Author: Tom Mitchelhill, CoinTelegraph; Translated by: Baishui, Golden Finance
The Bitcoin power law — a mathematical model that suggests the price of bitcoin will continue to grow over time — has become the subject of intense debate, with critics slamming it as “deeply flawed” and saying it is more like a “horoscope” than a predictive model for cryptocurrency prices.
Consultant and Bitcoin advocate Adrian Morris noted that while the Bitcoin Power Law has been touted as a predictive model for Bitcoin’s future price, its plausibility has been greatly exaggerated by its advocates.
On the other hand, Italian physicist Giovanni Santostasi, the discoverer of Bitcoin’s power law, pointed out that Bitcoin’s power law is undeniable and only needs to be witnessed with one’s own eyes.
Bitcoin’s power law works by plotting Bitcoin’s historical price data on a “log-log” scale — the log of price versus the log of time is plotted along the line that best fits the data.
Power law proponents, including Santostasi and his colleague, mathematician Fred Krueger, say the law suggests that the price of Bitcoin should continue to grow at a relatively steady rate long into the future.
The Bitcoin power law indicates that the price of Bitcoin will continue to grow. Source: Bitbo
Power laws are common in nature and have been applied to a variety of natural phenomena, from the growth of teeth and claws of animals, the distribution of wealth in society (the well-known Pareto principle) to mapping the severity of earthquakes and tornadoes.
Santostasi noted that the power law is not limited to Bitcoin’s price, but can also be found in a variety of Bitcoin-related data, including the growth of the network’s hash rate and the growth rate of new Bitcoin wallet addresses over time.
Santostasi said the power law can be reflected in many of Bitcoin's properties. Source: Giovanni Santosasi
Bitcoin Power Law: Statistics or Physics?
But Morris did not believe in power laws, and he received a lot of criticism for that.
He accused Santostasi’s power laws of “overfitting” mathematical data in an attempt to explain what are human systems.
Morris argues that any study of Bitcoin data falls within the realm of statistics, rather than physics, which is more concerned with the nature and properties of matter and energy.
"It was a magic trick, and [Santostasi] was just performing a sleight of hand. That's it," Morris said.
“He put a statistics rabbit in the hat and pulled a physics rabbit out.”
However, Santostasi refuted this argument, saying that while humans are clearly involved in the maintenance and growth of Bitcoin — both the network and market value — it can still be considered a physical system, albeit one with human involvement.
“It’s still a physical system because there are fundamental physical limitations, such as the number of interactions we humans can have and the amount of information we transmit,” Santostasi said.
Furthermore, Santostasi noted that many of Bitcoin’s key data points — including its difficulty adjustment algorithm, various machine-based feedback loops and miners’ energy requirements — can be considered to fall within the realm of physics.
Santostasi points to the work of British physicist Geoffrey West, who wrote the book
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Santostasi further emphasized this assertion, adding that the study of Bitcoin data falls squarely within the disciplines of “social physics” or “econophysics,” which use mathematical tools to study social networks and their influence.
Therefore, Santostasi said that Bitcoin’s price performance since its inception is completely consistent with the power law and can therefore be used as a powerful tool to simulate its future growth.
Morris: Power law is more like a "horoscope"
Morris’s next major criticism of the power law is that it exploits “hindsight bias” and encompasses such a wide range of data that it cannot be relied upon to make useful predictions about the future.
Morris concluded that the power law is more like a "horoscope" than a predictive model.
"Based on the power law, the price of Bitcoin in 2045 could be $200,000. Or it could be $10 million. It's not very predictive," he said.
“It’s dishonest to say that the price is likely to be within six standard deviations, implying that it’s highly predictable,” Morris added.
"The power law is just looking back at the past with hindsight bias and using math to confirm that bias. It's really just confirmation bias modeled graphically."
Bitcoin advocate and cyber economist Timothy Peterson offered a similar critique of the power law in a May 23 post to X, saying that the power law and the Never Look Back (NLB) indicator cannot be considered “models” that can be used to make predictions.
"They are based on time, and time is not an independent variable. They are historical relationships, but they are not models," he said.
Source: Timothy Peterson
How does the Bitcoin power law break down?
Santostasi acknowledged that Bitcoin’s power law, like all power laws, is not a completely perfect predictive tool, and any outsized sustained change that causes its price to fall below or exceed the current trendline in any dramatic way could overturn the power law.
He noted that as of today, Bitcoin’s price would need to drop to the low $30,000s for an extended period of time before the power law would be overturned.
“People will see for themselves whether this is no longer working,” Santostasi said, noting that any significant deviation from the trend would be empirical evidence of failure.
Likewise, he said, the advent of “hyperbitcoinization,” which could look like the U.S. accepting Bitcoin as its currency and pushing the price above $250,000 in a matter of weeks, would also invalidate the model.
