structure
(immaculate) conception: an exploration of intuitions behind systems and thoughts
framing
functional programming
category theory as a level of abstraction above other maths
sets, algebra, topology
(de)composition
on intuition of composition
some simple examples
movement
cooking
any set of actions that can be tied together
eg open the door, then walk into the room
but if the door is open i dont need to open the door, so maybe it’s
check if the door is open
if it’s open, walk in the room
if it’s not open, open the door, then walk in the room
what i’m trying to do is to communicate some of the reason why i’m attracted to some of these ideas
dare you to see composition all around you and imagine if it looks
physics of systems?
What is a system?
a process that takes some inputs and produces some outputs
transformer
system dynamics example?
A system is composed of components. A component is something you understand.
howard aiken
functional and formal decomp
dsm
physics of thought?
let’s say thoughts and language are interchangeable for now
semantic triples, resource description framework
thoughts are essentially references to other thoughts
why is a raven like a writing desk
physics of logic?
Propositions
curry howard lambek isomorphism
type theory
logic
types of category
physics of causality?
Space time requires us to think about movement as something that traverses both space and time and because of that that’s where composition comes from the idea that transformation happens and something stays invariant
(formal) construction: intro to category theory
what is a category?
dots and arrows
identity
it is raining -> it is raining
composition
it is raining -> it is cloudy -> earth has clouds
associativity
it is raining -> it is cloudy -> earth has clouds -> earth has an atmosphere
commutative diagram
what emerges from this structure?
isomorphism
it is raining <-> rain is falling from the sky
user ids <-> ssns VS user ids -> first names
universal properties
everything as relational
terminal, initial objects
“bestness” and uniqueness
limits, products
enriched categories
morphisms with structure
$\infty$-categories
morphisms between morphisms (and beyond)
(can anyone see the punchline?)
categories of categories
Cat: a category whose objects are categories
functors
maps between categories
morphisms in Cat
natural transformations
morphisms between functors
“translations between translations”
some sketches: examples like logic, co-design, system dynamics, etc
conversation
concerns
consequences