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
Lots and lots of experimenting.
Let’s say you wanted to find a formula for how wire length affected voltage and current.
You’d start by… getting a piece of wire and a power source, preferably of constant voltage. You then stick an ammeter and run current through differing lengths of wire, and chart your measurements on a graph.
You get a straight line pointing down! This tells you that if voltage is constant, current is inversely proportional to length, or I α 1/L.
Now you do the same thing for voltage, adjusting the power source until the current read about the same value each time and then taking the voltage across the wire sections. You plot them on another graph and you get another straight line, pointing up this time! This tells you that when current is constant, voltage is proportional to length, or V α L.
Putting these two together you get V α IL, or V = kIL, where k is a constant.
And then to test your formula you run a bunch more tests and see if your measurements line up with your expected values! If they line up fairly well (and k is indeed a constant) you’ve got the beginnings of a mathematical formula.
TL;DR lots and lots and lots of experimenting.
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