The uncertainty principle states that there exists a limit to the precision with which two certain physical properties of a particle can be measured simultaneously. Those two properties are called complementary variables.
Heisenberg was the first to propose the existence of such a limit and in 1972 he stated that the more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa. The uncertainty principle must not be confused with the observer effect: On the one hand, the uncertainty principle is due to the matter wave nature of all quantum objects and is inherent in the properties of all wave-like systems. It occurs whenever any interaction between classical and quantum objects takes place. The uncertainty principle applies whether an observer was involved or not and it has nothing to do with the accuracy of the device. On the other hand, the observer effect can be reduced to insignificance by using better instruments or observation techniques. This is because the observer effect is the result of using instruments that alter the state of what they measure. It simply states that the act of measuring certain systems will inevitably affect those systems. Sources: Uncertainty principle. (n.d.). Retrieved December 21, 2014, from http://en.wikipedia.org/wiki/Uncertainty_principle Observer effect (physics). (n.d.). Retrieved December 18, 2014, from http://en.wikipedia.org/wiki/Observer_effect_(physics) Heisenberg - Quantum Mechanics, 1925-1927: The Uncertainty Principle. (n.d.). Retrieved December 18, 2014, from http://www.aip.org/history/heisenberg/p08.htm
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Saccheri (1667 – 1733) was a philosopher and mathematician. He is renowned for "Euclides ab omni naevo vindicatus" which translates to "Euclid Freed of Every Flaw" which was his last publication and the second work in non-Euclidean geometry.
Saccheri's wanted to establish the soundness of Euclidean geometry by means of a reductio ad absurdum proof (proof by contradiction) of any alternative to Euclid's parallel postulate. He assumed it to be false, and intended to find a contradiction. Euclid's postulate is equivalent to the following statement: "the sum of the internal angles of a triangle is 180°". Saccheri considered that the sum of the angles is more than 180° which implied that straight lines are finite (contradicting Euclid's second postulate) and hence Saccheri found a contradiction. He then considered that the sum of the angles is less than 180° and couldn't find a direct contradiction. Instead he derived non-intuitive statements from it that allowed him to conclude that "the hypothesis of the acute angle is absolutely false because it is repugnant to the nature of straight lines". Saccheri's 'assumptions ad absurdum' are now theorems of elliptic and hyperbolic geometry. Source: Giovanni Girolamo Saccheri. (n.d.). Retrieved December 21, 2014, from http://en.wikipedia.org/wiki/Giovanni_Girolamo_Saccheri The use–mention distinction is a foundational concept of analytic philosophy, according to which it is necessary to make a distinction between using a word (or phrase) and mentioning it. This distinction is also a crucial aspect of natural language which allows communicating information about language itself. Research on the use-mention distinction can benefit many areas such as computational linguistics, natural language processing, and artificial intelligence. 1. John is a doctor.
2. John begins with the tenth letter of the English alphabet. There is a difference between the interpretations of the two sentences. Sentence 1 states that a certain person (named John) is a doctor. If we interpret sentence 2 in the same fashion, it would state: " a certain person (named John) begins with the tenth letter. That interpretation makes no sense. It is not the person John himself who begins with the tenth letter; rather it is the word, "John", that begins with the tenth letter. We interpret Sentence 2 so that it states: the word John begins with the tenth letter. To talk about the person named John (as in sentence 1 above), we use the word which refers to him viz. John. However, we sometimes want to talk, not about the person, but about his name (the word which we use to refer to the person). In Sentence 1 the word John is used to refer to a certain person. In Sentence 2 the word John is simply mentioned. Source: Use–mention distinction. (n.d.). Retrieved December 18, 2014, from http://en.wikipedia.org/wiki/Use–mention_distinction |