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In 1967, Simon Kochen and Ernst Specker proved mathematically that even for a single quantum object, where entanglement is not possible, the values that you obtain when you measure its properties depend on the context. So the value of property A, say, depends on whether you chose to measure it with property B, or with property C. In other words, there is no reality independent of the choice of measurement. It wasn't until 2008, however, that Alexander Klyachko of Bilkent University in Ankara, Turkey, and colleagues devised a feasible test for this prediction. They calculated that if you repeatedly measured five different pairs of properties of a quantum particle that was in a superposition of three states, the results would differ for the quantum system compared with a classical system with hidden variables. That's because quantum properties are not fixed, but vary depending on the choice of measurements, which skews the statistics. "This was a very clever idea," says Anton Zeilinger of the Institute for Quantum Optics, Quantum Nanophysics and Quantum Information in Vienna, Austria. "The question was how to realise this in an experiment." Now he, Radek Lapkiewicz and colleagues have realised the idea experimentally. They used photons, each in a superposition in which they simultaneously took three paths. Then they repeated a sequence of five pairs of measurements on various properties of the photons, such as their polarisations, tens of thousands of times. A beautiful experiment They found that the resulting statistics could only be explained if the combination of properties that was tested was affecting the value of the property being measured. "There is no sense in assuming that what we do not measure about a system has [an independent] reality," Zeilinger concludes.

"Forget quantum physics, forget relativity. Inklings of an ultimate theory might emerge from an unexpected place "

"The human brain is capable of 1016 processes per second, which makes it far more powerful than any computer currently in existence. But that doesn't mean our brains don't have major limitations. The lowly calculator can do math thousands of times better than we can, and our memories are often less than useless - plus, we're subject to cognitive biases, those annoying glitches in our thinking that cause us to make questionable decisions and reach erroneous conclusions. Here are a dozen of the most common and pernicious cognitive biases that you need to know about"

"DISCOVER THE SIMPLE WORLD OF HIGH LEVEL MATHEMATICS!"

IMAGINARY is your place for open and interactive mathematics. You can explore great programs, enjoy beautiful picture galleries and create hands-on math exhibits. Share your own ideas and modules. Stage your own exhibitions.

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The Khan Academy is a not-for-profit 501(c)(3) with the mission of providing a world-class education to anyone, anywhere. We are complementing Salman's ever-growing library with user-paced exercises--developed as an open source project--allowing the Khan Academy to become the free classroom for the World.

RANDOM.ORG offers true random numbers to anyone on the Internet. The randomness comes from atmospheric noise, which for many purposes is better than the pseudo-random number algorithms typically used in computer programs. People use RANDOM.ORG for holding drawings, lotteries and sweepstakes, to drive games and gambling sites, for scientific applications and for art and music.

Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems.

Wolfram has long been a trusted name in education-as the makers of Mathematica, Wolfram|Alpha, and the Wolfram Demonstrations Project, we've created some of the most dynamic teaching and learning tools available. We are pleased to offer the best of all of our technologies to you here in the Wolfram Education Portal, organized by course. In the portal you'll find a dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more built by Wolfram education experts.

Access the Wolfram|Alpha platform at multiple levels-from individual results to complete Wolfram|Alpha output pages. The API operates as a high-performance REST-style webservice, with convenient bindings for popular languages and platforms.