ROBERTSÂ How is it possible that Cal Tech’s basketball team was considered better than UCLA’s basketball team in the 1950s? That was the part I was amazed at.
MLODINOW At least the early part of the decade. That was harder to understand than the Girl Named Florida Problem. I think in those days basketball was nothing–imagine saying that the Cal Tech curling team is better than the UCLA curling team. Since nobody really cares about curling it’s just a quaint fact that someone at Cal Tech, probably in the faculty, would care about curling well enough to organize a team. Maybe I’m exaggerating a little bit, but in the 50s I think it was a much different sport and a much different sports world. Not to belittle their team; I think they had some really good players from the looks of it and maybe Cal Tech cared more about recruiting players for sports than they do today. Maybe our world in general is a little looser about things and you could invest the time to play sports more even if you were at a high-powered place like Cal Tech; not to be as pressured–to just study. I guess it was just a different world in some ways–a nice world–back then that could happen. Now college basketball is just a huge and money generating industry that no one would allow a school like Cal Tech–by allow it I don’t mean that there’s some individual disallowing it but the world will not allow, it’s not loose enough to allow, a school that’s not completely focused on that sport to have a good team in that sport. Everything is too high-powered today.
ROBERTS Yes. Of all the things in your book, that was the most staggering.
MLODINOW You should see the movie Quantum Hoops; it’s a documentary about the Cal Tech basketball team. I recommend it.
ROBERTS I didn’t know there was such a movie.
MLODINOW It’s on DVD; I’m thinking it must be available from NetFlix.
ROBERTS Yes, I’ll get it.
MLODINOW It’s very amusing–it is for me because of my connection to Cal Tech–but I think for the general public, it’s a very amusing film.
ROBERTS We were talking about unexpected things. If you looked at the Cal Tech basketball team, if you just looked at basketball in the 1950s, you would think, ’Well, Cal Tech–that’s as it should be.’ But then all of the sudden, 20 years later, it’s so very different.
MLODINOW I think in those days it was more like a club, like a sport, like what you think of as a kids’ fun activity and now the athletes for basketball are heavily recruited and bribed in one way or another, and the huge amounts of money at stake for the school for them. It’s a totally different calculus and it’s sad in a way, isn’t it? I think everything is like that today.
ROBERTS I guess what I’m saying is that there was something–you’re in the 1950s, it’s 1956–very few people saw that there was something hidden in basketball that could lead to what it became.
MLODINOW And if you were the superstar of that time you also didn’t get the rewards of what became today and it’s a little bit late for you now, right? I know in the bathroom in the Cal Tech cafeteria there was a framed article about him, I can’t remember his name, one of the superstars of the 50s who was one of the best basketball players to ever live–I think they claim that even today–who basically probably never even made a living from it, or not a good living.
ROBERTS Yes, that kind of brings us back to the very beginning. I feel like somehow the times have changed and people are smarter. Now you can make a living from what you’re doing. You’re writing this very entertaining intellectual history; finally there’s a market for it. Finally people are smart enough to be at your level so that you can write a book that you respect but you can get a wide enough audience.
MLODINOW Are you saying that in the 50s that couldn’t have been done? I don’t know.
ROBERTS Well, nobody did it; let’s put it that way.
MLODINOW No, nobody did it. I don’t know why.
ROBERTS As I said before we started recording, you’re the first person to ever do this. Will you be the last? I don’t know but you’re the first. You’re the first person to write intellectual histories that actually are popular and that people want to read, that they’re not forced to read by their teachers. It’s not just a tiny group of people reading them. Professors of course write them but they’re not well written and it’s just their job to write them; they get a salary from the government to write those books. You’re not getting any salary. You’re an entrepreneur and it’s just so different. Your books have to be popular or your job goes away. It’s just a different level of competence; your books are just infinitely more accessible, infinitely better than a professor would normally write. A professor is subsidized and that’s what is basically comes down to. Practically everybody who writes about science is subsidized but you’re not.
When the TV show The Simpson came along I would talk about IQ scores in my class and I talk about the fact that they had been rising and so forth. And I say, ’Well you know there is evidence that people are getting smarter and one example is The Simpsons; this is at a higher level than other TV shows that came before it.’ Now maybe that’s not so important, how intelligent is an animated show, but I think what you’re doing is very important and I think it may be a sign of increased intelligence. There’s enough of a market now for what you’re doing. There wasn’t before.
MLODINOW I’m certainly glad that there is and that people appreciate the way I put things.
ROBERTS I’m glad because that means you can do so much more of it.
MLODINOW Yes, and I look forward to that. It’s a great privilege to be able to do that.
ROBERTS When I was a freshman at Cal Tech I was always looking for books like yours but they just didn’t exist. So I ended up reading The New Yorker for my intellectual history. That was very narrow; they never did a good job of covering science. They never talked about geometry or DeMoivre, Laplace, or Gauss. They didn’t cover those people. But those people are important. But you do; finally we have someone. It’s great.
These days, Caltech is the preferred moniker, to distance CIT from Cal Poly.
Interesting on numbers and such.
BTW, a segue back to your Taubes series …
It’s “Do We Really Know What Makes Us Healthy?”, by Gary Taubes, all about the problems built into epidemiological studies, and it’s online at
https://crab.rutgers.edu/~mbravo/prospective.pdf . It’s fourteen pages long, and worth every minute of the time it takes to read it, in my opinion. Here’s one brief sample:
“Smoking and lung cancer is the emblematic success story of chronic-disease epidemiology. But lung cancer was a rare disease before cigarettes became widespread, and the association between smoking and lung cancer was striking: heavy smokers had a 2,000 to 3,000 percent the risk of those who had never smoked. This made smoking a ‘turkey shoot,’ says Greenland of U.C.L.A., compared with the associations epidemiologists have struggled with ever since, which fall into the tens of a percent range. The good news is that such small associations, even if causal, can be considered relatively meaningless for a single individual.”
Taubes devotes a lot of space, usefully, to the problem of “healthy-user bias” — the fact that people “who faithfully engage in activities that are good for them — taking a drug as prescribed, for instance, or eating what they believe is a healthy diet — are fundamentally different from those who don’t.” So, for example, there was the Coronary Drug Project, which found that not only did those who took their prescribed drugs faithfully cut their risk of heart-disease almost by half, this was also true of those who took their placebo faithfully.
Also online is Sue Hughes’ two-page summary of the Taubes article, titled “New York Times Magazine focuses on pitfalls of epidemiological trials,” at
https://www.theheart.org/article/813719.do .
I’m curious about Mlodinow’s teaching style, and also the popularity of his courses at Cal Tech.
I remain in the camp that believes the explanation to this problem is wrong!!!! Here is my analagous problem. Imagine sex is determined by casting a die. Odd is girl, even is boy.
Q: What is the probability that a pair of dice thrown will result in two odd numbers if at least one lands on an odd number?
A: 1/3
Now imagine a 1000-sided die. Let the number 999 represent the name Florida.
Q: What is the probability that a pair of dice thrown will result in two odd numbers if at least one lands on the number 999?
A: 999 / 1999. To see this, draw a table with x = 1 to 1000 on the horizontal axis and y = 1 to 1000 on the vertical axis. Now just count down the column 999 and across the row 999, and add up the outcomes representing the intersection of two odd numbers.
As faces of the die are removed (representing the increasing popularity of the name), the probability slowly approaches the limit 1/3. But of course, no name occurs with frequency 0.5, so any time a name is given, the probability is much closer to 1/2 than it is to 1/3.
This is where Mlodinow went wrong. He explains that the fact that Florida is a rare name is the key to this problem when in fact you get essentially the same result even with the most popular name in the U.S.
Even the most popular names for children occur with a frequency of about 1 in 150 to 1 in 170 (ignoring sex). So let’s say you have a 170-sided die. Even numbers represent boys, odd represent girls, and the number 169 represents the name Emma which was the most popular girls name in the U.S. in 2008. What are the odds that a family with two children has two girls, if one of their children is named Emma. (I’m ignoring the possibility of boys named Emma). The answer is 119/339 or very close to 1/2.
So the relative popularity of a particular name is somewhat irrelevant. The real reason for the dramatic difference between the two problems (the one resulting in probability 1/3 and the one approximating 1/2) is that the basic building blocks of the sample has changed. Instead of a sample consisting of families, when a name is given to a particular child we are now looking at a sample consisting of individual children. So the frequency of girls is always about one half, but the frequency of two-children families with girls is about 3/4. When the families with two children are looked at more closely, we see that 2/3 have one girl and 1/3 have two girls, but this fact tells us something about the distribution of characteristics among families, not among girls.
Mlodinow’s error is in the last phrase of the sentence in the second full paragraph on p. 113: “That leaves us with just (boy, girl-F), (girl-F, boy), (girl-NF, girl-F), and (girl-F, girl-NF), which are, to a very good approximation, equally likely.” In fact, the odds for (B, GF) and (GF, B) are 1/3 each, while the odds for (GNF,GF) and (GF, GNF) are 1/6 each. Let’s look at it step-by-step.
First, we are told that a woman is pregnant with fraternal twins. There are four equally likely outcomes: (B,B), (B,G), (G,B), and (G,G). So the odds that both twins are girls is 1/4.
Second, we are told that at least one of the twins is a girl. There are now three equally likely outcomes: (B,G), (G,B), and (G,G). So the odds that both twins are girls is 1/3.
Third, we are told that some girls are named Florida, but we don’t yet know how many girls are so named. Let’s assume for a moment that half of all girls are named Florida. (B,G) thus has two equally likely outcomes: (B,GF) and (B,GNF). Each is thus 50% of 1/3, or 1/6 likely. Similarly, (G,B) has two equally likely outcomes, (GF,B) and (GNF,B), each of which has a 50% of 1/3, or 1/6 chance of happening. (G,G) has four equally likely outcomes, (GF,GF), (GF,GNF), (GNF,GF), and (GNF,GNF), each of which is 25% of 1/3, or 1/12 likely to occur.
Fourth, we are told that at least one of the twins is a girl named Florida. (B,G) can thus only be (B,GF) and has a 1/3 chance of being the outcome. Similarly,(G,B) can only be (GF,B), and has a 1/3 chance of being the outcome. (G,G) can thus only be (GF,GF), (GF,GNF), or (GNF,GF), each of which has a 33% of 1/3, or 1/9 chance of happening.
Finally, we are told that Florida is a very rare name, and nobody (except maybe George Foreman) is going to name both twin girls Florida. So, (G,G) can now be only (GF,GNF) or (GNF,GF) each of which has a 50% of 1/3, or 1/6, chance of happening. The 1/3 chance that both twins are girls has not changed because of any additional information. Simple, eh?