Let’s say you have a division. You’ve got 3/2, where 3 might be acres and 2 might be brothers so from there you could deduce that the division just means that the 3 acres of land will be distributed between two brothers. Summation and multiplication are quite straight forward, but what the hell does one do with multiplication and exponentiation? If I got 20 N-m of torque, wtf does the multiplication tells me there? If something follows a square root?
Please feel free to add any other operations to these. Thanks!
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A N-m is a force multiplied by a distance. If you hold a meter-long stick horizontally and hang a weight of 1 N on the end of it, then you are supporting 1 N-m (at your wrist).
But it can also be 2 N * 0.5 m, etc, which is the same torque.
For exponent you can think of it as area of a square or volume of a cube for the first couple.
If you have a square that’s 200 feet by 200 feet it’s area is 200×200 or 200^2 which is 40,000 feet.
If you have a cube that’s 200×200 and is 200 feet tall you get 200x200x200 or 200^3 which is 8,000,000 feet.
But, exponents in essence are simply a short hand way of denoting specific multiplication problems.
9x9x9x9x9x9x9x9x9 is the same as 9^9.
Multiplication is just synthatic sugar for summation. 5*3 is the same as (5+5+5).
Exponentiation is just synthatic sugar for multiplication. 5^(3) is the same as (5*5*5) which is the same as (5+5+5+5+5) + (5+5+5+5+5) + (5+5+5+5+5) + (5+5+5+5+5) +(5+5+5+5+5)
Rooting is just the opposite of exponentiation. ∛ ( (5+5+5+5+5) + (5+5+5+5+5) + (5+5+5+5+5) + (5+5+5+5+5) +(5+5+5+5+5)) is 5
20Nm of torque means you are applying a force on an object that is equivalent to attaching a 1m long pole to the object and rotating it with a 20N force.
20N is the same as 20kgm/s^(2) and is the amount of force that, when applied to a 20kg rock during 1 second makes the rock go from stationary to moving at a speed of 1 m/s (ignoring friction).
A newton meter torque measured by applying one newton of force against a hanging arm. This measures twisting force, so it isn’t newton times meter, it is just the more newtons you can throw against that arm the more twisting force you have. The meter is just the length of the arm. The American customary unity is foot pound, it is the same idea, put a pound of force against an arm 1 foot long.
You may find it interesting to know that early mathematics was literally just geometry. Algebra and equations didn’t exist. Even the number zero didn’t exist. Mathematics was basically always constructed as a word problem and generally mathematical operations were performed to find a value equal to some length.
I say this to imply that mathematics, in general, was all physically realizable at first.
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