What makes food healthful?

The USDA and most nutritionists recommend eating a diet with lots of fruits and vegetables.  In the old guideline, the recommendation was to “strive for five” servings of fruits and vegetables.  The new guideline advises us to fill half of our plates with fruits and vegetables. Food writer Michael Pollen (see essay here) tells us to “Eat food. Not too much. Mostly plants.”

The question then is why?   Food consists of the three macronutrients – fat, carbohydrates and protein, water, fibre, minerals, vitamins, other micronutrients (more on this later),  and ash (non-digestible stuff).  You need water everyday. Your energetic requirements come out of the macronutrients.  There are a number of essential amino acids, fatty acids, vitamins and minerals you need.  Fibre is thought to be important for digestion but you could live without it.  In principle, you could obtain all of your nutritional requirements by eating raw animal products (cooking and drying may destroy some vitamins like vitamin C).  You could also just eat hamburgers and a multi-vitamin supplement  but most health conscious people would recoil from such a diet.  Thus there seem to be three dietary situations: 1) malnutrition, where you miss some of the essential nutrients, 2)  nutritional sufficiency, where you obtain all the essential nutrients, and 3) healthful eating, which is 2) plus lots of fruits and vegetables (and perhaps other things like olive oil, etc).

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National Elk Refuge

Right outside of Jackson, Wyoming is the National Elk Refuge, which was established in 1912.  It is the wintering ground for a herd of ten thousand elk as well as eight hundred bison.  During winter, the elk come down from the mountains to the Jackson Hole valley where the snow is thinner so they can access grass more easily.  You can take a horse drawn sleigh right out to the herd with the Grand Tetons as the the backdrop. Here are some pictures.

Productivity and ability

What makes some people more productive then others?  Is it innate ability, better training, hard work?  Although the meaning of productivity is subjective,  there are quantifiable differences between researchers in measures of productivity such as the  h-index.    Here I will argue that a small difference in ability or efficiency can lead to great differences in output.

Let’s consider a simple and admittedly flawed model of productivity.  Suppose we consider productivity to be the number of tasks you can complete and let P represent the probability that you can accomplish a  task (i.e. efficiency).  A task could be anything from completing an integral, to writing a program, to sticking an electrode into a cell, or to finishing a paper.  The probability of completing N independent tasks is T=P^N.  Conversely, the number of steps that can be completed with probability T is N = \log T/\log P.  Now let P = 1-\epsilon, where \epsilon is the failure probability.  Hence, for high efficiency (i.e. low failure rate),  we can expand the logarithm for small \epsilon and obtain N \propto \epsilon^{-1}.  The number of tasks you can complete for a given probability  is inversely proportional to your failure rate.

The rate of change in productivity with respect to efficiency increases even faster with

\frac{dN}{d P}\propto \epsilon^{-2}

Hence, small differences in efficiency can lead to large differences in the number of tasks that can be completed and the gain is more dramatic if you have higher efficiency.  For example, if you go from being 90\% efficient (i.e. \epsilon = .1) to 95\% efficient (i.e. \epsilon = .05) then you will double the number of tasks you can complete. Going from 98\% to 99\% is also a doubling in productivity.  The model clearly disregards the fact that tasks are often correlated and have different probabilities for success.  I know  some people who have great trouble in revising and resubmitting papers to get published and thus they end up having low measured productivity even though they have accomplished a lot.   However, it seems to indicate that it is always worth improving your efficiency even by a small amount.

Dyson on Econtalk

Freeman Dyson is the guest on Econtalk this week. Dyson has long been one of my favourite physicists.  The podcast was mostly superficial chit chat but there were some interesting moments.  For example, when the host asked Dyson what he was most proud of Dyson thought about it for a moment and said it was his books.  He said that even today, he’ll get emails from young people who say his that his books greatly inspired them.  Dyson then went on to say that he’d mostly been a dabbler all of his life who just worked on things because they were fun so he never felt that he made a deep contribution to science.  The then added that he was second most proud of was his work on Project Orion, which was to build a nuclear bomb propelled spaceship.  He felt that we would already be visiting other worlds by now if the project had been allowed to be completed.  However, he also noted that the environmental issue made such an idea impossible today.

The podcast only touched briefly on Dyson’s climate change skepticism, of which he has received the most attention lately.  (Steve Hsu has a nice collection of posts on Dyson.)  I would classify Dyson’s position more as climate change action skepticism.  He doesn’t dispute that greenhouse gases can perturb the climate system, he just believes we simply don’t know enough to be able to act in a knowledgeable way.  He fears that any action we take could have more severe consequences.  For example, a tax on carbon could slow economic growth, which could lead to more hardship than global warming.  He favours proposals that have fewer risks such as increasing energy efficiency and changing farm policy to be less wasteful.

I’ve always felt that Dyson should have gotten a Nobel prize for his work on QED.  Silvan Schweber’s book QED and the Men Who Made It, is partly a tribute to Dyson’s under-appreciated contribution. Dyson didn’t get it in 1965 with Feynman, Schwinger and Tomonaga because the Nobel prize is limited to three people.  I thought that the ideal time to give it to him retroactively was in 1999 when  t’Hooft and Veltman received it for renormalization in electroweak theory.  The prize could have been generalized to renormalization in QED and electroweak theory.  However, one could argue that this would then exclude other important contributors like Fadeev and Popov.  This all then goes back to my other idea of abolishing the Nobel prize entirely since results never exit in pure isolation.