I gotta disagree with some of my fellow Bitcoiners. From where I stand Bitcoin does not disprove the regression theorem, rather it’s an interesting and very illustrative example of it.
Bitcoin’s value early on came from the novelty - people who liked the concept from a technical point of view wanted them just enough to engage in some - mostly tongue-in-cheek - trades. One often cited example is the two pizzas that went for 10000 Bitcoins in May 2010. But this is actually a rather late example, there were lots of trades with large and small amounts of Bitcoins before then, but in 2009 especially nobody really knew what a Bitcoin was worth. (To a lot of people it was worth absolutely nothing, which is why a significant percentage of 2009 coins should probably be assumed lost.)
The breakthrough was right around a year ago when exchanges like MtGox appeared on the scene. While trading Bitcoins for US dollars was not new, the fact that MtGox published a Bitcoin “price” was and it was significant because now people knew what you could expect to get for your coins. Selling anything for Bitcoin was no longer guesswork, but simply a matter of looking at the current market rate.
Once Bitcoins had an organized exchange market, trade started to shift from joke transactions to actual merchants accepting Bitcoins for their goods. By February 2011 the Trade page had grown to over a hundred companies and was moved to the wiki, because it had become to complicated to maintain otherwise. (Now, only four months later, it lists over 600 companies.)
Acceptance was what triggered speculation. People saw that the currency was starting to be used as such and suddenly they seriously considered the possibility that it might find widespread adoption some day. Speculation is the reason why the exchange rate went up more quickly (16x since February) than the acceptance (6x since February). Jörg Guido Hülsmann has a good YouTube video on deflation explaining that interest rates can’t go negative so instead currencies appreciate quickly as people anticipate deflation.
So here is why Bitcoin is a great example for the validity of the regression theorem. Bitcoin’s exponential growth could have started 18 months earlier in 2009, but it took one and a half years before anybody used Bitcoin as a money. Bitcoins couldn’t develop monetary value while it didn’t have non-monetary value. And non-monetary value was hard to come by. Clearly a lot of the early trades were irrational, it was only when this irrationality was captured in a somewhat stable market rate that other people started using Bitcoin. You can accept Bitcoin, even if you don’t believe in the concept if you know you can sell them to somebody else at a certain rate. The more that happened, the more the demand for Bitcoins for monetary uses developed and eventually vastly outgrew the early non-monetary demand.
One thing to point out is that this same principle is hard to imagine happening with paper money. Early transactions consisted of tens of thousands of coins for value that is today only fractions of a coin, so Bitcoin’s divisibility and transportability were critical properties. Another reason for the hard-to-explain early demand is the fact that Bitcoin is the first implementation of a peer-to-peer network solving the decentralized, anonymous agreement problem, so some geeks wanted to own Bitcoins not because they thought it had a chance to become an actual currency, but purely to own a piece of history. Again, this stuff didn’t make Bitcoins expensive, it just gave them some value that was bigger than zero.
Disclaimer: This is not investment advice, I’m merely intested in this debate. In fact I would recommend against Bitcoins as an investment, since even if the economics are sound, it can still fail technically, socially, etc. At the same time I do invest time and effort in Bitcoin myself, mostly because I’d like it to succeed - independent of what I think its chances are.