Claude Opus 5.5 explains math bounds beyond the universe's 2^308 operation limit — and what physics would unlock them
teortaxesTex · x · 2026-10-27
teortaxesTex quotes a post noting a new math bound only kicks in at 2^65536 boolean variables — vastly beyond the observable universe's 2^308 historical operation count (Seth Lloyd estimated 10^120 operations since the Big Bang). The attached screenshot shows Claude Opus 5.5 (High) answering in detail:
- How far away we are: the ETH algorithm beats brute force only past n = 2^65536, needing 2^(2^65536) steps — you'd need a universe where doubly-exponential steps are routine.
- Just bigger universes: our cosmological constant caps the information budget (10^122 bits); with Λ=0, Dyson-style eternal computation becomes possible, but any finite budget has its own galactic threshold.
- Different rules: nonlinear quantum mechanics (Abrams-Lloyd) solves NP-complete in polynomial time; closed timelike curves (Aaronson-Watrous) solve all of PSPACE; Malament-Hogarth spacetimes yield hypercomputation; measurable infinite-precision reals enable analog encoding.
Conclusion: our physics closes every one of these doors. teortaxesTex muses: seeing mathematical truths strictly useless in our tiny physics, is there another physics?
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