Megan McArdle is blogging about weight set points at Asymmetrical Information. The new book by Gina Kolata might be worth checking out. She’s a science journalist who generally does a good job.
Reductionists (get it?) who sniff at various dieting strategies and insist that weight control is a simple matter of "eat less/exercise more" annoy me. They are correct only on on the most superficial and least useful level. Readers know that I occasionally serve as kitchen-table engineering consultant to my husband, who gets paid to control processes among other things. I have an idea — next time he is explaining the latest problem involving material clogging up the piping in the pilot system he’s working on (may’nt be more specific, sorry, this is Based On A Real Process), how about I try opening my eyes wide and innocently suggesting, "There is nothing complicated here. Surely this is just a simple matter of making sure that more material flows out of the pipe than you put into it."
Assume a spherical dieter. (This is engineering school shorthand, paraphrased from the punchline to an old joke about a physicist working as a consultant to the dairy industry, and it means In what is about to follow, please do not bother me with extraneous details, as I have already made a host of assumptions intended to simplify the problem to the bare essentials that are necessary and sufficient, if not actually to solve the problem, then to make a desired rhetorical point about said problem. Note that this requires a little bit of double think since, of course, I’m about to accuse my opponents of oversimplifying the problem. I, on the other hand, am simplifying the problem just exactly enough. For my purposes.)
Here is where the oversimplifying people agree with me. You have to burn 3500 calories to lose one pound of fat. So for every pound of fat that is lost over a period of time T,
(average rate of calorie burning – average rate of calorie intake) = 3500/T [1]
or, more precisely if less linearly,
-d(weight of fat)/dt = (1 lb/3500 kCal) * (rate of energy burning – rate of energy intake) [2]
[UPDATE. I can’t believe I left this out. Rather obviously, there should be a third term in those parentheses: rate of calorie excretion. Some weight loss programs, e.g. the new OTC drug alli or bulimia, rely heavily on inducing the body to excrete some of what’s taken in. So it really shouldn’t be rolled up into a "net" energy intake.]
Energy intake is straightforward to measure, and straightforward if nontrivial to control. It’s that rate of burning part that’s tricky, unless we want to enclose our dieter in a (spherical, frictionless) bomb calorimeter.
The oversimplifiers and I continue to agree on a corollary to that equation: When the spherical dieter’s weight is unchanging, i.e., when d(weight of fat)/dt = 0,
rate of energy burning|t<0= rate of energy intake|t<0 [3].
So anyway, let’s suppose that before beginning a weight control program (t < 0), our spherical dieter’s weight is constant, so that Equation [3] holds. At time t = 0, our dieter begins a program of controlled eating, s.t.
rate of calorie intake (t) = f(t) [4]
where f(t) is some function of t; perhaps it can be approximated as a constant (more jesuitical assumptions here, heh, just wait till August 15), s.t.
rate of calorie intake (t) = F [5].
(F stands for Food. There, that’ll be easy to remember.) And in the meantime, let’s say that before t<0, the rate of calorie intake could be approximated as a constant F0. OK?
Here is where our oversimplifying friends part company with us: They assume that if there is no change in physical activities other than eating, the rate of burning does not change. That leads to the following equation
-d(weight of fat)/dt = (1 lb/3500 kCal)*(F0-F)
— did you notice how neatly the tricky-to-measure part, rate of burning, has dropped out of the calculation? What’s been substituted for it is the rate F0 of energy intake before the diet started. Now, according to this line of thinking, all you have to do is eat less than you did before. Exercising isn’t necessary, continue the oversimplifiers, although of course (they say) it will help you lose weight even faster, according to the following equation
-d(weight of fat)/dt = (1 lb/3500 kCal)*(F0-F) + X
where X is "the extra weight you’ll lose per unit of time because you’re exercising," no further details supplied. Anyway, even if X is zero because there’s no exercise, the problem is simple, say they. Just pay careful attention to F, so that you can keep it always below F0, and weight loss has to follow, according to the second law of thermodynamics or something like that. If it doesn’t, obviously you weren’t careful enough to keep F below F0. Right?
There’s a glaring inconsistency inherent in this argument: the clue is right there in the problem. Can you find it? More on this in another post.
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