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moritz comments on Harry Potter and the Methods of Rationality discussion thread, part 13, chapter 81 - Less Wrong
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There could be multiple factors that govern the strength of wizardry. For example the base could be a trained component like muscle strength, but the total observable strength also depends on your ability to control it. If you have very fine control over the magic (ie very precise wand movements, nearly perfect self control for spells that require it), you can make your magic flow much more efficiently. A bit like pulling a lever into the exactly correct direction, or a bit in the wrong direction -- it'll still work, but requires more strength.
If it worked like that, there’s still the question of “what component?” Muscles becoming stronger as a result of exercising them is a complex behavior, governed by many genes. Harry’s reasoning towards one “magic marker gene” suggests that is not the case.
I can think of all sorts of possible explanations, I just can’t see one that looks really reasonable; since we have no actual explanation about how stuff works, you need a lot of assumptions for anything and stuff tends to be arbitrary. If you think about it, all substances being combinations of four elements, or Lamarckian inheritance, are plausible explanations if your only observations are on the level of “some stuff burns” and “water quenches fire” or “children kinda look like parents”.
(“Inventing” new charms is mentioned several times, but there are basically no details about how that works. Harry just changes how to apply a couple of existing charms, and he seems to have figured out how he might pick ingredients for potions, but even there he’s not told where the gestures and ritual come from.)
Maybe using magic doesn't strengthens your magic the way that physical exercise strengthens your muscles, but rather similar to a river carving its way through the landscape -- the more water flows, the deeper the river bed becomes.
Such a mechanism wouldn't require any more genetic information, because it's not a property of the individual magic user.