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..
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 seems too simple, but on the other hand I cannot believe that the goodness of fit is just coincidence; is there something truly at play here that we haven't fully come to understand?
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..