The BTC Scaling Law

[BTCdragosfera]

I just posted an article on Medium about the BTC Scaling Law. Please let me know what you think.
Here is the link: https://medium.com/quantonomy/btc-scaling-law-model-has-been-right-for-the-last-15-years-real-price-and-model-comparison-5dee5bb495f6

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[NotATether]

The law is not clear to me exactly, but it seems to be a variation of Moore's law. Price to time, I believe in this case?

But that also means that the price will eventually flat-line, *some time* over the next couple decades. I mean it can't keep growing in price constantly, forever like this. Moore's law itself has already flat-lined (despite chip manufacturers not wanting to admit it).

[BTCdragosfera]

The main graph that illustrates the BTC scaling law is this.

[BTCdragosfera]

The law is not clear to me exactly, but it seems to be a variation of Moore's law. Price to time, I believe in this case?

But that also means that the price will eventually flat-line, *some time* over the next couple decades. I mean it can't keep growing in price constantly, forever like this. Moore's law itself has already flat-lined (despite chip manufacturers not wanting to admit it).

It is a power law, that are well-known in physics. Moore's law is an example but there are many other similar relationships in nature and man-made systems. You can listen to this talk here: https://www.ted.com/talks/geoffrey_west_the_surprising_math_of_cities_and_corporations

The law can be expressed in 2 ways 1) As a power law, that means one quantity as a power of another Price=10^-17 * (days from Genesis Block)^5.82 or 2) as a Scale Law log10(Price)=5.82 *log10(days from Genesis Block)-17. It is the same law just written in two different ways. The second way shows the relationships between scales (logs reveal the scale of the price and the scale of the time) is a simple linear relationship (the parameters mentioned here were calculated using a simple linear regression over the logs of price and logs of time). Phenomena that show power law behavior look like straight lines in a log-log graph (log on the x-axis and log on the y-axis).

Usually, assets are never graphed over a log-log graph but BTC is unique because it seems to follow this universal law. There is something deeper going on with how BTC scales up. It is not random but follows some universal law. By the way, networks show often power law characteristics. It is something that should be known more in the BTC community. I will discuss more about this topic in the following days.

[BTCdragosfera]

The law is not clear to me exactly, but it seems to be a variation of Moore's law. Price to time, I believe in this case?

But that also means that the price will eventually flat-line, *some time* over the next couple decades. I mean it can't keep growing in price constantly, forever like this. Moore's law itself has already flat-lined (despite chip manufacturers not wanting to admit it).

The log of the price as a function of time (log in the y-axis and linear in the x-axis) is not going to look like a straight line but a convex curve (bending downwards). This indicates BTC is slowing down with time when looked over linear time because as the log-log graph reveals what scales up linearly with the log of price is the log of time, so scales. In other words, every time BTC scales up by a factor of 10 we need an equivalent scaling of time so 10 days, 100 days, 1000 days, and so on. This looks like a slowing down in our linear understanding of time or diminishing returns. It is ok because even if this means the 1000x returns in a few years are behind us, it shows the system is stable and robust. Power laws are typical of robust and nonfragile systems. To answer your comments there is no real ceiling also because it represents the price of BTC in dollars and the dollar is inflationary and can go easily to zero relative to BTC. Inflation is already part of the model given we had considerable inflation in the last 15 years. I expect the system to continue similarly for a few more decades but we will see.     

[NotATether]

Usually, assets are never graphed over a log-log graph but BTC is unique because it seems to follow this universal law. There is something deeper going on with how BTC scales up. It is not random but follows some universal law. By the way, networks show often power law characteristics. It is something that should be known more in the BTC community. I will discuss more about this topic in the following days.

That certainly makes sense. I was thinking it would be more like the rainbow chart (https://www.blockchaincenter.net/en/bitcoin-rainbow-chart/).

I guess someone should make a calculator for this, cause interactive things make it much easier for others to understand the graph and how this thing works, I guess.

[BTCdragosfera]

I have a similar rainbow chart. See here for an example. I'm also working on a website that will make it interactive and help with BTC Scaling Law weighted DCA.

https://www.reddit.com/r/Bitcoin/comments/18z04kp/15_years_of_btc_power_law/

In this case, I don't compare the model price with with real price (it is just another way to show the power or scaling law) but I show the model price and the real price as a function of time. The Rainbow chart is actually a ripoff of the famous Trolololo model. In fact, my model is also related to the Trolololo model. I developed it independently from Trololo as a power law model but then I realized that is exactly what Trolololo was trying to describe even if he didn't recognize it as a Power Law. The fact it is a Power Law makes the model incredibly meaningful given Power Laws have a lot of consequences and significance in science. It is astounding that BTC follows a Power Law and it is something that should be well-known and mentioned in all the media. But for some reason it seems like very few people are aware of it and even less understand the significance. My post here is trying to spread the news. This is not just ANOTHER model. It is the BTC Scaling Law, something fundamental to the nature of BTC itself.

[franky1]

firstly the article is not about bitcoin scaling. its about bitcoin price

secondly the chart is an illusion because it depicts a straight diagonal using "log" chart to pretend price goes exponential. yet thats just manipulation of the axis
(using rough numbers from memory. not exact)

                                                                                                        low       high    low
we are no longer in the first halving cycle where the market went from $0.03 to $30 to $4 1000x max
we are no longer in the second halving cycle where the market went from $4 to $1200 $450 300x max
we are no longer in the third halving cycle where the market went from $450 to $20k $2.8k 44x max
we are near end of the fourth halving cycle where the market went from $2.8k to $70k $15k 25x

as you can see each cycle the multiplier declines. and things get less volatile
thus the chart should not be manipulated as straight diagonal exponential line. but instead natural form of a curve

if you put a knee on a weight scale (change the axis of chart) you change the physics of law and change the perception of reality

[BTCdragosfera]

I'm sorry but you don't understand what is going on here.

It is all about scale of course. The law in the graph is log10(Price)=5.82 * log10(days from GB)-17. The chart in the link compares the prediction based on this law for each day since the exchanges opened up to today with the market price of BTC. The middle line of that graph is a simple linear relationship to show that the 2 prices (model and real) are on average identical.
 
The log10 in the law is all about scale because it emphasizes the size, or magnitude, factors of 1, 10, 100, and 1000 both in the price and in the time. There is something fundamentally wrong with what you said above and your understanding of what this is all about.

What you are misunderstanding is that if the law is plotted as a function of time it would be a straight line in a log-linear graph. It would not be, it would be curved as the log10 of the price of BTC is in a log-linear chart.

But what is fundamental to understand is that IT IS a straight line in a log-log graph when we plot the BTC Scaling Law in a Scale of Price, log10(price), vs Scale of Time, log10(time), chart like here:

https://www.reddit.com/r/Bitcoin/comments/18z04kp/15_years_of_btc_power_law/

What you are discussing is what is called a log-linear chart where an exponential would look like a straight line. A power law of the form y=A*time^n (that is another way to write log10(y)=C*log10(x)+B) looks like a straight line in a log-log graph not in a log-linear chart.

It is not an illusion but on the contrary one of the most fundamental and important aspects of BTC, up there with the creation of BTC itself. I'm not kidding about this. I gave a link about the importance of Power Laws in nature and human-made phenomena in the other posts. You can also google power laws to understand why it is amazing that BTC is a power law.

https://www.youtube.com/watch?v=XyCY6mjWOPc

[franky1]

nice try, but no..

try again. you got 2 more chances to get it right before i laugh
you want to make it look exponential because YOU chose to display the data in log format

naturally its not log format.
YOU just the scaled it in YOUR chosen scale of log.

thus YOU are manipulating the results and YOU drew the lines ontop the chart to make YOUR (empty) point
however real world data is more of a curve where the multiplier per cycle DECREASES

good luck with your attempts, but dont waste too much time on it.. because ultimately you dont decide the data path..
the data does its own thing

also..
you got black chartlines outside(below the bounds) of the green min lines YOU drew
you got black chartlines outside(above the bounds) of the red max lines YOU drew

thus rendering your lines void of sticking to data mins and max's

here.. even i can use your chart and create a purple curve

which sticks more to the "max"'s than your line

(how many times does YOUR red line touch the max... once, at the end)
(how many times does my purple line touch the max... six, start to end)

[BTCdragosfera]

I'm not even sure what you are talking about at this point and discussing things with you is a waste of time.

I don't think you have the basic knowledge to understand what a log-log graph is, what a power law is, and what it is represented in the graph. You have to understand that I have a Ph.D. in Physics and I have worked with this kind of graph for decades. I gave you enough information for you to understand if you try and if you want to truly understand.

You can watch this video so you can learn something:

https://www.youtube.com/watch?v=7jUp1rR-Q4I

I'm not sure what you don't get. The blue line is a line that shows on average the predicted prices and the real price match. You need to understand that is an average match, it is a general trend and not a perfect match of course. The model just determines the general trend.

The green and red line represents a deviation from the trend and it is obvious to anybody with minimal math knowledge that they indicate statistically where the bottom is and how to identify areas where the price is oversold or overbought. It doesn't even matter that the bottom is really identified by the green line (even if it is a nice feauture of the model). All what matters is that we identify areas where it is a good idea to buy and areas where it is a good idea to sell.

It doesn't matter if the price of the tops goes above the red area. The idea is that if the price is close to or above the red region then it is time to sell. You don't have to catch the exact top to have a good predictive model just a way to determine if you are paying a premium or you have a discount over the trend. There is nothing drawn by hand as you did but it is all based on statistical analysis and properties of BTC.

The model is simply on purpose but it is based on the true properties of the BTC Scaling Law, or that BTC behaves like a power law.

It is obvious to me you don't have the knowledge or skill to discuss seriously this topic. Maybe you want to try to understand and learn something instead?

[BTCdragosfera]

nice try, but no..

try again. you got 2 more chances to get it right before i laugh
you want to make it look exponential because YOU chose to display the data in log format

naturally its not log format.
YOU just the scaled it in YOUR chosen scale of log.

thus YOU are manipulating the results and YOU drew the lines ontop the chart to make YOUR (empty) point
however real world data is more of a curve where the multiplier per cycle DECREASES

good luck with your attempts, but dont waste too much time on it.. because ultimately you dont decide the data path..
the data does its own thing

also..
you got black chartlines outside(below the bounds) of the green min lines YOU drew
you got black chartlines outside(above the bounds) of the red max lines YOU drew

thus rendering your lines void of sticking to data mins and max's

here.. even i can use your chart and create a purple curve

which sticks more to the "max"'s than your line

(how many times does YOUR red line touch the max... once, at the end)
(how many times does my purple line touch the max... six, start to end)

You don't get the general trend to be in the middle of the black curve if the model doesn't give an overall average path of the price. It is obvious if you understand math.

The deviation at 50 % from the general trend aligns almost perfectly with all the bottoms and with the majority of the price data points during bears.
The 200 % premium lines show areas where the price is overbought. It doesn't catch perfectly the tops but instead of coming out with something arbitrary to determine where the tops are it simply says it is time to sell because we are close to the tops.

Models are just that simplified representation of the true phenomena. They need to be simple to try to explain the majority of the data. The middle line itself has a R^2 of 0.92 that means the model explains 92 % of the variability of the data. Given the large oscillations around the trend, this is pretty remarkable.

One can also write a code to show what would have happened to an investor that followed the model to go in and out of the market when the price reached the green line for the first time in the cycle (to buy) and then the red line (to sell). It can be shown easily the investor would have multiplied their BTC holdings by 100x. Not the USD dollar value but the BTC itself would have multiplied by many fold.
 
Again, I'm sorry you don't understand the basic math of this model. I tried.

[franky1]

goodluck
you had another chance.. but nope you doubled down..

[BTCdragosfera]

goodluck
you had another chance.. but nope you doubled down..

You are funny. I don't need your chances, but you could have learned interesting things if you were open enough and tried to understand the knowledge I shared with you. Thanks for the good luck, you need it too.

[odolvlobo]

Unimpressive. A model is cannot be made simply by fitting a curve.

The main problem with your "model" is that it changes over time. If you fit the curve in the past, you got different parameters. If you fit the curve next year, you will get different parameters. It's a useless "model".

[BTCdragosfera]

Unimpressive. A model is cannot be made simply by fitting a curve.

The main problem with your "model" is that it changes over time. If you fit the curve in the past, you got different parameters. If you fit the curve next year, you will get different parameters. It's a useless "model".

1) We do that all the time in Physics. Here, for example, listen to this talk:

https://www.youtube.com/watch?v=XyCY6mjWOPc

But it shows you don't understand what is done. It is very frustrating to explain these things to people here. You guys do not even ask questions on how the model is created or why is significant. Just making uninformed statements without any real rational foundation.

I'm going to try no matter what to explain and spread the message, but have you ever heard of Kepler's Laws? How do you think he found them? By exactly fitting the log of the distance of the planets vs the logs of the time it takes the planet to go around the sun. This is how he discovered one of the most important laws in astronomy. Kepler's model of the solar system is still used today.

Tell me again how fitting doesn't allow us to make a model?

2) One can calculate the parameters of the fit with time. You can add more and more data to the analysis and then calculate the parameters. You can show that the parameters converge to a stable value with time. As you have more and more data the model becomes stable and that is what the model is after 15 years of data. I made a prediction 5 years ago using the same model and my model is basically the same after 5 years.

https://www.reddit.com/r/Bitcoin/comments/9cqi0k/bitcoin_power_law_over_10_year_period_all_the_way/

Here is the update:

https://www.reddit.com/r/Bitcoin/comments/18z04kp/15_years_of_btc_power_law/

3) The usefulness of the models doesn't depend much at all on the parameters changing slightly. In fact, it can tell us where the bottom are almost perfectly. I have the evidence to show this is the case because in November I made several public posts on my X account and on FB calling the bottom close to $16000 dollars, exactly when the model said so (when everybody was saying we were going to 10 K).

It is not the first rodeo my friend I have been one of the first BTC price modelers and one of the few that has been right over all this time.

[BTCdragosfera]

Unimpressive. A model is cannot be made simply by fitting a curve.

The main problem with your "model" is that it changes over time. If you fit the curve in the past, you got different parameters. If you fit the curve next year, you will get different parameters. It's a useless "model".

But the worst part is that people who do not understand that BTC follows a Scaling Law and why this is amazing about BTC do not understand something fundamental about BTC.
It is one of the most important characteristics of Bitcoin. It makes it a unique asset, something that doesn't behave randomly but it is more like a force of nature.

Maybe the math is difficult for people but anybody with even a small of mathematical understanding and intuition should realize how relevant and exciting this is.

BTC is programmed to be an asset that grows in time, not sure even Satoshi could realize when it created it that the progression of the price would be so incredibly predictable and would follow a well-known behavior of complex systems.

I want to say that this property of BTC is the essence of BTC itself, it is not just another model, it is the equivalent of Kepler's Laws.

[BTCdragosfera]

It would be fun when in a few years from now people will read these posts and they will shake their heads and wonder why some people didn't understand why this is so relevant and fascinating about BTC.

For whoever wants to learn something interesting here is why it is amazing BTC is a power law:

https://www.youtube.com/watch?v=HYQT9_ymsVY

[franky1]

goodluck
you had another chance.. but nope you doubled down..

You are funny. I don't need your chances, but you could have learned interesting things if you were open enough and tried to understand the knowledge I shared with you. Thanks for the good luck, you need it too.

i understand more then you know. but your choice of log scaling your choice of line positioning does not relate to the actual hard data

just check the multiplier per cycle of each halving cycle
the multiplier decreases.. thus curve

you made a chart to scale in YOUR log dimensions but that scale wont last long because bitcoin wont exponential to the extent predicted in the next cycle
i say it wont last long because your references show your straight line was using 5.84509376
now its 5.82 meaning its already slipping out of alignment and needed to change a constant.. thus no longer a constant and thats before even the next market cycle completely messes with your "math" again

also even with change.. .. the "explains 92% variance" .. previous references had it at >93%. so your slipping already
so even after adjusting you are still less accurate then before which shows the current number is not accurate even after adjusting it to try to bring it back into alignment.. because it didnt achieve its re-alignment even after adjusting the log

anyways
here is a better log chart

[BTCdragosfera]

goodluck
you had another chance.. but nope you doubled down..

You are funny. I don't need your chances, but you could have learned interesting things if you were open enough and tried to understand the knowledge I shared with you. Thanks for the good luck, you need it too.

i understand more then you know. but your choice of log scaling your choice of line positioning does not relate to the actual hard data

just check the multiplier per cycle of each halving cycle
the multiplier decreases.. thus curve

you made a chart to scale in YOUR log dimensions but that scale wont last long because bitcoin wont exponential to the extent predicted in the next cycle
i say it wont last long because your references show your straight line was using 5.84509376
now its 5.82 meaning its already slipping out of alignment and needed to change a constant.. thus no longer a constant and thats before even the next market cycle completely messes with your "math" again

also even with change.. .. the "explains 92% variance" .. previous references had it at >93%. so your slipping already
so even after adjusting you are still less accurate then before which shows the current number is not accurate even after adjusting it to try to bring it back into alignment.. because it didnt achieve its re-alignment even after adjusting the log

anyways
here is a better log chart

Sorry, you still don't understand.

Just somebody who doesn't understand math will argue about a parameter for a fit that changes slightly over several years. I also told you that the parameter converges to a particular value over time. You can do that by yourself and show as you get more and more data the parameter becomes stable. It also depends on where you calculate the fit given the large outliers during the bull run skew the data. One can do more sophisticated things like giving less weight to the outliers and the parameters then become even more stable. All things that I'm sorry to say you probably don't get either. You can see clearly that the 50 % discount line in fact goes through a majority of data points. So if one fits only the bear markets you will see even a more clearer power law trend.

The other thing you don't get is that the small change in parameters doesn't matter in terms of predicting the scaling of the price. Scaling means we care about changes from 1 to 10 to 100. It is about orders of magnitude. So if a prediction using a parameter of 5.82 says $70,000 and another using a parameter of 5.83 says $75,000 is basically the same number in terms of magnitude. You could even use 6 as the parameter it doesn't matter. These values are derived from regression and are always an approximation.

That is what the model is trying to do, predict how long it takes for the price to go up another factor of 10, but you miss that completely because you do not understand what scaling is about.

I feel I'm talking to a flat earther and I have to explain basic things and the flat earther insists on debating using his 4th-grade understanding of science.

It is obvious that you don't understand math even in pointing out that a R^2 of 0.92 is different from a R^2 of 0.93, lol. It is within statistical error to have such a small change given the data is random locally.  It doesn't say anything about the model becoming less precise because that is the same value from a statistical point of view. Why don't you take a class in stat and come back?

Also, you don't get what power laws tell us and the significance of them. I bet you didn't watch the videos I linked because you are hard-headed and arrogant and don't want to learn a thing even from people who have much better professional experience in these things than you do. Can you ask what you do for a living?