OP post on Bitcointalk.org: The BTC Scaling Law
During the last few weeks, I have been increasingly involved in studying a new model by an astrophysics professor turned neuroscientist, which describes bitcoin according to Power Laws.
Giovanni Santostasi, aka BTCdragosfera described a model where he explains why Power Laws governing price and other Bitcoin metrics (such as Active addresses and hash rate) are not a random fact but actually the symptoms of something else, namely Bitcoin being "not a common asset but more similar to natural phenomena ruled by universal Power Laws due to recursive, infinite feedback loops fundamental to the system".
Bitcoin is more similar to a city and an organism than a financial asset.
Santostasi first posted his mumblings on Reddit more than 5 years ago:
This post went almost unnoticed: Giovanni set it aside a little bit, focusing on other things, namely his new venture on Neurosciences, but kept working on the idea and finally published the following paper:
The Bitcoin Power Law Theory
If you prefer the video format, hear a video Summary of the Theory:
The material is not very well organized, so I will try to explain the ideas better in this thread.
The Power Law is only the first part of his full BTC model, where it also models a range for bitcoin price and a bubble indicator to detect excessive price movements:
Yes, of course, you have already seen that Rainbow Graph, and actually Trolololo chart is a Power Law chart.
The innovation of Santostasi's article is that Bitcoin is considered a financial system that behaves like a natural system according to well-defined laws. These laws are Power Laws. In this sense, the article is not a "model" about Bitcoin but a coherent "Bitcoin theory."
According to Santostasi:
Quote
In modern science, the term "theory" refers to scientific theories, a well-confirmed type of explanation of nature, made in a way consistent with the scientific method, and fulfilling the criteria required by modern science. Such theories are described in such a way that scientific tests should be able to provide empirical support for it, or empirical contradiction ("falsify") of it. Scientific theories are the most reliable, rigorous, and comprehensive form of scientific knowledge,[1] in contrast to more common uses of the word "theory" that imply that something is unproven or speculative (which in formal terms is better characterized by the word hypothesis).[2]
(This is from Wikipedia - Ed.)
<...>
It is a full theory because it explains the entire behaviour of Bitcoin. It has several points and explains the interaction of all the on-chain parameters,
it even explains why the bubble exists and why we have a bottom. He makes predictions that make the theory falsifiable.
In science, a model is a representation of an idea, an object or even a process or a system that is used to describe and explain phenomena that cannot be experienced directly. Models are central to what scientists do, both in their research as well as when communicating their explanations.
A model is very similar to a hypothesis, so it is an initial mathematical formula or algorithm to try to replicate some of the behaviour of the subject studied.
A theory is the ultimate way to understand a phenomenon: it is complete in the sense that it tries to explain all the observed behaviour.
In this case, how the on-chain parameters work, how the adoption is growing (via a virus-like mechanism), and how the adoption affects the price (via Metcalfe law).
How the price brings in more miners, how the hash rate is related to price, how the Difficulty Adjustment kicks in and creates an inhibitory loop that creates stability for the system, and so on and on
People do not comprehend it yet: it tells us everything we need to know about Bitcoin, and there is a corollary that even explains the bubbles and their relevance. It can be improved and made better, but it is coherent and complete: it is really a big deal.
(I made some little readjustments to make the sentences more readable)(This is from Wikipedia - Ed.)
<...>
It is a full theory because it explains the entire behaviour of Bitcoin. It has several points and explains the interaction of all the on-chain parameters,
it even explains why the bubble exists and why we have a bottom. He makes predictions that make the theory falsifiable.
In science, a model is a representation of an idea, an object or even a process or a system that is used to describe and explain phenomena that cannot be experienced directly. Models are central to what scientists do, both in their research as well as when communicating their explanations.
A model is very similar to a hypothesis, so it is an initial mathematical formula or algorithm to try to replicate some of the behaviour of the subject studied.
A theory is the ultimate way to understand a phenomenon: it is complete in the sense that it tries to explain all the observed behaviour.
In this case, how the on-chain parameters work, how the adoption is growing (via a virus-like mechanism), and how the adoption affects the price (via Metcalfe law).
How the price brings in more miners, how the hash rate is related to price, how the Difficulty Adjustment kicks in and creates an inhibitory loop that creates stability for the system, and so on and on
People do not comprehend it yet: it tells us everything we need to know about Bitcoin, and there is a corollary that even explains the bubbles and their relevance. It can be improved and made better, but it is coherent and complete: it is really a big deal.
Introduction: What is a Power Law?
According to Wikipedia:
Quote
In statistics, a Power Law is a functional relationship between two quantities, where a relative change in one quantity results in a relative change in the other quantity proportional to a power of the change, independent of the initial size of those quantities: one quantity varies as a power of another.
Power Laws can be written in 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 follow Power Laws.
The Power Law has a few important features.
- Scale invariance: Power Laws remain valid when the involved variables change the order of magnitude.
- Lack of well-defined average value: Power Laws have a median but lack a mean value.
- Universality: Power Laws with the same exponent produce similar dynamics.
The first property is that a Power Law drawn in a log-log chart, or a chart where both axes are on a logarithmic scale, is a straight line with slope A, B intercept, and S as a shift parameter.
Please note that a straight line in a log-log plot is necessary, but there is insufficient evidence for Power Laws. Determining a Power Law existence only because there is a straight line fitted in a log-log chart is an unsatisfactory approach to the statistical method.
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bitcoin price plotted against time
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