Answering the question “what does a physicist do?” can be difficult.  Even the much more modest question “what do you do?” is pretty hard.  Over the course of my relatively brief physics theory career, I have studied sonar, traffic patterns, cloud formation, parasite epidemics, low-temperature magnetic structures, and the electrical properties of DNA, to name a few things.  These topics have seemingly nothing in common, but they represent only a small sampling of the kinds of research you could find in the physics theory department of any major university.

And really, these subjects don’t have much in common.  But that’s okay, because physics theory isn’t really a topic.  It’s more of an approach, or a set of strategies for problem solving.  Someone trained in physics theory is not valuable because they have learned a lot of useful information, but because they have acquired a way of reasoning that is useful for solving complicated problems.

Acquiring new ways of thinking is what physics theory is all about.  In this post I want to illustrate the value of a “physics theory approach” to a problem by discussing an example where reasoning without it can get you a very wrong answer.

Not long ago I read Matt Ridley’s The Red Queen: Sex and the Evolution of Human Nature.  It was a very interesting book, full of complex and important ideas.  But in my mind too many of its conclusions were based on “common sense”; which can be a dangerous thing.  An idea that seems correct often is, but is certainly not guaranteed to be.  There are plenty of strange and counterintuitive phenomena out there, and their explanations cannot be rooted out by common sense.  Sorting strange fact from sensible fiction takes quantitative reasoning, and that’s what physics theory was designed for.

Somewhere around the fourth chapter of The Red Queen, the author starts talking about factors that can influence the gender of an unborn child.  During the course of his discussion, the author mentions that “merely by ceasing to breed once they have a boy … people would have male-biased sex ratios at birth.”  At first sight, the idea seems sensible.  After all, if every couple decided to stop having children once they had a boy, then every family would have at least one male child and maybe the result would be a male-biased gender distribution.  But on second thought, maybe the opposite should happen.  If everyone keeps having children until they have a boy, then you could have families with 9 girls and only one boy.  They should bias the gender distribution in the other direction, right?  So which is it?  Will a society produce more boys than girls simply by considering them to be more valuable?

To construct an argument that could be physicist-approved, we need to come up with a quantitative prediction for how many boys and girls would result from a society where couples have children until they have a boy, and then stop.  Let’s enumerate all the possibilities.  For a given couple, the sequence of their children could be {boy}, or {girl, boy}, or {girl, girl, boy}, or {girl, girl, girl, boy}, … and so on.  What is the probability for each of these sequences?  The probability for a given child to be either a girl or a boy is 50% (or 1/2).  So the probability of the outcome {boy} is 1/2.  The probability of the outcome {girl, boy} is 1/2 * 1/2 = 1/4.  For {girl, girl, boy} it’s 1/2 * 1/2 * 1/2 = 1/8 (or 12.5%).  And, in general, the outcome with n children has the probability .  We can make a diagram of all possible outcomes that looks something like this:

A diagram of possibilities for a couple's children. Bottom (blue) paths represent a male child, which ends the sequence of children. Top (pink) paths represent a female child, which cause the couple to continue having children. Each blue line has a percentage indicating the likelihood of that sequence.

Every couple will have one boy.  But how many girls, on average, will they have?  Well, according to our chart, there’s a 50% chance they will have no girls, a 25% chance they will have one girl, a 12.5% chance that they will have two girls, and so on.  Summing all possible outcomes gives

(average number of girls per family) =

You can plug the first eight terms or so into your calculator to get a good approximation to the answer, or you can remember what you learned about infinite series from calculus.  Either way, the answer is exactly one.  That is, nothing happens to the gender distribution: on average, every family has one girl and one boy.

If you think this was a fun problem, you can try to see what happens when you modify the “child birth rules” a little bit.  For example, maybe every couple stops either when they have their first boy or when they have 5 children total.  Or if every family keeps having children until they have two boys (the “tree” of possibilities is a little more complicated here, but you can still draw it out).  You’ll find that nothing changes the inevitable: your cultural values have no effect on the ratio of male to female babies.

This answer seems obvious in hindsight, but it really wasn’t.  We needed quantitative reasoning to be our King Solomon, judging between a number of different sensible arguments.  Of course, I’m not saying that non-quantitative arguments are never valuable or correct; they very frequently are.  It’s just that physics theory has trained me not to trust them.

And in case you’re wondering, yes, I did have the audacity to contact Matt Ridley and inform him of the error in his book.