Hi everyone!
Basically what the title asks. I was wondering if there was some sort of one to one pairing between certain phenomena and math concepts. For example, I’ve heard that multiplication is an indication of interaction between two variables.
Another good example of what I mean is Maxwells equations. How was he able to figure out all the details to comprehensively describe electromagnetism? How did he know what math tool to use to depict a real world phenomena?
How can one read these equations and discern what would happen in reality?
Thanks for your time yall!
In: Physics
>How can one read these equations and discern what would happen in reality?
With a good deal of training. That’s a problem I’m actually facing now, and it’s not easy.
So the easiest way to explain this is by pointing out a very crucial fact:
Everything described by math is a MODEL of reality, not reality itself. An approximation. And the job of people developing these models is to make sure that they fit reality as close as possible, but everyone knows they will not be perfect. And sometimes they’re imperfect on purpose, because making them perfect would be too complex. Otherwise we would have wrapped up science by now, nothing more to do
As for how it’s done, there are functions and operations in math that represent some specific things, universally. It’s difficult to talk specifics because that would require explaining the math, and that’s beyond ELI5, but there are universal ways to describe amounts of stuff, how they change, how they move, how they can interact.
Because they have specific meanings, you can put them in different combinations to make them represent more complex things. It’s sort of like a language.
As simple example, if something is changing in proportion to how much of it there is (which most things do), you use the e^x function, because that’s what it does mathematically.
A slightly more complex example. If you want to specify that something isn’t created or destroyed, say water flowing through a piece of pipe, there’s a specific operation that universally describes an amount of “stuff” moving, which you can then define to be water by putting in appropriate numbers. You then specify using that operation that amount entering plus amount exiting equals 0. You have just defined a conservation of mass law, water cannot pop into existence or disappear inside the pipe, only enter through one side and exit the other.
And now for something interesting. But what if you say it’s not 0? Does that break physics? You’re saying that water can be literally conjured from vacuum, quantum style?
No, because remember, it’s not reality, it’s a model of reality. What you can claim is that there’s a water source or drain there. In actual reality, that would be another water pipe of some sort, or a hole in the pipe, and the water keeps existing somewhere and you should keep track of it. But because it’s just model of this one piece of pipe, you can just say “yeah, a specific amount of water just appears or disappears”.
Mathematically it’s literally indistinguishable from magic, and by just looking at the equation you wouldn’t be able to tell where the water comes from and goes. You need the context of what you’re reading to actually understand what it represents, physically.
That’s where the training comes in. You learn to recognise these contexts without being explicitly told. You see some specific symbols in a specific combination and recognise “oh, that’s a liquid”. Then you logically assume that it will obey laws of liquids, that you know.
And if something weird and unusual is going on, then the person making the model has to specify for everyone reading.
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