I think the simpler solution to the apparent disconnect between the regression theorem and cryptocurrencies is that cryptocurrencies break the regression theorem. I like Mises and all, but really? People are trying to apply the economics of the 1940s to the monetary system of today...
The regression theorem is account of how money arise from a barter economy. The theorem is irrelevant to bitcoin.
That sounds wrong, but maybe I do not understand the theorem, so lets review what I thought it was.
My understanding is that according to the theorem money arises when something useful (such as data aka information) turns out to be so useful that lots of people not only agree that it is useful but also start to use it as an intermediary in trade.
So, like, maybe once upon a time someone figured writing was so useful that instead of trading a loaf of bread for a shoelace they traded a loaf of bread either for a note saying "pay the bearer on demand one loaf of bread" or a note saying "pay the bearer on demand one shoelace".
Pretty soon more and more people were trading items for information in various variations of such techniques.
Along came computers, a new medium to write on with new writing tools, so people started trading goods for entries in databases.
And so on.
Did I get it wrong?
-MarkM-
Horribly wrong, I'm afraid. You are confusing the concept of money with the concept of tokens.
In your example, the notes aren't valuable except as they embody promises that they can be redeemed for stuff, that is, they are tokens.
Money (in this context) is something (either actually present or in token form) that is widely accepted in trade. Doesn't matter much what the thing is, or why it is widely accepted, just so long as it is.
Kiba is right that regression isn't important here. I would go another step and say that regression wasn't ever important anywhere. Money was in wide use all around the world for thousands of years before anyone thought they needed to invent a story to retroactively rationalize how it happened.
For bitcoin to be successful, it just needs to be better than the alternatives for at least one use, and I'm sure each of us can think of several things that bitcoin does better than any existing financial system.
By the way, discussing this sort of stuff is really hard. When we say money, we are usually referring to a token (cash in the wallet) or a token for that token (checking account, etc), or something even further removed (ATM card/check/savings account). For extra fun, as we peel away the stack of tortoises, we find out that the bottom token (cash) isn't a token
for anything. It is just a token.