How do we know math isn’t wrong? Like it works but could it only work due to our perception?
In: Mathematics
The first thing to understand is that math is not a part of science. Math doesn’t rely on the real world to be right or wrong. It’s right or wrong on its own. Math is right if it is internally consistent, regardless of whether it is useful for something in the real world. What’s neat is that much of math *is* useful in the real world.
Basically, the way math works is you make up a few simple rules. You then take those rules and see where they lead the more you play with them. If you find a set of rules that does interesting things, you’ve found some interesting math. If you find a set of rules that can describe things in the real world, then you’ve also found something that may be useful, besides also being interesting.
It can’t really be wrong. Math is a thing we created much like language. So you’re basically asking how do we know english isn’t wrong.
You can think of math as a language and we use it to describe things in the physical world or to describe financial transactions or whatever. Over time many people agree on the basic definitions and properties of that language [ 2^4 = 16 and Sin(45) = 0.707]. So the “language” is correct if we all understand it and use it in a consistent way. How do you know that the meaning of a specific word isn’t wrong? Because most everyone who uses that language agrees on it meaning and the way the word should be used. Then when you get to the question of… does this equation correctly describe this physical phenomenon, you are in the realm of physics and we’ve all agreed on the language we are using to solve that problem in physics.
Math is an internally consistent set of rules. We use it for convenience and apply it to the real world, but math does not itself describe reality.
1=1 in math. 1 apple = 1 apple in math if we define an apple as a unit.
But in the real world apples are not equal. They can be different sizes, quality, types, etc.
So the math is correct as math. It is not correct when applied to the real world.
Math is a tool. It can be used incorrectly.
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