just start writing

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composition is a consequence of causality

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

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

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what are we asking

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

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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

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

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

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

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causality as a chain

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

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

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rooted in possible worlds logic

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judea pearl uses directed acyclic graphs explicitly

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logic made up of steps

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

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

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

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under the hood

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why is logic made up of steps

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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.

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

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a fundamental question

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

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much like the question of whether mathematics is discovered or invented

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

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things

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transformations

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to be

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

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dot with an arrow pointing to itself

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to transform

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

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

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examples

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mixing paints

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deniz is alive

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two eggs becomes an omelette

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but there might be many paths here

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two transformations, one after the other

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composition

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three transformations, done in any order

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associativity

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what are some interesting findings in this language

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isomorphism

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