Higher-order Exponential Growth?

[Zangelbert Bingledack]

Hyperinflation (inverted) looks like this on a log chart, which means it is double-exponential or more:






...Meanwhile we are starting to see curving up on a log-scale chart of BTC price - note how similar the patterns are, with the little bump first and then the huge run up to total collapse of fiat...in fact the two charts align almost uncannily well if you look at the bumps, though of course Bitcoin's chart has yet to complete:





My theory is that regular exponential growth (straight line on a log chart) is from the viral effect of the Bitcoin "meme," while higher order exponential growth - that is, exponentially faster doubling times - is the viral effect + a herd-instinct-based stampede. This latter one is where bubbly-ness can be introduced. However, it seems to still be mild. Here is the best Bitcoin economist I've seen, arguing against a bubble right now:

http://konradsgraf.squarespace.com/blog1/2013/4/6/hyper-monetization-questioning-the-bitcoin-bubble-bubble.html

One thing he misses, though, is that the store of value function of Bitcoin is probably the main reason for the price rise now, even though it is ultimately backstopped by currency usage.

[chriswilmer]

One thing I could never figure out about hyperinflation (such as in the Germany example), is why take it so far? By the time 10 million paper marks equaled 1 gold mark, wasn't it obvious it wasn't worth the energy to run the printing press anymore? Also, I assume the decision to print more and more was made in a top-down way, and with the "double exponential" inflation, that seems to imply that the decision maker was eventually updating his ideas on how much to print multiple times per day.

[Zangelbert Bingledack]

I'm guessing the actual printing was just done to print the amounts necessary to keep up with people needing more (if they print too slow the whole charade ends that much earlier), so I assume the real action is in why merchants raise their prices at a double- or higher-order exponential rate.

[Krabby]

I like this one better;

[chriswen]

But, the time scales are different.

[Vandroiy]

Well. With just the exponential of last week a single Bitcoin reaches a trillion dollars by christmas.

I'm too lazy to look at the superexponential part. It would be some absurd number shortly.



Just don't draw straight lines on logscale for prediction purposes except when predicting very unstable human insanity. Doing a superexponential instead does not make it any better.

[sgbett]

It's never obvious exponential stuff, until afterwards.

Everything seems fine until a point where it's way too late to do anything. Take consumption for example, if some resource consumed at a rate that doubles every year. Then everything might tick along fine for hundreds of years, then bam in two years you go from oy having ever used 25% of the total supply ever over all that time to using it all.

Humans aren't geared to intuitively grasp exponential growth. This article is a cracking good read! Exactly what I have been looking for to understand what I felt but could rationalise why!

[yokosan]

Nice post, a new spin on a common topic. Upboats.