The Bitcoin power law, a mathematical framework suggesting that Bitcoin’s price will continue to rise over time, has sparked intense discussion. Detractors label it as “deeply flawed,” likening it more to a “horoscope” than a reliable price prediction model for the cryptocurrency.
Adrian Morris, a consultant and Bitcoin supporter, expressed to Cointelegraph that while the Bitcoin power law has been promoted as a forecasting tool for Bitcoin’s future price, its supporters have significantly exaggerated its credibility.
Conversely, Italian physicist Giovanni Santostasi, the individual behind the discovery of the power law’s application to Bitcoin, defended its validity, stating that its existence is evident to anyone who looks closely.
The Bitcoin power law operates by charting Bitcoin’s historical price data on a “log-log” scale, plotting the logarithm of price against the logarithm of time along a line that best fits this data. Advocates of this law, including Santostasi and mathematician Fred Krueger, contend that it indicates Bitcoin’s price is likely to increase at a relatively steady rate for the foreseeable future.
The Bitcoin power law indicates ongoing price growth for Bitcoin. Source: Bitbo
Power laws are frequently observed in nature and have been applied to various phenomena, from the growth of animal teeth and claws to wealth distribution in societies, famously known as the Pareto principle, as well as measuring the intensity of earthquakes and tornadoes.
According to Santostasi, the power law extends beyond just Bitcoin’s price; it can also be identified in a broader array of Bitcoin-related metrics, including the network’s hashrate growth and the increasing number of new Bitcoin wallet addresses over time.
Santostasi asserts that the power law applies across many aspects of Bitcoin. Source: Giovanni Santostasi
### Bitcoin Power Law: Statistics or Physics?
However, Morris, a skeptic of the power law, has voiced multiple criticisms. He accused Santostasi of “overfitting” mathematical data to explain systems that are fundamentally human in nature. He argues that analyzing Bitcoin’s data is rooted in statistics rather than physics, which is primarily concerned with the characteristics and behavior of matter and energy.
“This is a magic trick, and [Santostasi] is performing a sleight of hand. That’s all there is to it,” Morris remarked.
In response, Santostasi dismissed this claim, asserting that while human involvement is crucial for the maintenance and growth of Bitcoin—both in terms of its network and market value—it can still be interpreted as a physical system influenced by human actions.
“It remains a physical system because there are inherent physical constraints, such as the number of interactions we can have and the amount of information we exchange,” Santostasi explained. He further emphasized that several key aspects of Bitcoin, such as its difficulty adjustment algorithm and the energy consumption of miners, can be classified as elements of physics.
Santostasi referenced the work of British physicist Geoffrey West, particularly his book, *Scale*, as essential reading for anyone unconvinced by the presence of power laws in human systems.
### The Power Law: A Horoscopic Perspective?
Morris’s subsequent major critique of the power law asserts that it exploits “hindsight bias” and encompasses such a broad spectrum of data that it lacks the reliability needed for future predictions. He concluded that the power law resembles a “horoscope” more than a genuine forecasting model.
“Based on the power law, Bitcoin’s price in 2045 could be $200,000 or it could soar to $10 million. That’s not particularly predictive,” he stated. “It’s misleading to claim that a price could fluctuate within six standard deviations and still have a high predictive value,” Morris added.
Timothy Peterson, a Bitcoin advocate and network economist, echoed similar concerns in a May 23 post on X, arguing that both the power law and the Never Look Back (NLB) metric cannot be classified as models suitable for making predictions. “They are based on time, which is not an independent variable. They reflect historical relationships but do not function as predictive models,” he noted.
Source: Timothy Peterson
### How Could the Bitcoin Power Law be Disproved?
Santostasi acknowledged that, like all power laws, the Bitcoin power law is not an infallible predictive tool and could be invalidated by any significant and sustained shift that causes Bitcoin’s price to drop below or spike above the current trend line dramatically. He indicated that, as of now, Bitcoin’s price would need to settle at around $30,000 for an extended duration for the power law to be challenged.
“People will see for themselves if this model ceases to hold,” Santostasi remarked, adding that any substantial deviation from the trend would serve as tangible evidence of its invalidation.
He also noted that the phenomenon of “hyperbitcoinization,” which could occur if the United States adopted Bitcoin as its official currency, resulting in a price surge to over $250,000 in a matter of weeks, would similarly invalidate the model.
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