Trichaotic (Detail) by Eric J. Heller. In this detail we see two manifestations of chaos. The sky is a random wave, corresponding to the quantum manifestation of classical chaos. The mountain range is a stroboscopic accumulation of the motion of a chaotic rotator.

Subjective probabilities are ignorance probabilities: they enter the picture when relevant facts are ignored, and they disappear, or degenerate into trivial probabilities (either 0 or 1), when all relevant facts are taken into account (which is of course practically impossible in most cases). The so-called "uncertainty" principle of quantum mechanics, on the other hand, guarantees that quantum-mechanical probabilities cannot be made to disappear. As David Mermin has pointed out, "quantum mechanics is the first example in human experience where probabilities play an essential role even when there is nothing to be ignorant about."

It is unfortunate that Werner Heisenberg's original term "Unschärfe," the literal meaning of which is fuzziness, has come to be translated as "uncertainty.'' What makes atoms occupy as much space as they do (rather than no space at all) is not our subjective uncertainty about the positions of atomic electrons relative to atomic nuclei but the objective fuzziness of these relative positions.

Quantum-mechanical probabilities may therefore be characterized as objective. This characterization should not be confused with the objectivist's definition of probabilities as relative frequencies. While it is true that probabilities can be measured only as relative frequencies (and therefore only approximately), a specific type of event is not more probable because it happens more often; rather, it happens more often because it is more probable.