It’s interesting that you choose dividing by zero as your comparison to infinity, because there are infinite possible solutions to x/0.

It seems to me that by introducing infinites and infinitesimals to mathematics, mathematicians did something similar to how algebra made addition and multiplication “live together” despite their incompatability. By giving definition to something that sometimes can and sometimes can’t work with other parts of math, mathematicians brought the outside in, and fenced the universe.

I also find myself wondering if anyone thinks giving zero a name was a mistake. Zero is the reason there’s an x/0 asymptote.

As someone who read the book, you can answer this question: how often was zero (or nothingness) included in the paradoxes in the book? Without having read it, I’m guessing all of them hinge on some weirdness of 1 (unity), zero (null) or infinity.

It’s interesting that you choose dividing by zero as your comparison to infinity, because there are infinite possible solutions to x/0.

I think if you ask a mathematician what x/0 is, they’ll say “undefined” or “that’s not a valid question”. But if you ask how many natural numbers there are they’ll say “infinity” (or ℵ-zero). But we could have defined x/0 as “foo” to see what resulted, like sqrt(-1) is i. But I think not much results and so people don’t bother, and maybe we shouldn’t have bothered with infinity either.

(I don’t think the same about infinitesimals though! Analysis is a valid field of study!)

how often was zero (or nothingness) included in the paradoxes in the book?

There’s one of the silly 1==2 tricks where a divide-by-zero is obfuscated. There’s a number that involve infinite series, or infinite processes. The chapters on formal systems, voting, physics, etc don’t involve such things though, so I wouldn’t say that they’re all based on it.

It’s interesting that you choose dividing by zero as your comparison to infinity, because there are infinite possible solutions to x/0.

It seems to me that by introducing infinites and infinitesimals to mathematics, mathematicians did something similar to how algebra made addition and multiplication “live together” despite their incompatability. By giving definition to something that sometimes can and sometimes can’t work with other parts of math, mathematicians brought the outside in, and fenced the universe.

I also find myself wondering if anyone thinks giving zero a name was a mistake. Zero is the reason there’s an x/0 asymptote.

As someone who read the book, you can answer this question: how often was zero (or nothingness) included in the paradoxes in the book? Without having read it, I’m guessing all of them hinge on some weirdness of 1 (unity), zero (null) or infinity.

I think if you ask a mathematician what x/0 is, they’ll say “undefined” or “that’s not a valid question”. But if you ask how many natural numbers there are they’ll say “infinity” (or ℵ-zero). But we could have defined x/0 as “foo” to see what resulted, like sqrt(-1) is

i. But I think not much results and so people don’t bother, and maybe we shouldn’t have bothered with infinity either.(I don’t think the same about infinitesimals though! Analysis is a valid field of study!)

There’s one of the silly 1==2 tricks where a divide-by-zero is obfuscated. There’s a number that involve infinite series, or infinite processes. The chapters on formal systems, voting, physics, etc don’t involve such things though, so I wouldn’t say that they’re all based on it.