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?