Metcalfe's Law: Bitcoin Price and Adoption Analysis for the Future

[Wary]

I think you are just playing at definitions and missing the larger point.  As rate of adoption increases beyond linear, rate of price appreciation will increase beyond the current exponential.  Until we pass the 50% point on the S curve, the rate of price appreciation should therefore accelerate, not diminish.

If you don’t believe me or don’t get it, I don’t have time to try to convince you, sorry. (c)-you know who  

[Raystonn]

I have updated the graph with the latest data.  We continue to have higher lows on the Metcalfe data.  I have also added a zoomed chart to the first post.  We can clearly see we're working ourselves into a tighter and tighter range on adoption.  We should see a large price move upward when we break above the Metcalfe high of June 1st.

[saddambitcoin]

i believe we will go super exponential this year and hit $10,000. 

just around the corner...

[Bitcoin_is_here_to_stay]

I am afraid I do not understand what are "unique addresses" - I first thought these are bitcoin addresses, somehow filtered. But if so, how they can ever be declining?

[chriswilmer]

I am afraid I do not understand what are "unique addresses" - I first thought these are bitcoin addresses, somehow filtered. But if so, how they can ever be declining?

I think it's unique addresses used in transactions PER DAY.

[Bitcoin_is_here_to_stay]

I am afraid I do not understand what are "unique addresses" - I first thought these are bitcoin addresses, somehow filtered. But if so, how they can ever be declining?

I think it's unique addresses used in transactions PER DAY.

Thanks, that makes sense .

[FattyMcButterpants]

i think metcalfe's law is wrong. it assumes all nodes are equally valuable, which is pretty controversial. here is a good rundown of why:

http://spectrum.ieee.org/computing/networks/metcalfes-law-is-wrong

perhaps growth is not quadratic, but rather n log(n), where network size = n.

[painlord2k]

i think metcalfe's law is wrong. it assumes all nodes are equally valuable, which is pretty controversial. here is a good rundown of why:

http://spectrum.ieee.org/computing/networks/metcalfes-law-is-wrong

perhaps growth is not quadratic, but rather n log(n), where network size = n.

The nodes joining the network first are the nodes receiving the most benefit, others will follow.
The nodes joining first are not, usually, the largest.
Often , the traffic increase a lot when some subset of nodes is able to form closed loops where there is a positive feedback loop.

[aminorex]

logistic adoption occurs repeatedly, as btc breaks into widening circles of transactors.  expect the adoption curve to be fractal.  there have been periods in the past when superexponential fit the price better than exponential.  i expect that the latent network was adding a markov blanket in those times.

[TheJuice]

Which is following which? Higher prices = more attention = more addresses used?

[Raystonn]

Which is following which? Higher prices = more attention = more addresses used?

It depends on where you look in the graph.  Sometimes prices leads adoption.  Sometimes adoption leads price.  In the center of the graph you can clearly see adoption heading up without price.  Eventually price follows up and rejoins adoption.  So there can be periods of divergence due to speculation.  But historically they always converge again.

[nicoin]

Could we make a parallel to the internet itself using domain names instead of wallets? Not sure about this but just asking as this is the speculation forum

domain names 2002-2014, not far from an s-curve
http://www.registrarstats.com/GeneratedFiles/ChartImages/TldHistoryCom_7192014.png?32ad38f3-de49-4ea5-8946-10d708ec470c
It's getting flatter, have you tried to buy a domain name lately? Anything made with actual words or short or remotely nice sounding is already taken.

not sure how we value the internet, perhaps market cap tech/web companies 2006-2014 (sorry this graph suck no time to find a better one)
http://www.statista.com/statistics/216657/market-capitalization-of-us-tech-and-internet-companies

http://www.caseyresearch.com/sites/default/files/resize/AMZNSharePricing-490x355.jpg

Where we are on the adoption curve (avail as live charts on coinometrics)
http://www.genibits.com/wp-content/uploads/2014/04/Fitch_Bitcoin_Transaction-Volumes.jpg

[JstnPwll]

Any chance of getting some updated data?

[Swordsoffreedom]

Any chance of getting some updated data?

That's a good question hard to believe that a six month old chart is already getting outdated 

[aminorex]

i think metcalfe's law is wrong. it assumes all nodes are equally valuable, which is pretty controversial. here is a good rundown of why:

http://spectrum.ieee.org/computing/networks/metcalfes-law-is-wrong

perhaps growth is not quadratic, but rather n log(n), where network size = n.

It is probably ~n*log(n) in the early phase, and ~n*log(n) -> n in the mature phase, but in the hockey-stick phase, it is closer to n^2, while the highest value links are being aggregated to the network.

[SlipperySlope]

I have a thread on the logistic model as applied to bitcoin prices here . . .

https://bitcointalk.org/index.php?topic=366214.0

and a shared spreadsheet with graphs here . . .

https://docs.google.com/spreadsheet/ccc?key=0ArD8rjI3DD1WdFIzNDFMeEhVSzhwcEVXZDVzdVpGU2c

The math of the logistic (S-Curve) model is simple. f(x) = 1 / (1 + e^-x). On a linear graph you get the familiar S-curve, but that is not very useful yet for bitcoin because prices have increased on average 10x every year so a log graph is best right now.

If bitcoin prices were to exactly follow the logistic function then the following properties would hold . . .

1. At the beginning starting from zero adoption, the growth is approximately exponential, decreasing rapidly near the midpoint.

2. At the midpoint of adoption, the growth is linear.

3. At the ending with full adoption, the growth is zero, decreasing rapidly after the midpoint.

Note that currently prices are substantially lower than my model projects. I do not believe that we are yet near the midpoint of adoption - so I expect either to revise the model lower or to witness a surge in prices sometime in the next few months.

[InwardContour]

I'm not an expert at all but what I can say is that the adoption is still at the beginning and it's far away from the midpoint.

[Raystonn]

Any chance of getting some updated data?

Here is the latest:

[freedomno1]

I've been analyzing further.  When we hit the vertical stage of the adoption S curve, rate of adoption will go exponential.  Metcalfe will go super-exponential at that point, along with price.

Funny how human psychology makes most humans buy when the price is rising , but no one dares buying when the price is low after a bubble. Even when it's pretty obvious a new bubble will come.

I mean right now we are sitting on 600s but people will only really start buying once we past 1000 or so. And then once we peaked at about 5000 or so, people will stop buying until we are once again past the previous ATH rather than just buying during the downtrend.

You know markets people want to wait for a strong momentum movement before they start piling onto the ride
Otherwise looking back you just spent 2 to 3 months going sideways well unless you started at 420 to 600 then that was a nice 30% return in a short time period

[aminorex]

The math of the logistic (S-Curve) model is simple. f(x) = 1 / (1 + e^-x).

It's the sort of math that can emerge out of a lot of complexity.  The CDF of a gaussian, for example, is a sigmoid a la style du logistique, but the gaussian arises as described by the central limit theorem, as the asymptotic distribution of a mean of (functionally) random processes.  And that concept of randomness may conceal a chaotic process - arguably always does, given axiomatic physical determism.  Or it might just be, for example, a lotka-volterra system in which the quasiperiodic factors are on incomensurate time scales, and hence not evident above the noise of observation.

Given that the system described (the living economy) is an agent system physically, I don't think you can have a satisfactory understanding of the domain of applicability of a simple model, unless you can show how it is caused by the agent interactions.  When I say satisfactory, I mean a model such that you know when it must apply, and when it may or must fail to apply.

Make no mistake, I like the model.  I think it is useful - until it is no longer useful; and, I think it is even more useful to have a principled understanding of why and (hopefully, even) when it will cease to be useful.  Meanwhile, it can serve as a pretext or stimulus to hypothesize theories which explain why the model is presently applicable, an important creative process, but one which should include in its scope hypotheses which imply evanescent application.

TL;DR: I just don't want anyone to be mislead into thinking that because a model is elegantly simple, and a good fit, that therefore it is reliable.  It is often a precondition of, or indicator of reliability.  It is rarely an assurance of reliability.  When the model is the result of a sound theory, then reliability is indicated more strongly, and its conditions begin to be understood.