Math: from Anxiety to Hostility

There’s a dustup happening between science writer John Horgan and several popular authors in the Skeptical (with a capital-S) community. Horgan’s arguments are pretty dull, but one point caught my eye: he argues that grand cosmological theories are pseudoscience, no better than psychoanalysis or transhumanism. The alleged reason is because they are “untestable.” But lurking beneath this inch-deep argument is an implied hostility to mathematical theory. Math hostility is extremely widespread, even among scientists and engineers. I think it’s a form of xenophobia; people fear what they don’t understand.

But here’s the thing: mathematical theories are built for the sole purpose of thinking precisely and avoiding contradictions. If you believe a set of physical laws are true, then you have to accept the mathematical system that is built from those laws; otherwise you commit a contradiction. In some cases, as with string theory, it may be necessary to insert some untested propositions in order to complete the theory’s mathematical structure (disclaimer: I’m no string theorist, but I’ll do my best with what I’ve gleaned about it from popular literature). By doing this, a hypothesis is born. It’s not arbitrary — it’s constrained by the mathematics inherited from known physical laws. If you can’t think of any way to test the hypothesis, that’s no reason to stop working on it. This is what we call “reasoning”, you keep doing the math until you figure out some way to test it.

That’s what science is: thinking really hard about the world, devising explanations that help us understand things, expunging contradictions, and (where possible) connecting independent lines of evidence. Folks like Horgan tend to get stuck on simplified explanations of science, like the falsifiability criterion, and mistake those explanations for prescriptive rules of “the game”. But the practice of science is a phenomenon, and the falsifiability criterion is just one of many post hoc theories developed to explain that phenomenon. Like a lot of science spectators, Horgan doesn’t get that. He looks at sophisticated modern theories and says something I’ve seen many times before:

Some string and multiverse true believers, like Sean Carroll, have argued that falsifiability should be discarded as a method for distinguishing science from pseudo-science. You’re losing the game, so you try to change the rules.

I’m tempted to codify this phrasing and name it the “Crank’s Gambit”: the claim that a well established branch of science has gone rogue, has abandoned the true principles of scientific method, and now they want to retroactively change definitions in order to cover up their fraud. This pattern of argument is well represented among science deniers; I recently addressed it in my response to “memristor skeptics” in my own research field.

Apparently Horgan has held this view for a long time. Krauss (quoted by Coyne) describes the gist of Horgan’s book, the End of Science, as

John Horgan was a respected science writer years ago up until he wrote a book entitled The End of Science, which essentially argued that much of physics had departed from its noble traditions and now had ventured off into esoterica which had no relevance to the real world, and would result in no new important discoveries—of course, this was before the discovery of an accelerating universe, the Higgs Boson, and the recent exciting discovery of gravitational waves!

That description, “esoterica with no relevance to the real world,” is the most common complaint against highly abstract or mathematical theories. It echoes the sentiment from one comment made on my memristor post: “Who the hell is still believing that the ‘memristor’ – the so-called fourth basic component of electronic circuits – exists in physical reality? …the ‘memristor’ is nothing else but a mathematical curiosity.” These comments betray an underlying suspicion that mathematics cannot describe the real world. In my previous post I quoted Tesla, who said something similar in reaction to general relativity:

Today’s scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality…. The scientists of today think deeply instead of clearly. One must be sane to think clearly, but one can think deeply and be quite insane.

For the past week I’ve been at a conference where mathematicians mingle with circuit engineers, and several conversations have turned toward the deep seated mistrust of mathematics that we encounter in our own professional fields. There are many who genuinely believe that if you aren’t building and measuring something, then what you are doing is fake. But this view is so dysfunctional. For one thing, it’s often prohibitively expensive to build and measure interesting things. For another thing, it’s impossible to know what would be interesting to build and measure, unless you’ve invested a lot of rigorous thought beforehand. That’s what theory is for. As for those who are so skeptical of it, my best guess is that they simply don’t get the math, and they resent what they don’t understand.

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