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MagnetoHydroDynamics comments on Harry Potter and the Methods of Rationality discussion thread, part 20, chapter 90 - Less Wrong Discussion
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Because a stateless system is always simpler than a stateful one.
If it assigns magical ability to living brains with wizard genes, that is strictly lower Kolmogorov-complexityi than identifying a wizard at birth, tagging them and then withdrawing power when they 'die'.
(Stateless means no hidden variables; everything can be decided locally.)
Examples of powerful stateless systems: The basic logic gates, the Link Layer of the Internet (barring traffic control utilities), Lambda Calculus, and others.
You seem to confirm my point. It's a basic logic gate: (wizard genes & alive) = magical ability. remembering that the person was once dead is an extra complication.