## Monday, July 11, 2011

### Calories in vs. calories out?

Note: this post may be triggering to readers with eating disorders. I've put it behind the jump.

Also note: there is math talk, including differential equations, in this post. Don't panic. I've explained the math in English.
Over at Consumerist, commenter RecordStoreToughGuy_StarCommandSeasonOneisLive! writes:

I have an amazingly fool-proof weight loss plan that is GUARANTEED to work. I'll phrase it in the form of a simple Mathematical equation: E - C = WEIGHT LOSS*, where E is energy expended and C is calories. If you expend more energy than you take in, you'll lose weight.**
*I am not good at math, so this equation is probably expressed incorrectly, but I'm guessing you get the point.
**Energy levels vs. Caloric intake vary from individual to individual; some individuals may need to expend way more energy than they take in than others to achieve goals.
A lot of people say this when the subject of weight loss comes up. "It's simple math! Calories in vs. calories out!" But the math really isn't simple at all.

Weight loss is more accurately modeled as a system of differential equations: dW/dt = f(E,C), dE/dt = g(E,C, W) and dC/dt = h(E, C, W), where W is weight, E is energy expended, and C is calories taken in.  f, g, and h are all probably nonlinear functions.

In English, the change in your weight depends on the difference between what you eat and how much energy you expend. But the energy you'll expend tomorrow, and the calories your body would naturally be hungry for tomorrow, change based on on how much you move and eat today, and on what you weigh today.

In even shorter English: weight loss is a moving target. Everything affects everything else.

The problem is that we don't know exactly what f, g, and h are. Or in English, we have no idea exactly how everything affects everything else.

You can hold C constant or near-constant. So you can make dC/dt zero, or at least fairly small. That takes care of h. In English, that means you can eat a fixed (or nearly fixed) number of calories every day, so the amount of calories you take in isn't affected by anything else. (At least in theory, or if you are in a medical study where your diet is rigidly controlled by others. In real life, good luck forcing yourself to eat an identical number of calories every day for any length of time.)

You can exercise -- but the amount of energy you actually burn during exercise is hard to actually measure. And your resting metabolic rate (RMR) -- how much energy your body uses just to stay alive -- is completely outside your direct control. There are certain ways of measuring RMR, which are fairly accurate. But it's expensive and somewhat difficult to make those measurements. And energy consumption is quite variable between individuals. Lean body mass affects it; body fat affects it; sex affects it; age affects it; the amount of exercise you usually do affects it. But even these factors don't explain all of the variability. Some of it is probably genetic.

People argue that f is simply E-C, or in English, that weight loss is simply burning more calories than you consume -- but that's not true. For one thing, water weight varies a lot depending on what you eat, how hydrated you are, and what your hormones are doing. But a bigger factor is how your body stores and accesses energy. And that's a really complicated topic. It depends in part on your body's secretion and breakdown of insulin and glucagon. People devote entire careers to teasing out some understanding of this. If we knew exactly how it worked, we'd have a magic weight loss pill.

There's plenty of empirical evidence to show what range of caloric intake and exercise amount is likely to result in a healthy weight. But it's not an exact science. At all.

Izzy said...

"Weight" in this context just a rough way to measure body fat percentage. Normally measuring your percentage of body fat with any degree of accuracy requires prolonged immersion in water inside a specially designed tank, but if you take height and gender into account you can estimate body fat within an acceptable margin of error just by stepping onto a scale. Having body fat above a certain percentage is correlated with all sorts of medical problems, including the leading cause of death in our country.

Weight delta may not be well correlated to the actual difference between energy absorption and expenditure, but the correlation does exist, and bodyweight scales represent the best effort to accuracy ratio in tracking changes to our dietary health.

Eat less, exercise more, be healthier. That is the point. Who cares if the numbers line up?

Tor Hershman said...
This comment has been removed by the author.
Tor Hershman said...

'Splain in Engrish.