> But how does that translate to something useful in the real world?
I think this is a by-product of the way we are taught maths at the very start; that it must somehow relate to real things. We start our understanding of maths by using real world objects like apples and we show how addition works and subtraction. I think perhaps it sticks in our head that everything must somehow relate to real objects and the real world.
We somehow get past that when we are introduced to things like square roots and integrals and higher mathematical concepts, but even with those we often try and relate them back to the real world.
I wonder of there are other ways to start teaching maths that doesn't start by using balls or apples? How would that work?
Perhaps not really great examples - I mean you can relate to the length of a diagonal line in a square room, but you can't really relate to the square root of three apples, can you? I'm not trying to say that those example don't relate to the physical world. My point is we abstract more and more away from the "real world" until you get something like this post.
What about complex numbers - the square root of -1, incredibly, is useful in electronics and other real physical systems, but you cannot really relate it to physical objects - or at least not obviously. Or more incredibly something like Banach Tarski [1].
I think this is a by-product of the way we are taught maths at the very start; that it must somehow relate to real things. We start our understanding of maths by using real world objects like apples and we show how addition works and subtraction. I think perhaps it sticks in our head that everything must somehow relate to real objects and the real world.
We somehow get past that when we are introduced to things like square roots and integrals and higher mathematical concepts, but even with those we often try and relate them back to the real world.
I wonder of there are other ways to start teaching maths that doesn't start by using balls or apples? How would that work?