Suppose I said, “I have this clock that I really like. It’s a very nice clock. So, I am going to measure everything I can in terms of the times registered on this clock.”
“OK,” you might say, while wondering what the big deal is.
“In fact, I am going to measure all speeds as the time it takes to travel a standard unit of distance.”
“Uh, hold on.”
“And this means that, contrary to what you learned in Big University, zero is not a speed! Because the right way to think of speed is the time it takes to travel 1 standard distance unit, and an object that never moves never travels.”
Now, you might try to argue with me. You could try to point out all the things that my screwy definition would break. (For starters, I am throwing out everything science has learned about inertia.) You could try showing examples where scientists I have praised, like Feynman or whoever, speak of “a speed equal to zero”. When all that goes nowhere and I dig in further with every reply, you might justifiably conclude that I am high on my own supply, in love with my own status as an iconoclast. Because that is my real motivation, neither equations nor expertise will sway me.
Yes, it’s time for another installment in my occasional series, Friends Don’t Let Friends Learn Topic X from Eliezer Yudkowsky. For those who don’t know, Yudkowsky is an autodidact and fanfiction writer who, like E. L. James, portrays insufferable characters as admirable and thereby gives the whole medium a bad name. Unlike James, he also fills his work with bad science. Because he scratches an emotional itch for people enamored of the idea that they are above emotion, he has become influential in circles you would rather avoid.
Among many other things that Yudkowsky has famously attempted to explain is the concept of probability. The bit I want to zoom in upon today is the time that he argued that 0 and 1 are not probabilities. He grounds this headscratcher in the statement that you can’t turn a probability of 1 into a ratio by the function $f(p) = p/(1-p)$, because you’d be dividing by 0. This and everything that followed is just getting high off his own supply. One could try showing how he presumes his own conclusion. One could try showing how he breaks the basic idea that probabilities by their nature add up to 100% (given an event E, what can Yudkowsky say is the probability of the event E-or-not-E?). One could even observe that the same E. T. Jaynes he praises in that blog post uses 1 as a probability, for example in Chapter 2 of Probability Theory: The Logic of Science (Cambridge University Press, 2003). If you really want to cite someone he admires, you could note that Eliezer Yudkowsky uses 1 as a probability when trying (and failing) to explain quantum mechanics, because he writes probability amplitudes of absolute value 1.
As an academic, I have to hold myself back from developing all those themes and more. But the additional wrongness that comes in when he turns to quantum mechanics is worth pausing to comment upon.
Yudkowsky loves to go on about how the map is not the territory, to the extent that his fandom thinks he coined the phrase, but he is remarkably terrible at understanding which is which. Or, to be a little more precise, he is actively uninterested in appreciating that the question of what to file under “map” versus “territory” is one of the big questions that separate the different interpretations of quantum mechanics. He has his desired answer, and he argues for it by assertion.
He’s also just ignorant about the math. Stepping back from the details of what he gets wrong, there are bigger-picture problems. For example, he points to a complex number and says that it can’t be a probability because it’s complex. True, but so what? The Fourier transform of a sequence of real numbers will generally have complex values. Just because one way of expressing information uses complex numbers doesn’t mean that every perspective on the problem has to. And, in fact, what he tries to do with two complex numbers — one amplitude for each path in an interferometer — you can actually do with three real numbers. They can even be probabilities, say, the probability of getting the “yes” outcome in each of three yes/no measurements. The quantumness comes in when you consider how the probabilities assigned to the outcomes of different experiments all fit together. If probabilities are, as Yudkowsky wants, always part of the “map”, and a wavefunction is mathematically equivalent to a set of probabilities satisfying some constraint, then a wavefunction belongs in the “map”, too. You can of course argue that some probabilities are “territory”; that’s an argument which smart people have been having back and forth for decades. But that’s not what Yudkowsky does. Instead, through a flavor swirl of malice and incompetence, he ends up being too much a hypocrite to “steelman” the many other narratives about quantum mechanics.