to the universe itself. We can know the universe but through interaction. Any modelling in terms of something lower-level than interaction is but a matter of convenience for symbol-manipulation; it doesn't reflect the structure of the universe, but provides a tool for the mind to manipulate more easily; if it reflects the structure of anything, it is the structure of the minds that build the models.

For instance, mathematicians wondered for a long time whether the the continuum hypothesis was true. Well, they found out that the hypothesis was irrelevant to most mathematics. It's a feature of particular set theoretical models of mathematics, that some may possess, that some may not possess, and that may even be undefined in other models. We can build all the usual structures of higher mathematics without relying on the continuum hypothesis, and we can even build all of them without resorting to set theory at all. For instance, we can build mathematics on top of such a formalism as category theory, where the CH doesn't even have a meaning. My dad, a mathematician bent on the aesthetics of plane geometry, taught me the meta-level concept of intrinsicness of a mathematical concept: alignment is intrinsic to the projective geometry, but not the choice of the hyperplane at infinity; the origin is not intrinsic to an affine plane, but to an arbitrary coordinate system chosen on it; distance is intrinsic in euclidian geometry but not in affine geometry, etc. What matters in a mathematical structure is its intrinsic properties. Sometimes, it is easier to explore a structure and to prove intrinsic properties of it by introducing arbitrary intermediate objects such as a coordinate system and a metrics; but these intermediate objects are features of the demonstration and are not intrinsic to the structure being explored.

This justifies my views that:
* if you can't write it down, you don't really understand it.
* mathematical truth only makes sense relative to a model, to be chosen for its *usefulness* or its correspondence to our intuition.