Graham's number. Graham's number, named after Ronald Graham, is a large number that is an upper bound on the solution to a problem in Ramsey theory. The number gained a degree of popular attention when Martin Gardner described it in the "Mathematical Games" section of Scientific American in November 1977, writing that, "In an unpublished proof, Graham has recently established ... a bound so vast that it holds the record for the largest number ever used in a serious mathematical proof. " The 1980 Guinness Book of World Records repeated Gardner's claim, adding to the popular interest in this number. According to physicist John Baez, Graham invented the quantity now known as Graham's number in conversation with Gardner himself.
While Graham was trying to explain a result in Ramsey theory which he had derived with his collaborator B. Graham's number is unimaginably larger than other well-known large numbers such as a googol, googolplex, and even larger than Skewes' number and Moser's number. Context . Graviton. Theory The three other known forces of nature are mediated by elementary particles: electromagnetism by the photon, the strong interaction by the gluons, and the weak interaction by the W and Z bosons. The hypothesis is that the gravitational interaction is likewise mediated by an – as yet undiscovered – elementary particle, dubbed as the graviton.
In the classical limit, the theory would reduce to general relativity and conform to Newton's law of gravitation in the weak-field limit. Gravitons and renormalization When describing graviton interactions, the classical theory (i.e., the tree diagrams) and semiclassical corrections (one-loop diagrams) behave normally, but Feynman diagrams with two (or more) loops lead to ultraviolet divergences; that is, infinite results that cannot be removed because the quantized general relativity is not renormalizable, unlike quantum electrodynamics.
Comparison with other forces Gravitons in speculative theories See also Interconnectedness. Interconnectedness is part of the terminology of a worldview which sees a oneness in all things. A similar term, interdependence, is sometimes used instead, although there are slightly different connotations. Both terms tend to refer to the idea that all things are of a single underlying substance and reality, and that there is no true separation deeper than appearances. Some feel that 'interconnectedness' and similar terms are part of a contemporary lexicon of mysticism, which is based on the same core idea of universal oneness. Economic The economic interconnectedness, so called economic globalization, has evolved and developed ever since the time immemorial with the countries bartering in prospect of finding mutual interests and gains. There are number of categories on economic interconnectedness.
"Globalization means international interdependence with disadvantages as well as advantages. Religion The mystics[who?] Politics Implications See also Polysemy. Charles Fillmore and Beryl Atkins’ definition stipulates three elements: (i) the various senses of a polysemous word have a central origin, (ii) the links between these senses form a network, and (iii) understanding the ‘inner’ one contributes to understanding of the ‘outer’ one. Polysemy is a pivotal concept within disciplines such as media studies and linguistics.
Polysemes A polyseme is a word or phrase with different, but related senses. Since the test for polysemy is the vague concept of relatedness, judgments of polysemy can be difficult to make. In vertical polysemy a word refers to a member of a subcategory (e.g., 'dog' for 'male dog'). A closely related idea is metonym, in which a word with one original meaning is used to refer to something else connected to it.
Examples Man The human species (i.e., man vs. animal)Males of the human species (i.e., man vs. woman)Adult males of the human species (i.e., man vs. boy) Mole Bank Book Newspaper The newspaper fired its editor. Who is winning the 'crypto-war'? 15 March 2014Last updated at 20:12 ET By Gordon Corera Security correspondent, BBC News In the war over encryption between the NSA and privacy activists, who is winning? Ladar Levison sits exhausted, slumped on a sofa with his dog Princess on his lap. He is surrounded by boxes after he moved into a new house in the suburbs of Dallas, Texas, the previous day. He describes his new home as a "monastery for programmers".
Levison and co-workers plan to live and work there as they create a new email service which will allow people to communicate entirely securely and privately. It is a new email service because Levison himself shut down his old one - called Lavabit - after a visit from the FBI. It began with a business card in May of last year. A tussle with the FBI led to a court ordering Levison to hand over the keys to his email service. Levison knew that it would take time for the FBI to input the keys and that gave him the chance to shut down his entire system. What is encryption? Alfred North Whitehead. In his early career Whitehead wrote primarily on mathematics, logic, and physics.
His most notable work in these fields is the three-volume Principia Mathematica (1910–13), which he co-wrote with former student Bertrand Russell. Principia Mathematica is considered one of the twentieth century's most important works in mathematical logic, and placed 23rd in a list of the top 100 English-language nonfiction books of the twentieth century by Modern Library. Whitehead's process philosophy argues that "there is urgency in coming to see the world as a web of interrelated processes of which we are integral parts, so that all of our choices and actions have consequences for the world around us.
" For this reason, one of the most promising applications of Whitehead's thought in recent years has been in the area of ecological civilization and environmental ethics pioneered by John B. Cobb, Jr. Life Whewell's Court north range at Trinity College, Cambridge. Views on education William James. William James (January 11, 1842 – August 26, 1910) was an American philosopher and psychologist who was also trained as a physician. The first educator to offer a psychology course in the United States, James was one of the leading thinkers of the late nineteenth century and is believed by many to be one of the most influential philosophers the United States has ever produced, while others have labelled him the "Father of American psychology". Along with Charles Sanders Peirce and John Dewey, he is considered to be one of the greatest figures associated with the philosophical school known as pragmatism, and is also cited as one of the founders of the functional psychology.
He also developed the philosophical perspective known as radical empiricism. James' work has influenced intellectuals such as Émile Durkheim, W. E. B. Du Bois, Edmund Husserl, Bertrand Russell, Ludwig Wittgenstein, Hilary Putnam, and Richard Rorty. Early life Career Writings Karl Popper. Karl Raimund Popper CH FBA FRS (28 July 1902 – 17 September 1994) was an Austrian-British philosopher and professor at the London School of Economics. He is generally regarded as one of the greatest philosophers of science of the 20th century. Popper is known for his rejection of the classical inductivist views on the scientific method, in favour of empirical falsification: A theory in the empirical sciences can never be proven, but it can be falsified, meaning that it can and should be scrutinized by decisive experiments.
If the outcome of an experiment contradicts the theory, one should refrain from ad hoc manoeuvres that evade the contradiction merely by making it less falsifiable. Personal life Family and training Karl Popper was born in Vienna (then in Austria-Hungary) in 1902, to upper middle-class parents. He worked in street construction for a short amount of time, but was unable to cope with the heavy labour. Academic life Honours and awards Critical rationalism. Critical rationalism is an epistemological philosophy advanced by Karl Popper. Popper wrote about critical rationalism in his works, The Open Society and its Enemies Volume 2, and Conjectures and Refutations. Criticism, not support Critical rationalists hold that scientific theories and any other claims to knowledge can and should be rationally criticized, and (if they have empirical content) can and should be subjected to tests which may falsify them.
Thus claims to knowledge may be contrastingly and normatively evaluated. They are either falsifiable and thus empirical (in a very broad sense), or not falsifiable and thus non-empirical. Those claims to knowledge that are potentially falsifiable can then be admitted to the body of empirical science, and then further differentiated according to whether they are retained or are later actually falsified. In this sense, critical rationalism turns the normal understanding of a traditional rationalist, and a realist, on its head. 1. The Open Society and Its Enemies. The Open Society and Its Enemies is a two-volume work on political philosophy by Karl Popper.
Written during World War II, it failed to find a publisher in the United States and was first printed in London by Routledge in 1945. The book was published in Russia in 1992. Popper criticises theories of teleological historicism in which history unfolds inexorably according to universal laws, and indicts as totalitarian Plato, Hegel and Marx for relying on historicism to underpin their political philosophies.
The work was on the Modern Library Board's 100 Best Nonfiction books of the 20th century. Publication A veritable who's who of philosophy and the social sciences were involved in its path to publication, as Popper was writing in academic obscurity in New Zealand for the duration of World War II. Synopsis In The Open Society and Its Enemies, Popper developed a critique of historicism and a defense of the open society, liberal democracy. Legacy See also