Ladder Paradox
Updated 2026-08-05
INTRODUCTION
English translation pending.
CORE DEFINITION
An infinite divisibility puzzle attributed to Max Black, closely related to Zeno's paradoxes of motion, in which the base of a ladder is moved forward by half the remaining distance at each step. The construction suggests that infinitely many discrete moves must be completed to reach a finite point, which clashes with the intuition that infinite steps take infinite time. The mathematical resolution invokes convergent series and limits. The qualification is that the puzzle concerns intuitions about completing infinity rather than a genuine physical impossibility.
SCAFFOLDING EFFECT
Reduce cognitive load
- Use Limit Reasoning: Replace step-by-step intuition with the limit that the sequence approaches. - Use Infinity Sorting: Distinguish potential infinity, an ongoing process, from actual infinity, a completed totality. - Use Convergence Check: Test whether an endless process still sums to a finite value before declaring it impossible.
Anchor fast decisions
Each step is defined as a fixed fraction of what remains, so the distances form a geometric sequence whose partial sums approach a finite limit. Infinitely many terms therefore add up to a finite total, which is why the moving ladder covers the whole interval. The paradox arises because intuition treats infinitely many steps as necessarily taking infinitely long, conflating the count of operations with the total magnitude they accumulate.
MINIMUM ACTION
In progress 0/1Practice this model in one real situation:
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Source support: Explicit
- zh.wikipedia.orghttps://zh.wikipedia.org/wiki/%E6%A2%AF%E5%AD%90%E6%82%96%E8%AB%96verified
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