## What did you do during lockdown? I estimated my equilibrium energy intake

If it moves, it’s biology. If it smells, it’s chemistry. If it doesn’t work, it’s physics. Or, at least, so the saying goes.

But, as I often tell my postgraduate research students, if it’s physics, it must work. If the theory and the experiment disagree, one, or the other, or both, must be wrong. So, we re-check our calculations, re-check our measurements, track down the source of the discrepancy, and, finally, find data and model agree. That’s physics.

This underlying confidence in physics gave me the temerity to launch on the self-experimentation that led to my latest research paper. I wanted to establish my equilibrium energy intake, that is, the daily dietary energy intake needed for me to maintain a fixed body weight. Signs everywhere recommend 8700 kJ, but I suspected it was less for me; I thought I was taking in that, or less, but still putting on weight. How wrong I was.

Back in 1897 Atwater wrote, “At first thought it might seem very easy for a man to find whether he gains or loses body material on a given diet, and with any particular kind of work, by simply weighing himself on accurate scales.” That was indeed my first thought. I would stick to a given diet. I would do a regular amount of work. Regulating both of these was assisted by being in covid lockdown, which began for me in Australia in March 2020. I checked I had accurate scales and weighed myself systematically each day (wake up, urinate, undress, weigh). My first thought was that finding my equilibrium intake would be “very easy”. How wrong I was.

In a physics lab, to maintain a sample at a low temperature, I first cool it to below the desired temperature. Then, I supply heat at a constant rate. The sample temperature goes up and equilibrates at a new value. If that is too low, I add more heat, and vice versa. This was the approach I applied to my own body. Change the amount I was eating (measured in kJ). Was my weight going down? Then I wasn’t eating enough. Was my weight going up? I was eating too much. Was my weight staying the same? Bingo! I had found the equilibrium energy input.

Easier said than done. The problem was the variability in the weight data. Even when I had checked the scales weren’t the source of variation, my energy intake was identical from day to day over a fortnight, my activity was much the same each day, still my weight fluctuated significantly. Why? My spouse reckons hormones. My impression is that, while there may be a little inhomogeneity in the energy value of the food, it is probably not much; rather, it was day-to-day variations in my activity, which was not monitored very precisely, that caused the fluctuations. Certainly week-by-week I could account for some systematic variation: after running on Tuesday and Saturday, my weight was usually less on Wednesday and Sunday. Perhaps other variations in my activity accounted for the other fluctuations in my weight.

After sixteen weeks and no clear result, I pulled the plug on the experiment, thinking it a failure. But, being a physicist, I decided to mathematically model the data, using the simplest model I could conceive. That model accounted for the data well – the residual fluctuations in the data falling evenly above and below the model. The model gave me not only my equilibrium intake, but a second piece of information as well, the amount by which my weight changes if the energy input is above or below the equilibrium value.

In the end, it worked. That’s physics.

Roger Lewis, senior professor, School of Physics, Faculty of Engineering and Information Sciences, University of Wollongong, Wollongong NSW 2522, Australia.

Competing interests: See research paper