randomness
https://plus.maths.org/content/taxonomy/term/260
enInformation is sophistication
https://plus.maths.org/content/information-sophistication
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Marianne Freiberger </div>
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<p>Kolmogorov complexity gives a high value to strings of symbols that are essentially random. But isn't randomness essentially meaningless? Should a measure of information assign a low value to it? The concept of sophistication addresses this question.</p>
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<p><em>This article is part of our <a href="https://plus.maths.org/content/information-about-information">Information about information project</a>, run <a href="https://plus.maths.org/content/information-about-information#fqxi">in collaboration with FQXi</a>. Click <a href="https://plus.maths.org/content/can-you-measure-information">here</a> to find out about other ways of measuring information. </em></p><p><a href="https://plus.maths.org/content/information-sophistication" target="_blank">read more</a></p>https://plus.maths.org/content/information-sophistication#commentscomplexityinformation about informationInformation theoryrandomnesssophisticationTue, 24 Mar 2015 17:31:53 +0000mf3446318 at https://plus.maths.org/contentInformation is complexity
https://plus.maths.org/content/information-complexity
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Marianne Freiberger </div>
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<p>There are many ways of saying the same thing — you can use many words, or few. Perhaps information should be measured in terms of the shortest way of expressing it? In the 1960s this idea led to a measure of information called <em>Kolmogorov complexity</em>.</p>
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<p><em>This article is part of our <a href="https://plus.maths.org/content/information-about-information">Information about information project</a>, run <a href="https://plus.maths.org/content/information-about-information#fqxi">in collaboration with FQXi</a>. Click <a href="https://plus.maths.org/content/can-you-measure-information">here</a> to find out about other ways of measuring information. </em></p><p><a href="https://plus.maths.org/content/information-complexity" target="_blank">read more</a></p>https://plus.maths.org/content/information-complexity#commentscomplexityinformation about informationInformation theoryrandomnessTue, 24 Mar 2015 16:56:10 +0000mf3446317 at https://plus.maths.org/contentFreedom and physics
https://plus.maths.org/content/freedom-and-physics
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Marianne Freiberger </div>
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<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/5/12_jan_2012_-_1525/icon.jpg?1326381914" /> </div>
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<p>Most of us think that we have the capacity to act freely. Our sense of morality, our legal system, our whole culture is based on the idea that there is such a thing as free will. It's embarrassing then that classical physics seems to tell a different story. And what does quantum theory have to say about free will?</p>
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<p><em>In the latest poll of our <a href="https://plus.maths.org/content/science-fiction-science-fact-reports-frontiers-physics">Science fiction, science fact project</a> you told us that you wanted to know whether there is such a thing as free will. This is one of the articles we've produced in response. Click <a href="https://plus.maths.org/content/science-fiction-science-fact-there-free-will">here</a> to see more articles on free will.</em> </p><p><a href="https://plus.maths.org/content/freedom-and-physics" target="_blank">read more</a></p>https://plus.maths.org/content/freedom-and-physics#commentsFrontiers of physicsmathematical realityfree willNewtonquantum mechanicsquantum uncertaintyrandomnessThu, 12 Jan 2012 11:19:01 +0000mf3445628 at https://plus.maths.org/contentKeeping track of immunity
https://plus.maths.org/content/keeping-track-immunity
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Adam Kucharski </div>
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<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/5/13_may_2011_-_1139/icon.jpg?1305283193" /> </div>
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<p>Dengue fever does the opposite of what you might expect. Unlike for many diseases, if you've had this tropical virus and recovered, you might be worse off, as a second exposure to the dengue virus can be life threatening. So keeping track of the strains of the diseases is an important problem which can be solved with the help of a little randomness.</p>
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<p>Dengue fever does the opposite of what you might expect. Unlike many diseases, if you've had this tropical virus and recovered, you might actually be worse off. In the aftermath of an infection like chickenpox, your new antibodies will step in to stop a repeat of the illness. However, a second exposure to the dengue virus can be far more severe than the first, even life threatening. </p><p><a href="https://plus.maths.org/content/keeping-track-immunity" target="_blank">read more</a></p>https://plus.maths.org/content/keeping-track-immunity#commentsmedicine and healthrandomnessstochastic modelFri, 20 May 2011 09:25:23 +0000mf3445482 at https://plus.maths.org/contentUnderstanding Uncertainty: Pure randomness in art
https://plus.maths.org/content/understanding-uncertainty-pure-randomness-art
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David Spiegelhalter </div>
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<p>This article is based on a talk I gave at the recent <a href="http://www.kettlesyard.co.uk/exhibitions/cage.html">John Cage exhibition</a> in the Kettles Yard gallery in Cambridge. Cage is perhaps best known for his avant-garde music, particularly his silent 1952 composition <a href="http://en.wikipedia.org/wiki/4′33″">4′33″</a> but also for his use of randomness in <em><a href="http://en.wikipedia.org/wiki/Aleatoric_music">aleatory music</a></em>. But Cage also used randomness in his art.</p>
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<br class="brclear" /><p><div style="text-align:center;margin-right: auto; margin-left: auto; width: 90%; font-size: 15px; border: 2px solid #9a7a9f; padding: 5px;">This article is adapted from material on the <a href="http://understandinguncertainty.org">Understanding Uncertainty website</a>.</div></p><p><a href="https://plus.maths.org/content/understanding-uncertainty-pure-randomness-art" target="_blank">read more</a></p>https://plus.maths.org/content/understanding-uncertainty-pure-randomness-art#commentsCMSmathematics and artrandomnessunderstanding uncertaintyWed, 15 Dec 2010 11:16:29 +0000mf3445382 at https://plus.maths.org/contentOuter space: A question of tactics
https://plus.maths.org/content/outer-space-question-tactics
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John D. Barrow </div>
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<p>In many sports a particular tactical conundrum arises. The team captain has to choose the best order in which to use a group of players or set-plays in the face of unknown counter choices by the opposition. Do you want to field the strongest players first to raise morale or play them last to produce a late run for victory? John D. Barrow shows that randomness holds the answer.</p>
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<p>Left, right or centre?</p><p><a href="https://plus.maths.org/content/outer-space-question-tactics" target="_blank">read more</a></p>https://plus.maths.org/content/outer-space-question-tactics#commentsmathematics in sportouterspacerandomnessstrategyFri, 03 Sep 2010 15:41:16 +0000mf3445301 at https://plus.maths.org/contentHow to protect your privacy
https://plus.maths.org/content/how-protect-your-privacy
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<p>How would you feel if your private health record were revealed to insurance companies or prospective employers? These days our details are kept on all sorts of different databases and cleverly cross-referencing them can reveal intimate information about individuals. So what can be done to protect privacy? We talk to Cynthia Dwork from Microsoft Research, whose talk at the ICM showcased some mathematical tools to keep our details safe.</p><p><a href='http://plus.maths.org/content/sites/plus.maths.org/files/podcast/queries_0.mp3'>How to protect your privacy</a></p>https://plus.maths.org/content/how-protect-your-privacy#commentsrandomnessstatisticsTue, 24 Aug 2010 10:01:44 +0000mf3445292 at https://plus.maths.org/contentRandom, but not by accident
https://plus.maths.org/content/os/latestnews/jan-apr10/quantum/index
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<p>Researchers from the University of Maryland have devised a new kind of random number generator that is cryptographically secure, inherently private and — most importantly — certified random by the laws of physics. Randomness is important, particularly in the age of the Internet, because it guarantees security. Valuable data and messages can be encrypted using long strings of random numbers to act as "keys", which encode and decode the information. Randomness implies unpredictability, so if the key is truly random, it's next to impossible for an outsider to guess it.</p>
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<p>Researchers from the University of Maryland have devised a new kind of random number generator that is cryptographically secure, inherently private and — most importantly — certified random by the laws of physics.</p><p><a href="https://plus.maths.org/content/os/latestnews/jan-apr10/quantum/index" target="_blank">read more</a></p>https://plus.maths.org/content/os/latestnews/jan-apr10/quantum/index#commentsquantum cryptographyquantum entanglementrandomnessMon, 19 Apr 2010 23:00:00 +0000plusadmin5213 at https://plus.maths.org/contentUnderstanding uncertainty: Infinite monkey business
https://plus.maths.org/content/infinite-monkey-businesst
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David Spiegelhalter and Owen Smith </div>
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<p><strong>David Spiegelhalter</strong> explains that waiting for an infinite number of monkeys to produce the complete works of Shakespeare is not just a probabilistic certainty, it also gives us an insight into how long we can expect to wait for a rare event to happen.<br />
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<p>The idea that an infinite number of monkeys typing at random on an infinite number of typewriters will eventually produce the complete works of Shakespeare apparently <a href="http://en.wikipedia.org/wiki/Infinite_monkey_theorem">dates from 1913</a>, and has appeared <a href="http://en.wikipedia.org/wiki/Infinite_monkey_theorem_in_popular_culture">repeatedly in popular culture</a> ever since.
When the BBC Horizon team dec<p><a href="https://plus.maths.org/content/infinite-monkey-businesst" target="_blank">read more</a></p>https://plus.maths.org/content/infinite-monkey-businesst#comments54CMSgeometric distributioninfinite monkey theoreminfinityrandomnessrare eventShakespeareunderstanding uncertaintywhat is infinityMon, 01 Mar 2010 00:00:00 +0000plusadmin5167 at https://plus.maths.org/contentPlay the quantum lottery
https://plus.maths.org/content/play-quantum-lottery
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How to win with quantum uncertainty </div>
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<p>Unlucky with balls? Try atoms.</p><p><a href="https://plus.maths.org/content/play-quantum-lottery" target="_blank">read more</a></p>https://plus.maths.org/content/play-quantum-lottery#commentsgamblingquantum mechanicsquantum uncertaintyrandomnessMon, 23 Apr 2007 23:00:00 +0000plusadmin2629 at https://plus.maths.org/contentCoincidence, correlation and chance
https://plus.maths.org/content/coincidence-correlation-and-chance
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Andrew Stickland </div>
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How much evidence would you need before buying into a get rich quick scheme? Do high ice cream sales cause shark attacks? And just how likely was it that you were ever born? <b>Andrew Stickland</b> finds out that, when it comes to probability, our instincts can lead us seriously astray. </div>
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<p><a href="https://plus.maths.org/content/coincidence-correlation-and-chance" target="_blank">read more</a></p>https://plus.maths.org/content/coincidence-correlation-and-chance#comments31biascausationcorrelationrandomnesssurvivorship fallacyTue, 31 Aug 2004 23:00:00 +0000plusadmin2252 at https://plus.maths.org/contentRunning a lottery, for beginners
https://plus.maths.org/content/running-lottery-beginners
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John Haigh </div>
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There are many different types of lottery around the world, but they all share a common aim: to make money. <b>John Haigh</b> explains why lotteries are the way they are. </div>
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<p><i>To appreciate why Lottery formats are what they are, consider how you would design an ongoing Lottery from scratch. Your aim is to maximise the total profit, within the legal constraints that all tickets are treated equally.</i></p><p><a href="https://plus.maths.org/content/running-lottery-beginners" target="_blank">read more</a></p>https://plus.maths.org/content/running-lottery-beginners#comments30combinatoricslotteryrandomnessFri, 30 Apr 2004 23:00:00 +0000plusadmin2247 at https://plus.maths.org/contentThe UK National Lottery - a guide for beginners
https://plus.maths.org/content/uk-national-lottery-guide-beginners
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John Haigh </div>
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In the early days of the UK National Lottery, it was quite common to see newspaper articles that looked back on what numbers had recently been drawn, and attempted to identify certain numbers as "due" or "hot". Few such articles appear now, and <b>John Haigh</b> thinks that perhaps the publicity surrounding the lottery has enhanced the nation's numeracy. </div>
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<p><i>The UK National Lottery began in November 1994. Optimistic statisticians hoped that the surrounding publicity might increase interest in ideas of chance and probability, and perhaps even enhance the nation's numeracy.</i></p><p><a href="https://plus.maths.org/content/uk-national-lottery-guide-beginners" target="_blank">read more</a></p>https://plus.maths.org/content/uk-national-lottery-guide-beginners#comments29combinatoricslotteryrandomnessMon, 01 Mar 2004 00:00:00 +0000plusadmin2243 at https://plus.maths.org/contentLooking out for number one
https://plus.maths.org/content/looking-out-number-one
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Jon Walthoe </div>
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You might think that if you collected together a list of naturally-occurring numbers, then as many of them would start with a 1 as with any other digit, but you'd be quite wrong. <b>Jon Walthoe</b> explains why Benford's Law says otherwise, and why tax inspectors are taking an interest. </div>
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<p>So, here's a challenge. Go and look up some numbers. A whole variety of naturally-occuring numbers will do. Try the lengths of some of the world's rivers, or the cost of gas bills in Moldova; try the population sizes in Peruvian provinces, or even the figures in Bill Clinton's tax return. Then, when you have a sample of numbers, look at their first digits (ignoring any leading zeroes). Count
how many numbers begin with 1, how many begin with 2, how many begin with 3, and so on - what do you find?</p><p><a href="https://plus.maths.org/content/looking-out-number-one" target="_blank">read more</a></p>https://plus.maths.org/content/looking-out-number-one#comments9Benford's Lawdistribution of digitsfraud detectionlogarithmrandomnessscale invariancestatisticsuniform distributionTue, 31 Aug 1999 23:00:00 +0000plusadmin2391 at https://plus.maths.org/contentWhat a coincidence!
https://plus.maths.org/content/what-coincidence
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Geoffrey Grimmett </div>
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Coincidences are familiar to us all but what are the so-called laws of chance? From coin tossing to freak weather events, <b>Geoffrey Grimmett</b> explains how probability is at the heart of it all. </div>
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