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this post was submitted on 03 Jul 2023
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Showerthoughts
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A "Showerthought" is a simple term used to describe the thoughts that pop into your head while you're doing everyday things like taking a shower, driving, or just daydreaming. The best ones are thoughts that many people can relate to and they find something funny or interesting in regular stuff.
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I think it is more than that, the shower is a proper refuge where external stimuli is severely limited. Sounds are limited by the running water, temperature is controlled by the water, visuals are limited, and no one is generally barging in.
When I was studying math at University I had a remarkable number of eureka moments in the shower where suddenly infinity made sense. Smart phones didn't really exist then but showers still held power as a great place to think
This dude literally understood infinity in the shower...
After finishing up calculus and differential equations taking real analysis was a trip! Basically opening up the box that is calculus and seeing why taking the derivative of a function means dropping the exponent and so much more. It frequently dealt with infinity and we went from writing long equations to solving word problems involving infinite doors. It was great
Limits are cool 😁 They open the door to all the 20th century maths and physics. I still don't understand how infinity is treated to get the result that the sum of all natural numbers is -1/12 though. That must use some different definitions, but I'm not sure what.