Last time I wrote about the distinction between so-called ‘pure’ and ‘applied’ mathematics. I figured that someone would have written a “mathematical apology” for applied mathematics, but I was a little surprised that the most cursory of internet searches revealed three such documents, here, here, and here.
So many copies floating around… shoot!
This time, I wanted to take the distinction a little further, or make it broader, or narrower… well, whatever it is that I am doing now, that is what I wanted to do. Why not talk about the differences between work in mathematics and work in the lab-based sciences? Oh, sure, one could look at the differences between work in mathematics and work on cybernetic organisms or poetry, or anything you like, but for fields such as physics and chemistry, which are heavily reliant on mathematics, the differences in work structure are stark.
For one, there is no laboratory in mathematics. As leading sentences go, this will do as well as any other, and, in the style of all leading sentences, at least part of it is incorrect. There is a lab for mathematics, I suppose: I do ‘experiments’ on a sheet of paper, or on the blackboard. I want to show that this sequence converges, so I ‘hypothesise’ that is does, and then try to remember some test for uniform convergence, and which is the sanest choice to make.
I then get confused with dominated convergence, what a Lebesgue integral even is, and soon forget who I am, what I am doing, and where I have put my socks. True story! I then convince myself that the thingy (whatever it was… a sequence? Could be!) converges, and my ‘experiment’ is a success.
But this is a bogus link, more bogus than you could come to expect from a Trudgian post. For our colleagues in the lab sciences, they have to be in the lab for hours at a time. They have to spend hours and hours poring over data. They have to come in on a Saturday if the pump for the liquid beryllium (who knows: that could be a real thing!) was being repaired on Friday. They have to stick around till 7pm if the system was down earlier in the arvo. That’s a lot of extra hours at the workplace. They don’t get much of a choice in it.
The next time we, as mathematicians, get stuck because we realise there is an error in our proof, we will be frustrated, sure, but we can take solace in the fact that we can down tools now, come back tomorrow, and have another go. We may even call in to our colleagues down the hall and invite ‘em out for a drink after they’ve finished in their proper lab. We don’t need to stay in at the office past home time, since our equations will look after themselves overnight. This point is sometimes missed by people who should know better, and I hope to talk about this more next time.