$300 Fermi Model Competition

I’m not sure if this is what you’re looking for, but here’s a fun little thing that came up recently I was when writing this post [LW · GW]:

Summary: “Thinking really hard for five seconds” probably involves less primary metabolic energy expenditure than scratching your nose. (Some people might find this obvious, but other people are under a mistaken impression that getting mentally tired and getting physically tired are both part of the same energy-preservation drive. My belief, see here [LW · GW], is that the latter comes from an “innate drive to minimize voluntary motor control”, the former from an unrelated but parallel “innate drive to minimize voluntary attention control”.)

Model: The net extra primary metabolic energy expenditure required to think really hard for five seconds, compared to daydreaming for five seconds, may well be zero. For an upper bound, Raichle & Gusnard 2002 says “These changes are very small relative to the ongoing hemodynamic and metabolic activity of the brain. Attempts to measure whole brain changes in blood flow and metabolism during intense mental activity have failed to demonstrate any change. This finding is not entirely surprising considering both the accuracy of the methods and the small size of the observed changes. For example, local changes in blood flow measured with PET during most cognitive tasks are often 5% or less.” So it seems fair to assume it’s <<5% of the ≈20 W total, which gives <<1 W × 5 s = 5 J. Next, for comparison, what is the primary metabolic energy expenditure from scratching your nose? Well, for one thing, you need to lift your arm, which gives mgh ≈ 0.2 kg × 9.8 m/s² × 0.4 m ≈ 0.8 J of mechanical work. Divide by maybe 25% muscle efficiency to get 3.2 J. Plus more for holding your arm up, moving your finger, etc., so the total is almost definitely higher than the “thinking really hard”, which again is probably very much less than 5 J.

Technique: As it happened, I asked Claude to do the first-pass scratching-your-nose calculation. It did a great job!

Related Manifold question here: