Bad Math and the Evil Dr. Weight-loss

Occupy Math has always advocated using math to solve problems and protect yourself from scams. A recent post discussed the issue of how math models can be used for good or evil. In this post, Occupy Math will examine the problems with our mental math concerning weight loss. Most weight loss techniques cannot possibly work or only work temporarily and are followed by weight gain. The reason for this is rooted in the difference between linear systems and non-linear systems.

If some is good, more is better. Not!

Most people instinctively believe the statement “if some is good, more is better”. This statement is the soul of linear models. A linear model is one that, if you graph it, makes a line. To say it another way, the output of the system is proportional to its input. Weight loss is one of the things people think is linear that absolutely is not. Most doctors will tell you that if you want to lose weight then you should exercise and eat less. The reason they believe this is that it does work for some people and, here’s another big problem, doctors don’t really believe people are individuals. The idea that different things work for different people is foreign to most doctors. Letís look at an example of how weight loss doesn’t follow a simple, proportional model.

The NBC show The Biggest Loser follows contestants through very large weight losses, with the goal to be the person that loses the most weight. A follow-up study by a done by a National Institutes of Health researcher found that the process changed the contestants so that their bodies became far more efficient at absorbing calories and packing them away as fat. Occupy Math’s point? Since the way the contestantsí bodies absorbed calories changed, the simple linear model “less calories means less weight” is horribly wrong.

The way your body reacts to calories is not linear.

A mathematician who finds a new non-linear system immediately starts trying to figure out why the system is non-linear. In the case of your body’s reaction to calories, it turns out that we know where to look to solve a part of the mystery. Here comes an analogy. If you ignore things like dimmer switches, a light is on or off. It does not slowly brighten in response to you pressing on the switch – rather it abruptly changes state from on to off or off to on. The important idea here is that of a state change. On and off are states of the light and the switch makes it jump back and forth – a very simple non-linear system. What, I hear you ask, are the light switches in our calorie handling systems?

Microbiota are a huge deal in science right now. Occupy Math is sure there will be multiple Nobel Prizes. It turns out that the way your body absorbs calories is influenced a great deal by the bacteria in your gut. An article in the December 2015 issue of Cell examined the gut bacteria of mice made to live in cold and warm environments. The cold mice had their guts elongate 50%, the villi in the guts that absorb nutrients grew, and mice became much better at sucking calories out of food. The warm mice – genetically identical lab strains – did not exhibit these changes. The gut bacteria were very different in the two sets of mice. Finally, normal mice could acquire the cold gut length characteristics by just co-habiting with the cold mice in normal conditions. This happened unless the cold mice’s gut bacteria were cleared out with antibiotics. This is how we know the gut bacteria were critical to the changes in the mice guts.

The mouse experiments demonstrated that gut bacteria can control the efficiency of absorbing calories in their host organism.

Other research has shown that what you eat has a big effect on your gut bacteria and that your body has the ability to encourage or discourage different types of bacteria. Antibiotics, high sugar diets, not enough vegetables, and on and on all matter. This means that your bacterial gut load is a “light switch” that changes the way your body responds to calories. In extreme conditions – like a reality TV show on weight loss – you can flip the switch hard enough that it breaks. By losing a lot of weight, the contestants changed themselves into people who gain weight on a near-starvation diet. The change is already known to be durable and may even be permanent.

Almost all the money spent on diet research is spent on figuring out how to convince people to buy a specific diet product. A widespread and effective technique for convincing people to try a given diet is the testimonial. People saying that the diet worked for them and before-and-after pictures are simple, effective types of testimonial. Mathematical analysis shows that testimonials are horribly dishonest in this case. The dishonesty lies in the manipulation of probability.

Suppose that you live in a society that has a love of coins that flip and land on “heads”. A company who makes coins and want people to prefer their coins takes coins and flips them ten times. They count the number of heads in each trial (so far this is a fair test). They then test 100,000 coins and base their advertisements on the 20 best outcomes. Wow and gee-whillickers, that creates a bias! It is horribly dishonest. With 100,000 trials the 20 best will be mostly heads even if the coin favors tails! Given that different people respond differently to different weight-loss programs, it will be easy to find people to do testimonials that show extraordinary weight loss by just cherry-picking against the natural variation in results.

Cherry picking the best results makes testimonials totally dishonest.

Understanding simple probability can help you understand why testimonials absolutely cannot be trusted, but the situation is even worse. The contestants on “The Biggest Loser” would have made good testimonial examples the day the show was filmed. A few months later they were fighting weight gain with almost no hope of victory. The fact that diet testimonials happen at a single point in time is another type of bad math. A “point model” or single sample test isn’t too meaningful. If you are concerned about your health or your appearance for more than a week, then what matters is the longer term results of the diet. If your diet program doesn’t come with a study including a three-year follow-up on a fair sample of the people that used it, then there is no reason to think it will work for anyone – and even if it does work for some people, that doesn’t say it will work for you.

Occupy Math’s look at how the diet industry uses bad math to cheat their customers, combined with blithe ignorance among medical professionals trying to help their patients lose weight, has put us at the bottom of a pretty deep well. One thing we are now sure of is that making yourself uncomfortable to lose weight has a good chance of making your body fight back so that it becomes harder for you to lose weight. Following the adage that it can always be worse, it also turns out that – at least for some people – the goal weight for good health is not calibrated correctly.

Recent research shows that if you divide people into four weight categories, underweight, normal, overweight, and obese then the overweight people have the longest average life span. The standards for dietary health were not created by an evidence-based process and, in fact, may have been based on the way Hollywood actors looked at the time the standards were compiled. The old food pyramid – the one that wanted you to eat lots of grains – was based on the need to sell agricultural products more than on information about human health This mis-calibration of the model means that many people – beyond those with problems like anorexia – are trying, under medical advice, to maintain a less-than-healthy weight. The regulatory systems in their bodies are probably fighting back. These systems have evolved for eons with the goal of keeping you in good shape; they might not like being overruled by an MD. It is important to note that all the “a little overweight is better” information that Occupy Math found was from northern countries. People living in different climates may have different outcomes.

A final point that Occupy Math wants to include is that:

counting calories is pretty much useless.

Calories are a single number measure of the “health” of a type of food. Using calorie count alone ignores the effect of the other nutrients in the food, it does not take into account your personal genetics or microbiome state, and in general ignores important context. Eating so that you, personally, feel good is an excellent first step. Checking which feel-good diets let you keep your weight at a good place is a viable second step. If you want a third step, a varied diet with lots of cooked vegetables is good for more types of people than most – but please remember you are an individual! Occupy Math finds that his weight behaves better when he gets enough sleep – a factor unrelated to calorie counts.

People can use calorie counts in an abusive fashion. Many people behave, for example, as if diet soda somehow compensates for a bacon double cheeseburger. It doesn’t – and on more levels than just calories. Your body and microbiome can take a metabolic look at diet soda and trigger cravings. Bacon cheeseburgers and diet soda both probably increase your cancer risk in ways not encoded in calorie counts. Dietary health is pretty complicated and “less calories are good” is a terrifically over-simplified model of the situation.

A primary goal of this post is to give you information about the bad, dishonest, and deceptive math used by the diet industry. The post also tries to inform you about the importance of your microbiome. The big mathematical payoff is the idea of non-linearity and state changes (which are one of the big types of non-linearity). Occupy Math actually found a number of other cool things while researching this post and owes his wife, Wendy, and his editor, Charlotte, a big thank you for turning up several of the supporting articles. The rest of the material has been deferred to a future post on not oversimplifying your models, possibly entitled “Kids Need Dirt”. Do you have examples of non-linear phenomena that are cool or deadly if ignored? Tweet or comment and they may well find their way into a future Occupy Math.

I hope to see you here again,
Daniel Ashlock,
University of Guelph,
Department of Mathematics and Statisticscalories


2 thoughts on “Bad Math and the Evil Dr. Weight-loss

  1. Excellent article, particularly the “debunk” about calorie count.

    Now let me offer you an opportunity to research a phenomenon I have never seen even mentioned, let alone explained.

    I am 92 years old and in good health. So I must be doing some right things and avoiding some wrong things.

    I have never exceeded 125 lb in weight. If I eat too much I simply get sick with looseness problems I’d rather not discuss. I’ve no idea what would happen if I ate too little. I have an extremely sensitive gut – probably have IBS. Decades ago I found that my ideal daily ration of sugar is ZERO, of red meat nearly the same. Doctors have seen my prominent ribs and prescribed huge diet supplements like what they call the “Army milkshake” incorporating raw eggs, dried milk powder, and so on. Probably 500 calories per cupful. No weight gain but lots of IBS.

    I live alone and make sure to eat extremely well. I buy no processed food and cook everything to avoid transmitted illness. A typical supper meal will feature three to five (multi-color) foods and fish. I take a multi pro-biotic.

    So there is your friendly challenge, comprising two parts:

    1. An intelligent person has studied his body and his diet for decades and has identified a diet that supports his activities just fine without disturbing his sensitive guts. It took about 40 years to do it! It might help others.

    2. Others must be in the same situation but, since doctors don’t recognize it, cannot (and probably need not) gain weight. You could research this and publish your results helpfully.


    Frank Gue, B.Sc., MBA, P.Eng.
    Burlington, Canada.



    1. Your story is related to active research our consulting company is doing – without giving away too much, it sounds like you are a good example of figuring out which diet makes you fell healthy. Pro-biotics are a factor that I didn’t mention – they steer your gut bacteria toward good places – thanks for making them appear in the comments!

      I will look into what you say – and pass it on to more biological colleagues. Occupy math is, well, mathy, but I may find an angle.



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