Really interesting. The super-exponential part really hit home, as I remember people figuring out that bitcoin was in super-exponential growth in the first week of April. Still, it doesn't really indicate how one should trade. Bubbles don't have to pop, it's just that the super-exponential behavior has an expiration date and "something" happens afterwards that is different.
The real issue to understand is where the super-exponential growth is coming from; what is the factor that is the main driver causing the exponential growth.
For example: Is the underlying cause for this exponential behavior (up or down) "debt" related? If it is debt related, then it is artificial, it is manipulated, it is an illusion. On the other hand, if it is not caused by debt, but rather natural market forces, and "not leveraged", then there is no reason to believe that the growth is in any way artificial or unsustainable, in reality the price at any moment would reflect the "true" price; thus, bubbles would essentially not be formable. Basically it all comes down to debt and leverage. Debt adds risk. The more debt-leverage involved, the more the debt-related risk associated with it, exponentially. Most people are deceived by debt because they just look at the money, and they forget to think about risk. If you want a stable financial market, eliminate ALL debt. This means you have to actually save money and be productive in order to create wealth. Debt is borrowing money that you don't have...essentially it is like a race analogy.
Race Analogy: The person with debt "jumps the gun" and runs out in front of everyone else and gives the appearance of being a better athlete, yet he is not any better than the rest, and once it if finally discovered when they review the race....they have to start the race all over again...Once it is discovered that someone used debt and are not paying it back, there is a financial crisis and a "reset" of the financial race.
There's another, maybe simpler, explanation for why
it's different for Bitcoin (yeah, yeah, bears I know. It's never different). Let's make the simplifying assumption that there is, at a give time, a fair but unknown evaluation of a commodity, and that the market attempts to discover it (pretty standard, right).
If our current ideas about the eventual importance of Bitcoin are even remotely right, then the current evaluation is still several orders of magnitude below that eventually "fair" evaluation. Note: it's okay that this is the case, markets take their time, and there's obviously a lot of risk.
Anyway, the argument in favor of double exponential growth is that because the gap is so huge between current evaluation and (what I stipulated as ) the eventually fair evaluation, any shift in market perception must result in huge growth, whether it corrects back afterwards or not.
If in some other, more mature, market the evaluation goes from, say, 95% of the fair value to 99% of the fair value, it can do so at more reasonable pace. Double exponential growth in those cases probably is a sign that a correction will happen.
In our case, if we're at 1% of the eventual evaluation, and try to go to, say, 50%, it
has to be a at a breakneck pace. Sure, usually double exponential growth means correction in our little market as well, but the way it seems to go is a frantic race that increases price 10-fold, then corrects back to half of that, or maybe a third. So what's left of the initial growth is still pretty impressive.
