Solomonoff’s theory of inductive inference, the foundation of algorithmic information theory and universal inductive reasoning, aims to construct a completeness-based predictive framework rooted in all Turing machine interpretations. However, its core conclusion is that Solomonoff induction is uncomputable, due to the necessity of considering all Turing machines. The derived understanding is that any computable inductive method is incomplete because it can only explore a finite hypothesis space, thus failing to capture all patterns.
A thought-provoking perspective is to extend the concept of “completeness” implied by Solomonoff induction to understand the Bitcoin network as a unique socio-technical system. This article aims to explore how the Bitcoin network possesses a kind of “completeness” arising from its inherent uncertainty, and to analyze how this “completeness” distinguishes it from other blockchain projects.
The core argument lies in the fact that the Bitcoin network, due to endogenous uncertainty generated by the individual games of its participants, exhibits characteristics that cannot be precisely replicated or predicted. Even if the same code were used to restart the Bitcoin network, or if one returned to its genesis and redeployed it, the specific state of today’s Bitcoin network could not be reproduced. This is not only due to the complexity of its code, but more importantly to the joint shaping of its unique evolutionary path by factors such as historical transaction records, participant distribution, computing power, adoption level, community consensus, and ever-changing external environments. These factors interact unpredictably at different times and under different conditions, resulting in a vast possibility space for the future state of the Bitcoin network.
This unpredictability is key to Bitcoin’s “completeness.” Similar to Solomonoff induction’s attempt to encompass all explanations, the Bitcoin network, as a decentralized system driven by the behaviors of countless independent individuals, does not evolve in a fully deterministic way. The emergent behaviors arising from individual game-play make the Bitcoin network resemble a natural ecosystem or human culture, constantly adapting and evolving in an uncertain environment.
Drawing an analogy between Bitcoin’s “completeness” and the completeness of human culture is enlightening. Human culture is not a pre-defined, closed system, but one shaped over a long historical process by countless individuals through creation, communication, and transmission. Its form and meaning are dynamic and difficult to fully predict. Similarly, the Bitcoin network continuously absorbs new ideas, technologies, and applications throughout its development, and its value and significance evolve through interactions with the real world. This dynamic interaction with the real world enables Bitcoin to be not just a technological tool, but a phenomenon rooted in and symbiotic with reality.
By contrast, other blockchain projects are often more focused in design toward specific application scenarios and make different trade-offs in consensus mechanisms, governance structures, and so on. This leads to them being more deterministic or controllable in some respects. However, such determinism also brings limitations, making it difficult for them to fully reflect and adapt to the complexity and uncertainty of the real world, thus rendering them “incomplete” in a certain sense. They are more like precisely designed tools serving specific purposes, but lack the Bitcoin network’s ability to form a unified, unpredictable whole with human society.
Therefore, the “Solomonoff-completeness” of the Bitcoin network does not refer to its computational completeness in protocol, but rather to its authenticity as a socio-technical system. This is due to its endogenous uncertainty and deep coupling with the real world, showing a dynamic nature that is difficult to fully predict or replicate. This “authenticity” allows it to grow and enrich itself continuously in an uncertain world, like nature and human culture, rather than being a deterministic, closed, tool-like system. This unique completeness is a vital source of Bitcoin’s long-term value and resilience.
Further thought is needed on how to precisely define and measure this kind of “completeness,” and whether such endogenous uncertainty also brings potential risks and challenges. Nevertheless, viewing Bitcoin as a complex adaptive system co-evolving with human society and examining it from the perspective of “completeness” offers a new angle for understanding its essence and its place in the future world.
