# A smaller risk is valuable even when it is not zero Mathematical illustration; not a forecast. Consider a deliberately simplified model: a civilization faces the same independent probability p of extinction in each interval. After n intervals its survival probability is (1 − p) raised to n. For any fixed p strictly between zero and one, that probability tends toward zero as n grows without bound. The calculation is not an estimate of humanity’s actual risk; it illustrates why finite-time resilience and guaranteed eternity are different claims. Canonical page: https://givegigs.com/wiki/necro-chapter-immortality-versus-risk Last updated: 2026-11-09T18:58:12.584Z Parent topic: [necromancer-neuroscience](https://givegigs.com/wiki/necromancer-neuroscience) ## Contents - [Overview](#wiki-section-overview-1) - [Chapter notes](#wiki-section-chapter-notes-2) - [Dossier section](#wiki-section-dossier-link-3) ## Overview Mathematical illustration; not a forecast. This page expands the “A smaller risk is valuable even when it is not zero” chapter in the neuroscience collection. ## Chapter notes Consider a deliberately simplified model: a civilization faces the same independent probability p of extinction in each interval. After n intervals its survival probability is (1 − p) raised to n. For any fixed p strictly between zero and one, that probability tends toward zero as n grows without bound. The calculation is not an estimate of humanity’s actual risk; it illustrates why finite-time resilience and guaranteed eternity are different claims. Real hazards are not necessarily independent or constant. Risk may change with technology, institutions, environment, and events. The toy calculation therefore cannot prove that humanity must go extinct. It does show why a claim of reaching an immortal attractor needs stronger justification than observing that the annual risk seems very small. The team should ask which specific hazards a measure reduces, which it introduces, whether the risks are correlated, and what evidence supports the comparison. Declaring victory over all chance would skip that work. A more resilient future can be a major achievement without the organization claiming a mathematical guarantee it cannot establish. The reverse-apocalypse is strongest as an ongoing commitment to improve those conditions and preserve the ability to revise the plan. If future theory supports a different conclusion about indefinite survival, the team can examine it. Until then, certainty about forever is neither required for useful action nor something this initiative can honestly sell. ## Dossier section [Open this exact section in the Necromancer dossier](/necromancer#immortality-versus-risk). The original chapter status is “Mathematical illustration; not a forecast.” ## Sources - [Necromancer dossier section](/necromancer#immortality-versus-risk) --- This article is collaboratively maintained. Check the canonical page and cited sources for the latest context.