The Perfect Diet Plan

Several years ago I bought a book called Games for the Superintelligent by James F. Fixx.  It contains all kinds of games and puzzles that usually require some twist or non-intuitive creative leap to solve.  The book contains an introduction entitled, "The pleasures of intelligence, and some incidental perils," that relates some amusing anecdotes featuring very intelligent people.  One of the stories theorizes a creative way to lose weight as follows.

Intelligence can cause trouble, too, by teasing the mind into supposing it can solve problems that in fact may defy solution.  One bright man, a person who on occasion enjoys a drink or two, addressed himself to the problem of losing weight while continuing to drink, with, in his own works, the following results.

"Losing weight, of course, is a matter of burning up more calories than you take in.  A calorie, as everyone knows, is defined as 'the amount of heat required to raise the temperature of one gram of water one degree centigrade'

 "Let us take a good glass of Scotch and soda.  Since a gram of water is pretty close to 1 cc (to make it simple), put in plenty of ice and fill it up to about six or seven ounces, making it, say, 200 cc.  Since it contains melting ince, its temperature must be 0 degrees centigrade (negleting the temperature lowering effects of alcohol, Scotch, and gas).

"Sooner or later the body must furnish 7400 calories (200 cc * 37 degrees C) to bring it up to body temperature.  Since the calorie-counter books show Scotch is 100 calories per shot, and club soda as 0 calories, we should be able to sit around all day, drinking Scotch and soda, and losing weight like mad.

 "P.S.: I tried this and it didn't work."  So much for the power of pure reason.

When I read this, I immediately saw the flaw in the proposed diet plan and why it did not work.  The author was too quick to give up on reason and logic because they were not the problem.  The author never reveals the flaw.  It bothered me that a book supposed to be for the superintelligent contained an error like this.  I thought of writing the author, until I saw that the book was published in 1972.  I am sure that the author did receive mail about this and I was far too late.  The author says that some problems defy solutions.  He may be right, but this one is not an example of a problem that defies solution.  His concluding remark, "So much for the power of pure reason" disturbed me the most.  There is absolutely nothing wrong with the reasoning in this case or with reasoning in general.  The reasoning is sound and the math is all correct.  There is just one tiny factual error that invalidates the whole argument.

The fact that I caught the error means nothing more than me knowing a trivial fact that the Scotch drinker and the author did not.  It does not make me more intelligent than either of them.  It does, however, illustrate how easy it is to make errors that can lead to completely wrong conclusions, even for intelligent people.  I am not sure how common the knowledge of the key fact is in this case.  The only reason that I remembered it is because of an experiment I did in a seventh grade science class.

In my science class we were attempting to measure the caloric content of food by burning it and measuring the rise in temperature of a beaker of water.  My partner and I burned a piece of a walnut.  After performing the required calculations we came up with a figure of something like 3500 calories for the walnut piece.  I was pretty sure that this could not possibly be correct.  I showed our results to the teacher, explaining that I thought we made a mistake somewhere.  He said that we probably got it right because it was a reasonable answer.  He then explained the key fact that reveals why the Scotch drinker's diet does not work.

If you already know the fact I learned that day in seventh grade science, then you already know why the diet does not work.  The Scotch drinker was using calories (with a little "c") to calculate how much energy the body would have to expend to raise the temperature of the Scotch and soda while the Calories in the Scotch (with a big "C") are actually kilocalories.  A food Calorie is 1000 of the calories defined as the amount of heat it takes to raise the temperature of 1 gram of water 1 degree Celsius.  So the 7400 calories he thought he was burning were only 7.4 Calories, hardly enough to make any difference at all for weight loss.  An equivalent way to look at it is that the Scotch contains 100,000 calories (with a little "c").  Either way, he was consuming much more than he was burning.

Now that I know more about the Calorie content of walnuts, I think my seventh grade measurement was too low.  It should have been more like 20-30 Calories rather than 3.5.  This may have been partly because we did not completely burn the walnut and because the heat transfer from flame to water was not perfectly efficient.  Some of the heat escaped into the air and some of it heated the beaker.  It could also be that we made an arithmetic error or that the walnut was smaller than I remember.  I have no way now to go back and check.  My science teacher, however, knew the results typically attained from past classes so he knew that our results were in the ballpark.  At least they were not off by a factor of 1000 as the Scotch drinker's were.