instruction:
In this task you will be given a text passage from a trivia quiz. You should choose the category this question belongs to from these categories: History, Science, Social Science, Fine Arts, Literature. You can only choose one category, so if in doubt, please choose the closest match.
question:
This rule holds if the operator algebra for some set of observables is non-trivial; that is true because it is derived via the Schwarz inequality applied to the expectation value of the commutator of two observables operators. It formally bounds the product of the dispersions in two observables. An adapted form of this law applies to energy and time; it applies directly to any two components of spin, but it is best known in its application to position and momentum, the product of the standard deviations of which is at least h-bar over two. FTP, name this principle from quantum mechanics that limits the precision of measurements.
answer:
Science

question:
The lemma named for this person states that if a prime number divides a product, then it divides a factor of that product. Janos Bolyai and Nikolai Lobachevsky developed a system that was notable for not following all of this person's rules. A so-called orchard is named for this person because of his algorithm for finding greatest common divisors. A book he wrote states that if a line segment intersects two lines, then the lines meet on the side of the segment where the interior angle sum is less than two right angles, the last of his five postulates. Name this mathematician whose Elements was a standard text of geometry.
answer:
Science

question:
Alonso de Vargas suppressed a rebellion against this man, which saw Juan de Lanuza beheaded afterward. Antoine Perrenot de Granvelle was one of this man's main advisors, and he signed the treaty of Vervins with France. His secretary, Antonio Perez, was involved in the murder of Juan de Escobedo, the private secretary of this man's half brother. Alexander Farnese would help this man reconquer the southern Netherlands after the Duke of Alba had failed to subdue the Dutch revolt, and Don Juan of Austria would help him defeat the Ottomans at Lepanto. A son of emperor Charles V, he would rule from the Escorial palace. FTP, who was this Spanish king who saw the Spanish armada defeated
answer:
History