Bitcoin's Power Law: Unveiling the Network's Hidden Dynamics

Bitcoin's Power Law Model: A Deeper Dive

Last month, we explored the power law model proposed by Italian physicist Giovanni Santostasi, which suggests that Bitcoin's price follows a power law. Further investigation reveals that not only does price fit this model, but so does the number of Bitcoin addresses over time.

Giovanni's research is part of a broader trend using network theory to model Bitcoin. The Bitcoin network, crucial for decentralized consensus, mirrors the internet's Metcalfe's Law, where value increases with network size. Measuring network size can be done through nodes, with full nodes keeping a copy of the blockchain and validating transactions. Giovanni uses a broader approach, considering Bitcoin addresses as nodes and transactions as links, leading to a larger network size.

However, using addresses as nodes has implications. Some behaviors, like a user sending bitcoins to multiple controlled addresses or using mixing services, increase the number of addresses without boosting adoption. Despite these edge cases, the number of addresses serves as a rough proxy for Bitcoin usage.

While the power law model establishes a statistical fit between external measures and Bitcoin, it doesn't explain the underlying economic forces driving these measures. To truly understand Bitcoin's value and price, we must identify the core economic constructs determining buying and selling behavior. A structural economic model could help, categorizing buyers into short-term traders, long-term holders, corporations, and nation-states, each with unique objectives, time preferences, budgets, and risk appetites.

Combining physical and social sciences in future research could amplify the power law model, offering a more comprehensive understanding of Bitcoin's dynamics. This exciting area of study holds great potential for advancing our knowledge of this innovative cryptocurrency.