Mathematics

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The dust library - physics-math - 03 January 2012. Read full article Continue reading page |1|2 Specks of dust are as unique as snowflakes – but no one had ever paid much attention to what individual particles are made of.

The dust library - physics-math - 03 January 2012

Until now THE dusty old library is a bit of a cliché. But take away all the books and you are left with something rather interesting, in its own small way. Welcome to the dust library. Dust means different things to different people. Dust is hugely diverse. Our knowledge of dust is also diverse, if a little haphazard. As with many great scientific breakthroughs, this one was serendipitous. "Usually, if you see dust, you avoid it," says Katherine Cilwa, then a graduate student in Coe's lab and now at the University of Michigan, Ann Arbor.

So what can this unusual library tell us? Anyone counting will also have noticed that there are already more components than particles. New Scientist Not just a website! More From New Scientist Stephen Hawking's new theory offers black hole escape (New Scientist) Promoted Stories. Is It Time to Overhaul the Calendar? Forget leap years, months with 28 days and your birthday falling on a different day of the week each year.

Is It Time to Overhaul the Calendar?

Researchers at Johns Hopkins University in Maryland say they have a better way to mark time: a new calendar in which every year is identical to the one before. Their proposed calendar overhaul — largely unprecedented in the 430 years since Pope Gregory XIII instituted the Gregorian calendar we still use today — would divvy out months and weeks so that every calendar date would always fall on the same day of the week. Christmas, for example, would forever come on a Sunday. "The calendar I'm advocating isn't nearly as accurate" as the Gregorian calendar, said Richard Henry, an astrophysicist at Johns Hopkins who has been pushing for calendar reform for years.

"But it's far more convenient. " New versus old The trouble with designing a nice, regular calendar is that each Earth year is 365.2422 days long, leaving extra snippets of time that don't fit nicely into a cycle of 24-hour days. A Fun DIY Science Goodie: Proof Yourself against Sensationalized Stats. For my book Brain Trust, I interviewed Keith Devlin, NPR’s “Math Guy,” a World Economic Forum fellow, and math professor at Stanford.

A Fun DIY Science Goodie: Proof Yourself against Sensationalized Stats

And being a mathematician, Devlin thinks about things differently than the world at large. For example, in his very good monthly column Devlin’s Angle, he quotes the following problem, originally designed by puzzle master Gary Foshee: “I tell you that I have two children, and that (at least) one of them is a boy born on Tuesday. What probability should you assign to the event that I have two boys?” Does this sound like a bunch of confounding mumbo jumbo meant to obscure the obvious fact that the other kid has exactly 50/50 chance of being a boy and so if one kid’s definitely a boy, the probability of them both being boys is one in two? Yes, yes it does.

But that’s not the case. Without the “Tuesday” part, this is a famous problem first published in Scientific American by the venerable mathematician and puzzler Martin Gardner. Yikes. Cool so far? The High-Stakes Math Behind the West's Greatest River. Ultimate Fighting vs. math: no holds barred - Ideas. Burning Desire for Efficiency. Ever wonder how efficient it is to heat water?

Burning Desire for Efficiency

Of course you have! Ever measured it? Whoa, mister, now you’ve gone too far! I recently devised a laser-phototransistor gauge to monitor my natural gas meter dial—like ya do. As a side benefit, I acquired good data on how much energy goes into various domestic uses of natural gas. Heating Basics The amount of energy it takes to heat water is so well-established, that it is the basis for several prominent units of energy. So if I want to take 500 mℓ of water from 18°C to boiling, I need to expend 82×0.5 kcal to get the job done, or 171.6 kJ.

Measuring the Gas My natural gas meter usually receives little attention from me—which is saying something for a person as measurement/data crazed as myself. Rather than parking myself outside for days on end to keep track of my gas gauge, I bought a cat-toy laser pointer and modified it to be powered by a constant 5-volt power supply. Contraption attached to gas meter. Stove-top Boil I was surprised. An Adventure in the Nth Dimension. On the mystery of a ball that fills a box, but vanishes in the vastness of higher dimensions Brian Hayes The area enclosed by a circle is πr2. The volume inside a sphere is 4/3πr3. These are formulas I learned too early in life. Having committed them to memory as a schoolboy, I ceased to ask questions about their origin or meaning. Some 50 years after my first exposure to the formulas for area and volume, I have finally had occasion to look into these broader questions. In those childhood years when I was memorizing volume formulas, I also played a lot of ball games.

The mathematician Richard Bellman labeled this effect “the curse of dimensionality.” A few months ago I was preparing an illustration of Bellman’s curse for an earlier Computing Science column. In the end I chose a different and simpler scheme for the illustration. (In this context “ball” is not just a plaything but also the mathematical term for a solid spherical object. But what about the n-ball? Seven equations that rule your world - physics-math - 13 February 2012.

Essay: Nature's Secrets Foretold. By now, all aficionados of physics news — and quite a few people who don’t know physics from phonics — have heard about the discovery of the Higgs boson.

Essay: Nature's Secrets Foretold

It’s the biggest news in physics ever tweeted. And it came after a long wait. For more than three decades, the Higgs has been physicists’ version of King Arthur’s Holy Grail, Ponce de Leon’s Fountain of Youth, Captain Ahab’s Moby Dick. It’s been an obsession, a fixation, an addiction to an idea that almost every expert believed just had to be true. But despite years of searching, using the most complex machines ever built on the planet, the Higgs remained as elusive as a World Series ring for a Chicago Cub.

Asked why the Higgs boson is so important, most physicists reflexively respond that it’s a piece of the cosmic substance that endows elementary particles with mass. In fact, the Higgs is responsible for the structure of the universe as we know it. In essence, the Higgs field split the electro­weak force’s personality. Mathematics: Mapping a fixed point. 22.11.11 - For fifty years, mathematicians have grappled with a so-called “fixed point” theorem.

Mathematics: Mapping a fixed point

An EPFL-based team has now found an elegant, one-page solution that opens up new perspectives in physics and economics. Take a map of the world. Now put it down on the ground in Central Park, against a rock on Mount Everest, or on your kitchen table; there will always be a point on the map that sits exactly on the actual physical place it represents. Obvious? Not for mathematicians. Think outside the map Surprisingly, this theorem works for all kinds of maps, from a diagram of a metro route to a map of spaces used in quantum physics.

The challenge for the mathematicians was to find that fixed point. Turning the page In 2008, a thirty-page article, full of technical jargon, almost arrived at a proof. Source:A fixed point theorem for L1 spaces, U. Link: On Points. Tallis in Wonderland Raymond Tallis pinpoints the mathematics/reality divide.

On Points

Readers of this column will have had a hint of my views on the limitations of the ability of maths and physics to capture lived experience – in particular in ‘Time, Tense and Physics: The Theory of Everything But…’ in Issue 81. Here, I want to focus on something absolutely central to the interpretation of the world in which we live in terms of mathematics: the notion of a point – in particular, a point in space.

Points, which lie at the heart of the mathematisation of space (and, subsequently, of space-time), achieved this elevated status via the discipline of geometry. Those of you who remember your early encounters with Euclid may recall, amidst memories of fear, humiliation, boredom and the other accompaniments of the pedagogic experience, that Euclid begins with a series of definitions and axioms. Wrinkled doughnut solves geometrical mystery - physics-math - 30 April 2012. This may be the weirdest doughnut you have ever seen, but it solves a long-standing geometrical puzzle that evaded mathematicians including Nobel laureate John Nash, who inspired the film A Beautiful Mind.

Wrinkled doughnut solves geometrical mystery - physics-math - 30 April 2012

Topology is the branch of mathematics concerned with the geometric deformations of objects. According to its rules, a certain type of flat square - in which opposite edges have been mathematically linked - is equivalent to a holed-doughnut, or torus, because one can easily be turned into the other. First, form a cylinder by joining the top edge of the square to the bottom edge, then bend that cylinder into a circle and join its two open ends. There is just one problem: for the two ends to meet, the torus must be stretched in a way that distorts the original shape of the square. Any horizontal lines on the original square will be stretched on the torus, while vertical lines will remain the same. Molecular doughnut 3D printout The method of wrinkling is known as convex integration theory. Font for digits lets numbers punch their weight - physics-math - 12 May 2012. THE symbols we use to represent numbers are, mathematically speaking, arbitrary.

Font for digits lets numbers punch their weight - physics-math - 12 May 2012

Now there is a way to write numbers so that their areas equal their numerical values. The font, called FatFonts, could transform the art of data visualisation, allowing a single infographic to convey both a visual overview and exact values. "Scientific figures might benefit from this hybrid nature because scientists want both to see and to read data," says Miguel Nacenta, a computer scientist at the University of St Andrews, UK, who developed the concept with colleagues at the University of Calgary, Canada.

Infographics are all the rage as a means to display information now that computers can gather and sort vast reams of data. However, fancy charts and images often obscure the actual data behind them. For single digit numbers, this was fairly straightforward. To represent numbers with multiple digits, the team devised a system of nested digits. New Scientist Not just a website! More From New Scientist. How to Beat the Odds at Judging Risk. In Their Prime: Mathematicians Come Closer to Solving Goldbach's Weak Conjecture. One of the oldest unsolved problems in mathematics is also among the easiest to grasp.

In Their Prime: Mathematicians Come Closer to Solving Goldbach's Weak Conjecture

The weak Goldbach conjecture says that you can break up any odd number into the sum of, at most, three prime numbers (num­bers that cannot be evenly divided by any other num­ber except themselves or 1). For example: 35 = 19 + 13 + 3 or 77 = 53 + 13 + 11 Mathematician Terence Tao of the University of California, Los Angeles, has now inched toward a proof. He has shown that one can write odd numbers as sums of, at most, five primes—and he is hopeful about getting that down to three. The weak Goldbach conjecture was proposed by 18th-century mathematician Christian Goldbach.

Mathematicians have checked the validity of both statements by computer for all numbers up to 19 digits, and they have never found an exception. Next, Tao hopes to extend his approach and show that three primes suffice in all cases. The Search for a More Perfect Kilogram. The perfect kilogram is getting lighter. Can science find a better measure? Photo: Christopher Griffith; kilogram models by Jim Zivic The official US kilogram — the physical prototype against which all weights in the United States are calibrated — cannot be touched by human hands except in rare circumstances.

Sealed beneath a bell jar and locked behind three heavy doors in a laboratory 60 feet under the headquarters of the National Institute of Standards and Technology 20 miles outside Washington, DC, the shiny metal cylinder is, in many ways, better protected than the president. “Everything is a potential contaminant,” says Patrick Abbott, a NIST physicist responsible for maintaining it. The American prototype is one of some four dozen such national standards around the world, and each of those, in turn, is accountable to an even higher authority: a regal artifact called the international prototype kilogram.

This state of affairs is intolerable to the guardians of weights and measures. Agreement to tie kilogram and friends to fundamentals - physics-math - 25 October 2011. After decades of worry, toil and argument, metrologists have officially begun the process of tying the definitions of four basic units to nature's fundamental constants. The General Conference on Weights and Measures (CGPM) in Paris, France, has unanimously agreed on a proposal that would lead to reform of the mole, kilogram, kelvin and ampere, according to the international system of units (SI). That puts us on the cusp of a historic change in the way science sizes up the world.

If the next CGPM, in four years' time, confirms the plan, it will amount to the biggest change to the SI units for a century. Proponents of the switch are thrilled. "Not a single vote against! Metal shock Nearly all measurements we make are ultimately based on the SI, with a chain of laws and rules leading back to just seven base units.

The first sign that the SI was flawed was noticed in 1949 in a check on a lump of metal kept inside a vault at the International Bureau of Weights and Measures (BIPM) in Paris.