Original Topic: Giovanni Santostasi - The Bitcoin Power Law TheoryAuthor: fillippone
Everything you wanted to know about The Bitcoin Power Law Theory, but were afraid to ask!OP post on Bitcointalk.org:
The BTC Scaling Law
During the weeks wey pass, I been dey increasingly involve in studying a new model by an astrophysics professor wey turn neuroscientist, wey dey describes bitcoin according to Power Laws.
Giovanni Santostasi, aka
BTCdragosfera don describe a model where he don explains why Power Laws governing price and other Bitcoin metrics (such as Active addresses and hash rate) no be random fact but actually e fit be symptoms for something else, namely Bitcoin being "no fit be common asset but fit dey more similar to natural phenomena wey universal Power Laws dey rule due to recursive, infinite feedback loops fundamental to the system".
Bitcoin dey more similar to a city and an organism than a financial asset.
Santoshi first post he mumblings for Reddit for more than 5 years ago:
This post go almost unnoticed: Giovanni put am aside small, con focus on other things, wey na he new venture for Neuroscience, he continue dey work on the idea then con finally publish am for the following papers:
The Bitcoin Power Law TheoryIf na the video format you want, hear a video Summary of the Theory:
The material no dey very well organized, so I go try explain Wella for this thread.
The Power Law na the only first part of he full Bitcoin model, where e also be model range for Bitcoin price and bubble indicator to take detect excessive price movement:
Yes, of course you don already see that Rainbow Graph, and actually
Trolololo chart na Power Law Chart.
The innovation of Santostasi's article be say Bitcoin dey considered as financial system wey dey behave like natural system according to well defined laws. This laws na Power Laws. In this sense now, the article no be "model" about Bitcoin but part of "Bitcoin theory."
According to Santostasi:
For model science, the term "Theory" dey refer to scientific theories, well confirmed type of explanation of nature ,made in a way wey be say e dey consistent with the scientific method, and e fulfill the criteria wey dey required by modern science. That type of theories dey described for way wey be say scientific tests go fit provide empirical support for am, empirical contradiction ("falsify") of am. Scientific theories na the most reliable, rigorous, and comprehensive form of knowledge,[1] unlike all them this common words wey we de use "theory" we de imply say something no de proven or de speculative (wey be say formal terms de characterized by the word hypothesis).[2]
(This na from Wikipedia - Ed.)<...>
Na full theory because e dey explain the entire behavior of Bitcoin. E get several points and e dey explain the interactions of all the on-chain parameters,
E dey even explain why the bubble dey exist and why we get bottom. He dey make predictions wey dey make the theory falsifiable.
For science, model na representation of Idea, object or even process or system wey dem dey use to take describe and explain phenomena wey dem no fit experience directly. Models na central to wetin scientists dey do, both their research and when communicating their explanations.
A model dey very similar to a hypothesis, so na the initial mathematical formula or algorithm wey try to replicate some of the behaviour for subject studied.
Theory na ultimate way to take understand phenomenon: E dey complete in the sense that e dey try to explain all the observered behavior. For this case , how the on-chain parameters dey work, how the adoption take dey grow (via a virus-like mechanism), and how the adoption effect take dey affect price (via metcalfe law).
How the price take dey bring more miners, how the hash rate take dey related to the price, how the Difficulty Adjustment dey kick in and e dey create inhibitory loop wey creates stability for the system, like that like that
People never comprehend am yet: E dey tell us everything wey we need to know about Bitcoin, and dey get corollary wey dey even explain the bubbles and how dey take dey relevant. E fit dey improved or do am make e dey better, but e dey coherent and complete: na big deal e really be.
(I do some little readjustments to make the sentences make e dey more readable)
Introduction: wetin be Power Law?
According to Wikipedia:
For statistics, power law na functional relationship between two quantities, where one relative change for one quantity results for relative change for the other quantity proportional to the power of the change, independent of the initial size of those quantities: one quality dey different from the power of another.
Dey fit write power law for the following form:
Y=10^B*(x+S)^A
or:
log(y)=A*log(x+S)+B
A lot of natural, sociological, mathematical, physical and psychological phenomena dey follow power laws.
The power law get few important features.
- Scale invariance: Power Laws still dey valid when the involved variables change the order of magnitude.
- Lack of well defined average value: Power Laws get meridian but e lack mean value.
- Universality: Power law wey get the same exponent dey produce similar dynamics.
The first property be say power law wey dey draw for log-log chart, or chart where both axes dey on logarithmic scale, na straight line with slope A, B intercept,and S na shift parameters.
Abeg know say straight line for log-log plot dey necessary, but them no too get evidence for Power Laws. To determine Power Law existence only because say the straight line fit log-log chart na unsatisfactory approach to the statistical method.
|  |  |
| bitcoin price plotted against time | A graph you might have already seen Log bitcoin price, plotted against time |
|  |  |
| Now both axis are Log, and a linear relationship appears | The previous graph slightly reworked |
Abeg know say those 4 graphs represent the exact same data. The blue line na the same as the red one.
This only difference na wetin you dey see, and dey fit capture am best by the red line for the log-log chart, wey dey appear to describe the Bitcoin prices.
For reality, the explanatory power na the same for all the graphs but the linear scale "undervalues" the errors for the first steps of the graph and e dey "overvalue" the errors for the last steps , as the price don increase four orders of the magnitude.
The log-log charts dey evenly "decompresses" the charts price and e time dimension, and the best-fit function dey appery for straight line.
I do those graphs myself to take check the reality of the claimed properties of the log-log chart.
If you wan understand Wella wey Power Laws be and why them dey everywhere for science, Abeg look them this links:
|  |  |
| Geoffrey West: The surprising math of cities and corporations | Why do Power Laws Work so Widely? | Episode 2207 | Closer To Truth |
Giovanni Santostasi don already publish article wey dey answer few questions and e dey correct our misconception about PLT (Power Law Theory):
Common Misconceptions and Fallacies Regarding the Bitcoin Theory of BitcoinThey get this rendition of the "Bitcoin clock" using the power laws: the beautiful spiral well dey represent the soundness of the theory.
Bitcoin price no be the only variable wey get governing power law; addresses and hash rate also dey governed by similar laws.
E add beauty to the model, as we fit fine "cross" relationship.
They get this beautiful YouTube video about the relationship between these quantities:
Addresses and Prices dey tied via Power Law with something wey resemble Metcalfe Law.
HashPower and Price de linked via Power wey strongly supporta price via mining Hardware cost.
The major point of this model no be say scarcity no dey considered anywhere for the model . The PLT no consider S2F relevant for the price determination
Of course, the author soon con enter disagreement with PlanB:
In
this article Giovanni explain why scarcity no dey play any role for price determination:
Scarcity no be wetin dey drive Bitcoin price
<...>
Here 2 models, the power law model wey get zero assumption on scarcity, just based on those observations for the price to dey increase na something wey dey predictable. Scarcity no dey part of the model at all. The other, S2F where scarcity na the main driver, in fact, e assume say scarcity dey increase with time. The power law (with no assumption on scarcity) dey lead to " hurry up get some BTC now". As you fit see S2F instead say you fit get in anytime con still make the same gains, no matter if you even join 10 years ago (for the same amount of 4 years HOLDING time)or 10 years from now( again for the same HOLDING time ). Both investors go make 10x return over this time. While you notice say for the Power Law model e dey important to join as soon as possible. So you see how people use scarcity argument dey take lead to illogical conclusions wey fact no support?
If you want dive deep for this matter, they get video for here:
Why BTC stock-to-flow model based on scarcity dey worse than wrong, na compete nonsense.
Santostasi never even finish yet. First he dey try organise the knowledge wey dey scattered over few articles and X posts .
The first output go be scientific paper, possibly peer-reviewed, and a more educational book wey dey talk he theory in details
Resources:
