A log trend line (more precisely: linear regression on log charted price history) is a nice little tool to get a feeling for where we are at any point in time compared to the historic trend, and where we're going to be, very very roughly, in a few months or a year from now.
I don't think Bitcoin's long term trendline is going to be straight on a log graph - I think it's going to trace an S curve
graphed in log space.
http://bitcoincharts.com/charts/mtgoxUSD#igDailyzczsg2011-11-01zeg2013-12-30ztgSzm1g10zm2g25zlThrow away the data from before November '11, while the exchanges were trying to figure out how to operate, and what do you see?
I know, I know
I participated in the previous discussion of that idea. Didn't we conclude that the well known S shaped "tech adoption" curve would still be a straight line when mapped to log. Why does BTC deserve a "super S", if I may ask?
If we define "super S" as faster than exponential growth over the early portion of the S-curve, then I think we can rationalize this (doesn't mean its correct though).
Assumptions:
- bitcoin adoption,
x, is small compared to its theoretical potential adoption
- the amount of people that hear about bitcoin is proportional to the number of bitcoin users (who keep bringing it up).
- the probability that after hearing about bitcoin, a person becomes a user, is
kI don't feel like being rigorous, but I think we can roughly see that bitcoin growth could then be modelled by the differential equation:
dx / dt = k x, which of course has the familiar "exponential growth" solution.
But, I think we can be reasonable sure that
k is *not* constant, but instead depends on how many users there currently are. I say this because I have noticed that the general "guy at the bar" is much more interested and eager to talk about bitcoin after the November media blitz, than prior to this. Prior to the April growth spurt, no one really cared at all.
So, lets say:
k = c x and then our differential equation becomes:
dx / dt = c x^2, which has a hyperbola as a solution.
[uberbull]This means that we will eventually approach a singularity where the bitcoin price becomes infinite. The only way for this to happen is for the USD to go to zero as well.[/uberbull]