# On infinity

## Axiom of Choice

- video from Mathologer
- Link to previous site
- Banch Tarsky Paradox from veritasium

## Law of Excluded Middle

- From ancient greeks
- Assumes every question has an answer
- Is equivalent to AoC

## Computability

- computability & physical universe
- Intuitionism - mathematics as human process rather than discovering nature
- Robert Harper Lectures
- logicomix

### Goedel's incompleteness theorems

You can never know everything. eg. Can God think of a question so difficult that not even God can answer?

## Continuoum Hypothesis

Cantor's argument controversy - people kind of debate about it

CH is independent of ZFC

## Computable Unierse

- Quantization
- Plank limits

### Simulation Hypothesis

TODO: Link to source.

There are counter arguments attacking each of the assumptions, but for me it's that each time you simulate something time slows. This implies that there's a limit to the limit to the depth of simulations.

## Recursion

Talking about simulations, in computation we have this idea of recursion which is a function calling itself. To me links with self-awarenes, a reflective property.

- HOTT infinite tower of types
- fast growing higherarchies
- Dune quote - plans within plans within plans within plans
- or.. a feint within a feint

- self organising systems
- atoms organising into self-replicating mollecules (DNA)
- DNA organising into self-replicating organisms (individuals)
- individuals organising into self-replicating groups (tribes / communities)

- fractals

## Complexity

Maximum complexity is at the middle point between the small and the large.

Geometric average between size of the universe and size of strings is around 1m - weird that no?