Bitcoin Forum

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

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 main graph that illustrates the BTC scaling law is this.
https://i.ibb.co/C6n28k8/Model-Valuation-A1.png (https://ibb.co/MfR6SYS)

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.

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.     

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.

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.

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

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

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
https://talkimg.com/images/2024/01/12/36ZhJ.png
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)

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?

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.

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.

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.

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.

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

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
https://talkimg.com/images/2024/01/12/3ROBI.png

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?

that was your final chance and you dug down deeper in your hole, 3 times..

goodluck with life. you will need it.
the price will not continue exponentially .. the hard data shows the multiplier is closing

..
your theory is not of the bitcoin data.
your theory is about YOUR manipulation of how YOU display data, by YOU displaying it using YOUR decided numbers that are not even EVER going to be a constant. thus self defeats math.

you would have a palatable point if you could come up with a true constant.. but you cant.

even when you say you refined the number due to added time/added data.. your refined number ended up giving less accurate results. thus debunks your theory

---

funniest part is your medium article that references a twitter that references a Reddit.. shows the Redditor actually say that bitcoin wont exponentially continue on a straight line but would actually 'taper off'

The redditor is me, hardhead, lol. I'm the author of these reddit posts. I have even linked them above. I tried to explain to you like 100 times that an exponential in a loglinear chart looks like a straight line, this is a LOG-LOG chart. The equation is price=A (days from Genesis Block)^n, does this look like an exponential to you? Why do you talk about math when you don't know anything? Go back to school or look at some math videos online. At this point, you are just a troll.

I'm not sure why I even answer you. It is a straight line in a log-log plot. In a log-linear plot it would be curved and indeed is tapering off, the same equation, lol. There is no data manipulation of any kind, lol. What are you even saying? Why do you talk about stuff you don't understand?

first of all

that chart in this topic YOU post is not a standard LOG
i linked a standard log which shows the curve

that chart in this topic YOU post is not a standard LOG
heck even using your variable your lines dont even match up with the market data.
greens dont touch the bottoms reds dont touch the tops

infact looking at the old reddit theory vs this topics graph.. the mis-alignment is worse now by a huge factor
in short your theory is breaking more and more

YOU MANIPULATED the log using a metric that MAKES IT STRAIGHT... FOR NOW
how ever previous time and in future that metric has to change..
you manipulate a chart to temporarily display as if on a line but cant do it using a constant. which means the theory you present does not stay on a straight line forever


it will not be exponential it will taper off..

stop pretending it will stay on that constant line where the price multiplies exponentially

just look at the real data and do real math. not chart manipulation..

real math of real price data.. not image voodoo

you made the chart image to fit a narrative.
its equal to people that photoshop to make the pictures of themselves look taller

you would only have validation if the metric you used was a unbreakable constant.. however its a variable. thus debunks whole theory

..
by being a variable that changes over time proves curve power law not line power law

..
im just gonna say
5.97    5.845    5.82   in just a few short years. shows how you have not proved a constant line. you have actually proved a curve instead
bitcoins market cycle is a known factor of 4 years.
so each new metric adjustment occurs every 4 years.
yet even one of YOUR numbers has not even lasted even one whole 4 year cycle. meaning your model deviates more frequently. whch debunks your theory

..
your theory does not show knowledge of math. it shows display of graph image manipulation that does not prove itself 4+ years later using the same manipulated numbers.

Fitting allows you to make a model, but a curve fitting is not a model. Kepler's Laws describe the characteristics of the orbits of the planets, but they are not the model itself.
Here's another astronomical example. Hubble observed that the red shifts of galaxies are roughly proportional to to their distance. Here is the graph: https://en.wikipedia.org/wiki/Hubble%27s_law#/media/File:Hubble_constant.JPG
Note that neither the graph nor Hubble's constant are the model. They are observations that support the model of the the expansion of the universe.

Likewise, your curve mimics Bitcoin's price over time, but it does little to explain its nature. It is not a model. Does your model provide any explanation of why the price behaves the way it does?


Your parameters are not converging to a stable value. Specifically, your n is not constant. It is falling over time. It was 5.9762 five years ago and it is 5.82 today. If you do the curve fitting for the first 5 years, I'm sure that n will be greater than 5.9762, and I predict that in 5 years it will less than 5.82. How does your model explain that?


Perhaps "useless" is an exaggeration. I say "useless" because it explains nothing. Furthermore, like all tools based solely on back-testing, the fact that your curve fits past data allows it to predict the past, but it says nothing about predicting the future.

Why do you want to argue with somebody who uses math for his daily work?
I don't get it.
The chart has been explained over and over. It is just another expression of the relationship of the log10 of price vs the log10 of time. I gave you links to the reddit post where the relationship between log of price and the log of time is shown. I'm the author of that reddit post.

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

The chart here is EXACTLY the same relationship but now time is expressed in terms of the predicted price.
It shows how the 2 prices agree in average.

If you plot Price=A*days^n in a log-linear chart will taper, if you plot it in a log-log chart it will look like a straight line.

I still don't get what you think has been manipulated. Listen I don't want to discuss any more with you because, notwithstanding my attempts to educate you, it doesn't work because you are as arrogant as ignorant.
It is a waste of time.

Are you a physicist or an astronomer? I'm.

I tell you that in physics we make models all the time by simply fitting data. If you find a relationship between y and x that is a model. It is a mathematical model. Here the modelling assumes that the behavior of BTC is a power law. The R^2 shows that this mathematical model can explain 92 % of the behavior of BTC.

I gave you a link so you can learn about power laws and their significance in nature. Just discovering BTC is a power law is an incredible discovery that changes everything about the nature of BTC.

The title of the video is:
Why do Power Laws Work so Widely?

Watch it and then we can discuss maybe, you will learn something anyway. Here is again:

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

If you listen to the video it is said over and over that physicists create models of power laws by fitting data. Most of these power laws are not understood in terms of what causes them (because these systems are so incredibly complex) even if there are some attempts to do that. Nobody knows exactly why metabolism rates in animals follow a power law but it is a model of how metabolism works and it can be used in biology to make a lot of interesting inferences.

When Kepler discovered the power law that governs the motion of the planet he didn't have any idea what caused that but it was not useless. It could be used to predict eclipses and other important things. They are called laws for a reason.  Imagine you saying to him it was useless because it was just derived by fitting.

He had the idea of using logs which at that time was revolutionary. His discovery lead eventually Newton to find the law of gravitation. Yes, finding a deeper cause is what you do in the progression of understanding how a phenomenon works but it starts in making mathematical models of the process itself.
But one can learn a lot of things by knowing the system will behave in this way. It would be great to find out why BTC is a power law and what is the underlying cause but that is extremely difficult in the case of networks like BTC. Maybe eventually somebody will figure out, but they would have to start from recognizing it is a power law.

I made a prediction 5 years ago about BTC moving along a power law and this has been true since (in fact from the start of BTC history).

Again another person arguing with me that 5.94 is different from 5.82. IT IS NOT for god sake! Just people who have no clue on how statistical models are created will say that.

First of all the n value I calculated 5 years ago was just after a local peak and the outliers of the bubble skewed a bit the value, second the difference between the 2 predictions is insignificant for example with n = 5.94  we get after 5500 days that the nominal price is $62K with the value of n = 5.83 we get $59 K that is 3K difference, lol. Do you realize how stupid that remark is?
It doesn't matter much at all in particular given the entire idea is to focus on scale that is what we care is rounding to the next magnitude so even 80 or 90 are basically 100 in this exercise.
How do you know the parameters are not converging did you do the math? No.

Here is a graph on how exactly the parameter n is converging as you add more and more data. It is stabilizing. Most of the oscillations are actually due to the bubbles. One can eliminate them by using methods like RANSAC (look it up) and it will be even more stable. Here the graph showing how n is converging (going flat).

https://i.ibb.co/7YBpH1V/ModelN.png (https://ibb.co/w08QTzC)

A power law model is all about understanding how long it will take to go up by a factor 10 and the model tells us BTC is a scale-invariant system and tells us exactly how long it will take.
Please watch the video, google power laws, and try to understand something if you care about BTC.

Also, this model allowed us to tell the bottom in November. I made public posts telling everybody we reached the bottom of $16K. Tell me again how useless this is.

Not just that but if somebody had used the model to buy at the bottom indicated by the area of discount in the chart and sold at the the areas of premium, even with an updated n (that is exactly what you do when you work with mathematical models, you update them with new data) you would have a strat with 99 % success rate and 950 profit factor (as I programmed it in Tradingview given it can only use past data when you do backtesting). USELESS???? LOL.

Why do you insist on discussing this with me as you want to teach me without having worked on these models of BTC since 2014? I do this for a living.
I don't get it.

Not sure why people come here and debate with somebody who has a Ph.D. in Physics and worked in science for 30 years, modelled BTC for 10 years, with such arrogance without understanding what they are talking about. I don't want to appeal to authority but if you discuss things you don't understand with a professional you should have a little bit more humility and be open to try to understand by asking questions instead of making useless claims.

It's working until it stops working just like the 100 or 200 Moving Average which was supposedly to hold Bitcoin at $22k in 2022. What happened? It broke and Bitcoin went as low as $15k.
So everything will work until one day, when it will suddenly stop working. I am sure it was the same case with the PlanB guy or something? I don't remember his name exactly.

funny part is he admits in his other forums that the number(he wrongly calls constant) was 5.97 then now 5.82.. and then in the SAME WEEK he is already also talking about 5.8

imagine what he is going to say in the next halving cycle

second funny part is he is so desperate to try making his manipulations go viral that he is making many accounts and retweeting and reposting himself

oh and he is purporting to be a physicist now not a mathematician..
third funny part is in the scientific model it actually involves peer review but he cries when people do review and call him out on his broken theory

fourth funny part is he cries about working on it for a decade.. if the formulae even had merit. the constant would work for itself and prove it over time without needing any adjustments

EG E=mc² is still E=mc² a century later

It has worked for 15 years. What I'm trying to explain is that we are dealing with a power law. I gave many links to people, please really look at the videos because there is incredibly valuable info. Power Law are stable and actually, as the system grows it becomes more stable. It is not another formula.

It doesn't matter if it 5.82, 5.89, or even 6.
I told you it is converging to a particular value. Also small variations in the value do not make any difference in the predictive power of the model.

Did you see the graph I posted in the previous response?
No, so please do not continue with the same nonsense.

It is a statistical derivation anyway.
Do you know what that means? We are dealing with a stochastic system so you are not going to get perfect constants, the data is messy.

You are not in a position to peer review anything because you are not my peer. I posted here in the hope of discussing with somebody who understands these kinds of things and having a constructive discussion, instead the people who replied so far seem to have no basic knowledge of math.

I don't want to insult you but it is completely evident you have no clue of what you are talking about. Again, I said it is like a flat earther discussing with a professional Astronomer.

Physicists are applied mathematicians. We are as good at math as a mathematician but we know more about how to apply it to the real world.

Everybody should know about this profound property of BTC.

showing links to the same falsehoods is not proof. its just circling the same trashcan
your "law" has changed over the years. and even with changes becomes LESS accurate

even a toddler can see how your lines dont even match the lows and highs of the market even after you edit the chart(adjusting numbers variably) to try to make the chart fit a straight line

The links is to a mathematical proof that the value converges. You don't understand why that is fundamental to prove the model works.
Why do you argue? It is like me walking in a baseball professional team and telling them how to play basketball.

The top line is not supposed to match the highs of the market. It is evident they don't follow a trend. The decay can also be modelled but it is not what the lines are trying to do. They are trying to do the second best thing that is to identify places where the price is too high and it is a good idea to disinvest.

These are areas that show that if the price goes above 200 % of the trend line is time to sell. I tried to explain this to you 1000 times. It is a reference point. It gives a simple recipe for DCA. The bottom line perfectly indicates the bottom instead it catches all the major bottoms and in fact, the general path during bear follows the bottom line. It is stochastic again so please do not tell me a few points went below because it is completely idiotic.

I'm trying to do my best to teach you because I'm an ex-professor so I'm trying to be patient and calm but you are really really annoying.

your model breaks. becomes less accurate and doesnt use a constant..
your proving nothing

anyone can take any data and at one time manipulate it into appearing to conform to a straight line with a range of boundaries/buffer/outliers.
but if at a later date a peer takes your exact numbers and does it themselves and doesnt get the same results.. the theory is debunked

you endless showcasing that you have been working endlessly on it for 15 years shows its broke because you need to keep fixing it periodically

the top line doesnt, thanks for admitting it
however the blue (your supposed mid line) does not even follow the mid point of the market cycle
the green line doesnt even follow the bottom of the market

in short it has nothing to do with the market

you simply straightened a curve into a diagonal chart. and just drew a line for the axis not for the market data.
you then notice you cant get lines to fit the market data so then call it "undervalued" and "over priced" when the market data doesnt fit your silly theory

..
here is a thing though

you can look at the average hashrate of network over a period. look at current gen asics hashrate electric and hardware. and calculate the bitcoin price min and max dependant on dominant global countries electric price. and get a min/max mining cost.. and you will see the market has traded within that range

so not out of bounds of real economics

yep
2021 5k-75k was its global mining cost efficient/inefficient window and the market stayed inbounds
2022 10k-95k was its global mining cost efficient/inefficient window and the market stayed inbounds
2023 15k-110k was its global mining cost efficient/inefficient window and the market stayed inbounds

there are logical, social and economic reasons why the market stays inbounds of global min max mining
if no one on planet can mine for less no one wants to sell for less and everyone sees it cheaper to buy than mine so everyone is buying no one is selling causing a support line no one wants to cross
if everyone on planet can mine for less no one wants to buy for more and everyone sees it cheaper to mine to sell rather than buy, so everyone is mining/selling, no one is buying causing a resistance top line no one wants to cross

so when you then see the market hit those limits but not cross them you see the market is performing as expected when testing the boundaries

You are simply ignorant. Hard-headed and ignorant.
In fact, I checked your other posts and it is obvious you are ignorant.

You don't even know what shorting is and you want to come here and discuss mathematical modelling.

No, the trend doesn't have to go through the middle of what your eyes says is the middle. In the graph in this thread the middle line is y=x simply. It is the line when the two prices the real and the estimated price meet. Because the black line oscillates around this middle line it shows the model price is on average (the key is average) reproducing the real price. In 5 years from now, the graph will look almost identical, I tried to explain this to you and the only reason I still address it is because some other person will read this and need to know you say just idiocies after idiocies.

As data comes in one updates the model. Of course, if they change radically they are invalid but this model is simply becoming more stable and better.

I don't dictate what the price is doing. It is very obvious to anybody with a minimal amount of math knowledge that the bottom line is determining almost perfectly the bottom prices. You just show how idiotic your comments are by insisting it doesn't. The tops as discussed do not align and there is useful information that seem to indicate they decrease with each cycle. I explained already how we deal with this information (but it went above your head).

No, not everybody can make data go in straight line. I didn't make the data go in straight line, BTC is a straight line one a log-log chart (and this is in a sense a log-log chart given the black dots is the transformation of the data given the power law formula.

You know I talked with many people and you are one of the few people (there was another one a few years ago, not sure if it is you because you two have the same level of ignorance) who is insisting on something while showing a complete lack of understanding about basic concepts and ideas. Not sure if there is an option to block you, I'm looking for that in this antequate app but you are really being disruptive and contribute nothing to the discussion. Maybe I should just ignore you.



 

Your estimates are not very useful because they are so wide and also they don't tell us where the bottom is or the top, not even close.
Also, do not reveal anything about the behavior of BTC in terms of deep network and fractal properties. If you are not interesting in this discussion simply go back to explain to people (wrongly) what shorting is all about.

bitcoin is a curve on a LOG model

YOUR chart is not log .. you manipulated the log multiplier and even you cant use a constant. which shows bitcoin doesnt stay on a straight line because you need to alter the log number periodically

so it doesnt fit a model

its like you want to pretend clothes fit a particular mannequin model. but then endlessly rebuilding the mannequin model to try to ensure the clothes fit

im telling you and alerting others that you mess with the mannequin model, thus no way of knowing the true clothes size comparison/expectation

analogy
imagine you had weighing scales in your house and you want to tell your wife you can lose 8% weight by next year
you would happily turn the dial/adjust sprints/counter balance, under the scales to make 1kg=0.92kg

and then show her that the read-out says you are 8% lighter.. shouting "but the scales prove my weight" and getting angry if she even suggests you tweaked the measurements and not had constants to compare physics to your body weight

How many times I need to repeat myself? YES, BTC IS A CURVE ON A LOG-LINEAR CHART !!!! I know because that is exactly what a power law looks on a log-linear chart, that curve is EXACTLY a power law.

Here is you can see the same graph here, it curves, same equation, same model, different chart type. Learn something.

https://twitter.com/Giovann35084111/status/1746243124278804748/photo/1

When you plot the same graph on a log-log chart then it becomes a straight line. That is what power laws do.

https://twitter.com/Giovann35084111/status/1746082576337625380/photo/1

Do you get it now?

The graph I posted here is another type of graph where I calculated the price given by the model above and plotted on the x-axis and the real price on the y-axis. I know this is too difficult for you to comprehend but stop to say idiocies.

It is just 3 ways of showing the same thing.

There is nothing tweaked, there is nothing changed. These are models. If you don't understand it is your problem.

 

Have you ever analyzed data in your life?
Very such a thing called randomness and noise.
Try to measure the temperature in a room. Of course is going to change over time. What you do is measure over and over and then take an average. You can then plot a distribution of the noise level to see which kind of randomness you are dealing with, you can calculate standard deviations, and so on. Every measurement has noise. You want to teach me, what I taught in college how to do measurements, how to do an experiment and calibrate things, lol. Your example is stupid. You have no idea of what noise is, how to estimate errors, statistical methods and so on. In fact, you have no idea what a short is and you still wanted to debate that. You have Legendary status but you are simply a troll.



 

Also, stop harassing me, I'm serious now. Your comments are just trolling at this point and I initiated this thread. Just go and discuss with somebody else. I will look at the rules on the site and report you if necessary.

This graph addresses the comments of the skeptics that say the model will change the parameters over time and so it is not valid. The parameters change slightly as we add more data mostly because of the large deviations during the bubbles. It depends if you do the fitting near the top or bottom. This has nothing to do with the goodness of the model but the fact we have a phenomenon with a general trend and period of large deviations.

Anyway, I calculated the slope and y-intercept of the power law for each day in the last 7 years and created a model for each day using these parameters extrapolated to today and all the data for the real up today (so it is easy to compare all the models). I then averaged the model given the parameters oscillate around a mean value. I compare with the model today. This is the result:

https://twitter.com/Giovann35084111/status/1746312103089328281

As you can see the model today and the average over parameters up to 7 years ago is basically identical for all purposes. This shows the power law pattern is stable in time. This should resolve all doubts.

Of course, it doesn't guarantee that is going to work forever but even if does we will learn something about the dynamic of BTC. So far the power law has been respected and I will expect to work in the same for several years in the future.

what constant/formulae did you use this time

also
https://pbs.twimg.com/media/GDwrBxUbYAAr4M9?format=png&name=large

you only changed things from 7 years ago (mid way)
look on the right the blue line sits at 1.5 but the blue is ~1.25
meaning not a 8% error.. but at >20% error

and thats just from chart manipulation of flattening the curve.. before even adding in extra lines for mid, top bottom

Can't say I'm overly keen on the name.  If it's a power law, just stick with power law.  The word "scaling" is far more closely associated with network usage, not price.  I feel it just creates unnecessary confusion.

Aside from that, you have my support.  Ignore renowned troll franky1.  No one takes him seriously and the forum is a much nicer place with him added to your ignore list.

Yeah, I understand what you say, I didn't think about that, people may confuse "scaling" with network usage even if in this case I meant the scale of price (10,100,1000) and scaling of time. But I can see how this can lead to confusion. Scaling is a term we use in physics, and I was trying to emphasize that physics terminology. There is a good book by G. West called "Scale" that is all about this topic but I understand what you are saying.
Yeah, franky1 is a troll, very annoying.

That flatlining isn't totally true yet because they're pushing the chips and the transistors in the wafers to the absolute limit, I believe that they're getting closer to creating a transistor that's getting closer or about halfway close to the size of an atom so I don't believe that a plateau or a flatline in computing is ever going to happen, humans are a natural boundary pushing species so who knows what's next for us in computing power and this belief is shared with this one bitcoin scaling law too as it's definitely oddly similar to Moore's law, as time goes by, there's going to be more and more people that will either lose their bitcoins permanently through forgotten passwords, destroyed hardware wallets, voluntary bitcoin burning and other stuff and it's going to grow the same as bitcoin adoption together with the prices which means that a plateauing of the price is close to impossible.

 I find your work on the BTC Scaling Law intriguing. Renaming it the "BTC Scaling Model" to reflect the relationship between price scales and time scales is a logical step. Your model's approach to predict Bitcoin's growth over a significant period and magnitude using a power law framework is an innovative take in the crypto analysis space.

The use of model price as the x-axis and the real price as the y-axis is an interesting method to gauge the accuracy of your predictions. It's notable that your model aligns with the general trend of Bitcoin over an extended period, considering the volatility inherent in cryptocurrency markets.

The practical application of your model in identifying overvalued or undervalued phases of Bitcoin could be valuable for investors, provided it's used cautiously and in conjunction with other analysis tools. However, it's important to remember that no predictive model is foolproof, especially in a market as unpredictable as cryptocurrencies.

Your initiative to apply scientific and mathematical principles to financial market analysis is commendable and contributes to the evolving field of cryptocurrency analytics. I'm interested to see further developments and more detailed insights in your upcoming article.