Yes, but modeling is not just about collecting enough training data, but about discovering the underlying structure.
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Replying to @Plinz
Ahhh. I hadn't thought of it that way just yet. Thinking about flows of information certainly feels like I'm thinking about an underlying structure. But I'm not sure that everything has an underlying structure. Oh I just remembered another statement for my theory!
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Replying to @MagpieMcGraw @Plinz
This one I'm less confident in, but it's this: There is a minimum amount of information needed to complete any task. I get this from programming. A function cannot complete unless you pass it all the arguments.
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Replying to @MagpieMcGraw
That is an artifact of the programming language interface. A functional transition always occurs based on the transition function the system implements for its current state.
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Replying to @Plinz
These terms are getting a little too big for me now. Transition functions and graphs... I think this is where I have to take a break. But it was a fascinating discussion!
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Replying to @MagpieMcGraw
No, "flow" is to big, you only have an intuition. You need to decompose until every element of your model has a meaning that you can fully implement.
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Replying to @Plinz
I think about how information takes intermediate forms and how it undergoes changes when it's going from one place to another. But it's 1 am now I really need to get to sleep. I'll see your further replies in 9 hours.
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Replying to @MagpieMcGraw
A graph is a data structure that consists of a set of nodes and a set of links between them. A transition function is a mapping from all possible states of a system to their sucessor state.
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Replying to @Plinz @MagpieMcGraw
Every system is fully characterized by is state (variable) and its transition function (invarable). Systems allow us to describe dynamic patterns as trajectories through a state space. A change in the transition function means that we change the system and resulting state space.
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Replying to @Plinz @MagpieMcGraw
Those functions that can be expressed as finite sequences of mappings from finite ordered sets of bits to finite ordered sets of bits are called computable.
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All computable functions can be effectively computed by directed graphs implementing NAND gates (= digital computers). The conjecture that the set of effectively computable functions is the same for ALL ways of mapping bit vectors to bit vectors is the Church Turing thesis.
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Replying to @Plinz @MagpieMcGraw
It is possible to mathematically define hypercomputable functions that involve infinite vectors of bits. Such functions are required to describe continuous transitions (for instance in space and time) with infinite resolution.
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Replying to @Plinz @MagpieMcGraw
There is reason to doubt that our universe implements hypercomputation. There is disagreement in physics whether we live in a computable (fully discretizable) or hypercomputational universe.
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