> I’m going to update towards thinking that integers and square roots are much scarier, richer objects than I’d thought. I’ve updated to being more scared of re

> I’m going to update towards thinking that integers and square roots are much scarier, richer objects than I’d thought. I’ve updated to being more scared of real numbers than I used to be—they have all these sketchy properties like “almost none of them have finite descriptions”. Real numbers, and sets, and logical statements, have all started feeling to me like Cthuluesque monstrosities whose appearances are only tolerable because we only look at the pretty parts of them and don’t let ourselves look at the horrors that lurk below. I don't know much number theory but whenever I poke around at stuff like the Collatz conjecture, it seems like there is something profoundly weird about the interaction of addition/subtraction and multiplication/division. Like each of those pairs defines a totally separate universe and moving between them is irreducibly hard even though the members of both are "just" numbers. By that I mean you can have a number that you understand perfectly well one side (for example, as a set of factors in the world of multiplication). You move it to the other side and perform a trivial operation (say add one). And now you know nothing about it on the other side any more. Maybe this is just me knowing very little about the field.