Arithmetic and Butter

August 17, 2010

This is a guest blog post from Seth Roberts. Thanks Seth!


Last Tuesday I gave a talk called “Arithmetic and Butter” at the Quantified Self meeting in Mountain View. I had about 10 slides but this one mattered most:

[photo no longer available]

It shows how fast I did simple arithmetic problems (e.g., 2*0, 9-6, 7*9) before and after I started eating 1/2 stick (60 g) of butter every day. The x axis covers about a year. The butter produced a long-lasting improvement of about 30 msec.

I think the hill shape of the butter function is due to running out of omega-3 in Beijing — my several-months-old flaxseed oil had gone bad, even though it had been frozen. When I returned to Berkeley and got fresh flaxseed oil, my scores improved.

This isn’t animal fat versus no animal fat. Before I was eating lots of butter, I was eating lots of pork fat. It’s one type of animal fat versus another type. Nor is it another example of modern processing = unhealthy. Compared to pork fat, butter is recent.

Most scientists think philosophy of science is irrelevant. Yet this line of research (measuring my arithmetic speed day after day, in hopes of accidental discovery) derived from a philosophy of science, which has two parts.

First, scientific progress has a power-law distribution. Each time we collect data, we sample from a power-law-like distribution. Almost all samples produce tiny progress; a very tiny fraction produce great progress. Each time you collect data, in other words, it’s like buying a lottery ticket. I realized that a short easy brain-function test allowed me to buy a large number of lottery tickets at low cost.

Second, we underestimate the likelihood of extreme events. Nassim Taleb has argued this about the likelihood of extreme negative events (which presumably have a power-law distribution); I’m assuming the same thing about extreme positive events (with a power-law distribution). We undervalue these lottery tickets, in other words. Perhaps all scientists hope for accidental discoveries. I seem to be the first to use a research strategy that relies on accidental discoveries.

In the graph, note that one point (actually, two) is down at 560 msec. This suggests there’s room for improvement.

During the question period, a cardiologist in the audience said something about me killing myself — butter is unhealthy. The usual view.

I said I thought the evidence for the usual view was weak. He said, “The Framingham studies.” That was epidemiology, I said. It is notoriously hard to understand. My data was from something like an experiment. Much easier to understand.

(And the Framingham study is a terrible example of the supposed evidence. To quote from it: “In the period between the taking of the diet interviews and the end of the 16-year follow-up, 47 cases of de novo CHD developed in the Diet Study group. The means for all the diet variables measured were practically the same for these cases as for the original cohort at risk.”)

He replied that the reduction in heart disease in recent years was more support for the usual view. I said the recent decline in heart disease could have many explanations other than a reduction in animal fat intake. Many things have changed over the last 20 years.

There is epidemiological evidence that saturated fat is bad, yes, but it is not the Framingham study nor the recent decline in heart disease. And it really is difficult to interpret. The butter-is-bad interpretation could easily be wrong. The obvious problem is that, after people are told butter is bad, people who try hard to be healthy avoid butter. And they do a lot of other things, too, to be healthy. So butter consumption ends up confounded with a dozen other variables believed to affect your health. When I was growing up, my parents avoided butter because margarine was much cheaper. So butter consumption is confounded with income, another problem.

My tiny experiment, whatever its problems, was much easier to interpret.


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