Ⅰ. The core framework of Bayesianism

Belief = Prior Probability × New Evidence
Human cognition is like a probability engine:

  • Prior belief: Initial assumption based on historical experience

  • Likelihood: The strength of support of new evidence for the hypothesis

  • Posterior belief（Posterior）：Revised cognition after evidence iteration
    The rise of Bitcoin is an epic practical application of this formula.

Ⅱ. The prior belief of Bitcoin: The rebellious hypothesis of cypherpunks

Initial prior probability (2009):

P (Bitcoin succeeds) ≈ 0.001

Assumption foundation:

  • math

  • \small

    \text{Decentralized currency} = f(\text{Cryptography} + \text{Game Theory} + \text{Anti-authoritarianism})

  • Prior fragility：
    The vast majority viewed it as a 'geek toy',Prior probability approaches zero—until the first real transaction (10,000 BTC for two pizzas 🍕) provided initial likelihood evidence.

  • Ⅲ. The flood of evidence: The market as a likelihood function generator

    The survival of Bitcoin relies on continuous evidence shocks, constantly revising human collective beliefs:

  • Bayesian crisis point:

    • Mt. Gox incident (850,000 BTC stolen): Likelihood evidence strongly negates the 'safety assumption', posterior probability plummets

    • Each halving: Deterministic evidence of reduced new issuance, continuously enhancing scarcity likelihood value


    Ⅳ. The Bayesian nature of market prices

    The price curve of Bitcoin is essentially the probability integral of the posterior beliefs of global participants:

    math

    \small

    \text{BTC Price} = K \times \prod_{t=2009}^{now} \frac{P(\text{Survival}|E_t)}{P(\text{Death}|E_t)}

    • KEt: New evidence at time t (regulation/hack/technological breakthrough)

    • K: Network effect multiplier (Metcalfe's Law)


    Typical case：
    When the Fed raises interest rates (fiat currency yield ↑ evidence), participants lower their inflation-hedging likelihood estimate for BTC → posterior value probability ↓ → price drops


    The market generates arbitrage in the speed difference of Bayesian updates:

    • On-chain data provides prior adjustment signals for 'smart money' (e.g., large whale accumulation)

    • Retail investors' posterior updates lag → volatility increases


    Ⅵ. The ultimate Bayesian dilemma: the faith test of the 21 million cap

    The most revolutionary prior setting of Bitcoin—absolute scarcity (21 million cap)—is essentially an unfalsifiable hypothesis:

    • Supporting evidence: 12 years without inflation records → likelihood function strengthens credibility

    • Falsification risk: If a 51% attack modifies the rules, the posterior probability will collapse

    Hayekian metaphor：
    Bitcoin is humanity's first transformation of monetary theory into a falsifiable mathematical protocol,each block is a Bayesian test of Satoshi's prior。


    Conclusion: Cryptographic revelations under the prism of probability

    • For investors：
      Bitcoin's returns come from bearing the 'prior cognitive risk premium', requiring continuous calculation of P(Survival|New Evidence)P(Survival|New Evidence)

    • For philosophers：
      It exposes the fragility of human cognition—once we believed in the Lehman bond ratings with P≈1P≈1.

    • Ultimate prophecy：
      When the critical point of P(Bitcoin becoming a reserve asset) > 0.5 arrives, Bayesian updates will trigger a nonlinear leap.

    • 'Market prices are merely a temporary consensus of collective posterior beliefs,
      and code is humanity's most devout likelihood function to the god of probability.'