just start writing

composition is a consequence of causality

i’d like to reference some dead white men (DWMs)

i’d also like to reference some dead not-only-white not-only-men (DNNs)

what are we asking

in the original essay, wigner tries to answer the question of why mathematics seems to be the right, or best, language for physics

here, we will try to answer a question that either assumes mathematics is the right, or best, language for physics, or if it does not assume it, it at least feels like a question that sibling trajectory

why are composable steps at the core of every system we conceive of?

it’s not obvious that processes must be made up of composable steps

why is causality a chain? why is logic made up of steps?

causality as a chain

hume questioned the necessity of causal connection, saw it as a habit of mind

x causes y if, had x not happened, y wouldn’t have happened

rooted in possible worlds logic

judea pearl uses directed acyclic graphs explicitly

logic made up of steps

frege / bertrand russell / Whitehead, formal logic as stepwise derivation

ludwig wittgenstein logical form as mirrored in the structure of reality, atomic facts compose into more complex facts

brouwer in intuitionism, logic is a constructive mental activity, the steps come from the “mind’s unfolding”

under the hood

why is logic made up of steps

identifying invariance across time makes it so that if we can get from a to b, and we know we can get from b to c, then we know that we can get from a to c. but sometimes things come up on our way from a to b. that’s fine, but that lies outside of the boundary we draw of what we are going to consider. when we draw a boundary, we decide what compositions we care about, and what invariances we will trust.

this “invariance” is a lot like reducing side effects in functional programming

a fundamental question

is this “composition” something that we are discovering in the world, or something we’ve invented?

much like the question of whether mathematics is discovered or invented

what would it look like to have a language for this universal phenomenon we call composition

things

transformations

to be

first, this language must be able to state that things exist

dot with an arrow pointing to itself

to transform

in order for the language to represent more than a universe in complete stasis, we must support transformations

two dots with an arrow going from one dot to the other

examples

mixing paints

deniz is alive

two eggs becomes an omelette

but there might be many paths here

two transformations, one after the other

composition

three transformations, done in any order

associativity

what are some interesting findings in this language

isomorphism