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Bitcoin is more like a city and an organism than a financial asset. This assertion arises from Bitcoin's power law behavior. If you delve deep into the world of Bitcoin, you will develop a geometric intuition about Bitcoin's power-law price behavior.
Of course, this intuition is not enough; we need to further establish a complete theory of Bitcoin behavior that can explain all major on-chain parameters in a scientific, coherent, and falsifiable manner. This is what this article attempts to explore: the Bitcoin power law theory.
Bitcoin's operation is depicted by power laws for several reasons:
1. Initially, Bitcoin was accepted and adopted by the first users in the Satoshi Nakamoto circle. The "value" (now "price," which can be checked online 24/7) increased with the square of the number of users (network effects)—this is the confirmation of the theory known as Metcalfe's Law. Metcalfe's Law suggests that if each user in a network can connect with all other users, then the theoretical number of connections in the network when there are N users is close to N(N-1)/2, which is approximately N² in scale.
2. The rise in Bitcoin price brought in more resources, especially mining capacity. The price increase reduced the time for mining blocks, but due to "difficulty adjustment," the required hash rate for mining blocks iteratively changes. Since mining is almost unprofitable, the compensation mechanism needs to be directly proportional to the increase in price P=user² and the reward itself. Therefore, logically and dimensionally, hash rate=price² (which also aligns with empirical observations: the empirical value of the power is close to 2, and price=hash rate^1/2). Here, the physical significance of the hash rate is a comprehensive indicator of network processing power, security, mining difficulty, and energy consumption.
3. The increase in hash rate brings more security to the system, thereby attracting more users. While some people may not buy Bitcoin because of "security," it's evident that no one would invest significant effort in it if it weren't a secure system. Security, directly or indirectly, brings in new users.
4. Bitcoin differs from common S-curve growth (such as the growth curves of TV, refrigerators, cars, and phones); it follows a time-power-law growth of t=3. The difference lies in the fact that if there are significant inhibitory mechanisms, the power law becomes more pronounced. For Bitcoin, any type of investment's "difficulty adjustment" and risk serve as such inhibitory mechanisms. This understanding aligns with empirical observations.
In conclusion, we obtain the following power law model relationships: users=t³, price=users²=(t³)²=t^6, hash rate=price²=(t^6)²=t^12. This cycle repeats infinitely, creating bubbles—a crucial and necessary component of this cycle. The power law theory of Bitcoin opens a window for us to explain and predict Bitcoin's long-term behavior, leading to some interesting implications.
One of the most surprising and often misunderstood by most ordinary Bitcoin investors is scale invariance (or using fractals to understand "fractal and power law" reflexivity discount arbitrage explanations, "wild beast" cycles, quantification, and fractal trading principles).
Scale invariance is a typical characteristic of systems governed by power laws.
We can accurately predict that reaching 1 million BTC will take approximately 10 years. Although this sounds unbelievable, in the long run, core parameters like users, price, and hash rate are predictable—Bitcoin's scale has followed power-law growth by 9 orders of magnitude, so we shouldn't be surprised if it continues to follow power laws and grows by another 1-2 orders of magnitude.
Furthermore, scale invariance enables us to understand the role and importance of events, such as large institutional ETF investments flowing into the Bitcoin system recently—scale invariance tells us that these events won't significantly affect Bitcoin's price trajectory, but the system will continue its scale-invariant growth—this is one of the most shocking predictions of the theory.
Bitcoin's long-term future is unpredictable, but under the assumption that the power-law mechanism remains intact, this theory suggests that the path of Bitcoin's price is deterministic—unless we experience a catastrophic event, it won't change, especially during the expansion period of the next 1-2 orders of magnitude—this is only a small part of Bitcoin's overall historical growth. |
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Post time 19-4-2024 22:55:51