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glumph comments on Harry Potter and the Methods of Rationality discussion thread, part 12 - Less Wrong Discussion
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That doesn't mean the Founders could do the impossible. Saying that "it just uses your name" might be true, but it doesn't tell us how it can use your name. There must be a way that it works (although it may very well be that there is no consistent way-that-it-works that can be extracted from the text). Compare this to another example in which the creator of an artifact "thought about the problem" differently:
Broomsticks don't work the way we would expect them to work, because that's not how Celestria Relevo thought about the problem, but that doesn't meant there isn't a way that they work.
To clarify, what I believe is that magic works in a top-down way, not a reductionist way. If you were writing a computer program, you would have to specify where the name comes from and what to do in marginal cases. But the Founders believed that each individual came with an XML-tag name attached to them, and the map just tries to figure out that name.
I realize this is an incomplete theory because it doesn't explain what the map does in weird borderline cases (although I can make guesses). I am using this theory (which we can derive by comparing the map to Harry's pouch, and to broomsticks, and to Transfiguration) to reject hypotheses that involve a reductionist, computer-program approach to magic.
The Founders may have been Truenamers, in which case each person who walked in would have a singular name attached to them.
So the Map can't find married women?
The reason Voldemort brainwashed Bellatrix was in order to marry her in absolute secrecy, unconventionally taking her last name for his own (this is also the reason she is not married to Lestrange in MoR). As a result, his name will show up as "Tom Black" on the map, and Dumbledore's "Find Tom Riddle" instruction will do nothing.
My guess is that, in the world of HP:MoR, the Simulation Argument is true. Muggle science works within the boundaries of the simulation; magic operates directly on the underlying data structures, bypassing most of the Muggle-oriented interfaces by using debugging APIs. That's why it has rules that make some sort of sense, but that don't correspond to most laws of nature as Muggles understand them. Of course, the virtual machine that powers the "reality" of HP:MoR is fairly robust, which is why magic is relatively safe (i.e., you can't crash the whole of reality with a miscast Lumos), and also why magic is not all-powerful (those debugging APIs are still fairly limited).