mathematics

Science Art: Giant Animals: Modern and Extinct (detail), by Mary McLain

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These are prehistoric animals compared to their modern relatives and, for scale, a human. A human who’s interested in what they’re like… except when…

Look out! HELL PIG!

There are plenty more of the majestic giants (and some terrifying ones) at NPR’s Skunk Bear tumblog.

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Science Art: Jupiter's Rings by LORRI, 2007.

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The New Horizons Long Range Reconnaissance Imager (LORRI) snapped this photo of Jupiter’s ring system on February 24, 2007, from a distance of 7.1 million kilometers (4.4 million miles).

This processed image shows a narrow ring, about 1,000 kilometers (600 miles) wide, with a fainter sheet of material inside it. The faint glow extending in from the ring is likely caused by fine dust that diffuses in toward Jupiter. This is the outer tip of the “halo,” a cloud of dust …

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SONG: Thirty-Five Minutes (from Earth)

SONG: “Thirty-Five Minutes (from Earth)”.

ARTIST: grant.

SOURCE:Based on “NASA Windbots Could Explore Gas Giant Jupiter”, Sky News, 24 July 2015, as used in the post as used in the post “Windbots to explore Jupiter – the bumpier the ride, the better..”

ABSTRACT: The planet Jupiter is 35 light-minutes from Earth (give or take a couple of minutes depending on where in its orbit the planet is).

So a robot floating in the turbulent winds of Jupiter would take that long to send a mes…

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Science Art: Doree, Zeus, Faber by Edward Donovan

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Three names for one little fish. And those are just the beginning.

I found this one on the Scientific Illustration tumblog, which quoted Wikipedia on the doree (etc.):

John Dory, St Pierre or Peter’s Fish, refers to fish of the genus Zeus, especially Zeus faber, of widespread distribution. It is an edible benthic coastal marine fish with a laterally compressed olive-yellow body which has a large dark spot, and long spines on the dorsal fin. The dark spot is used to flash an ‘evil ey…

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Science Art: Her Majesty's Cochins; Imported in 1843, published 1904.

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These are ostensibly Cochin chickens, or forerunners of what we’d call Cochins today. They’re a breed with a *lot* of character, and are uniquely suited, temperamentally, for being “pet” chickens moreso than egg factories or walking meat supplies. Despite the name (after a part of India), they’re originally from China.

This picture is from The Asiatics; Brahmas, Cochins and Langshans, all varieties, their origin; peculiarities of shape and color; egg production; their ma…

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Science Art: Soaking Up the Rays of a Sun-Like Star, by NASA Ames/JPL-Caltech/T. Pyle, 2015.

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This is an artist’s impression of a planet just discovered by NASA’s Kepler mission that’s gotten the folks at SETI all excited.

It’s the most Earth-like planet yet discovered. Kepler 452b sits in the “Goldilocks” zone around its star, not too hot and not too cold, and is about the same size (or is a little larger) and made of something like the same stuff as the planet we’re sitting around on right now. It takes 365 days to orbit around its sun, too. NASA’s calling it ou…

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Viral science – things that spread fast.

10 March 2015 // 0 Comments

Nature skips past the blue-and-black dress to ask: Have you seen the one about viral scholarship?: In a paper due to appear in Management Science, Sharad Goel and his collaborators propose a mathematical definition of virality that quantifies the extent to which a concept is spreading between friends as opposed to via popular news outlets. Nature asked Goel, a computational social scientist at Stanford University in California, how his work applies to #TheDress. … What does ‘viral’ mean? When people say viral they can mean a lot of different things. It’s often a synonym for popular. People will say, “Look at this viral video”, when really it was something released by Taylor Swift or something like that. Something that’s a little bit closer to what I think of as viral, is something that’s not being promoted by a celebrity and that you wouldn’t ordinarily think is going to become very popular. Closer still — and […]

Science Art: D ß ist der schneck auß dem grund…, by Albrecht Duerer, from Four Books on Measurement (Underweysung der Messung mit dem Zirckel und Richtscheyt)

26 January 2015 // 0 Comments

Click to embiggen The full title of this appears to be: “D ß ist der schneck auß dem grund auf gezogen/mit allen notwendigen linien drauß er gemacht wirdet,” or “This is the spiral from the plan drawn into the room, with all necessary construction lines.” It’s from a volume on making three-dimensional shapes out of numbers.

Gödel music composition to debut at Gödel Prize celebration.

8 July 2014 // 0 Comments

Nature has more on the suitably self-recursive premiere of a uniquely mathematical piece of music: The piece, “The Hilbert Heartbreak Hotel” by Danish composer Niels Marthinsen, was the brainchild of computer scientist Thore Husfeldt of Lund University in Sweden and IT University of Copenhagen. “I probably have some latent frustration about the increasing fragmentation of the arts and sciences,” Husfeldt says, “so maybe it’s an attempt to bring together some strands of culture that I happen to enjoy very much.” … Marthinsen was a student of the Danish composer Per Nørgård, who in the 1960s explored the use of mathematics in composition with, for example, series of notes with the fractal-like property of self-similarity. So Marthinsen was a natural choice for commissioning the piece. “He said: ‘This is completely insane and I don’t have time at all, but of course we have to do it.’” Husfeldt recalls. “From there, the puzzle was to actually make […]

Ant colonies are smarter than Google.

27 May 2014 // 0 Comments

When it comes to finding new information, The Independent reports, those crazy, criss-crossing paths that ants take are more efficient than Google at processing new information: The joint Chinese-German study, which is published in Proceedings of the National Academy of Sciences, found that while individual “scout” ants may seem “chaotic” in their movements, they are leaving a trail of pheromones to allow following “gathering” ants to refine and shorten their journeys to food sources in the vicinity of the colony. As this journey is repeated again and again by worker ants carrying their loads, a “self-reinforcing effect of efficiency” creates a shorter trail, saving the colony the time and energy of “continued chaotic foraging”. “While single ants can appear chaotic and random-like, they very quickly become an ordered line of ants crossing the woodland floor in the search for food,” co-author of the study Professor Jurgen Kurths told The Independent. He added: “That transition between […]

1 in 25 Death Row inmates don’t belong there.

30 April 2014 // 0 Comments

Or so says a new analysis published in Nature. That’s 4% of condemned people who would be exonerated given enough time: Few convictions result in an exoneration, most of those convicted never manage to prove their innocence and many cases do not have their final outcomes recorded, so data are not available to researchers. Innocent people also frequently plead guilty in the hope of reducing their sentence, effectively eliminating themselves from any analysis. Therefore, quantifying exonerations is the only way to get a glimpse of the extent of wrongful convictions, says lead author Samuel Gross, a criminologist at the University of Michigan Law School in Ann Arbor. Gross and his colleagues analysed the rate of exonerations among prisoners on death row, whose outcomes are carefully tracked by the US Bureau of Justice Statistics in Washington DC. In a previous report, the researchers found that less than 0.1% of prison sentences are death sentences, yet capital […]

So a shark, a hunter-gatherer and a honeybee walk into a bar…

31 December 2013 // 0 Comments

…and they way they move, ScienceDaily says follows the same mathematical pattern: A mathematical pattern of movement called a Lévy walk describes the foraging behavior of animals from sharks to honey bees, and now for the first time has been shown to describe human hunter-gatherer movement as well. The study, led by University of Arizona anthropologist David Raichlen, was published today in the Proceedings of the National Academy of Sciences. The Lévy walk pattern appears to be ubiquitous in animals, similar to the golden ratio, phi, a mathematical ratio that has been found to describe proportions in plants and animals throughout nature. “Scientists have been interested in characterizing how animals search for a long time,” said Raichlen, an associate professor in the UA School of Anthropology, “so we decided to look at whether human hunter-gatherers use similar patterns.” … The Lévy walk, which involves a series of short movements in one area and then a […]

Polynesian polynomials? Islanders counted in binary.

17 December 2013 // 0 Comments

Nature has more on the math whizzes of the South Pacific: Binary arithmetic, the basis of all virtually digital computation today, is usually said to have been invented at the start of the eighteenth century by the German mathematician Gottfried Leibniz. But a study now shows that a kind of binary system was already in use 300 years earlier among the people of the tiny Pacific island of Mangareva in French Polynesia. The discovery, made by analysing historical records of the now almost wholly assimilated Mangarevan culture and language and reported in Proceedings of the National Academy of Sciences1, suggests that some of the advantages of the binary system adduced by Leibniz might create a cognitive motivation for this system to arise spontaneously, even in a society without advanced science and technology. Pure binary arithmetic works in base 2 rather than the conventional base 10, which many cultures have adopted possibly as a consequence of […]

Some critters are so small, they can’t make a species.

9 August 2013 // 0 Comments

That’s the argument Laboratory Equipment describes some mathematical taxonomists (there’s a discipline for you) are making – claiming that some kinds of plankton are individually so small and so *weird*, they’re impossible to divide into different species: A new mathematical theory from the Univ. of Bath is challenging one of the most basic ideas of biology: that the concept of a “species” applies to all creatures. In a paper, published in the Proceedings of the Royal Society B: Biology, an interdisciplinary team of scientists, including mathematician Tim Rogers, outline findings from a recent study into the mathematics of biodiversity. Small organisms, measuring less than one millimeter, form the bedrock of the global ecosystem and their diversity is crucial for ecological health and stability. With recent advances in genetic sequencing technology, ecologists had hoped to be able to count the number of different species of such creatures by looking for groups of organisms with similar genomes. […]

SONG: “Beautiful People” (a penitential Books cover)

9 June 2013 // 0 Comments

SONG: “Beautiful People” (penitential cover) [Download] (To download: double right-click & “Save As”) ARTIST: grant. SOURCE: This is a cover (a late one) making up for a late song in April. Now, I owe one more cover for May. Mea maxima culpa. This song was written by the curiously academic and oddly moving Books. ABSTRACT: I was searching for songs about science and this came up. What a peculiar and brilliant artifact – a math rock/electronica hymn to tangrams. I sort of fixated on the hymn part, and thought about what might happen if The Books were ever invited to A Prairie Home Companion, which is where I hear most of my songs of praise nowadays. It became kind of important to me that this be done all acoustically. I had a church organ part for the second chorus sprouting in my head, but since I don’t have a church organ in my living room […]

Science Art: Bodendruckapparat nach Pascal by Max Kohl

10 March 2013 // 0 Comments

Click to embiggen This is an illustration of a model of a paradox – they hydrostatic paradox, as demonstrated by Blaise Pascal. The paradox is that the pressure at the bottom of a column of water only depends on the height of the water, not the shape or the volume. Six tons of water and six ounces of water will exert the same pressure if they’re each in a vessel that’s only a foot tall. And, if you connect any vessels together, regardless of their shape, they’ll fill with water up to the same level. The big vessel won’t force water further up the small one. Seems weird. There’s a better explanation of what’s happening here. Max Kohl’s engraving I found on Wikimedia Commons.

Finding the influential few. In medicine, in politics, and in social networks….

19 February 2013 // 0 Comments

Nature looks at the star power of “network theory,” curious statistics that control all kinds of complicated systems. They’ve found that even really complex networks are shaped by an influential few: To demonstrate their technique, Yang-Yu Liu of Northeastern University in Boston and his colleagues looked at the entire human metabolic network and found that concentrations of about 10% of the body’s 2,763 metabolites could be used to determine the levels of all the rest. But the method could also be used in social networks to identify the people whose opinions determine everyone else’s, helping to predict the outcome of, say, a presidential election. Or it could help ecologists to single out the particular species to track to follow changes in an entire ecosystem, to name just a few potential applications. … Liu’s team tackled the problem by examining clusters of strongly connected components in a network, again represented by nodes with arrows connecting them. […]

Space statistics: Martian astronauts would see a 1-megaton collision

19 December 2012 // 0 Comments

MIT Technology Review crunches the numbers and figures that anyone who spends three years on Mars is going to witness an H-bomb-sized asteroid collision: Today. William Bruckman and pals at the University of Puerto Rico at Humacao do exactly this kind of analysis but with a twist. They derive impact probabilities for Earth but also for Mars. Their conclusion is that astronauts visiting Mars for just a few years are likely to witness a significant asteroid impact. … Their model suggests that Tunguska-type events of around 10 megatons should occur roughly once a century and smaller 1 megaton events once every 15 years. They say that both these predictions are compatible with crater counts and most other estimates. Emboldened by this success, they apply the same model to Mars, where impact rates are likely to be higher because of its proximity to the asteroid belt. Here’s the interesting part: these guys calcaulte that Mars experiences […]

Science Art: Jungle Allure by Diane Walker

26 August 2012 // 0 Comments

This painting was one of the winners of the Benoit Mandelbrot Fractal Art Contest 2007, a mathematical art contest. I suppose nowadays, fractal art seems very, very 1990s. But still – there’s something fun and dreamlike about it. As Dr. Mandelbrot himself says in his introduction to the gallery: “What distinguishes fractal geometry within mathematics is an exceptional and uncanny characteristic. Its first steps are not tedious, hard, and unrewarding, but playful and extraordinarily easy, and provide rich reward in terms of stunning graphics. To the mathematician, they bring a bounty of very difficult conjectures that no one can solve. To the artist, they provide backbones around which imagination can play at will. To everyone, a few steps in about any direction bring extraordinary pleasure. Nothing is more serious than play. Let’s all play.”

If you were an MIT math student, you’d fix the lottery too.

10 August 2012 // 0 Comments

Boston Globe blows the lid off an M.I.T. syndicate that appears to have made a cool $8 million fixing the lottery: [Massachusetts Inspector General Gregory W.] Sullivan’s report details the way a handful of math and science wizards, including Massachusetts Institute of Technology undergraduates looking for an interesting school project, turned Cash WinFall into a nearly fulltime business, spending $40 million on tickets over a seven-year period and winning an estimated $48 million. And lottery officials were happy about the huge sales to these sophisticated gamblers, bending and breaking lottery rules to allow them to buy hundreds of thousands of the $2 tickets, Sullivan found. If anything, lottery officials were envious, with one supervisor asking in an e-mail: “How do I become part of the club when I retire?” The scheme revolved around using large numbers of ticket sales to trigger a period in which the odds of winning big increased. At least, as far […]

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