Units, Human Power Draw, and The Deepest Fact You Will Read On This Blog

Today I Learned:
1) A watt is 1 Joule/second. I should have known there would be a stupidly simple relationship between the two.

2) Fact 1 leads to fact 2. I know, from previous lectures and other sources, that the human body generates approximately the same amount of heat as a 100 watt lightbulb. That also means it's drawing about the same amount of power (though chemically instead of electrically). That means we can peg the approximate power consumption of the human body at around 100 jouls/second... which finally gives me a meaningful reference point for a joule -- about 1/100th the energy required to power a human body for 1 second.

3) The sum of all the whole numbers is -1/12. Yeah, (1 + 2 + 3 + 4 + ...) = -1/12. This is probably the most ridiculous, bizarre, and potentially insightful fact (if I can really get why it's true) I think I've ever written in this TIL series. And yes, I know it's obviously false; and yes, it's actually true.

This 'fact' was discovered hundreds of years ago by a well-meaning monk, and was the subject of much debate for a century and a half. I think the mathematicians eventually came to the consensus that it's true, but the real kicker is that this sum comes up ALL THE TIME in physics, and the identity (1 + 2 + 3 + 4...) = -1/12 makes the physics come out to the physically correct, experimentally-verifiable answer. This is the first time I know of that a physical experiment has confirmed a mathematical result*.

There's a nice video about this... thing here: https://www.youtube.com/watch?v=w-I6XTVZXww. Personally, I think the proof in the "extra footage" video linked from the above video is more convincing. Check them both out, though! *I say this with some glibness -- again, I think sure mathematicians were convinced well before it turned up in physics... but it certainly is what convinces me.