Most of you can't picture in your head as I (and some others here probably) can, so I need to show you chart for you to get that "Ah ha" epiphany.

I lack the math software to do a proper log-logistic curve fit. Here follows my eyeballing and rough fit to the change in slope.

The run from Oct to Jul 2011 had a slope of 2/7mos and from Jan 2012 to Jan 2014 had a slope of 2/24 mos. The cumulative distribution function shown superimposed in blue below is 1/1+(1/x)^0.5. Thus from x=0 to x=0.25 for the Oct to Jul 2011 run has a slope of 1/1+sqrt(1/0.25) = 1/3 = 0.33 and from Jan 2012 to Jan 2014 is from x=0.25 to x=0.50, thus 1/1+sqrt(1/0.5) = 0.41. So 0.33-0 = 0.33 and 0.41 - 0.33 = 0.08. And 0.33/0.08 = 4 and 24/7 = 3.5. So we can see ratios of the slopes match closely. So this is a reasonable curve fit as the proportional vertical heights also match. A quantitative fit would be more accurate. The accurate fit is probably a bit less steep in the early portion and less flat in the latter. So this would be more favorable than the one I overlaid.

Any way, if this theory is correct, then you can clearly see that Bitcoin will stop rising as fast and that it is due to fall down in price significantly before it rises again and more slowly than the past. From here on the slope from x = 1 to x = 1.5 is only 0.05, thus 5/8 of the rate of increase we've on the log 10 chart since Jan 2012. Note that is 5/8 of a rate of increase that is exponential in the power of 10.

It is roughly saying we won't significantly surpass $1000 in 2014. I don't know where the correctly fitted curve would be right now, so I can't project where the price should be now and where it will be nominally. I think the slope projection is more close to accurate, so we can say that if the theory is correct (that distribution of money holders is a power law distribution as the cited research and common knowledge says it always is), then price appreciation will slow down specifically to 0.05 units on the log 10 chart per month where 1 unit is 10X appreciation. So if we bottom at $400, then price after 20 months should be $4000. Again this is a very rough eyeballed fit and would expect the refined fit to have a slightly higher slope maybe 0.06, so make that 16 months instead.





What is hard to understand? Reed's Law is another way of stating Metcalf's Law. It is quite clear that in a network with N nodes, there arre N^2 possible interconnections. Thus the value of the network interaction is N^2. How hard is it to understand that without communication and interaction, there is no leverage of each other. How can I use your knowledge if I can't interact with you? Why do we become smarter by posting in this forum. Etc..

Apologies I was intending to make following correction and then we had a brown out and I fell asleep.



The red line below is a power law distribution for B=0.5 which you can see above is the value of B I fitted.



What that distribution says is that the rich hold most of the percentage of wealth, which we know is in fact always true. And the fitting of the cumulative distribution function to BTC price is the theoretical claim that earlier adopters will be more wealthy (by now) than later ones.

The research I cited points out is that the masses use money as a unit-of-exchange, not as a store-of-value.

However does the Metcalf's law value of money (which Peter R has shown BTC mcap and thus price is tracking) where the value is proportional to the square of the number of nodes in the network nullify my use of a power law distribution? I.e. do the wealthy not create (proportional to their wealth) more network nodes (e.g. unique active BTC addresses) than the masses?

I see the really diehard power users (e.g. SlipperySlope and Peter R) are both talking about creating a new node every day. Thus this anecdotally supports that the power law distribution applies correctly here.

Thus I think we need to take this theory seriously. It might be the correct growth curve. The linear one with a least squares fit seems really out-of-touch with historical data. It totally ignores the shape of the earliest adoption curve up to July 2011. Risto's explanation was the early adopters were bad speculators and bid the price up too much, but my interpretation is they are the most wealthy now and they were the most powerful because they are early adopters. The least squares fitting of a line to a curved adoption could possibly be (confirmation bias in play as) an (emotional "to the moon") attempt to force a linear projection on a growth curve which obviously was not always linear. Has it become linear since January 2012?

I very much doubt it!

Convince me? Risto how do you analytically defend your linear least squares fit that makes you so sure of everything and gives you the audacity to browbeat all the bears?

Add: why don't stocks follow this log-logistic curve? Maybe they do (?), if we don't compress the early adopters into a single event IPO. Also can a stock issue have network effects, i.e. does Metcalf's law apply to company shares? Seems to me yes if the shareholders network amongst themselves, but much less so than a network of money holders.

Add: Fact is the slope during the runup to July 2011 was 0.33 per month. Since Jan 2012, it has been 1/4 of that 0.08 roughly. Why should we expect the slope to not decline again? Why should the pace of adoption remain constant? Seems intuitively unlikely to me. Pace of adoption should slow as we slog into the less astute demographics. Larger mass with more inertia grows more slowly than smaller mass with nimble inertia.

You put a lot of weight in your humongous pride, as if someone presenting analytical discussion is worried. I am not worried about the BTC price. I could careless because I don't own any BTC nor am I itching to buy any. And you put a lot of weight in arbitrary curve fits.

And people who think they know every thing for sure (and you don't even enumerate the arbitrary assumptions in your model), eventually get a lesson in respecting chaos. Maybe not this time. No one knows. But eventually yes.

I hope you realize the following chart is arbitrary BS.




And why not drawn like this? A least squares fit is an arbitrary choice of slope, because the curve you are fitting is not very linear. The 2011 outlier is your big problem with choosing this arbitrary fit. And we can't really trust that early data back in 2010.

The green line looks much more accurate to me. It removes that bubble from 2013 and follows a trendline from before the bubble started. Or we stay with the purple trendline, in which case the price is almost down to the purple line.

You need to update your chart. The price is now lower than shown.





Also refer to my upthread post quoted below pointing out that adoption (and thus BTC ≅ adoption^2) is likely log-logistic, not logistic. Thus we see the first slope to 2011 was higher, then the slope from 2012 to 2014 was the purple line, and now we may be ready to transition into an even lower slope, such as the green line.