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In my previous post about weight control I noted that there was a glaring inconsistency that is inherent in the argument of oversimplifiers who say that to lose weight, a dieter need only carefully make sure that he takes in fewer calories in the future than he takes in now at his current stable weight.

The glaring inconsistency:  Before the diet, the dieter’s weight is stable (if too high) without any careful attention.

Oh sure, there are plenty of people whose weight is increasing if they don’t pay attention, who have to carefully control their calories so that they don’t gain.  Most of these are people who used to be fatter.  (I’m one.)   But the argument is generally about someone whose weight is stable before they begin weight loss.  And there are lots of those people.  Fat ones and thin ones.  I was one for years.  My weight was the same, slightly over the overweight/obese boundary, before and after three pregnancies.   Never budged more than a pound on either side, without really paying any attention to it.  My husband is one too.  He does not have to do anything conscious to keep his weight constant.  It’s always the same healthy weight. 

That’s the set point idea that Megan was blogging about.  The evidence for it is simple:  Lots of us stay the same without paying careful attention to our calorie intake.  But get this — if the assumptions of the oversimplifiers were correct, that without exercise rate of energy burned is essentially constant, it ought to be much more difficult to remain at a constant weight than to gain or to lose.  It ought to require near-constant vigilance to remain precisely balanced on the knife-edge of the equation (rate of energy burned = rate of energy intake).  And yet, it is easy.  The hard part is falling off, at least to one side.

Clearly there are nonlinearities here.  Rate of energy burned is some function of rate of energy intake, or else both are functions of some third thing.

So take the rate of energy burned apart.   Let’s turn our spherical dieter into a spherical exerciser, and start thinking less about mass/energy balance than about thermodynamics.

Rate of burning = power exerted by body + rate of heat dissipated from body

Did I miss anything here?  I don’t think so, but this doesn’t seem to be the most useful partitioning of the energy balance.  Let’s think like engineers instead of physicists. 

Rate of burning = power exerted by acts of will + (power exerted + heat dissipated) involuntarily

The first term is a function of things like how many steps we take over the course of the day, how often we go to the gym, how fast we move while we do our housework, that sort of thing.  Also how heavy we are, because a lot of that power is the power necessary to accelerate and decelerate our own bulk!  To a great extent, we can increase and decrease that first term.  By definition, there’s nothing we can do directly to influence the second term.  It includes stuff like how much heat our body puts out while it’s breathing and digesting.  And there is no basis for believing that it is constant.   What if our body had a secret mechanism that tunes the second term down when the first term goes up?  Then taking the stairs instead of the elevator wouldn’t help much now, will it?

I happen to think it’s more likely that our body’s mechanisms tend to tune the second term up when the first term goes up — we’re told that muscles burn energy at rest, so anything that encourages your body to build muscle (cf. picking up heavy stuff and putting it down again) ought to cause your body to generate more heat. 

But I also think it likely that the second term depends on other things.  Like the difference between calories taken in and calories excreted — that whole idea that "your metabolism slows down when you eat less."   Or on what macronutrients you’re eating:  why wouldn’t the fat/carbohydrate/protein/fiber ratios that go into your mouth affect your personal engine efficiency?   

So let’s update the equation. 

-d(weight of fat)/dt = (1 lb fat/3500 kCal)*(power exerted by acts of will + involuntary power + involuntary heat + energy excreted – energy consumed)

where power exerted by acts of will is a knowable function of what you do, energy consued is a knowable function of what you eat, and — here’s the tricky part — involuntary power, involuntary heat, and energy excreted are essentially unknowable functions of what you eat and what you do.

And that’s not even getting into the idea that (what you eat) and (what you do) are themselves rather complicated functions of each other, some involving feedback loops.   Who’s got less willpower when she’s tired?  Anyone?  Who’s got experience with the "you can’t eat just one" aphorism, besides Frito-Lay and Alcoholics Anonymous?  Hmm?

So.  No, it’s not that simple.  And so people who have trouble losing weight are not stupid gluttons.  They’re struggling with a complicated controls problem. 

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.

The house is a mess.  I have a very strong temptation to blog about that, perhaps constructing a post about the order in which I will attack the various tasks involved, instead of getting off my butt and simply cleaning it up.  I am happy to report that after some struggle, I have prevailed against that temptation.

…Damn.