# The straw that broke the camel’s back

Oct 18 JDN 2459141

You’ve probably heard the saying before: “It was the straw that broke the camel’s back.” Something has been building up for a long time, with no apparent effect; then suddenly it crosses some kind of threshold and the effect becomes enormous.

Some real-world systems do behave like this: Avalanches, for instance. There is a very sharp critical threshold at which snow suddenly becomes unstable and triggers an avalanche.

This is how weight works in many video games, and it seems ridiculous: In Skyrim, for instance, one 1-pound cheese wheel can mean the difference between being able to function normally and being unable to move. Fear not, however: You can simply eat that cheese wheel and then be on your way.

But most real-world systems aren’t like this. In particular, camels are not. Yes, zero pieces of straw will not break a camel’s back, and some quantity of straw will. No, there is not a well-defined threshold at which adding just one piece of straw will kill the camel. This is one of those times where formal mathematical modeling can help us to see things that we otherwise couldn’t.

If this seems too frivolous, consider that this model need not be about camels: It could be about the weight a bridge can hold, or the amount of pollution a region can sustain, or the amount of psychological stress a person can bear. I think applying it to psychological stress is particularly appropriate at the moment: COVID-19 has suddenly thrust us all above our usual level of stress, and it’s important to understand where our limits lie.

A really strict formal model useful for engineering purposes would be a stress-strain curve, showing the relationship between stress (the amount of force applied) and strain (the amount of deformation of the object). But for this purpose there are basically two regimes to consider:

Below some weight y (the yield strength)the camel’s back will compress under the weight, but once the weight is removed it will return to normal. A healthy camel can carry up to y in straw essentially indefinitely.

Above that point, additional weight will begin to strain the camel’s back. But this damage will not all occur at once; a larger amount of weight for a shorter time will have the same effect as a smaller amount of weight for a longer time.

The total strain on the camel will thus look something like this, for exposure time t: (w-y)t

There is a total amount of strain that the camel can take without breaking its back. This has units of momentum, so I’m going to use p.

What is the amount of straw that breaks the camel’s back? Well, that depends on how long it is there!

w = p/t + y

This implies that even an arbitrarily large weight is survivable, if experienced for a sufficiently small amount of time. This may seem counter-intuitive, but it’s actually quite realistic: I’m not aware of any tests on camels, but human beings have been able to survive impacts of 40 g for a few milliseconds.

If you are hoping to carry a certain load of straw by camel over a certain distance, and need to know how many camels to use (or how many trips to take), you would figure out how long it takes to cover that distance, then use that as your time parameter to figure out the maximum weight a camel could carry for that long.

So what would happen if you actually added one piece of straw at a time to a camel’s back? That depends on how fast you add them and how long you leave them there!

# What do we mean by “obesity”?

Nov 25 JDN 2458448

I thought this topic would be particularly appropriate for the week of Thanksgiving, since as a matter of public ritual, this time every year, we eat too much and don’t get enough exercise.

No doubt you have heard the term “obesity epidemic”: It’s not just used by WebMD or mainstream news; it’s also used by the American Heart Association, the Center for Disease Control, the World Health Organization, and sometimes even published in peer-reviewed journal articles.

This is kind of weird, because the formal meaning of the term “epidemic” clearly does not apply here. I feel uncomfortable going against public health officials in what is clearly their area of expertise rather than my own, but everything I’ve ever read about the official definition of the word “epidemic” requires it to be an infectious disease. You can’t “catch” obesity. Hanging out with people who are obese may slightly raise your risk of obesity, but not in the way that hanging out with people with influenza gives you influenza. It’s not caused by bacteria or viruses. Eating food touched by a fat person won’t cause you to catch the fat. Therefore, whatever else it is, this is not an epidemic. (I guess sometimes we use the term more metaphorically, “an epidemic of bankruptcies” or an “epidemic of video game consumption”; but I feel like the WHO and CDC of all people should be more careful.)

Indeed, before we decide what exactly this is, I think we should first ask ourselves a deeper question: What do we mean by “obesity”?

The standard definition of “obesity” relies upon the body mass index (BMI), a very crude measure that simply takes your body mass and divides by the square of your height. It’s easy to measure, but that’s basically its only redeeming quality.

Anyone who has studied dimensional analysis should immediately see a problem here: That isn’t a unit of density. It’s a unit of… density-length? If you take the exact same individual and scale them up by 10%, their BMI will increase by 10%. Do we really intend to say that simply being larger makes you obese, for the exact same ratios of muscle, fat, and bone?

Because of this, the taller you are, the more likely your BMI is going to register as “obese”, holding constant your actual level of health and fitness. And worldwide, average height has been increasing. This isn’t enough to account for the entire trend in rising BMI, but it reduces it substantially; average height has increased by about 10% since the 1950s, which is enough to raise our average BMI by about 2 points of the 5-point observed increase.

And of course BMI doesn’t say anything about your actual ratios of fat and muscle; all it says is how many total kilograms are in your body. As a result, there is a systematic bias against athletes in the calculation of BMI—and any health measure that is biased against athletes is clearly doing something wrong. All those doctors telling us to exercise more may not realize it, but if we actually took their advice, our BMIs would very likely get higher, not lower—especially for men, especially for strength-building exercise.

It’s also quite clear that our standards for “healthy weight” are distorted by social norms. Feminists have been talking about this for years; most women will never look like supermodels no matter how much weight they lose—and eating disorders are much more dangerous than being even 50 pounds overweight. We’re starting to figure out that similar principles hold for men: A six-pack of abs doesn’t actually mean you’re healthy; it means you are dangerously depleted of fatty acids.

To compensate for this, it seems like the most sensible methodology would be to figure out empirically what sort of weight is most strongly correlated with good health and long lifespan—what BMI maximizes your expected QALY.

You might think that this is what public health officials did when defining what is currently categorized as “normal weight”—but you would be wrong. They used social norms and general intuition, and as a result, our standards for “normal weight” are systematically miscalibrated.

In fact, the empirical evidence is quite clear: The people with the highest expected QALY are those who are classified as “overweight”, with BMI between 25 and 30. Those of “normal weight” (20 to 25) fare slightly worse, followed by those classified as “obese class I” (30 to 35)—but we don’t actually see large effects until either “underweight” (18.5-20) or “obese class II” (35 to 40). And the really severe drops in life and health expectancy don’t happen until “obese class III” (>40); and we see the same severe drops at “very underweight” (<18.5).
With that in mind, consider that the global average BMI increased from 21.7 in men and 21.4 in women in 1975 to 24.2 in men and 24.4 in women in 2014. That is, the world average increased from the low end of “normal weight” which is actually too light, to the high end of “normal weight” which is probably optimal. The global prevalence of “morbid obesity”, the kind that actually has severely detrimental effects on health, is only 0.64% in men and 1.6% in men. Even including “severe obesity”, the kind that has a noticeable but not dramatic effect on health, is only 2.3% in men and 5.0% in women. That’s your epidemic? Reporting often says things like “2/3 of American adults are overweight or obese”; but all that “overweight” proportion should be utterly disregarded, since it is beneficial to health. The actual prevalence of obesity in the US—even including class I obesity which is not very harmful—is less than 40%.

If obesity were the health crisis it were made out to be, we should expect that global life expectancy is decreasing, or at the very least not increasing. On the contrary, it is rapidly increasing: In 1955, global life expectancy was only 55 years, while it is now over 70.

Worldwide, the countries with the highest obesity rates are those with the longest life expectancy, because both of these things are strongly correlated with high levels of economic development. But it may not just be that: Smoking reduces obesity while also reducing lifespan, and a lot of those countries with very high obesity (including the US) have very low rates of smoking.

There’s some evidence that within the set of rich, highly-developed countries, obesity rates are positively correlated with lower life expectancy, but these effects are much smaller than the effects of high development itself. Going from the highest obesity in the world (the US, of course) to the lowest among all highly-developed countries (Japan) requires reducing the obesity rate by 34 percentage points but only increases life expectancy by about 5 years. You’d get the same increase by raising overall economic development from the level of Turkey to the level of Greece, about 10 points on the 100-point HDI scale.

Now, am I saying that we should all be 400 pounds? No, there does come a point where excess weight is clearly detrimental to health. But this threshold is considerably higher than you have probably been led to believe. If you are 15 or 20 pounds “overweight” by what our society (or even your doctor!) tells you, you are probably actually at the optimal weight for your body type. If you are 30 or 40 pounds “overweight”, you may want to try to lose some weight, but don’t make yourself suffer to achieve it. Only if you are 50 pounds or more “overweight” should you really be considering drastic action. If you do try to lose weight, be realistic about your goal: Losing 5% to 10% of your initial weight is a roaring success.

There are also reasons to be particularly concerned about obesity and lack of exercise in children, which is why Michelle Obama’s “Let’s Move!” campaign was a good thing.

And yes, exercise more! Don’t do it to try to lose weight (exercise does not actually cause much weight loss). Just do it. Exercise has so many health benefits it’s honestly kind of ridiculous.

But why am I complaining about this, anyway? Even if we cause some people to worry more about eating less than is strictly necessary, what’s the harm in that? At least we’re getting people to exercise, and Thanksgiving was already ruined by politics anyway.

Well, here’s the thing: I don’t think this obesity panic is actually making us any less obese.

The United States is the most obese country in the world—and you can’t so much as call up Facebook or step into a subway car in the US without someone telling you that you’re too fat and you need to lose weight. The people who really are obese and may need medical help losing weight are the ones most likely to be publicly shamed and harassed for their weight—and there’s no evidence that this actually does anything to reduce their weight. People who experience shaming and harassment for their weight are actually less likely to achieve sustained weight loss.

Teenagers—both boys and girls—who are perceived to be “overweight” are at substantially elevated risk of depression and suicide. People who more fully internalize feelings of shame about their weight have higher blood pressure and higher triglicerides, though once you control for other factors the effect is not huge. There’s even evidence that fat shaming by medical professionals leads to worse treatment outcomes among obese patients.

If we want to actually reduce obesity—and this makes sense, at least for the upper-tail obesity of BMI above 35—then we should be looking at what sort of interventions are actually effective at doing that. Medicine has an important role to play of course, but I actually think economics might be stronger here (though I suppose I would, wouldn’t I?).

Number 1: Stop subsidizing meat and feed grains. There is now quite clear evidence that direct and indirect government subsidies for meat production are a contributing factor in our high fat consumption and thus high obesity rate, though obviously other factors matter too. If you’re worried about farmers, subsidize vegetables instead, or pay for active labor market programs that will train those farmers to work in new industries. This thing we do where we try to save the job instead of the worker is fundamentally idiotic and destructive. Jobs are supposed to be destroyed; that’s what technological improvement is. If you stop destroying jobs, you will stop economic growth.

Number 2: Restrict advertising of high-sugar, high-fat foods, especially to children. Food advertising is particularly effective, because it draws on such primal impulses, and children are particularly vulnerable (as the APA has publicly reported on, including specifically for food advertising). Corporations like McDonald’s and Kellogg’s know quite well what they’re doing when they advertise high-fat, high-sugar foods to kids and get them into the habit of eating them early.

Number 3: Find policies to promote exercise. Despite its small effects on weight loss, exercise has enormous effects on health. Indeed, the fact that people who successfully lose weight show long-term benefits even if they put the weight back on suggests to me that really what they gained was a habit of exercise. We need to find ways to integrate exercise into our daily lives more. The one big thing that our ancestors did do better than we do is constantly exercise—be it hunting, gathering, or farming. Standing desks and treadmill desks may seem weird, but there is evidence that they actually improve health. Right now they are quite expensive, so most people don’t buy them. If we subsidized them, they would be cheaper; if they were cheaper, more people would buy them; if more people bought them, they would seem less weird. Eventually, it could become normative to walk on a treadmill while you work and sitting might seem weird. Even a quite large subsidy could be worthwhile: say we had to spend \$500 per person per year to buy every single adult a treadmill desk each year. That comes to about \$80 billion per year, which is less than one fourth what we’re currently spending on diabetes or heart disease, so we’d break even if we simply managed to reduce those two conditions by 13%. Add in all the other benefits for depression, chronic pain, sleep, sexual function, and so on, and the quality of life improvement could be quite substantial.