CoinWorld reported:
Author: Tom Mitchelhill, CoinTelegraph; Translation by: Bai Shui
The Bitcoin power law—a mathematical model indicating the continuous growth of Bitcoin prices over time—has become a subject of intense debate, with critics denouncing it as fundamentally flawed and likening it more to “horoscopes” than a predictive model for cryptocurrency prices.
Advisor and Bitcoin advocate Adrian Morris points out that while the Bitcoin power law is touted as a model for predicting future Bitcoin prices, its validity has been greatly exaggerated by its proponents.
On the other hand, Italian physicist Giovanni Santostasi—the discoverer of the Bitcoin power law—asserts that the power law is undeniable and can be witnessed firsthand.
The power law operates by plotting Bitcoin’s historical price data on a “log-log” scale—where the logarithm of price is plotted against the logarithm of time, along a line that best fits the data.
Supporters of the power law, including Santostasi and his colleague, mathematician Fred Krueger, argue that the law indicates that Bitcoin’s price should continue to grow at a relatively stable rate for a long time into the future.
The Bitcoin power law suggests that Bitcoin prices will continue to rise. Source: Bitbo
Power laws are common in nature and have been applied to various natural phenomena, from the growth of animal teeth and claws, the distribution of social wealth (the well-known Pareto principle), to the mapping of the severity of earthquakes and tornadoes.
Santostasi notes that power laws are not limited to Bitcoin’s price; they can also be found in various Bitcoin-related data, including the growth of network hash rates and the rate of new Bitcoin wallet addresses over time.
Santostasi states that power laws can be reflected in many attributes of Bitcoin. Source: Giovanni Santostasi
Bitcoin Power Law: Statistics or Physics?
However, Morris does not believe in the power law, leading him to make numerous criticisms. He accuses Santostasi’s power law of “overfitting” mathematical data in an attempt to explain what is fundamentally a human system.
Morris contends that any study of Bitcoin data belongs to the realm of statistics rather than physics, which is more concerned with the properties and attributes of matter and energy.
“This is magic; [Santostasi] is just performing tricks. That’s all,” Morris asserts.
“He pulls a statistical rabbit out of a hat and then pulls out a physical rabbit.”
However, Santostasi refutes this argument, stating that while humans are indeed involved in the maintenance and growth of Bitcoin—including network and market value—it can still be viewed as a physical system, despite human involvement.
“It is still a physical system because there are fundamental physical limits, such as the number of interactions we humans can engage in and the amount of information we can transmit,” Santostasi explains.
Furthermore, Santostasi points out that many key data points of Bitcoin—including its difficulty adjustment algorithm, various machine-based feedback loops, and miners’ energy requirements—can be considered part of the physics domain.
Santostasi refers to the work of British physicist Geoffrey West, who has written on this subject.
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Santostasi further emphasizes this assertion, adding that the study of Bitcoin data completely falls within the disciplines of “sociophysics” or “econophysics,” which utilize mathematical tools to study social networks and their impacts.
Therefore, Santostasi claims that the price trajectory of Bitcoin since its inception aligns entirely with the power law and can thus serve as a robust tool for simulating its future growth.
Morris: Power Law is More Like a “Horoscope”
Morris’s next major criticism of the power law is that it employs “hindsight bias” and encompasses such a broad range of data that it cannot reliably make useful predictions about the future.
Morris summarizes that the power law resembles a “horoscope” rather than a predictive model.
“According to the power law, Bitcoin’s price could be $200,000 in 2045. It could also be $10 million. That’s not very predictive,” he states.
“To say the price could be within six standard deviations means it has high predictability, which is dishonest,” Morris adds.
“The power law merely revisits the past with hindsight bias and uses mathematics to validate this bias. It is essentially confirmation bias modeled graphically.”
Bitcoin advocate and network economist Timothy Peterson expressed similar criticisms of the power law in a post on X on May 23, stating that the power law and the Never Look Back (NLB) metric cannot be regarded as “models” useful for making predictions.
“They are based on time, which is not an independent variable. They are historical relationships but not models,” he says.
Source: Timothy Peterson
How Could the Bitcoin Power Law Fail?
Santostasi admits that the Bitcoin power law, like all power laws, is not a perfect predictive tool; any significant sustained change that causes its price to deviate sharply below or above the current trend line could overturn the power law.
He points out that Bitcoin’s price would need to fall to a low of $30,000 over a prolonged period for the power law to be invalidated.
“People will see for themselves whether this no longer holds true,” Santostasi states, noting that any significant deviation from the trend would serve as empirical evidence of failure.
Similarly, he adds, the emergence of “superbitcoinization” could render the model ineffective, which might resemble the U.S. adopting Bitcoin as its currency and pushing the price above $250,000 within weeks
