Understanding the universe is a universal (if you’ll forgive the term) human desire. This is the attraction of science, natural theology, and much of philosophy — as well as pseudoscience. As I mentioned in a previous post, I read The Language God Talks by Herman Wouk last fall. The book covers a lot of ground for its small size, but the central focus is on a set of conversations, real and imagined, between the author and Richard Feynman, the Nobel-winning theoretical physicist. They have similar cultural backgrounds, both being Jewish New Yorkers whose families immigrated from Russia, but while Feynman was an atheist and famously had little patience for religion or literature, Wouk remains intensely interested in the Talmud and remains faithful to his Orthodox roots.
“The language God talks” is the phrase Feynman used to refer to encourage Wouk to learn calculus. Calculus, of course, is the branch of mathematics that deals (in general terms) with rates of change — differential calculus — and accumulation — integral calculus. For example, speed and acceleration are rates of change (“derivatives”): speed is how much distance something is traveling in a given amount of time, and acceleration is how much the speed changes with time. Energy is an accumulation (“integral”): think about how much effort it takes to push a sofa across a carpet, and how the farther you push it, the more effort you expend. Modern science is full of calculus, to the extent where most aspiring scientists take at least one calculus class in high school or college. Theoretical physicists (which I am, and which Feynman was) especially require a lot of calculus of particularly advanced sorts with mind-bending names like “multivariable calculus”, “differential equations”, and the like.
Feynman was likely also referring to a famous quote from Galileo:
Philosophy is written in this grand book — I mean the universe — which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering about in a dark labyrinth. (from The Assayer, 1623)
(Aside: I find it interesting that Feynman the atheist evokes God, while Galileo the devout Catholic doesn’t.)
I definitely can’t disagree with Galileo or Feynman here: while you can go a long way towards understanding science without getting into the math, you will reach a limit if you wish to actually make testable statements about the functioning of the universe. However, I think this is also where many people become daunted in their path towards understanding: math carries a stigma in our culture, which Wouk does address in passing in his book. The allure of the shortcut to enlightenment leads people away from the “hard” path, the path of real science, into pseudoscience, crackpottery, and perhaps even to a rejection of science itself.
On the other hand, I don’t think one needs to be a scientist or mathematician to love science and to understand the universe up to a certain point. The perennial popularity of books by scientists intended for a general audience shows how interested non-scientists are. One bone I have to pick with Feynman is his frequent impatience with people who want to learn about science but don’t have the time, motivation, or whatever to actually get into the math. I think it’s worthwhile to explain science, even the tricky bits, in language at a slight remove from what professionals use to talk to each other. Although I think it would be nice if everyone learned a little bit of calculus (and it would certainly make my job easier at times!), I don’t want that to be a road block in the path to general scientific literacy.
Part of my motivation for musing on this topic is that I’m thinking of directions to take this blog, now that the class “Science Vs. Pseudoscience” is at an end. I’m not going to stop writing about pseudoscience, but I think I want to write more about science itself: how it works, its importance to a literate society, and just interesting topics in general. (Also, if this post is rambling, I blame being hopped up on medication to treat the nasty infection I’ve got.) I think by broadening the intent of the blog, I will find more to write about and hopefully update more often, but also I hope it will be more interesting to others.