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SilasBarta comments on Open Thread: July 2009 - Less Wrong
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The Perceptual Control Theory crowd here (pjeby, RichardKennaway, Kaj) will probably respond with some kind of blackbox control systems model.
I don't have a complete answer, but I can tell you what form it takes.
The quantum states in your body become entangled with a new Everett branch, branches being weighted by the Bohr probabilities. This is what your choice to find the derivative (or not) feels like. These new, random values get filtered through the rest of your architecture into coherent action, as opposed to the seizure you would have if this randomness were not somehow filtered.
I know, not much at the nuts-and-bolts level, but I hope that provides a good sketch.
In a deterministic classical universe, all can be the same for minds and beliefs and decisions as it is in our world. Any good argument should generalize there.
"Entanglement" is the black box there, and PCT, as set out in the materials I've linked to in past posts, is the general form the real answer will take.
The more general answer, but too general to be of practical use, is the one that several people have given already. At some point the hardware bottoms out in doing the task instead of thinking about it.