Topic: rpietila Wall Observer - the Quality TA Thread ;) - page 112. (Read 907212 times)

What would you prefer on a personal level as a miner in the short and long term? An increase in transactions or an increase in exchange rate? What about for bitcoin overall?

Mathematically there shouldn't be unless at least Moore's Law died. You want to correlate mHash/$ and mHash/Watt, i.e. those are both increasing faster than Moore's Law I think?

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http://www.marketoracle.co.uk/Article47164.html

Here is a graph of Bitcoin Hash Rate growth for the last couple of months as presented by Bitcoin Wisdom. I believe from news announcements that mining is not only now industrialized, but becoming more vertically integrated as manufactures operate their own miners during that crucial period where return on capital investment is possible.

There appears to be little correlation this year between bitcoin price and the mining difficulty.

I reiterate my thesis that the larger this COIN event, the more coins that get locked up in a vault and never transact. All the buying and selling churn for COIN will occur off-chain. Thus it removes transactions from Peter R's Metcalf Law model of the market cap. Whether you believe that model is predictive is another issue. In short, COIN could make a lot of investors happy and boastful, but it has a cost to upside growth. It is expedient but destructive. It is top-down not decentralized.

My thesis is fairly simple. The network effects value of Bitcoin is the decentralized potential for every user to transact with any other user. For example, imagine two off-chain entities that refuse to interopt (we are then going backwards, i.e. analogous to paywalls on internet urls, e.g. subscription magazines). As that is taken away with too much investment focus and top-down off-chain activity, the headroom of Bitcoin's market cap is declining, i.e. log-logistic. The fascist bastardization of the internet is well underway too. We hackers have a lot of work to.

For me it is common sense. Bitcoin is being sought primarily as an investment, not as a tool. The internet was sought primarily as tool.

I think we need a crypto-currency that is sought by the majority of the population not as an investment, but rather as a tool. The investors will certainly follow, just they did for the internet or how Warren Buffet admires rapper Jay-Z. We shouldn't totally dismiss what was learned from Dogecoin.

I hope readers appreciate I have shared my secrets to a large extent. We will never know who copied and ran with them. Was it me? You will never know but I will.   lol. Peace. (it also helps to preserve my life I suppose, don't cha think 'Satoshi' is reading this)

P.S. In short, fuck the SEC! (and every other alphabet soup top-down molasses)

That is far out of my depth (and available time to dig) too. I defer to animorex perhaps. Or perhaps SlipperySlope.

Yes, I see your point and you might be right.  There's probably some more advanced ways to analyze the question of "what is the most accurate growth model?" objectively, as well as the question of "what would it take to invalidate the exponential growth model?"  But I don't have the skillset.  

For example, perhaps we could assume the adoption process is exponential Brownian motion [like the plot I showed earlier], estimate the hidden values for mean drift and volatility from the number-of-TXs-per-day time series, and calculate some sort of p-value for the fit.  But I'm way out of my depth now.  I wonder if there's anyone here who has a deep understanding of SDEs and things like the Black Scholes equation, etc.  

If it is true the "number of users is increasing exponentially (so far), the number of transactions is NOT" this would be congruent with my thesis that Bitcoin is abnormally skewed towards investors and not sufficiently balanced to (transaction) adopters.


We have more history now so what we see now is more supported (by data) than what they saw historically. That doesn't necessarily make it more predictive, as it depends on our characterization of possible noise and other supporting logic for which model should be predictive.


Your subjective bias is fooling you here. Mathematically false because there was never a mathematical confirmation that the predictive model was correct in the first place. We are simply picking straws blindfolded unless we have historically complete examples and or some other well supported logic from which to argue which predictive model should be correct.


I argue this proposed model is invalidated because it is internally inconsistent. It is based on the notional of investment value of market cap as a starting point, yet you are modeling the Metcalf Law adoption value which is based not on investment adoption but rather on transaction adoption. In other words there is a category error here.

P.S. thanks so much for applying the effort for the examples and sharing. It really helps to discuss from your effort as I think it helps raise understanding.

Not only implicitly but explicitly as well, yes:  A bad fit of a structurally representative model is far more predictive than a good fit of an unrepresentative model, because it is a compressive attractor.  There are some statistical tests you can use to discriminate, but knowing structure beforehand gives you a lot more leverage than structural estimation after the fact, because noise.

There are certainly some intuitions to support log-logistic, but they aren't compelling to me. Still have not taken time to think this one through properly, after all this time.  Summer has been crazytown.  And I've been indulging myself with distractions.

Yet, events in the world will never be entirely modeled by anything so simple.  COIN will be a liquidity event at a magnitude far larger, relative to current market cap, than was the advent of exchanges - which precipitated the superbubble.

My mathematical point to Risto is that the relatively lesser fit of 0.73 for the log-logistic exponential model is entirely meaningless because precisely the choice of model is what matters. So aminorex and Peter R have supported my argument.

P.S. kudos to Peter R's generative essence abstraction.

loved your example. will steal it. thanks

Not at all.  There is a great deal of psychological research that shows how our human minds try to find patterns that aren't really there.  A fantastic book on this topic is "Thinking Fast and Slow" by Daniel Kahneman.

IMO, the growth rate for bitcoin would need to decline strongly (or retreat over a long period) to truly invalidate the exponential growth model.  Here's a model that fixes bitcoin's market cap at inception at $500,000.  The "rationale" is that Satoshi spent approximately 2 years building it, and the market-value for Satoshi-level talent is $250,000 / year.  



I'm not arguing for this model, just pointing out that if growth slows to a more modest (but still exponential level), arguments could still be made that we are on trend.  IMO it would take a failure to reach a new ATH by 2017, or a sustained (1 year+) fall below $250, for me to say that "bitcoin growth has halted."  

...

It's so easy to be fooled by randomness.  Here's several simulations of the same underlying exponential growth model.  But instead of solving a regular differential equation to get a smooth exponential curve, I'm solving a stochastic differential equation that adds process noise.  The people in Alternate Universe #1 who get to ride the upper purple curve will think bitcoin is the most fantastic thing!  The people riding the bottom blue curve are going to make up story after story about how it's failing.  But in all cases, the only difference was randomness.  

I agree re waiting, but by December it should be clear (at least short term), don't you agree?
In addition, Steve Reed's graph shows -0.7 deviation from expectation (lowest yet).
I was basing my assertion on prior OP post:

No we just use the number of transactions per day and the number of unique addresses used per day as proxies for the number of users. It is highly likely they are strongly correlated.

Do we guesstimate the number of users from client/wallet downloads, key site (BTCT/blockchain) traffic, and Google search trends? Or what?

We don't actually have a reliable way to measure the number of bitcoin users.  The Metcalfe Value plots I prepare assume that it's correlated with the number of TXs per day and the number of unique addresses used per day.  The plot below shows that both of these two proxies for the number of users has indeed been increasing exponentially (along with bitcoin's market cap).  Today it appears that a "concave down" function would fit better than a straight line, but late last November people were arguing for a concave up (super exponential) model.   So we must wait and see.  The ups-and-downs away from exponential growth look like noise to me and are not yet significant enough to invalidate the model.  

This doesn't make sense, either, though. If any statistically significant amount of employees decided to be paid in Bitcoins and then they refused to spend their Bitcoins because their coins keep appreciating in value then they'd save themselves out of a job. If nobody is buying, how can you sell your wares?

In short, the proposition is at least a tad dubious.

while I agree that number of users is increasing exponentially (so far), the number of transactions is NOT, which was posted earlier.
Possible explanation-the absence of accurate statistics, but then the whole argument is mute.

Exponential growth is not some "arbitrary function."  It is the solution to a very simple--and very meaningful--differential equation.  It occurs whenever the growth rate of something is proportional to the size of the thing that's growing: e.g., the population of bunny rabbits in a park, bacteria in a petri dish, or users of a social networks.      

Here's a simple model for bitcoin adoption:

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Let N by the number of bitcoin users.  Assume that on average each user converts k non-users every year.  Each year (Δt) the change in the number of users (ΔN) is then clearly k N.  This allows us to write the differential equation¹:

  ΔN/Δt = k N

The solution to this equation is:
  
   N(t) = N₀ e^{k t}

Where N₀ is the initial number of users and N(t) is the number of users at a later time t (which clearly grows exponentially with time).  
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Note that this is exactly the same rationale that we'd use to explain the growth of an intially-small population of bunny rabbits introduced into a park with abundant food:


The exponential function comes from a very simple and very reasonable underlying dynamical model.  You can't just say "maybe bitcoin growth is a trig function" or "maybe it's a Bessel function"--you need to refine the original differential equation with new reasonable dynamics, and then solve it to determine what the "function might be."  For example, the "logistic function" arises by noting that things do not grow exponentially forever.  Instead, the growth rate often slows down and then approaches zero when N reaches some saturation value N_sat.  The simplest way to model this is by adding the following term to original differential equation:

  ΔN/Δt = k N (1 - N / N_sat)

The solution to this is the logisitic function that SlipperySlope is using.  

For bunny rabbits, the saturation level is the equilibrium population of bunnies that the park in question can support.  For bitcoin…well time will tell.
 

TL/DR: The exponential growth model is the best/simplest model that explains bitcoin adoption to date.    

¹I should use an appropriate limiting procedure here.

Just for fun...

EQUITY GOLD TRUST filed their S-1 on 13 May 2003. 1 year, 5 months, 3 weeks, 5 days later GLD was issued.

The S-1 for COIN was 1 July 2013. So that would put us on the 27th of December 2014.

bitcoin value is an enigma; the values you quoted are arbitrary. Why? The transactional value (including exchange) is 2.9% for credit cards & paypal vs 2% (coinbase round trip). A lot of businesses can exist in this slice (2-2.9), but it is not a gigantic value proposition (if you ONLY consider transactions).
In fact, I would think that since the lower bound (2%) will have a natural trend to go down (to less than 1%), there is even less monetary reward in transactions.
I think that the store of value is much more interesting proposition for the increase of price of bitcoin (eventually-as it is failing right now, contrary to my expectations).