Speedup Theorem
Updated 2026-08-05
INTRODUCTION
English translation pending.
CORE DEFINITION
Proved by Manuel Blum, the theorem shows that for any total computable function there is no optimal program, since for any algorithm one can construct another that runs much faster on all but finitely many inputs. The result concerns asymptotic behavior under a given complexity measure rather than practical performance on real machines. The core claim is that optimization has no theoretical endpoint. The qualification is that the faster program may carry enormous constants, so the theorem does not imply that practical optimization is futile.
SCAFFOLDING EFFECT
Reduce cognitive load
- Use Ceiling Abandonment: Stop searching for a final optimal solution and treat optimization as open-ended. - Use Marginal Rule: Decide to stop optimizing when the marginal gain no longer justifies the cost. - Use Bottleneck Focus: Direct limited optimization effort at the path that actually constrains the system.
Anchor fast decisions
The theorem constructs, for any given program, a faster program by encoding additional information that shortcuts many inputs, so the improvement is real in the limit. Because the same construction applies to the new program, the process never terminates, which means no program is optimal in the asymptotic sense. Practical work stops for a different reason, since at some point each additional unit of effort yields less benefit than it costs.
MINIMUM ACTION
In progress 0/1Practice this model in one real situation:
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Source support: Explicit
- en.wikipedia.orghttps://en.wikipedia.org/wiki/Speedup_theoremverified
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