The Bitcoin power law, a mathematical framework suggesting that Bitcoin’s price will continue to rise over time, has sparked intense debate. Critics have dismissed it as “seriously flawed,” likening it more to a “horoscope” than a reliable predictive model for the cryptocurrency’s valuation.
Adrian Morris, a consultant and Bitcoin proponent, shared with Cointelegraph that while the Bitcoin power law has been promoted as a means to forecast Bitcoin’s future price (BTC), its credibility has been significantly overstated by its supporters.
Conversely, Giovanni Santostasi, the Italian physicist credited with identifying the power law in relation to Bitcoin, asserted to Cointelegraph that its validity is clear to anyone who examines the data.
The Bitcoin power law operates by graphing Bitcoin’s historical price data on a “log-log” scale—the logarithm of price plotted against the logarithm of time, following a line that best fits this data. Advocates of the law, including Santostasi and mathematician Fred Krueger, argue that it indicates Bitcoin’s price is likely to continue growing at a consistent rate for the foreseeable future.
The Bitcoin power law suggests persistent growth in Bitcoin’s price. Source: Bitbo
Power laws are prevalent in nature and have been observed in various phenomena, from the growth patterns of animal teeth and claws to the distribution of wealth in societies—known as the Pareto principle—and even in the severity of natural disasters like earthquakes and tornadoes.
Santostasi highlighted to Cointelegraph that the power law extends beyond Bitcoin’s price to encompass a variety of Bitcoin-related metrics, including the expansion of the network’s hashrate and the increase in new Bitcoin wallet addresses over time.
Santostasi asserts that the power law is visible across a range of Bitcoin’s characteristics. Source: Giovanni Santostasi
Bitcoin Power Law: Statistics or Physics?
However, Morris, a skeptic of the power law, has outlined several critiques. He accused Santostasi of “overfitting” mathematical data in an attempt to explain systems that are fundamentally driven by human behavior. Morris contended that any analysis of Bitcoin’s data belongs to the field of statistics rather than physics, which focuses on the properties and behavior of matter and energy.
“This is merely a magic trick, and [Santostasi] is performing sleight of hand. That’s the crux of the matter,” Morris stated.
In response, Santostasi dismissed this perspective, arguing that while human involvement is integral to the operation and growth of Bitcoin—both as a network and an asset—it can still be perceived as a physical system, albeit one influenced by human actions.
“It remains a physical system due to inherent physical limitations, such as the number of interactions humans can have and the volume of information we can communicate,” Santostasi explained.
He also pointed out that many critical data points related to Bitcoin, including its difficulty adjustment mechanism, various machine feedback loops, and the energy requirements of miners, can be classified within the realm of physics. Santostasi referenced the work of British physicist Geoffrey West, whose book *Scale* he considers crucial reading for those unconvinced of the existence of power laws in human systems.
Related: Physicist discusses how his ‘power law’ model predicts Bitcoin could reach $10 million by 2045.
Reinforcing his argument, Santostasi emphasized that the analysis of Bitcoin’s data falls under disciplines known as “social physics” or “econophysics,” which apply mathematical tools to examine social networks and their influences. Consequently, Santostasi believes that Bitcoin’s price movements since its inception align perfectly with a power law, serving as a potent model for forecasting its future growth.
Morris Claims the Power Law is More Like a “Horoscope”
Morris further criticized the power law for exploiting “hindsight bias,” asserting that its broad data scope renders it unreliable for making accurate future predictions. He concluded that the power law resembles a “horoscope” rather than a genuine forecasting tool.
“According to the power law, Bitcoin’s price in 2045 could be $200,000 or even $10 million. That’s hardly predictive,” he remarked. “It’s misleading to suggest that a price could fluctuate within six standard deviations and still be considered highly predictable,” Morris added.
Bitcoin supporter and network economist Timothy Peterson echoed a similar critique on May 23 via X, stating that the power law and the Never Look Back (NLB) metric should not be regarded as “models” suitable for making predictions. “They are time-based relationships, not independent variables,” he noted.
Source: Timothy Peterson
How Could the Bitcoin Power Law Be Disproven?
Santostasi acknowledged that, like all power laws, the Bitcoin power law isn’t an infallible predictive instrument and could be disproven by significant and sustained changes that lead to a price drop below—or a spike above—the current trend line. He indicated that for the power law to be invalidated, Bitcoin’s price would need to remain around $30,000 for an extended period.
“People will witness for themselves if this model ceases to hold true,” Santostasi remarked, asserting that any major deviation from the established trend would serve as empirical evidence of its invalidation. Similarly, he noted that the onset of “hyperbitcoinization,” where Bitcoin could be adopted as the official currency in the United States, potentially driving its price above $250,000 within weeks, would also invalidate the model.
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