Paradox of tolerance The tolerance paradox arises from a problem that a tolerant person might be antagonistic toward intolerance, hence intolerant of it. The tolerant individual would then be by definition intolerant of intolerance. Discussions Why Smart People Are Stupid Editors’ Note: The introductory paragraphs of this post appeared in similar form in an October, 2011, column by Jonah Lehrer for the Wall Street Journal. We regret the duplication of material. Here’s a simple arithmetic question: A bat and ball cost a dollar and ten cents. The bat costs a dollar more than the ball. How much does the ball cost? Cryptographers chosen to duke it out in final fight - physics-math - 13 December 2010 A competition to find a replacement for one of the gold-standard computer security algorithms used in almost all secure, online transactions just heated up. The list of possibilities for Secure Hash Algorithm-3, or SHA-3, has been narrowed down to five finalists. They now face the onslaught of an international community of "cryptanalysts" – who will analyse the algorithms for weaknesses – before just one is due to be selected as the winner in 2012. The competition, which is being run by the US National Institute of Standards and Technology in Gaithersburg, Maryland, is a huge deal for cryptographers and cryptanalysts alike. "These are incredibly competitive people. They just love this," says William Burr of NIST.
Dave's short course in trigonometry Table of Contents Who should take this course? Trigonometry for you Your background How to learn trigonometry Applications of trigonometry Astronomy and geography Engineering and physics Mathematics and its applications What is trigonometry? Trigonometry as computational geometry Angle measurement and tables Background on geometry The Pythagorean theorem An explanation of the Pythagorean theorem Similar triangles Angle measurement The concept of angle Radians and arc length Exercises, hints, and answers About digits of accuracy Chords What is a chord? Ptolemy’s sum and difference formulas Ptolemy’s theorem The sum formula for sines The other sum and difference formulas Summary of trigonometric formulas Formulas for arcs and sectors of circles Formulas for right triangles Formulas for oblique triangles Formulas for areas of triangles Summary of trigonometric identities More important identities Less important identities Truly obscure identities
World we see is make-believe, top British scientist says THE human brain creates its own version of reality, and the world we see around us is mostly make-believe, according to a top British scientist. Professor Bruce Hood will explore the limits of the human mind in a series of prestigious lectures for the Royal Institution of Great Britain, the oldest independent research body in the world, it was announced yesterday. The psychologist plans to induce false memories in audience members and use pickpockets to demonstrate how easily people are distracted, in a bid to prove how we have less control over our own decisions and perceptions than we like to imagine. "A lot of the world is make-believe. We're only aware of a fraction of what's going on," Hood told The (London) Times.
10 Mind-Blowing Theories That Will Change Your Perception of the World Reality is not as obvious and simple as we like to think. Some of the things that we accept as true at face value are notoriously wrong. Scientists and philosophers have made every effort to change our common perceptions of it. The 10 examples below will show you what I mean. 1. Great glaciation. Relplot: equation plotter Relplot constructs high-resolution PostScript or PDF plots of the solutions to equations on two variables. Unlike most other plotters, it can handle general equations and inequations, not just functions, and it can plot multiple equations at once. What can you plot? Multiple equations/formulas separated by commas: ,Logical operators for combining formulas: && & ||Relational operators: = < <= > >=Binary arithmetic ops: + * - / ^ modUnary arithmetic ops: |x| sqrt floor exp ln sin cos tan asin acos atan atan2 sinh cosh tanhBuilt-in variables: x y r thConstants: pi e 2 -.5 1.4e5 .7e01 πUser-defined function applications: f(e1,..., en)User-defined variables: a-z x^3 + y^3 = 3xy, r^2 = 9/2 Some interesting equations to try:
List of mathematical symbols When reading the list, it is important to recognize that a mathematical concept is independent of the symbol chosen to represent it. For many of the symbols below, the symbol is usually synonymous with the corresponding concept (ultimately an arbitrary choice made as a result of the cumulative history of mathematics), but in some situations a different convention may be used. For example, depending on context, the triple bar "≡" may represent congruence or a definition. Further, in mathematical logic, numerical equality is sometimes represented by "≡" instead of "=", with the latter representing equality of well-formed formulas. In short, convention dictates the meaning.
Imaginary friend Imaginary friends or imaginary companions are a psychological and social phenomenon where a friendship or other interpersonal relationship takes place in the imagination rather than external physical reality. Imaginary friends are fictional characters created for improvisational role-playing. They often have elaborate personalities and behaviors. Although they may seem very real to their creators, children usually understand that their imaginary friends are not real. The first studies focusing on imaginary friends are believed to have been conducted during the 1890s. Few adults report having imaginary friends; however, as Eileen Kennedy-Moore points out, "Adult fiction writers often talk about their characters taking on a life of their own, which may be an analogous process to children’s invisible friends