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RichardKennaway comments on Harry Potter and the Methods of Rationality discussion thread, part 26, chapter 97 - Less Wrong
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On the grounds that if the goblins can tell them apart, there must be some difference. Remember, something doesn't need to have a physical use to have value - see Bitcoin, or intellectual property, or stock options. Simple scarcity is sufficient to create value if people decide to value it.
"If people decide to value it" makes that a tautology. Leaving that aside, scarcity is necessary but not sufficient. The only surviving painting by a contemporary of Leonardo da Vinci of little renown will be valued, but less than one by Leonardo.
Silver has two stable isotopes, in roughly equal proportions. I doubt there's much monisotopically refined silver in the world. It would cost more to make it, but it wouldn't be worth more, unless someone wanted some that badly for a practical purpose.
As phrased it's tautological, but my point was the implication - people can choose to value whatever they want, value is not intrinsic to an item. Lack of scarcity does provide an upper cap, though - air will never be valuable on the surface of Earth - so if people have chosen to value something, then scarcity is the remaining factor needed for it to have value. (I phrased it poorly, but I think it's still strictly correct)
Neither air nor water are scarce on Earth; but clean air and clean water have value.
Actually, some cities have featured "air stations" or "air bars" due to smog, historically. I don't know if they still exist, I haven't heard of a contemporary one.