Posts Tagged ‘symbolic logic’
“Reality leaves a lot to the imagination”*…
Here’s a curious thought experiment. Imagine a cloud of quantum particles that are entangled—in other words, they share the same quantum existence. The behavior of these particles is chaotic. The goal of this experiment is to send a quantum message across this set of particles. So the message has to be sent into one side of the cloud and then extracted from the other.
The first step, then, is to divide the cloud down the middle so that the particles on the left can be controlled separately from those on the right. The next step is to inject the message into the left-hand part of the cloud, where the chaotic behavior of the particles quickly scrambles it.
Can such a message ever be unscrambled?
Today, we get an answer thanks to the work of Adam Brown at Google in California and a number of colleagues, including Leonard Susskind at Stanford University, the “father of string theory.” This team shows exactly how such a message can be made to surprisingly reappear.
“The surprise is what happens next,” they say. After a period in which the message seems thoroughly scrambled, it abruptly unscrambles and recoheres at a point far away from where it was originally inserted. “The signal has unexpectedly refocused, without it being at all obvious what it was that acted as the lens,” they say.
But their really extraordinary claim is that such an experiment throws light on one of the deepest mysteries of the universe: the quantum nature of gravity and spacetime…
Quantum entanglement, and what it might tell us about quantum gravity– the fascinating story in full: “How a tabletop experiment could test the bedrock of reality.”
[The arXiv paper on which this article reports, “Quantum Gravity in the Lab: Teleportation by Size and Traversable Wormholes,” is here.]
* John Lennon
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As we contemplate connection, we might spare a thought for George Boole; the philosopher and mathematician died on this date in 1864. Boole helped establish modern symbolic logic– he created symbols to stand for logical operations– and an algebra of logic (that is now called “Boolean algebra”). Boole made important contributions to the study of differential equations and other aspects of math; his algebra has found important applications in topology, measure theory, probability, and statistics. But it’s for the foundational contribution that his symbolic logic has made to computer science– from circuit design to programming– that he’s probably best remembered.
Happy Birthday (1894), James Thurber!!
Infinitely infinite…
The folks at Plus polled their readers for the questions they’d most like answered. The winner: “Does Infinity Exist?,” which cosmologist John D. Barrow answers…
This is a surprisingly ancient question. It was Aristotle who first introduced a clear distinction to help make sense of it. He distinguished between two varieties of infinity. One of them he called a potential infinity: this is the type of infinity that characterises an unending Universe or an unending list, for example the natural numbers 1,2,3,4,5,…, which go on forever. These are lists or expanses that have no end or boundary: you can never reach the end of all numbers by listing them, or the end of an unending universe by travelling in a spaceship. Aristotle was quite happy about these potential infinities, he recognised that they existed and they didn’t create any great scandal in his way of thinking about the Universe.
Aristotle distinguished potential infinities from what he called actual infinities. These would be something you could measure, something local, for example the density of a solid, or the brightness of a light, or the temperature of an object, becoming infinite at a particular place or time. You would be able to encounter this infinity locally in the Universe. Aristotle banned actual infinities: he said they couldn’t exist. This was bound up with his other belief, that there couldn’t be a perfect vacuum in nature. If there could, he believed you would be able to push and accelerate an object to infinite speed because it would encounter no resistance.
For several thousands of years Aristotle’s philosophy underpinned Western and Christian dogma and belief about the nature of the Universe. People continued to believe that actual infinities could not exist, in fact the only actual infinity that was supposed to exist was the divine.
But in the world of mathematics things changed towards the end of the 19th century… In mathematics, if you say something “exists”, what you mean is that it doesn’t introduce a logical contradiction given a particular set of rules. But it doesn’t mean that you can have one sitting on your desk or that there’s one running around somewhere.
And that was only the beginning; then came advances in physics and cosmology… Find out what happened, and whether infinities do in fact exist (plus, discover– finally!– the attraction of string theory) in “Do Infinities Exist?”
[TotH to 3 Quarks Daily]
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As we remind ourselves that there’s always room in Hilbert’s Hotel, we might spare a well-ordered thought for German mathematician and logician (Friedrich Ludwig) Gottlob Frege; he died on this date in 1925. Frege extended Boole’s work by inventing logical symbols, effectively founding modern symbolic logic. He worked on general questions of philosophical logic and semantics (indeed, his theory of meaning, based on distinguishing between what a linguistic term refers to and what it expresses, remains influential). But relevantly here, Frege was the first to put forward the view that mathematics is reducible to logic– thus creating the context in which mathematical infinites can “exist” (in that they do not contradict that logic)…
Use by…
James Kendall and his wife Rosie own and publish Brighton SOURCE Magazine. Recently, Rosie’s mother, a 90-year-old widow who lived through the Blitz, gave up her long-time home to move to assisted living. In the process of helping her make the transition, James documented the contents of his mother-in-law’s pantry, and gathered the photos in a collection he calls “Best Before…”
Waste not; want not.
[TotH to Kottke.org]
As we rethink the concept of slow food, we might wish a systematically-happy birthday to George Boole; the philosopher and mathematician was born on this date in 1815. Boole helped establish modern symbolic logic– he created symbols to stand for logical operations– and an algebra of logic (that is now called “Boolean algebra”). Boole made important contributions to the study of differential equations and other aspects of math; his algebra has found important applications in topology, measure theory, probability, and statistics. But it’s for the foundational contribution that his symbolic logic has made to computer science– from circuit design to programming– that he’s probably best remembered.
It’s kind of like a Sofia Coppola film…
Reader’s may remember Bacon Ipsum, the down-home alternative to Lorem Ipsum, used by designers for “greeking” in placeholder text.
Well, now there’s a cooler, more moderne choice: Hipster Ipsum: “Artisanal filler text for your site or project.” A sample…
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Head on over to Hispster Ipsum for the coolest of layouts…
As we affect a posture of amused indifference, we might wish a symbolically-logical Happy Birthday to mathematician Guiseppe Peano; he was born on this date in 1858. The author of over 200 books and papers, he was a founder of mathematical logic and set theory, to which he contributed much of the symbolic notation still in use.
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