Moore’s Doomsday Hypothesis

DoomsdayHypothesis.md

title	author	date	license	tags
Moore’s Doomsday Hypothesis	Pete Moore	2025-11-20	CC BY 4.0	AI safety open source existential risk philosophy ethics

A speculative model of existential risk in the age of open-source AI.

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Moore’s Doomsday Hypothesis

Abstract

This paper proposes a probabilistic model for the eventual self-destruction of humanity through the intersection of human malevolence and technological capability. The hypothesis asserts that if a small but non-zero fraction of individuals possess both the intent and the means to cause global extinction, then humanity’s survival time is inversely related to the product of these factors. Open-source artificial intelligence accelerates this convergence by exponentially expanding access to catastrophic capability.

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1. Definitions

Let:

• x: Fraction of the global population with a latent desire or willingness to destroy humanity, e.g. due to psychopathy, nihilism, or ideological extremism.
  $0 < x \ll 1$

• y(t): Number of individuals at time t who possess the technical capability to cause human extinction — for example, through AI-assisted bioweapon design, or synthetic pathogens.
  $y(t)$ increases over time as technology becomes more accessible.

• m(t): Mitigation factor representing defences against catastrophic misuse — including governance, AI alignment, surveillance, and psychological intervention.

• p(t) = x · y(t): Expected number of individuals both willing and able to destroy humanity at time t.

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2. The Hypothesis

Statement

When $p(t) \approx 1$, humanity reaches a critical threshold where the probability of extinction within a bounded future interval becomes non-negligible.
As $p(t)$ rises above 1, extinction becomes increasingly probable and, by $p(t) \ge 10$, effectively inevitable.

Probabilistic Formulation

If each potential actor represents an independent extinction risk, the survival probability $S(t)$ of humanity can be approximated as:

$$ S(t) = e^{-(x y(t) - m(t))} $$

and thus:

$$ \text{Risk of extinction} = 1 - e^{-(x y(t) - m(t))} $$

As technological capability proliferates ($y(t) \to \infty$) and mitigations lag ($m(t)$ grows sublinearly), extinction risk asymptotically approaches 1.

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3. Discussion

(a) The Paradox of Openness

Open-source AI, though motivated by transparency and decentralisation, accelerates $y(t)$ by removing access barriers.
It thereby transforms existential risk from state-level containment to individual-level accessibility.

(b) Stability of Human Nature

The psychological distribution $x$ remains approximately constant over time — there will always exist a small fraction of malevolent or deranged individuals.
Thus, technological democratisation is the primary accelerant.

(c) Ethical Implications

Traditional risk management assumes concentration of power in few hands; Moore’s Doomsday Hypothesis suggests that universal empowerment inevitably leads to diffuse existential risk.
When the means of destruction become as ubiquitous as intent, extinction becomes a statistical certainty.

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4. Conclusion

Human extinction does not require collective intent — only the alignment of capability with a statistically inevitable fraction of destructive will.
The hypothesis implies that the open dissemination of advanced AI, while noble in spirit, may ultimately ensure the demise of the species it seeks to empower.

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5. Addendum: Practical Corollary

Efforts to reduce existential risk must therefore focus on:

• Slowing the growth of $y(t)$ via containment and safety barriers.
• Reducing $x$ through social, educational, and psychological interventions.
• Expanding $m(t)$ — collective resilience mechanisms that scale at least as fast as capability.

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Appendix: Mathematical Derivation

Let $\lambda(t) = x y(t) - m(t)$ denote the effective hazard rate — the expected number of extinction-capable, willing individuals adjusted for mitigation.

Assuming independent risk events follow a Poisson process, the probability that humanity survives up to time t is:

$$ S(t) = e^{-\int_0^t \lambda(u) , du} $$

For simplicity, if $\lambda(t)$ changes slowly relative to time, we approximate:

$$ S(t) \approx e^{-\lambda t} $$

and the expected time to extinction is:

$$ E[T] = \frac{1}{\lambda} = \frac{1}{x y(t) - m(t)} $$

This makes clear that as $y(t)$ grows faster than $m(t)$, the expected survival time of humanity decreases hyperbolically — collapsing toward zero once the product $x y(t)$ surpasses the mitigative term.

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Authored by Pete Moore, 2025.
Licensed under Creative Commons Attribution 4.0 International (CC BY 4.0).