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JoshuaZ comments on Harry Potter and the Methods of Rationality discussion thread, part 8 - Less Wrong
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There's a limit though since we have a decent estimate for how many wizards and witches there are in the world. That gives a strict upper bound on the total number of levels unless some of the levels are completely empty, tthat is something like every 12th level witch is also a 13th level witch. And if that's the case it isn't clear why the levels are being countered separately.
If there are much more powerful levels of magic, our estimate of the number of witches could be wildly off.
How do you figure that? The double-wizard idea doesn't seem to be that there are apparent Muggles with some form of magic. It seems to be that that there are people who seem to be ordinary wizards but really have additional powers. So levels of wizardry should be strictly ordered.
regular wizards have little trouble concealing the existence of their entire culture from every muggle, so presumably double wizards could have similar levels of control over whether or not regular wizards can perceive them. Double witches might be a group that's separate from as well as a subset of regular witches
So the Witches (when compared to Double Witches) aren't analogous to Muggles (when compared to Witches); they're analogous to people. Although we have heard rumours to the contrary, we Muggles tend to just think of ourselves as people, and any Witches that there may be are a special class of people; however (according to some versions of the rumours) there are actually quite a few Witches whom we would never perceive and therefore never even count as people. Similarly, although Witches have heard rumours to the contrary, they tend to just think of themselves as Witches, and any Double Witches that there may be are a special class of Witches; however (according to some versions of the rumours) there are actually quite a few Double Witches whom they would never perceive and therefore never even count as Witches.
In canon, it sounded like some witches pretended to live ordinary lives, and others lived "off the grid" in the middle of nowhere. The same mix might happen with higher-order witches, with some attending Hogwarts, some pretending to be muggles, and others going unnoticed by anybody.
If there are an arbitrarily high number of witch-levels, then the limit is the earth's population, not the magical population. But that's only a potential limit, as witches of arbitrarily high level can support an arbitrarily high number of themselves on one planet (or go to other ones).