A literary and scientific approach to goal weight

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As I mentioned in my previous post, if you want to start a diet and exercise plan, you should first decide what your goal weight is, and how long you want to take to get to it. These can be moving targets: I first decided on a goal weight of 180 lbs (from my starting point of 205 lbs); when I got to it without too much trouble, I decided to shoot for 170, then 160, and eventually settled on a final goal weight of 155 lbs. I also decided that I wanted to lose about 1 pound per week, meaning that in an ideal world it would take a hair over a year to achieve the goal. This being the real world, it took more like one and a half years, but I got there eventually. Why it took longer, and how I measured my weight loss accurately, are two things for upcoming columns. For right now, let’s talk about why I ultimately chose 155 lbs for my goal weight.

The choice was based on a combination of scientific methodology and literary research. Literary first: I’m a connossieur of old science fiction stories. If you read old space operas from the 1930’s through the 1950’s, you come across purple prose like this:

Biff Harrison stretched himself up to the full height of his loose-jointed, 6’2” frame. Determination lit up his steely gray eyes. “What do the Centaurian’s want?”, he demanded through clenched teeth, his 185 pounds of hard muscle straining against the force field that held him and Dolores prisoner.

            Dolores cast her eyes demurely downwards: “Don’t make me say such awful things!” she responded in a doleful voice, her cheeks blushing a deep red…

You read similar sorts of things in modern romance novels. The heroes almost universally stand between 6’ and 6’ 4” tall, and weigh between 180 and 185 pounds. Picking the middle of the range, let’s say that our canonical romance/spacce opera hero stands 6’ 2” (1.88 m) and weighs 182 lbs (83 kg). Height varies with weight: shorter people tend to weigh less than taller ones simply by virtue of being shorter. But by how much?

Well, I stand 5’ 10” (1.78 m) tall. Should my weight be in proportion to my height? No, not at all. This is one of Galileo’s great contributions to science, referred to sometimes as the Galilean square-cube law. Weight is proportional to the mass of an object:  mass is proportional to volume times mean density. The mean density of most people is pretty similar, about the same as the density of water. Because of this, my weight should be proportional to my volume.

People are complicated shapes, so let’s consider a simple one. A cube with side length 1 meter has a volume of (1) cubed = 1 cubic meter. A cube with side length 2 meters has a volume of (2) cubed = 8 cubic meters. If the weight of the first cube is 100 pounds, the weight of the second will be 800 pounds because the volume is 8 times higher. (I know I’m mixing English and metric units here – sorry!)

Ideally speaking, then, since the cube of 1.88 is 6.64, and the cube of 1.78 is 5.6, if I want to look like the archetypal romance novel hero, the ratio of my weight to his should be in the proportion of 5.6 to 6.64. This is about 85%, and 85% of 182 pounds is 154 pounds. Voila!  I won’t claim that I look exactly like a scaled-down romance novel hero, but my proportions are decent, especially if you squint a little.

There are other ways of considering this. Galileo pointed out that the weight is supported by the cross-sectional area of the bones, which presumably are proportional to the total body area, i.e., to the square of the height rather than the cube. If I want to have the same “bone cross-section loading” as a romance novel hero, I should make weight proportional to surface area, or height squared, implying an ideal weight of 163 lbs. Indeed, this idea leads to the concept of the Body-Mass index, which is weight (in kilos) divided by height squared (in square meters). The healthy range for BMI is something like 20-25 range for adults, although there is dispute over the proper use of this metric. Under these considerations, the BMI of our typical romance hero is 23.4, whereas my BMI is 22, both in the ”healthy” range.  Either way, the implication is that for adult males of “average” height and build, body weight should change by about 7 lbs per inch of height, or about 4% per inch.

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