# blog

# What to Ask

This following is a list of questions I've put together in the event I ever end up doing research in mathematics. They represent some of the most important questions that appear over and over again in general mathematics.

I reserve the right to update, rearrange, or change the list at any time.

## The basics

- What can we count?
- How many of them are there?
- How big are they?
- Can you visualize it?

# Data vs Codata

## Infinite lists

OCaml and Haskell are both statically typed functional programming languages. Their type systems are very similar. They both have function types, algebraic data types, higher-order types (list *of* things, maybe/option types, tuple types). They both support type variants of the Hindley-Milner type inference algorithm.

But in Haskell, one often heralded featured is that data types can be "infinite". Haskellers love to showcase this clever one-linear which produces the fibonacci numbers:

```
fibs :: [Int]
fibs = 1 : 1 : zipWith (+) fibs (tail fibs)
```

read more...
# Infinity Plus One

## A school-yard argument

Everyone has, at some point during their childhood, found themselves in a contest to name the largest number. It starts off with perhaps a hundred, or a thousand, then a million, a billion, a trillion. Perhaps the savvy youngsters will know about quadrilions or quintillions.

But at some point, we run out of words for numbers. The argument continues with one-upsmanship. Your friend names a numbers. You tack "plus one" onto the end. They come back with "plus two". Maybe some multiplication gets thrown in there ("a *trillion* trillion!").

The game gets boring pretty quickly, though. You decide it's time to pull out your trump card: infinity!

Surely, you've won. No one can top infinity. It's bigger than the biggest number, after all. Your friend will have to forfeit.

Or so you think. But they comeright back at you: "Infinity plus one!"

read more...# The Halting Problem in Javascript

## The Specs for `Halt`

We suppose the existence of a function called `Halt`

. It takes one parameter: a function, we will call f, that takes 0 parameters. Then `Halt(f)`

returns `true`

if the call to `f()`

ever returns a value, and `Halt(f)`

returns `false`

if `f()`

loops infinitely.

An important part of this assumption is that `Halt(f)`

must always return `true`

or `false`

regardless of your choice of `f`

. It must not itself loop.