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    Here is a problem with truly huge numbers, thought to be unsolvable. 

    Imagine that you have 128 tennis balls, and can arrange them in any way you like. How many arrangements are possible? According to a new paper, the answer is about 10^250, also known as ten unquadragintilliard: that's a number so big that it exceeds the total number of particles in the universe.

    Such “configurational entropy” - a term used to describe how structurally disordered the particles in a physical system are - could lead to a model for the sort of maths that would be needed to solve bigger problems still, ranging from predicting avalanches, or artificial intelligence systems.

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  • 02/02/16--04:51: On Mathematical Models
  • When a system is well understood, a well-constructed mathematical model of that system can make realistic predictions based on the data sets fed into it. However, when a system is not well-understood, but one insists on making a mathematical of it, anyway, the holes in the database and the gaps in our knowledge must, necessarily, be filled with assumptions and estimates, instead of established principles and actual data.

    The poorer our understanding of the system, the greater the impact of those simplifying assumptions and arbitrary estimates on the modeled results.

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    A Sino-Italian workshop on Applied Statistics was held today at the Department of Statistical Sciences of the University of Padova. The organizers were Alessandra Brazzale and Alessandra Salvan from the Department of Statistical Sciences, and Giorgio Picci from the "Confucius Institute". 

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    “Beware of false knowledge; it is more dangerous than ignorance.” - George Bernard Shaw, Man and Superman, 1903.

    It ain’t what you don’t know that gets you into trouble. It’s what you know for sure that just ain’t so. Mark Twain (1835-1910)


    The Fallacy:

    The so-called “Greenhouse effect” is one of the most persistent fallacies in popular science. It is a flawed speculation left over from the late 19th century, when it was first entertained by such scientific luminaries as Joseph Fourier, John Tyndall, and Svante Arrhenius.

    In fact, however, the so-called “greenhouse gases” do not “trap” infrared energy radiated from the surface of the Earth, as proposed; they merely slow its inevitable return to outer space.

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    Football teams have been wearing numbers since Arsenal experimented with putting their players in numbered shirts in 1928 (it didn’t bring them much luck – they lost 3-2 to Sheffield Wednesday). But it was Manchester United that made the number seven shirt iconic by putting their best players in it – perhaps most famously David Beckham, who said:

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    After being one of the few who picked the Mets to make it to the postseason in 2015, NJIT Mathematical Sciences Professor and Associate Dean Bruce Bukiet has published his projections of how the standings should look at the end of Major League Baseball's 2016 season.

    And things look good for the Mets again.


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    The 'maths gender gap' was eliminated in the United States during the Bush administration under the No Child Left Behind program, and it has closed substantially in European countries and parts of Asia as well. Where do young women still lag in math? In societies with poor rates of gender equality, according to the American Economic Review.


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    Sometimes we all just want to take a day off, be it from work or school. In the classic 1980s movie “Ferris Bueller’s Day Off”, which is celebrating its 30th anniversary, the title character spent his day off gallivanting around Chicago, seeing the sights and even hijacking a parade.

    Unlike the super-confident Ferris, most of us would probably worry about getting caught if we took off like that. But is that fear really justified?

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    UK bookmakers will undoubtedly benefit from three of the home nations (England, Northern Ireland and Wales) making it to the Euro 2016 finals. But if you want to bet with your head, rather than your heart, where should you put your money?

    You might be surprised that there is sometimes a way that you can bet and be guaranteed to win. If you can find the right set of odds and put the right amount of money on each outcome, you will win back more than the total amount you bet, no matter what happens. For example, with the following odds, if you bet a total of £73 across the different teams left in the tournament, you’d be guaranteed to have a final balance of at least £99.

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    During the Pamplona, Spain, "Running of the Bulls" you won't need all of the ambulances that are placed along the route, so how do event organizers know where they should be? Statistics helps know. 

    Experts have studied the bull runs of the last six years (a total of 48 races) in order to identify the risks that exist. As you might anticipate, absent an extraordinary event, like a terrorist attack or alien invasion, the risk to one set, the runners and the bulls, are the bulls themselves, the runners and the route. Runners may incur slight injuries such a falls, scratches or breakages, or even being gored. The bulls can suffer physical consequences such as broken horns or hooves. 


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    A false history of science was used to initiate colonial education, in support of colonialism. This false history persists. In a recent article about decolonizing mathematics, for instance, Professor Karen Brodie asserts that, “Much, though certainly not all, of mathematics was created by dead white men.”

    This is not true.

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  • 01/07/17--02:27: The Three Cubes Problem
  • Two days ago, before returning from Israel, my fiancee Kalliopi and I had a very nice dinner in a kosher restaurant near Rehovot in the company of Eilam Gross, Zohar Komargodski, and Zohar's wife Olga. 
    The name of Eilam should be familiar to regulars of this blog as he wrote a couple of guest posts here, in similar occasions (in the first case it was a few before the Higgs discovery was announced, when the signal was intriguing but not yet decisive; and in the second case it was about the 750 GeV resonance, which unfortunately did not concretize into a discovery). As for Zohar, he is a brilliant theorist working in applications of quantum field theory. He is young but already won several awards, among them the prestigious New Horizons in Physics prize.

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    Lovely Lisa Long Leg and Heil Hitler Screaming Nazi once again visit the Stupid Donald Trump Follower’s office in the mathematics department:

    Lovely Liberal Lisa: Heil Trump!

    Stupid Donald Trump Follower: Well, that’s better than what we had before, but I am still not convinced such does anybody any favors.

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  • 01/30/17--03:58: Paradox: Triple Or Bust
  • Today I have a decision problem for you.

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    A few days ago I discussed the coin toss game ‘triple or bust‘. The game is between Alice and Bob. Alice start the game by writing a $ 1.00 IOU to Bob. Alice then makes at least six subsequent tosses with a fair coin. On each ‘heads’ Alice triples the IOU amount. On ‘tails’ she sets the IOU to zero.

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    Trevor Hastie, the Stanford University guru on Statistical Learning (he coined the term together with his colleagues Tibshirani and Friedman) is in Padova this week, where he is giving a short course on his pet topic and a seminar. I am happy to report this as this was partly made possible by the European Union-funded network of which I am the project coordinator, AMVA4NewPhysics. But most of the merit is of Prof. Giovanna Menardi, PI of the Padova node of the network, who organized it... And of course I am happy because I am learning from his insightful lectures!

    (Above, prof. Menardi introduces the lectures).

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    Mental Health Warning:Many World/Mind (MW/M) descriptions may aggravate mental conditions; suicidal ideation has been recognized as a pitfall along the path of Zen-like wisdoms by a wide range of authors as diverse as to include Carlos Castaneda. (Suggesting potential public health benefits of MW/M ethics, I suggest careful adoption in select high school trials and long term monitoring of suicide rates and depression [unpublished].)

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    The most crucial to happy gambling generally (apart from being prepared for losing, since you create a losing copy of yourself with certainty) is your Happy-Enough-Ceiling, where if you reach it, you leave with your winnings. The trivial example is entering the casino with three dollars and playing Martingale roulette, leaving as soon as four dollars are won – the Many Worlds/Minds (MW/M) tree then looks like this:

     

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    SOCK-PUPPET: All your talk about betting strategies is irrelevant to the casino. The casino takes the money from those who just lost and gives it to those who won, from black to red or red to black. On average, every 37 times the ball hits the zero and the casino takes all the money on the table.

     

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    In 1907,Francis Galton recorded the entries from a competition where people guessed the weight of an ox. After analyzing hundreds of estimates the statistician found that while individual guesses varied wildly, the median of the entries was surprisingly accurate, within one percent of the ox's real weight.

    Galton published the results and his theory of collective intelligence, the "wisdom of crowds," became part of the lexicon.

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