Seth's Blog

ROBERTS I think that if you take the different things that happened to you and you measured their effect, the effects will have a power-law distribution. A tiny number will have a huge effect . . .

MLODINOW Yes.

ROBERTS . . . and a large number will have very little effect. But I guess you could shift the slope of that power-law distribution if you were smart. My research with rats has involved measuring how long they hold the bar down when they press the bar and it turns out that has a power-law distribution.

MLODINOW That’s interesting. Why is it that they hold it down with a power-law distribution rather than, let’s say, a normal distribution?

ROBERTS Why? I think it’s because the way the cerebellum is constructed. I think it has to do with . . . the brain is a network and it’s much easier to get a power-law distribution out of a network than out of a non-network and it’s revealing of the mechanism that produces the bar presses. It’s revealing that it comes from a very networked structure and a little bit more than that, too. It’s not only networked, it’s also chain reactioning and it sheds some light on the mechanism that’s producing the bar presses and that mechanism is not so far from what we see in the cerebellum, which has these incredible density of neurons, highly interconnected neurons. So that’s the connection.

MLODINOW Interesting.

ROBERTS That’s the best I can say as to the why. Clearly evolution designed the brain to solve the problems that animals encounter and why does the cerebellum have the structure it does? Because this power-law distribution is a good idea. Normal distribution is probably too conservative, whereas the power-law distribution is . . . every now and then it’s searching much more widely.

MLODINOW Searching for . . . to see if holding it down less or more amount of time will have any effect, so the power-law you will have some of those explorations into holding it down not long or extra long and therefore sometimes discover something new, rather than really more narrow . . . in a narrow band holding it down a certain number of milliseconds or whatever.

ROBERTS I would guess that the brain has been shaped to produce the power-law distribution in those operations and I think there’s probably other patterns of variability in other aspects of behavior but this is the one we measured.

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In a YouTube post, Nassim Taleb makes an excellent point about misleading stock prices — they mask what really matters. Practically the same point made by Michael Lewis in an excellent article about a basketball player and misleading stats.

Thanks to Dave Lull.

What a difference an idea makes. A few weeks ago I came up with the idea that evolution shaped us to like umami taste, sour taste, and complex flavors so that we will eat more harmless-bacteria-laden food, which improves immune function. (I pompously call this the umami hypothesis.) It seemed so likely to be true that I started eating more fermented foods: miso, kimchi, yogurt, buttermilk, smelly cheese, and wine. To avoid stomach cancer and high blood pressure, I later cut back on miso, kimchi, and smelly cheese.

There have been other changes, too:

• After buying meat or fish, I don’t try to get home quickly to put it in the fridge
• I don’t worry that eggs have been in the fridge for 3 weeks
• When buying eggs and other perishables, I don’t try to get the freshest
• I don’t worry about leaving milk out

Bacteria and viruses from other humans pose a threat. This is why we find fecal matter so offensive. It’s why hand-washing by doctors matters. But I believe plant-grown and dirt-grown bacteria are harmless because the substrates are so different than conditions inside our bodies. As for meat-, fish-, and dairy-grown bacteria, I don’t think they are very dangerous. Has anyone gotten food poisoning from yogurt? I keep in mind how much stinky fish the Eskimos ate. Maybe I should do some controlled rotting experiments — leave meat at room temperature for varying lengths of time before cooking and eating it.

Preston McAfee, a Caltech economics professor, writes:

These schmucks are offering a bribe to the professor for using their text. It had to happen, but students in courses using their books ought to be extremely irate — you should feel the same way if your physician took a bribe from a pharmaceutical company for giving you a prescription.

If?

ROBERTS What did you think of The Black Swan on the same topic?

MLODINOW It’s on the topic of how little things can cause big changes, you mean, and . . .

ROBERTS And how poorly we understand what really matters.

MLODINOW  I haven’t read the book from beginning to end so it’s hard to comment on that.

ROBERTS What about his previous book? There are similar ideas in the two books.

MLODINOW I didn’t really notice that book when I started writing Drunkard’s Walk; I wasn’t aware of the book. I had looked–in the library–gone through tons of books that seemed somehow related to randomness and somehow that one didn’t stand out to me. Sometime later it came out in paperback and it got very popular. Then I rediscovered it, and yes, I agree with a lot of what he says in that first book, but I still never read it from cover to cover. I’m not the type who feels compulsive about reading everything that’s been written on the subject that I’m writing on.

ROBERTS Yes. I always think of his book as being about these very long-tailed distributions–not only about that, but they play a large role–whereas you didn’t mention long-tailed distributions in your book.

MLODINOW Not explicitly, but I did talk about that idea and certainly the idea that not everything follows a normal distribution and how important it is to note that, for instance in Hollywood–Hollywood box office receipts. But I think The Black Swan was exclusively about that, so in that sense it was a different topic.

[For readers who don’t know what that is, if you’re talking about the probability of events occurring--let’s say you’re talking about the probability of a movie making a certain amount of money--there may be a mean amount of money that a movie makes or that a movie of that type makes. Then there will be fluctuations around it; some movies will make more, some movies will make less. The normal distribution is a distribution of the revenues that would follow a bell curve and the long-tailed distribution differs. One of the important respects that it differs in is that it has a lot more results that are far from the average that you would expect in a normal distribution. So if the average movie makes $1,000,000 or to be more realistic let’s say the average movie makes $50,000,000 and if it was normally distributed you would have, depending on the variance, but let’s just say you would have a certain number that make 40 or would make 60 and another small number would make 30 or 70 and you have a very small number indeed--probably practically zero--that would make $500,000,000. In Hollywood the way it really works is there are more that differ that far from the median than you would have if it were a normal distribution. That’s what they call a long-tailed distribution--the number of occurrences that are far from the average is much higher than you would expect with the normal distribution. -- LM]

So that applies in many areas of life as well. I think that translated into what we were just talking about, it means that these little minor incidents can have major effects on you. It’s not all kind of pushed toward the mean effect, which is just going into my office and doing more physics.

ROBERTS Yes, I think that if you take the different things that have happened to you and you measured their effect, the effects will have a power-law distribution. A tiny number will have a huge effect and . . .

MLODINOW Yes.

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