A brief aside about Division, Fractions, and Pizza
Mathematics; the science of understanding, deconstructing, and synthesizing abstractions. However, it is not an all powerful art. It is impossible to obtain something from nothing. If one wishes to obtain something, something of equal value must be given. This is the law of equivalent exchange: the basis of all maths. In accordance with this law there is a taboo among mathematicians: divisions by zero. For what could equal the value of a free pizza?
In grade school you’re taught that to think of division in term of a question: “if you have A pizzas and B people, how does each person get if split evenly?” so that 2 divided by 4 is one half, 3 on 9 is one-third, etc.
You are then told that this equivalent to multiplying by a fraction, ie, 2 on 4 equals 2 by 1/4th equals 1/2. The intuition is simply: “if you break 2 pizzas into four pieces, it’s the same as having 2 pieces that are 1/4 of a pizza.”
For dividing by fractions, however, things are less intuitive.
you’re told that you’re supposed to “flip the numerator and—” — at that moment, the discussion is entirely abstract and you don’t have an intuition for why you follow certain rules. Now, under pizza logic, the question is: “if you have A pizzas, and break them into pieces of size B, how many people can you feed?” So 2 on 1/2 is 4, 2 on 1/10 is 20, etc.
Now for division by zero…
under the first version: if you break a pizza into no pieces, you have no pizza, because having a pizza is having a slice of size 1. But if you have a pizza, break into no pieces, then you can’t feed anyone… because serving someone the entire pizza is breaking into 1 piece. So division by creates free pizzas of potentially infinite number, which violates the law of equivalent exchange. Hence the taboo among mathematicians.
