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
OK I’m not a math or science person, just a humble word-fucker and snake of history, so I’m probably wrong about this but I feel like the above is really kind of obvious when you think about it for a few seconds.
Like:
- Math is a Language
- Languages can deal in Analogy/Metaphor
- What does a Spring Do? It stores and releases Energy
- How does Energy interact with Matter? It is stored and released by it[1]
- Therefore, at a sufficiently micro level, all matter can be described via analogy to springs.
- Graphs are analogy/metaphors which describe events as lines through an abstract plane of numbers.
- Therefore, at a sufficiently micro level, all matter(and material interactions[which are exchanges of energy{which is a wave-motion?}]) can be graphed as a spring would(the parabola); which is to say, can be described by the graph of a spring[2].
[1]so could one say Energy is a Wave and Matter its Medium? Or I guess Waves transfer Energy but aren’t, themselves, Energy. So how do Waves relate to Work(Thermo: the transfer of energy due to external macro factors; Physics: Displacement with direction)? Do Waves do Work, or are they Work, or are they analogous to Work?
[2]which: is the parabola a waveform?? Or part of one??? Parabolas always remind me of sine-waves, so maybe this is some bizarre and inexplicable innate bias of mine talking |:T