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fowlertm comments on Doubt, Science, and Magical Creatures - a Child's Perspective - Less Wrong
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It's also possible that, in concealing the information from your parents, you also managed to conceal it from the TF as well. It would be much, much harder to figure that out experimentally, given how little we know about the mechanisms by which purportedly magical beings interact with information.
True but my prior on that was about an order of magnitude lower than my prior on the tooth fairy being real at all. It's not necessary to explain the phenomena if it gets the info via parents.
In my household, it's well established that Santa Claus is in regular contact with the parents; Tooth Fairy lore is less well established, but that makes this a reasonable hypothesis. In yours, maybe not.
The straightforward way would be to simply ask the parents how the tooth fairy knows about the teeth before running the experiment.
The answer to that is "But maybe the parents are misinformed about the tooth fairies' abilities?" You can go on and on like this, but at this point I would stop praisuing the child for pursuing the ratinal method for solving problems, and strat educatting the child in the next lesson of rationality: 0 and 1 are not probabilities, all knowledge is probibalistic, and you need to do VoI calculations before rushing off to try to rule out narrow and increasingly unlikly options.
But the hypothesis where the TF's knowledge is more closely linked to the parents' is less natural; to me it feels like making excuses for a bad hypothesis.
Does it? Suppose for example that that the Tooth Fairy has every house with little children bugged and so hears verbal statements about loose teeth.
That would require monitoring what happens to loose teeth in deaf families
But the Tooth Fairy probably knows how to read lips, given its fixation with teeth.
That leads me to think of some ethically questionable testing scenarios.
Yes...
But seriously, there are simpler tests to do, or to do first. Try telling your parents not out loud, but in a written note. That would rule out audio bugging. Try telling an empty room, when no one else is around. That could rule out your parents. Try telling someone you know won't understand you. (Like a younger sibling.) Try miming it to your parents without using words. Try falsely telling your parents that a tooth fell out, when none did. Try telling your parents about your tooth that fell out, but not putting it under your pillow that night. Try giving your fallen-out tooth to a younger sibling and tricking him into pretending that that tooth was his to your parents. (Although that would probably mean giving up the income from that tooth.)
All in all, there are a lot of possible open tests that could be done, to narrow down the search space dramatically.
You have a limited number of teeth to experiment with.
That's where your little brother comes in.
But the point is that if we allow the Tooth Fairy to be sufficiently ill-defined, we can construct a version of it that allows for any negative experimental result. Benquo had a preconceived model of the "the Tooth Fairy" which was given some initial weight, and when it was contradicted by an experimental result then Occam's Razor strongly insists that we fall back on the null hypothesis*.
*(Unless there was some pre-existing good reason to suspect the "bugged house" hypothesis, which I doubt there was)
Perhaps the tooth fairy doesn't magically sense baby teeth under pillows, but she has to be sent a telepathic note from the child's parents first.