How has the concept of zero acceptance historically been controversial?

Question

I just watched Young Sheldon, and the episode discussing the zero dilemma really intrigued me.

In: Mathematics

Answer 1

It, and negative numbers, introduce uncomfortable paradoxes. All cultures basically understood zero could exist, but the axiom was ‘nothing can’t exist’. That is a whole ball of wax that includes ideas of things like ‘the void’. Zeno’s paradoxes can easily be broken if we accept the idea of zero, the void, nothing is a countable value. Even negative number made more sense even though they obviously didn’t exist. -1 + -2 = -3 and the like. 0 + 0 = …0. Any number times zero is magically turned into zero. I say it is paradoxical because to accept zero exists, then by definition it can’t be nothing. This isn’t new, all of computer science is based off of a self referential paradox, but that isn’t what we are talking about here.

Keep in mind that ancient peoples took math a lot more literally. Countable items existed because we needed to buy and sell, if you have zero transactions you don’t write anything down. In geometry you can accept you have zero subdivisions in a ratio (something like zero halfs) but you started out with *something* to create a half, you just don’t have any of them.

Due to the paradox of something that exists that doesn’t exist, people got religious about it, even calling those who considered zero to be ‘real’ atheists, or non believers. It was similar to the uproar against atomism, how can the void exist? Turns out the atomists were more right than wrong, but it kicked up a zeal in people. As Arabian mathematicians invented and worked with algebra, it became obvious that zero caused things to make sense. They started accepting the idea that math could include concepts that aren’t directly related to anything in our physical world. That evolution was important to ideas like ‘the imaginary plane’ (Euler) and powers higher than 3 (Descartes). Remember a power is a dimension, so 1 is a line, 2 is a ‘square’, and 3 is a ‘cube’. That last one gives us our three dimensional world. What the heck is the power of 4, well, it is a tesseract, and it does not exist in our world in anyway we can perceive.