Quantum babble

Here’s  a recent article from New Scientist about the discovery — creation, actually — of a new kind of particle called the “Majorana fermion” that physicists have supposedly been searching for for 75 years (who knew?!)

I more or less trust New Scientist, so it’s presumably legitimate, but it’s amazingly close to a parody of quantum gobbledegook. I know more than the average person about quantum physics, but I really can’t tell if someone’s pulling my leg here. I could just as well imagine this having been scribed by Stanislaw Lem, and it wouldn’t be entirely out of place as a wonky Spock-Kirk colloquy in Star Trek, explaining how hyperwarp communications or something functions.

What is a Majorana fermion?

It is named for the physicist Ettore Majorana, who found that a particle could be its own antiparticle.

If a particle has properties with values unequal to zero, then its antiparticle has the opposite values. What that means is that all the properties of a Majorana fermion, the charge, energy, what have you, it’s all zero. It is a particle, but it doesn’t have properties that we can measure. That makes it very mysterious. It also makes it difficult to find.

How did you find the Majorana?
We made one. The Majorana comes out of the superposition of an electron and a “hole” – the absence of an electron in a metal. By applying a magnetic field to semiconducting nanowires laid across a superconductor, you can move electrons along these wires, creating two points in space that each mimic half an electron. The electrons go back and forth, so the hole jumps from left to right. If it spends an equal amount of time on each side, then, quantum mechanically, it’s in a superposition of being on the left and right. If it’s stable, then we call it a particle.

I’ve had graduate level courses in relativistic quantum mechanics, but I can’t tell if this is a joke.

Who needs math?

According to a study by sociologist Michael Handel, summarised here by Jordan Weissman, 75% of American workers never use any mathematics more complicated than fractions in their work. (It goes without saying that most partake of recreational calculus, at least on weekends…) Writing in the NY Times last year, Andrew Hacker argued that most schoolchildren are wasting their time learning mathematics: They’ll never understand it, and they won’t be any the worse off for it. As for scientists, the great entomologist E. O. Wilson has recently taken to the pages of the Wall Street Journal to argue that

 exceptional mathematical fluency is required in only a few disciplines, such as particle physics, astrophysics and information theory.

For that matter, even Albert Einstein famously remarked to a schoolgirl correspondent

Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.

But that was after he’d mostly decamped from physics for sagecraft.

Wilson goes on to portray mathematical biologists as technicians, armed with useful tools and useless ideas. And if you need them, you just hire them. (It’s not like they have anything important to do with their time.) So what’s going on? Are mathematicians scamming the public, teaching algebra and other unnecessaries to justify their existence? I would suggest that there are several important issues that these wise men are ignoring or underplaying:

  • It may be true (as Hacker argues) that only a tiny techno-elite actually needs to know how a computer works, or how to compute the trajectory of a spacecraft, or how to program a Bayesian network. But when they’re 11 years old you don’t know who will have the interest or aptitude to join that elite. If you start sieving the children out early because they don’t seem like a likely candidate for that track — and let’s be honest, a lot of the tracking is going to be based on parental status and educational attainment — most of them will have no way to change tracks later on, because of the cumulative nature of mathematical understanding. Worth noting, in this context, is Handel’s observation (cited above) that skilled blue collar jobs are actually slightly more likely to require “advanced maths” (algebra and beyond) than skilled white collar jobs. So you can’t decide who needs the advanced maths based on the kinds of work they’re going into. Those without the education are simply more likely to be stuck at the lower rungs of whatever trade or profession they go into. (On the other hand, a larger fraction of white collar workers are in Handel’s “upper” (skilled) category, so an average blue collar worker probably needs less maths than an average white collar worker.)
  • Mathematics is a language. And what is discussed in that language is, as Hacker recognises, crucial to the fate of everyone in the world. Those who have not learned at least the rudiments of the language are excluded from the conversation. I am reminded of a friend who dismissed the value of learning to speak French, with the argument that “Everyone in France speaks English.” Now, France might have been a bad choice for his claim, but even if it were true, it puts you at a significant disadvantage to be surrounded by people who speak your language, while you can’t decipher their language to understand what it is they’re saying to each other.
  • Think about that Einstein quote: Everyone finds mathematics difficult when they’re pushing beyond their current knowledge. If we’re going to drop mathematics training when it becomes challenging, we might as well stop counting when we run out of fingers and toesies.
  • I would suggest that Wilson may be using more sophisticated mathematics in his work than he is aware. To paraphrase J M Keynes, practical biologists who believe their work to be quite exempt from any need for mathematics, are usually the slaves of some defunct mathematician. Modern biologists of bench and field are often quite attached to some mathematical and statistical machinery that happens to be some years old, and seemed impossibly abstruse when it first seeped in from the pure mathematics or theoretical statistics world. Many of the attempts to apply mathematical techniques in biology (or sociology or economics or whatever) will prove more clever than enlightening, but some will stick, and become part of the basic toolkit that the biologists who think they don’t need any sophisticated math do use. Wilson’s arrogant posture really reflects the fact that there are far more trained mathematicians who are intellectually flexible enough to try and figure out what the biologists are doing, and what the connections might be to their own field, than trained biologists willing to work in the other direction.

Mutually Assured Logical Destruction

or, What Dr. Tortoise said to Prof. Achilles

I remember reading a biologist — I’ve forgotten who it was — remarking that, in comparison to some other fields, arguments in biology rarely turn venomous, because no matter how certain you may be, based on current knowledge, you can expect that within a few years the question will be definitively resolved one way or the other. If you are indeed correct, science will not suffer for your having indulgent your colleague’s error, and neither will your reputation. And you might be wrong. It’s very difficult to hold to absolute confidence in your own beliefs when they concern a matter of fact, and the fact will be revealed. It is a bit like the logic of keeping the peace through nuclear deterrence.

This was most trenchantly put by the great German mathematician David Hilbert, who famously commented on Galileo’s “cowardly” recantation in the face of the Inquisition:

He was not an idiot. Only an idiot could believe that scientific truth needs martyrdom — that may be necessary in religion, but scientific results prove themselves in time.

Continue reading “Mutually Assured Logical Destruction”

Evolution turns political

… followed by arithmetic

There are two general attitudes that a scientifically-minded educated person could take to the resurgence of anti-Darwinian politics in the US over the past few decades. 1) Children deserve to know the truth, as best as careful thinkers have been able to determine it. Parents have no right to withhold the truth. We need to break the cycle of ignorance. Disrespect for standards of science and objective truth in one area will undermine science universally, making it more difficult for our society to benefit, materially and intellectually, from scientific progress. 2) Evolution is a story. It is abstract. It is a belief system that lends itself at least as much to social and political abuse as an fundamentalist sect, so maybe we shouldn’t be pushing it too hard — particularly not when there’s a conflict with parental beliefs and values. There’s plenty of science to learn — even biology — that won’t run up against conflict with home values. Where it’s a problem, let’s leave these abstract matters for when they are older and more qualified to make their own value judgements. (Given the difficulty of US schools recruiting competent science teachers, we might also add the very real harm that is likely to be done by teachers who genuinely don’t understand evolution, teaching corrupted or incomprehensible versions of the key ideas.) Continue reading “Evolution turns political”