Terence Tao

And there could be one outlier choice of a special number that you stick in that shoots off to infinity while all other numbers crash to earth, crash to one.

In fact, there's some mathematicians, Alex Kontorovich, for instance, who've proposed that actually these Caldatz iterations are like these similar automata.

If you look at what happened in binary, they do actually look a little bit like

like these Game of Life-type patterns.

And in an analogy to how the Game of Life can create these massive self-applicating objects and so forth, possibly you could create some sort of heavier-than-air flying machine, a number which is actually encoding this machine, whose job it is to encode, is to create a version of itself which is larger.

heavier-than-air machine encoded in a number that flies forever.

So Conway, in fact, worked on this problem as well.

Oh, wow.

So Conway, so similar, in fact, that was one of my inspirations for the Navi Stokes project, that Conway studied generalizations of the collapse problem where instead of

multiplying by three and adding one or dividing by two, you have more complicated branching rules.

But instead of having two cases, maybe you have 17 cases and then you go up and down.

And he showed that once your iteration gets complicated enough, you can actually encode Turing machines and you can actually make these problems undecidable and do things like this.

In fact, he invented a programming language for these kind of fractional linear transformations.

He called it FactRat as a play on FortRat.

And he showed that you can program... It was too incomplete.

You could...

You could make a program that if your number you insert in was encoded as a prime, it would sink to zero.

It would go down, otherwise it would go up, and things like that.

So the general class of problems is really as complicated as all the mathematics.

Yeah, if you want to do it, not statistically, but you really want 100% of all inputs for the Earth.