The Bitcoin power law, a mathematical framework suggesting that Bitcoin’s price will continue to rise over time, has sparked intense discussions. Critics have dismissed it as “seriously flawed,” likening it more to a “horoscope” than a valid forecasting tool for the cryptocurrency’s value.
Adrian Morris, a consultant and Bitcoin supporter, expressed to Cointelegraph that the claims surrounding the Bitcoin power law as a forecasting mechanism for Bitcoin’s future price (BTC) have been significantly exaggerated by its supporters. Conversely, Giovanni Santostasi, the Italian physicist who identified the power law in relation to Bitcoin, asserted that its existence is undeniable and that a simple observation is enough to acknowledge it.
The Bitcoin power law operates by charting Bitcoin’s historical price movements on a “log-log” graph, plotting the logarithm of price against the logarithm of time to create a line that best fits the data. Supporters of this power law, including Santostasi and mathematician Fred Krueger, argue that this model indicates Bitcoin’s price is likely to increase at a consistent rate for the foreseeable future.
The Bitcoin power law suggests ongoing price appreciation for Bitcoin. Source: Bitbo
Power laws frequently appear in natural phenomena, encompassing a variety of aspects, such as the growth patterns of animal teeth and claws, the distribution of wealth in societies (the well-known Pareto principle), and even the severity of earthquakes and tornadoes. Santostasi emphasized that the power law is not confined to Bitcoin’s price alone but can also be observed in various metrics associated with Bitcoin, including the network’s hashrate growth and the increasing number of Bitcoin wallet addresses over time.
Santostasi highlights that the power law is observable across numerous aspects of Bitcoin. Source: Giovanni Santostasi
Bitcoin power law: Statistics or physics?
Morris, a skeptic of the power law, offers a comprehensive list of criticisms. He has accused Santostasi of “overfitting” mathematical models to explain human behaviors. Morris contends that analyzing Bitcoin data falls within the domain of statistics, as opposed to physics, which focuses on the characteristics of matter and energy.
“This is simply a magic trick, with [Santostasi] performing a sleight of hand. That’s the essence of it,” Morris stated. In response, Santostasi refutes this claim, arguing that while human actions drive the growth and maintenance of Bitcoin—both in terms of its network and market value—it can still be classified as a physical system influenced by human factors.
“It remains a physical system, constrained by fundamental physical limitations, such as the number of interactions humans can engage in and the volume of information we can transmit,” Santostasi explained. Furthermore, he pointed out that many critical indicators of Bitcoin, including its difficulty adjustment mechanism, various machine feedback loops, and miners’ energy requirements, belong to the realm of physics.
Santostasi referenced the work of British physicist Geoffrey West, whose book Scale is essential for those who doubt the existence of power laws within human systems.
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Reiterating this perspective, Santostasi added that studying Bitcoin data fits firmly within the fields of “social physics” or “econophysics,” which employ mathematical tools to analyze social networks and their impacts. Consequently, he believes that Bitcoin’s price movements since its inception align perfectly with a power law, making it a robust tool for forecasting its future growth.
Morris argues that the power law is more akin to a “horoscope” than a reliable forecasting tool. He claims it exploits “hindsight bias” and encompasses such a wide array of data that it cannot yield useful predictions for the future. Morris concludes that the power law’s predictions are vague at best.
“According to the power law, Bitcoin’s value in 2045 could be $200,000, or it might reach $10 million. That’s hardly predictive,” he asserted. “It’s misleading to suggest that a price could fluctuate within six standard deviations and still be considered highly predictable,” he added.
Timothy Peterson, a Bitcoin advocate and network economist, echoed similar sentiments in a post on X on May 23, arguing that both the power law and the Never Look Back (NLB) metric should not be regarded as models capable of generating predictions. “They hinge on time, which is not an independent variable. They demonstrate historical relationships rather than act as predictive models,” he stated.
Source: Timothy Peterson
How could the Bitcoin power law be disproven?
Santostasi acknowledged that, like all power laws, the Bitcoin power law is not an infallible forecasting tool and could be invalidated by an extraordinary and sustained shift that drives its price significantly below or above the current trend line. He mentioned that for the power law to be disproven, Bitcoin’s price would need to remain around $30,000 for an extended period.
“People will see for themselves if this model no longer holds,” Santostasi said, noting that any significant deviation from the established trend would serve as empirical evidence of its invalidation. He also pointed out that the phenomenon of “hyperbitcoinization,” where the U.S. might adopt Bitcoin as its currency and rapidly push the price past $250,000, would similarly disprove the model.
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