For a long time, humanity’s pursuit of knowledge and truth was deeply influenced by formal logic. Especially before the emergence of Gödel’s incompleteness theorems, people tended to embrace the Platonic ideal world depicted in The Republic, believing that all things possessed clear, decidable truths—either true or false. However, Gödel’s incompleteness theorems struck like lightning across the night sky, revealing that within any sufficiently complex axiomatic system, there must exist “undecidable” self-referential problems that cannot be proven either true or false, thus breaking the binary cognitive framework.
The rise of Bayesianism provided a new approach to handling this uncertainty. It introduced the concept of “confidence,” placing our degree of belief in a proposition’s truth within a continuous probability interval [0, 1]. This allowed us to quantify uncertainty and dynamically update our beliefs based on new evidence. Further, we can conceive of an idea of “extended confidence,” which not only applies to traditionally decidable problems but also offers a unified description for the undecidable problems revealed by Gödel. For the former, the confidence tends toward 0 or 1; for the latter, confidence reflects the degree of uncertainty about their truth.
This concept of confidence proves powerful in explaining phenomena like “perception asymmetry” in computational complexity theory, such as the P/NP problem. NP problems are generally regarded as “uncertainty-solving” problems: finding a solution may be extremely difficult, but verifying a given solution can be relatively easy within polynomial time. This asymmetry between solving and verifying can be understood through confidence: we may have low confidence in the existence of an efficient solution to an NP problem, but once a candidate solution is found, our confidence in its validity can be rapidly increased through quick verification.
Bitcoin’s proof-of-work (PoW) mechanism provides an excellent real-world analogy. Miners expend massive computational power to find a nonce that satisfies difficulty requirements (similar to solving an NP problem), while the entire blockchain network only needs simple hash calculations to verify the nonce’s validity (similar to NP problem verification). The longest-chain consensus mechanism is built precisely upon such asymmetric verification-based confidence—the longer the chain, the more accumulated proof-of-work, thus regarded as more reliable and trustworthy. Similarly, the logic of private key signing and public key verification in asymmetric cryptography relies on the asymmetry between complex signature generation and simple signature verification, with the confidence in the signature reflecting the trust in information origin and integrity.
Inspired by Hofstadter’s Gödel, Escher, Bach: An Eternal Golden Braid (GEB), we can further explore applying the concepts of confidence and asymmetric verification to build an incentive system for “perceiving reality” in a system like BitAgere. GEB explores concepts such as formal systems, self-reference, and emergence, suggesting that complex holistic behaviors can arise from simple local rules and interactions. BitAgere could aim to digitally incentivize “perception” or “action” in the real world, using asymmetric verification mechanisms to ensure information reliability.
In such a system, “perceivers” or “actors” perform tasks that are difficult to verify directly, while a verification system efficiently evaluates their effectiveness. By linking incentive mechanisms (e.g., digital currency or reputation) to verification outcomes, the system can encourage participants to provide truthful perceptions and effective verifications, gradually building overall platform confidence.
For example, in a decentralized knowledge acquisition platform, users could submit “perceptions” about certain events, while other users could verify these perceptions through specific mechanisms (e.g., based on their own experiences or trusted sources). The incentive system would reward users who provide truthful perceptions and effective verifications, thus gradually building the platform’s overall confidence in its information.
In summary, from Gödel’s incompleteness theorems challenging traditional deterministic thinking, to the introduction of Bayesian confidence, to the application of asymmetric verification in computational systems and cryptography, we are witnessing an evolution toward a mindset that transcends binary judgment and embraces uncertainty. Applying this confidence-based perspective to the design of incentive systems—such as the envisioned BitAgere—could achieve more reliable reality perception and value consensus within complex systems, opening new possibilities for future technological and societal development.
