## Sunday, May 27, 2007

### The Fundamental Theorem of Weight Loss

Background:

"Low-Carb Diets Get Thermodynamic Defense", on Nature.com.

"Is a calorie a calorie? Biologically speaking, no" in Letters to Am. J. Clin. Nutr. 2004;80:1445-54.

Feinman RD and Fine EJ, Thermodynamics of Weight Loss Diets, Nutr. Metab. (Lond.) 2004 Dec 8;1(1):15.

Fine EJ and Feinman RD, "A calorie is a calorie" violates the second law of thermodynamics, Nutr. J. 2004 Jul 28;3:9.

Recently I gave my physics students the following scenario, basically just for fun:

Imagine what would happen if food scientists were to invent a kind of intense "supersweetener" with 3500 calories in a single ounce. If you were to ingest an ounce of this sweetener, then how much weight would you gain?

A few of the students knew offhand that 3500 calories is the equivalent of a pound of fat. So everyone figured, well, if you ingest 3500 calories, then you should gain a pound.

But obviously, if you ingest only one ounce of material, then your weight could not increase by any more than one ounce.

The students hated this answer! For one thing, many of them had forgotten (or never known in the first place) that mass is always conserved in chemical reactions. And they had also never really viewed human metabolism in the abstract as just one great big chemical reaction; even the biochemistry students were down in the details of ATP and such.

So I said, well, just imagine that you're standing on a scale when somebody hands you the ounce of supersweetener. As soon as they put it in your hand, the scale will tick up an ounce. And nothing more will happen when you swallow it. The scale doesn't know or care whether you're holding the supersweetener in your hand, or in your mouth cavity, or in your stomach cavity. And as you digest the supersweetener, the molecules will separate and go here and there, but until they emerge from your body and find their way into the environment, the scale reading won't change one bit.

There's a Fundamental Theorem of Calculus, a Fundamental Theorem of Algebra, and a Fundamental Theorem of Poker. I nominate the following as the Fundamental Theorem of Weight Loss:

Weight loss per day = mass in - mass out.

(You'll have to forgive the conflation of weight with mass; I'm assuming that all weight loss programs will take place in a static and uniform gravitational field, so that it will not cause a problem.)

According to the Fundamental Theorem of Weight Loss, if you want to lose weight, then your challenge is simply one of routinely defecating, urinating, sweating, vomiting, and exhaling more mass than you ingest on any given day. (You could also amputate something, deliver a baby, clip your toenails, get a haircut, or hawk a really big loogie.)

By the way, people suffering from eating disorders have long understood the Fundamental Theorem. With a ruthless logic, the anorexic minimizes the "mass in", while the bulemic maximizes the "mass out" using the ultimate weight-loss "foods", namely laxatives and purgatives, which trigger mass losses in excess of their own mass.

But if "mass in minus mass out" is all there is to weight loss, then why all the talk about counting calories? Don't calories make you fat?

Calories do in fact work well as an indicator of the kinds of foods that tend to make you fat. So in view of the Fundamental Theorem, calories must basically be a rating of how much the human digestive system "grabs onto" different foods. Eat a piece of celery, and most of its mass will find its way out of your body through defecation (cellulose passes through) or urination and respiration (much of the mass of celery is water). But eat a Snickers bar, and your body's going to say hey, let's hang onto that good stuff. Eat an extra two-ounce Snickers bar every day, at something like a fifty percent mass retention rate, and at the end of a year you'll be 20 pounds heavier.

So here's an idea: Instead of printing calorie counts on food labels, why not show the weight you will actually retain by eating the item in question? For example, the label on a candy bar with a net weight of 2 ounces could say something like, "Retained Weight 1 ounce." In other words, of the 2 ounces of input mass, your body's going to hang onto 1 ounce for the long term.

Labeling foods this way might make it easier psychologically for people to resist foods that are going to make them fat. The motivation factor would be clearer because you're no longer trying to avoid the abstract threat of a calorie; instead you're scoring yourself by the very same metric that shows up on the bathroom scale. If you knew exactly how much of that candy bar was still going to be with you in the morning, you might pass it up. (Thanks to the Fundamental Theorem, I can now visualize the act of eating a candy bar as amounting to a process of melting the chocolate down and smearing it all over my midsection. Want to eat a whole pizza? Why not just save time and staple it to your shirt front. Will that Twinkie go straight to your thighs? Well, not all of it - just half an ounce or so.)

Something else the students challenged me on is the question of exercise. Isn't the goal of exercising to burn calories? If "mass in minus mass out" is really all there is to weight loss, then how does exercising help you to lose weight?

Somehow, exercising must turn out to be an exercise in the expulsion of mass, the key mechanism presumably being breathing out CO2. CO2 molecules don't weigh much, but they weigh a lot more than the O2 molecules you breathe in to fuel the metabolic process--about 30% more.

There are charts that tell you how many calories you will burn by exercising in various ways for given lengths of time. But maybe the charts should cut to the chase and tell you how much mass you can expect to lose by exercising in various ways for given lengths of time. Personally, if my goal is to change what the scale says, then I'd prefer for everything in the conversation to be couched in the scale's units.

We might for example have a universal table like the following, which I sketched out using the rough conversion 8 Calories "=" 1 g of fat (sources here and here):

Butter: 90 grams retained out of every 100 grams consumed (sigh)
Bagels: 25 grams retained out of every 70 gram bagel consumed
Beef tenderloin: 1.2 ounces retained out of every 4 ounces consumed
Carrots: 0.2 ounces retained for every 4 ounces consumed
Jogging: 17 minutes to lose 1 ounce (for a 190-lb person)
Raking leaves: 33 minutes to lose 1 ounce (for a 190-lb person)
Rowing: 14 minutes to lose 1 ounce (for a 190-lb person)

***

Postscript: I first thought of the Fundamental Theorem of Weight Loss back in 2004, but this past semester was the first time I tried using the example in class. Well, my students were pretty skeptical of the whole notion. With my pride thus challenged, I went to the web later that night and found two experts, Dr. Richard Feinman of SUNY Brooklyn Health Sciences Center and Dr. Eugene Fine of the Albert Einstein College of Medicine, who have been publishing technical papers on metabolism and diet for quite some time. The papers linked to at the top are very much concerned with the question of whether "a calorie is a calorie is a calorie."

The two men were kind enough to respond to my emails, and I'm hoping that they will come to Bennington sometime to discuss their work. They verified the truth of the "mass in minus mass out" thesis - as an application of basic physical law, it could hardly have been wrong - and they also had many more interesting things to say. Two brief excerpts from their emails:

"Calories in the context of diet are a nutritional invention with many unfortunate and misleading consequences, but the concept has become so entrenched that it is impossible to discuss weight change without making reference to this usage." (Fine)

"This established, the remarkable thing is that, under most conditions, where careful measurements are made, a calorie IS a calorie, that is, the calories in food predicts weight gain or loss between diets. The above, however, means that this is not a thermodynamic effect but rather the specific characteristic of living systems." (Feinman)

So calories seem to work well as a proxy for mass retention.