ok listen as a kid i thought science had to be super rigorous 100% exact all the time but it turns out at high levels it is all approximations all the time, theres not really a point to this post i just want to spread awareness of something we have to do
the equation for force on a spring is pretty well known, kx^2 (quadratic, goes with the square of the distance). the graph looks like this
here comes part one of the bullshit: theres a mathematical technique called a taylor expansion where you can take any equation (as long as it doesnt do a few mathematically rude things) and turn it into a bunch of polynomials (a+bx+cx^2+dx^3), which makes things a lot mathematically simpler
part two of the bullshit: if you zoom in real small you can ignore most of the latter terms, so its basically just a x^2 equation
so basically if you draw any goddamn squiggle and zoom in REAL close it looks like a parabola and therefore any REALLY small thing acts like a spring
atoms in a molecule. bumps on a road. electrons in an atom (before you get to the nasty stuff). just now i was thinking about bubble wrap. a weight on a pendulum. probably, like, interpersonal relationships. its all springs. boing
i found out recently that the very first trees did not rot when they died because the microbes that decompose trees hadnt evolved yet…which makes sense but it’s weird to think about. this actually caused a huge change in the climate at the time and many of these trees turned into coal because of it…
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