I haven’t posted something to the blog in a while, but I’m glad to return with an important question, one you’ve asked yourself many times: “Should Jim use shampoo?”
While showering today, I realized that I use the stuff mostly out of habit. Even though I’m not sure it’s actually better for hair than plain ol’ soap, I’ve been so thoroughly brainwashed (or something-else-washed) by the Hair Care Industrial Complex that I’ll take its indispensability as a given. However, I also have to take as a given the length and amount of hair I have on my head nowadays. I should have done that long ago, in fact, which is why I wondered whether I’ve reached the point where it makes better overall sense to just use bar soap. But how to decide?
When in doubt, turn to math.
Start with the average diameter of human hair: via en.wikipedia.org/wiki/Hair, it’s 0.0017-0.018cm…let’s call it 0.01cm, though I expect mine is actually on the thin side.
Length of my hair: I cut it to about 0.15cm, and unless I get lazy, the longest it gets is about 0.3 cm…so let’s call it 0.2cm.
Combining these, and assuming each hair is a perfect cylinder, that yields an exposed surface area for each hair of π(0.01/2)^2+π(0.01)(0.2) = 0.006cm^2.
Head hairs/unit area skull: approx. 100/cm^2, via //www.baldingblog.com/category/density/page/5/, which I am glad exists even though I don’t ever plan to visit again.
Diameter of my skull: approx. 17.5cm, so if we assume it’s a perfect hemisphere, that gives an area of 0.5(4π(17.5/2)^2) = 480cm^2.
Coverage: Ahem. I’ll use my wife Kat’s charitable estimate of 60%, even though I think it’s thinned from its original (and presumably average) density, which would mean I should use a lower number to compensate.
So, the surface area of hairs I have left is 0.006*100*480*0.6 = 173cm^2, which is substantially less than the exposed skin surface of 480-π(0.01/2)^2*100*480*0.6 = 478cm^2.
The conclusion is clear. Now, will I get less soap in my eyes?