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Physicist Giovanni Santostasi argues that Bitcoin’s long-term price path is best understood not as an S-curve, a speculative bubble, or a simple exponential trend, but as a power law resembling patterns seen in cities, biology, and other natural systems. In an interview on the May 12 episode of the Coin Stories podcast, the director of the Scientific Bitcoin Institute said historical data points to roughly $1 million per coin in about eight years and $10 million in roughly 20 years.
Santostasi said his thesis centers on a nonlinear mathematical relationship between Bitcoin’s price and time since the network’s early trading history. He described Bitcoin’s price as proportional to time raised to a power of roughly 5.8 to 5.9, which is often rounded to six. He characterized the exponent as a “fingerprint” of the system rather than a curve-fitting artifact.
He explained the relationship in practical terms: the age of Bitcoin can be measured in days or years, and applying the power to that time produces the observed pricing pattern. He also argued that short-term volatility—driven by wars, crises, and liquidity shocks—appears as deviations around a deeper trajectory.
Santostasi said Bitcoin behaves more like a networked organism than a corporate asset. He compared Bitcoin’s growth to cities, which he described as expanding through bottom-up interaction and enduring far longer than corporations. In his view, cities follow power laws because their value emerges from networks of people freely interacting, building, and exchanging information.
He contrasted this with exponential growth, which he associated with systems that expand quickly but eventually face resource limits. Using corporations as an example, he said many corporations die within about 150 years, while cities such as Rome can persist for millennia. From that distinction, he suggested a provocative implication: corporations backed by Bitcoin could theoretically become more city-like in durability.
“This is one of the reasons why I want Saylor to start adopting this language of a power law,” Santostasi said, referring to Strategy executive chairman Michael Saylor. “He could say exactly that. We are turning corporations into cities.”
Santostasi also pointed to Bitcoin address growth as supporting evidence. He said Bitcoin addresses have grown as a power law with time cubed, while price responds to address growth roughly according to a square relationship, which he likened to Metcalfe’s Law. He said combining those relationships yields the observed price relationship of time to the sixth power.
He illustrated the logic with examples: “If you double the number of addresses, the price goes up to four. If you triple it, it goes to nine. So it’s a power law with the square.”
Under Santostasi’s framework, Bitcoin adoption should not be modeled primarily as an S-curve like consumer technologies such as refrigerators or televisions. He argued those products are not networks in the same way Bitcoin is, and that Bitcoin’s social, monetary, and technical layers make it closer to the internet or a city than to a household appliance.
While Santostasi presented the power-law path as data-driven, he stopped short of treating the forecast as certain. When asked how confident he is that Bitcoin could reach about $1 million per coin in roughly eight years and $10 million in roughly 20 years, he said the probability is near 90%, leaving room for failure conditions.
He said the path depends on continued capital inflows, larger institutional participation, and new pools of capital to keep the trajectory intact.
At press time, BTC traded at $80,963.
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