(computing, robotics) The observation that, contrary to traditional assumptions, reasoning (which is high-level in humans) requires very little computation, but sensorimotor skills (comparatively low-level in humans) require enormous computational resources.

(probability) A problem within the classical interpretation of probability theory, illustrating how the principle of indifference may not produce definite, well-defined results for probabilities if it is applied uncritically when the domain of possibilities is infinite.

(programming) The situation where a programmer sees less powerful programming languages than those he/she knows as lacking in important features, but more powerful ones as having bizarre or unnecessary features.

(topology) The non-intuitive fact that it is possible to turn a sphere inside out in a three-dimensional space with possible self-intersections but without creating any crease.

The proposition in hydrostatics that any quantity of water, however small, may be made to counterbalance any weight, however great; or the law of the equality of pressure of fluids in all directions.

(set theory) The paradox that a set defined to contain all sets which do not contain themselves can neither consistently contain itself nor not contain itself.

(philosophy) A philosophical problem whereby a man intends to walk a mile from a particular point, but an infinity of gods separately plan to obstruct him. One of them will raise a barrier to stop his further advance if he reaches the half-mile point, a second if he reaches the quarter-mile point, a third if he goes one-eighth of a mile, and so on ad infinitum. The paradox involves the fact that (i) the man cannot begin walking, because a barrier will stop him even at the shortest distance, but (ii) if he does not begin walking, no barrier will rise.

(philosophy) Any of a set of philosophical problems generally thought to have been devised by the Greek philosopher Zeno of Elea (c. 490–430 BC) to support Parmenides' doctrine that, contrary to the evidence of one's senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion.

plural of Zeno's paradox

(physics) A relativistic paradox concerning the concept of Born rigidity within special relativity, where an ideally rigid cylinder that is made to rotate about its axis of symmetry. The radius R as seen in the laboratory frame is always perpendicular to its motion and should therefore be equal to its value R₀ when stationary. However, the circumference should appear Lorentz-contracted to a smaller value than at rest. This leads to the contradiction that R = R₀ and R < R₀.