Seth's Blog

What to watch? Entertainment Weekly has a feature called Critical Mass: Ratings of 7 critics are averaged. Those averages are the critical response that most interests me. Rotten Tomatoes also computes averages over critics. It uses a 0-100 scale. In recent months, my favorite movie was Gran Torino, which rated 80 at Rotten Tomatoes (quite good). Slumdog Millionaire, which I also liked, got a 94 (very high).

Is an average the best way to summarize several reviews? People vary a lot in their likes and dislikes — what if I’m looking for a movie I might like a lot? Then the maximum (best) review might be a better summary measure; if the maximum is high, it means that someone liked the movie a lot. A score of 94 means that almost every critic liked Slumdog Millionaire, but the more common score of 80 is ambiguous: Were most critics a bit lukewarm or was wild enthusiasm mixed with dislike? Given that we have an enormous choice of movies — especially on Rotten Tomatoes – I might want to find five movies that someone was wildly enthusiastic about and read their reviews. Movies that everyone likes (e.g., 94 rating) are rare.

Another possibility is that I’m going to the movies with several friends and I just want to make sure no one is going to hate the chosen movie. Then I’d probably want to see the minimum ratings, not the average ratings.

So: different questions, wildly different “averages”. I have never heard a statistician or textbook make this point except trivially (if you want the “middle” number choose the median, a textbook might say).  The possibility of “averages” wildly different from the mean or median is important because averaging is at the heart of how medical and other health treatments are evaluated. The standard evaluation method in this domain is to compare the mean of two groups — one treated, one untreated (or perhaps the two groups get two different treatments).

If there is time to administer only one treatment, then we probably do want the treatment most likely to help. But if there are many treatments available and there is time to administer more than one treatment — if the first one fails, try another, and so on — then it is not nearly so obvious that we want the treatment with the best mean score. Given big differences from person to person, we might want to know what treatments worked really well with someone. Conversely, if we are studying side effects, we might want to know which of two treatments was more likely to have extremely bad outcomes. We would certainly prefer a summary like the minimum (worst) to a summary like the median or mean.

Outside of emergency rooms, there is usually both a wide range of treatment choice and plenty of time to try more than one. For example, you want to lower your blood pressure. This is why medical experts who deride “anecdotal evidence” are like people trying to speak a language they don’t know — and don’t realize they don’t know. (Their cluelessness is enshrined in a saying: the plural of anecdote is not data.) In such situations, extreme outcomes, even if rare, become far more important than averages. You want to avoid the extremely bad (even if rare) outcomes, such as antidepressants that cause suicide. And if a small fraction of people respond extremely well to a treatment that leaves most people unchanged, you want to know that, too. Non-experts grasp this, I think. This is why they are legitimately interested in anecdotal evidence, which does a better job than means or medians of highlighting extremes. It is the medical experts, who have read the textbooks but fail to understand their limitations, whose understanding has considerable room for improvement.

Three things, he said:

1. Finance professors have all been working for hedge funds. Their research has been about how to price derivatives and options. In other areas of economics, the research topics are much broader and include policy questions.
2. Macroeconomics hasn’t made progress since the 1930s.
3. Recommendations what to do about the crisis, even from economics professors, are based on very little they learned in graduate school. They hardly differ from opinions. Listening to his colleagues’ recommendations, he thought they would be backed up by something solid. They weren’t.

You’ve probably heard of the unexpected hanging paradox in which a man is ordered to be hanged during a certain week but must not know in advance the day of his hanging. The last possible day is Saturday. He must be hanged before Saturday because if he’s not hanged by then he will know that he is going to be hanged on Saturday. By the same logic he can’t be hanged on Friday . . . and so on. Yet he is hung on Wednesday.

American Idol producers have a similar problem during recent eliminations: There must be suspense. From six guys and six girls one guy, one girl, and one runner-up will be selected. This week, the first person selected, out of two girls and a guy, was a girl. This meant that at the next step — one person chosen from one girl and one guy — the guy would be selected because if the girl was selected, the remaining girls would have no chance. Making the remaining portion of the program much less interesting. As an EW.com commenter put it:

There was no suspense in the Kris Allen/Megan Corkey stand-off last nite. Allison had already gone through & if Megan had it would automatically eliminate the rest of the females. Wasn’t going to happen halfway through the show. That’s what they call a ‘gimme’.

The Wikipedia article on the paradox gives no practical applications.

ROBERTS  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.

Interview directory.

Tucker Max, who got great results from flaxseed oil, wondered what would happen if he ate more fermented food. He emailed me:

I have been reading your posts about bacteria in food, so I decided to try it on my own. I HATE Roquefort and other stinky cheeses, and I am not about to eat fermented meat, so the best thing I could find in Whole Foods was Kombucha tea. It is basically normal tea, with bacteria cultures growing in it. Sounds weird I know, but it actually tastes pretty good, especially the ones with natural fruit juices added. It has a sparkly, almost champagne-like taste feel in your mouth. It takes a little getting used to, but I really like it now. I like GT’s brand the best, but I think there are others.

Anyway, after a week of drinking two bottles a day, I have noticed
these changes:

1. My stool is…well, better. In every way. More regular, more solid, and something else very unusual–I only have to wipe once. For most of my life, I have to wipe twice, or sometimes three times, which I assumed was normal. But this week, the stool comes out and leaves virtually nothing behind. At least nothing that is showing up on the toilet paper. I am not sure what this means as I am not a poop expert, but I think it means my stool is “healthier” for lack of a better word.
2. I have more energy. Aside from subjectively feeling it, I can see the difference in my workout logs, just in this past week I’ve gone up more weight on exercises than I normally do.
3. I am feeling overall better. This could very well be placebo effect/confirmation bias as it is a very subjective measurement, but I just feel better. I feel generally healthier, if that makes sense.
4. But, I am having trouble sleeping. I feel like I am getting less sleep, not much, maybe 30 minutes less. I don’t know if this is due to increased energy because it might be anxiety –we are about to sell my movie, and it’s an anxious time in my life, so the cause may have nothing to do with the tea.

Right now, I think kombucha tea greatly improves my health and I am
going to keep taking it to see if there are anymore changes or if this
persists. This stuff I buy is not cheap, like $4 a bottle [$3/bottle in one Berkeley store], but I am going to keep drinking at least two a day, I like it that much. Plus, once you get used to the taste and texture, it’s really delicious.

The brand he bought is GT’S. I’ll comment on this in a later post — but I’ll say now that eating much more fermented food didn’t have any noticeable effect on my sleep.