Paradoxes

The 20-th century was the "No you Can't" century in which there were a number of Paradoxes that were discovered that "proved" that not all things were possible.

Physics

. Relativity -- Large Physics

1. No material particle can be accelerated to the speed of light.
2. The Speed of light is a constant and is not observed to be changed no matter the speed of the observer.
3. There is no absolute space frame, e.g. one can not determine if one is stationary relative to any absolute space.

. Quantum Mechanics -- Small Physics

1. Many measurements are intermingled in that one can not measure both with infinite accuracy, e.g. Position and Momentum.
2. The state of a system often is indeterminate, with no hidden values, and only exists when an observation collapses the state.
3. Small particles (or waves) sometimes seem to be Particles, when their position is measures, and Waves when their path is measured.

Arrow's impossibility theorem (for voting) -- There is no voting system that is a fair way of determining group Public Good from individual preferences if the system is meant to satisfy: "

1. unrestricted domain, -- It should yield a unique and complete ranking of societal choices for any set of individual voter preferences.
2. non-dictatorship, -- It cannot simply mimic the preferences of a single voter.
3. independence of irrelevant alternatives -- Changes in individuals' rankings of irrelevant alternatives (ones outside the subset) should have no impact on the societal ranking of the relevant subset.
4. Pareto efficiency, -- If every individual prefers a certain option to another, then so must the resulting societal preference order. (note: monotonicity, non-imposition, and independence of irrelevant alternatives together imply Pareto efficiency)

Practical Paradoxes

the following seem to be paradoxes, but are not proven.

. Democratic Trilemma -- Fishkin -- No democratic system seems to satisfy the following three objectives.

1. Participation -- All qualified members of the society shall participate in the determination of the policies of the society.
2. Equality -- They shall be equally deterministic of the policies.
3. Deliberation -- They shall spend sufficient time to thoughtfully evaluate the values and implications of their decisions.