Natural ChemE » November 12th, 2015, 2:27 am wrote:someguy1,

I'm curious about your outlook on what's interesting/used/etc. Basically I feel like you're dismissing the tools that we currently use in applied fields based on their obscurity in non-applied fields, which seems very strange to me.

Hypothetically, say that engineers were using mathematics effectively unreproducible in terms of the systems that you're talking about. Say that human progress is advanced by progress in these tools unknown to non-applied mathematicians. In this hypothetical case, would you be interested in such tools, or would their obscurity within non-applied fields continue to cause them to be disinteresting to you?

I've drawn the distinction among the formal hyperreals as defined in math, the informal infinitesimals used by physicists, and the non-infinitesimal mathematical theory of limits. I didn't say physics was wrong or bad in any way; on the contrary, I said it was perfectly normal because physicists are interested in studying the universe, and not so much in the fine points of logical rigor. Was that not a satisfactory description of the situation?

Where did I dismiss anything? On the contrary. I pointed out that physicists regard mathematicians as excessively devoted to logical purity at the expense of studying the world. Did I not say that? Did you not read it? Did you read it and think I said something else?

I specifically made the point that math sometimes leads physics; and that physics sometimes leads math. Or maybe I lost that point in some edit. I'm perfectly aware of it. Sometimes the nonrigorous tools of physics prove valuable. Newton's calculus was one such example. Normalization is another.

Where did I dismiss anything?