Pop analogies

I find it funny when people make analogies to things they don't know much about to clarify something, making an analogy that's absurd to anyone who understands the topic. This often "works" in a way, in that the person reading the analogy often also doesn't know anything about the topic and has similar misconceptions.

An example I've seen at every large tech company I've worked for is "pets vs. cattle", which relies on having no idea how cattle are treated: https://twitter.com/danluu/status/1306075761787322370 .

Another one is when people in tech make sports analogies: https://twitter.com/danluu/status/911518589638905856 . And this isn't limited to people in tech as we can see by this analogy between height in basketball and IQ by Scott Alexander: https://slatestarcodex.com/2015/02/01/talents-part-2-attitude-vs-altitude/ .

I ran into this one when I was writing the "other discussions" section of https://danluu.com/talent/ since I remembered that Scott had written a variety of things about talent and IQ. Unfortunately, all of the writing I could easily find with a search had issues like the one discussed below, which made me not want to link the posts.

I'm not going to a 2002 blog style point-by-point refutation of the analogy, but basically no part of the analogy makes sense. For example, at one point, Scott says:

> If somebody who was 6’6 complained that they’d never be able to beat the 7’0 players on the other side, we would tell them to brighten up. After all, Michael Jordan was “only” 6’6, and he’s maybe the greatest basketball player of all time, even though he often had to face off against people taller than himself.

>

> But if a team made entirely of 6’6 players faced off against a team entirely of 7’0 players, and both of them were really motivated and practiced really hard and had great coaches, I know who I would bet on.

> Most important, people all over the world innocently enjoy playing basketball, and they are right to do so. Everyone knows that taller players have an advantage, no one’s denying it. But at the levels most people play at, moderate height differences are surmountable by differences in training and technique, and large height differences are so rare as to not come up very often. Yes, the pro leagues are a different story. Yet somehow the 5’8 kid who scores a three-pointer still manages to feel good about himself. And we can be very impressed by Kobe Bryant and LeBron James, praise them for their determination and technique and competitive spirit, all while acknowledging that it’s not a coincidence that the one is 6’6 and the other 6’9 and neither of these is a normal-person height.

>

> All of this is crystal clear when we’re talking about basketball. But as soon as we switch back to talking about intelligence, we’re shouting at each other: “YOU SAY RAMANUJAN WAS REALLY HARD-WORKING, BUT I THINK HE HAD HIGH IQ, SO THERE!” Or “WELL IF SUCCESS COMES FROM INNATE TALENT, I GUESS I’LL JUST NEVER STUDY AGAIN.”

> ...

> Likewise, if we can just apply the same common reasoning we use for normal everyday activities like basketball to the question of intelligence, we might find it’s not so complicated and scary after all.

I think the point of the analogy is that, in aggregate, higher IQ people will be more productive than lower IQ people but I think I'd take the 6'6" side of the bet here. It depends on how you draft the teams, but if you either pick the best 6'6" players and put them up against the best 7'0" players or you randomly draft 6'6" NBA players and put them up against 7'0" players, I'd take the 6'6" team for sure and same for less selected populations, like college ball players, euro league players, etc. If you're picking uniformly at random from all people and not just pro or semi-pro basketball players, that's a bit iffier, but I think it's still decently likely that the 6'6" team would win. It's certainly close enough that if someone wanted to give me any kind of significant odds on the bet, I'd take the 6'6" side.

There are a couple of reasons to take the 6'6" side for every distribution mentioned except the last one and maybe even then. If we're picking top players, there are simply more 6'6" players than 7'0" players, so we can effectively select from a much larger pool of 6'6" players (this is, f course, the same point made in https://danluu.com/talent/ about why top chess, go, and shogi players tend to not be very tall, except that there's a significant advantage to height in basketball, so the top players are taller than average, but still much less tall than Scott expects them to be).

The other major reason is that height isn't an unallowed good in basketball. Taller players tend to be a lot slower and less agile. Shaq was famous for being extremely quick for someone who was 7'0" and was one of the greatest players of all time because he combined freakish speed and agility for someone his size with being 7'0", but 5 Shaqs in their prime probably wouldn't do all that well against a team of the top 6'6"-ish players playing today (James Harden, Kawhi Leonard, etc.), and that's if we make 5 copies of the top 7'0" player of all time. If we compare players today vs. other players today or all-time players vs. all-time players, there's no contest.  If we select players at random from pro or semi-pro populations, we'll get the same effect, just with less famous people. The 7'0" team might have a chance if we select from the population at random, but even there, the 7'0" team will still get dominated on speed and agility. If it's truly at random from the population, then you might be able to argue that the 7'0" team has significantly better odds because it's likely that more of the players will have played organized basketball at all, but that's a pretty different point than Scott is trying to make, and if we remove that by selecting for players who've played organized basketball, I'd bet on the 6'6" team.

Scott says this whole topic is "crystal clear" when talking about basketball and it's only muddled when we talk about IQ because people have weird ideas about IQ, but I think the topic is complex enough that, when talking about basketball, Scott has it wrong. I wouldn't say it's unclear, but it's not clear in the way he thinks it is.

This is a pretty typical example of how these kinds of analogies go. Someone has some point they want to make. Sometimes they have a compelling case if they make it directly and sometimes they don't but, either way, they decide to make an analogy to a topic they don't understand to "clarify" the point. But the clarification is basically just pretending that the thing they're making an analogy to works the way they believe the original topic works, so they end up making the direct case anyway since the actual knowledge an analogy could bring to the table is thrown away. It sort of makes sense if you substitute the terms in the analogy with meaningless placeholders like "foo" and "bar", but if you use the actual words used in the argument, then the analogy is nonsense to anyone who knows about the topic. There's a sense in which this "works" because most readers won't know anything about the topic, but there's something I find quite funny about that.