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An Infinitely High Stack of Blocks? Impossible!

2025-08-20

This paper explores a counter-intuitive physics problem: the stability of an infinitely extending stack of blocks. By analyzing torque and center of mass, the author demonstrates that finite-height stacks of blocks can remain stable even when their tops extend far beyond the edge of a table—a result that defies intuition. However, when attempting to extrapolate this to an infinitely high stack, the author finds that regardless of the limiting procedure used, the end result is either no stack at all or a stack that doesn't lean. This reveals the subtleties of limit operations when dealing with infinity and the limitations of intuition.

A Simple Violation of Determinism in Newtonian Mechanics: The Dome

2025-01-03

This paper presents a counterintuitive example in Newtonian mechanics where determinism fails: a mass resting at the apex of a specially shaped dome spontaneously moves without any external intervention. The author demonstrates, through mathematical solutions and physical reasoning, that this system allows for multiple solutions, some of which depict the mass initiating motion at an arbitrary time, with no Newtonian prediction for when or in what direction. Even simple Newtonian systems can exhibit acausal events, challenging the universality of causality in classical physics.