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Occam's razor is a principle attributed to the 14th-century English logician and Franciscan friar William of Ockham. The principle states that the explanation of any phenomenon should make as few assumptions as possible, eliminating those that make no difference in the observable predictions of the explanatory hypothesis or theory. The principle is often expressed in Latin as the lex parsimoniae ("law of parsimony" or "law of succinctness"): "entia non sunt multiplicanda praeter necessitatem", roughly translated as "entities must not be multiplied beyond necessity".

This is often paraphrased as "All other things being equal, the simplest solution is the best." In other words, when multiple competing theories are equal in other respects, the principle recommends selecting the theory that introduces the fewest assumptions and postulates the fewest entities. It is in this sense that Occam's razor is usually understood.

Originally a tenet of the reductionist philosophy of nominalism, it is more often taken today as an heuristic maxim (rule of thumb) that advises economy, parsimony, or simplicity, often or especially in scientific theories

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In quantum physics, the Heisenberg uncertainty principle is the statement that locating a particle in a small region of space makes the velocity of the particle uncertain; and conversely, that measuring the velocity of a particle precisely makes the position uncertain.

In quantum mechanics, the position and velocity of particles do not have precise values, but have a probability distribution. There are no states in which a particle has both a definite position and a definite velocity. The narrower the probability distribution is in position, the wider it is in momentum.Physically, the uncertainty principle requires that when the position of an atom is measured with a photon, the reflected photon will change the momentum of the atom by an uncertain amount inversely proportional to the accuracy of the position measurement. The amount of uncertainty can never be reduced below the limit set by the principle, regardless of the experimental setup.

A mathematical statement of the principle is that every quantum state has the property that the root-mean-square (RMS) deviation of the position from its mean (the standard deviation of the X-distribution):

\Delta X = \sqrt{\langle X^2 \rangle-\langle X \rangle ^2 } \,\Delta X = \sqrt{\langle X^2 \rangle-\langle X \rangle ^2 } \,     times the RMS deviation of the momentum from its mean (the standard deviation of P):

\Delta P = \sqrt{\langle P^2 \rangle-\langle P \rangle ^2} \,\Delta P = \sqrt{\langle P^2 \rangle-\langle P \rangle ^2} \,    and can never be smaller than a small fixed multiple of Planck's constant:

\Delta x \Delta p \ge \frac{h}{4\pi} = {\hbar \over 2} \Delta x \Delta p \ge \frac{h}{4\pi} = {\hbar \over 2}

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