Diet Science

I went on a diet at the start of Lent. But instead of just watching what I ate and just watching the scale, I decided to keep the daily record of my weight in a spreadsheet. It was amazing to watch the data unfold.

But not at first. In fact, for the first week, it seemed like my weight was a “random walk”. Give or take a pound and a half, I wasn’t sure I wasn’t doing anything except giving up donuts for Lent (which, in fact, I did. That was the start of the diet).

But by week two, it seemed that there was a difference, if slight. By week three I thought to use the spreadsheet’s graphing function, and plotted the data I had. It actually looked like there was a (slight) downward drift. By week four, I started to plot not only the data set, but also a “least squares” linear fit through the points. Sure enough, the line showed me an 82% correlation coefficient, and also told me that I had a real weight loss that was almost hidden at first by noise!

Noisy data. Go figure.

I used to teach university physics, many years ago, and sometimes I wish I could do that again, just to show the students the science behind this simple exercise. Really! Instead of those once-a-week labs, where students in the ’70s used 1940s equipment on a canned experiment that someone thought demonstrated something meaningful in the ’30s, there’s no reason that students couldn’t get more out of a simple bathroom scale.
Think of it.
Data gathering – the weigh in. Answer this – what is better science; weighing yourself daily, or weighing yourself just before breakfast when you can?
Data reduction – can you calibrate your instrument? Did you “zero-out” the scale? How do you know that the spring in the scale isn’t losing its spring slowly as you weigh something as heavy as you for a semester?
Data reduction – can better calibrations be done? How do you know that when the scale says 150, it really means 150, and that when it tells you you’ve lost 10 lbs, it isn’t really 9? Can you figure out a better way to view what the scale is tell you?
Data reduction – You carefully calibrate your scale, you make sure that the measurement is taken with as few varying factors as you can, and you find that there’s still noise in the data, because the human body is inconstant. We can easily fit a straight line though the data, and use that line to give us a better measure of our weight. What does that line tell us about our weight in a month? 6 months? 10 years? For me, the straight line currently says that sometime in September of 2009, I will weigh 0 lbs. What does this mean?
Data interpretation – Does an exponential curve fit the data set better? If it does, what does it mean? What assumptions are we making if we chose a particular curve, and especially what hidden assumptions are we making when we chose a curve to fit the data?
Data interpretation – How good is our curve when we extrapolate outside the range of the data?
Wisdom (and extra credit) – Apply these principles to the science behind global warming.

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