Followup to: Stuff that Makes Stuff Happen

Previous meditation: Does the idea that everything is made of causes and effects meaningfully constrain experience? Can you coherently say how reality might look, if our universe did not have the kind of structure that appears in a causal model?

I can describe to you at least one famous universe that didn't look like it had causal structure, namely the universe of J. K. Rowling's Harry Potter.

You might think that J. K. Rowling's universe doesn't have causal structure because it contains magic - that wizards wave their wands and cast spells, which doesn't make any sense and goes against all science, so J. K. Rowling's universe isn't 'causal'.

In this you would be completely mistaken. The domain of "causality" is just "stuff that makes stuff happen and happens because of other stuff". If Dumbledore waves his wand and therefore a rock floats into the air, that's causality. You don't even have to use words like 'therefore', let alone big fancy phrases like 'causal process', to put something into the lofty-sounding domain of causality. There's causality anywhere there's a noun, a verb, and a subject: 'Dumbledore's wand lifted the rock.' So far as I could tell, there wasn't anything in Lord of the Rings that violated causality.

You might worry that J. K. Rowling had made a continuity error, describing a spell working one way in one book, and a different way in a different book. But we could just suppose that the spell had changed over time. If we actually found ourselves in that apparent universe, and saw a spell have two different effects on two different occasions, we would not conclude that our universe was uncomputable, or that it couldn't be made of causes and effects.

No, the only part of J. K. Rowling's universe that violates 'cause and effect' is...

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...the Time-Turners, of course.

A Time-Turner, in Rowling's universe, is a small hourglass necklace that sends you back in time 1 hour each time you spin it. In Rowling's universe, this time-travel doesn't allow for changing history; whatever you do after you go back, it's already happened. The universe containing the time-travel is a stable, self-consistent object.

If a time machine does allow for changing history, it's easy to imagine how to compute it; you could easily write a computer program which would...

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