Science News


Mathematicians Create Objective Quality of Life Index PDF Print E-mail

The US comes second in a new quality of life index designed to be mathematically objective

Here's a thorny problem: to develop an objective way to rank countries according to the quality of life they offer their citizens.

There are various ways of approaching this problem. For example, the Economist Intelligence Unit compiles its quality of life index using surveys, a useful technique but one that is hard to show is objective. Another widely quoted index, the Life Quality Index is based on life expectancy at birth and the gross domestic product per person but is only able to rank countries by applying a correction factor for each country that some critics say is open to bias.

Is there another way? Andrei Zinovyev at the Institut Curie in Paris and Alexander Gorban at the University of Leicester in the UK think so, using a mathematical technique developed in the mid-90s that can cut through this kind of problem .

They chose several widely-measured and well-studied indices on which to base their index: GDP per capita, life expectancy at birth, infant mortality rate and the incidence of tuberculosis. This data from 2005 is available for 162 countries.

Zinovyev and Gorban then plot this data in four-dimensional space. To create a ranking, the important question is whether there is a linear function that reduces this four-dimensional dataset to a one-dimensional set. Unsurprisingly, the answer turns out to be no. "Any linear mapping will inevitably give strong distortions in one or other region of data space," they say. That's what makes this problem tricky.

However, in the mid-90s a group of mathematicians devised a technique for reducing the dimensionality of complex data sets. This technique is essentially equivalent to connecting various data points together with springs and allowing the system to relax; hence it's name: elastic mapping. The trick is to find an arrangement of springs that "flattens" the data set, or in other words, reduces its dimensionality.

And that's basically what Zinovyev and Gorban have done, creating what they call the Nonlinear Quality of Life Index in the process.

Here are the top and bottom 5 from 2005:

1. Luxembourg
2. USA
3. Norway
4. Ireland
5. Iceland
.
.
.
158. Zambia
159. Mozambique
160. Zimbabwe
161. Kenya
162. Swaziland

No real surprises there, although there are some interesting features of the list. For example Equatorial Guinea is ranked at 140 although its GDP per capita is more than Saudi Arabia's ranked at 37. That's because of Equatorial Guinea's appalling health statistics: 123 infant mortalities per 10,000 inhabitants, for example, compared to 21 in Saudi Arabia.

For similar reasons, Russia is ranked 71st despite having a GDP per capita that is significantly higher than other countries with a similar ranking.

Every list throws ups anomalies like this. The important point about this one is that it is done objectively and transparently.

That's important because these kinds of indices are widely used by economists and politicians as a measure of economic and social development and so used to determine spending polices and legislation.

Objectivity is hard to come by when making these kinds of decisions. If the people who matter would agree to use it, this index could help.

Ref: arxiv.org/abs/1008.4063: Nonlinear Quality of Life Index




Read more: http://feeds.technologyreview.com/click.phdo?i=ebc38b4dce144b3226db82650a7f2e0f

 
Rings 'n' Fingers PDF Print E-mail

The best of the rest from the Physics arXiv this week:

Lunar Palaeoregolith Deposits as Recorders of the Galactic Environment of the Solar System and Implications for Astrobiology

Toward A Quantitative Understanding of Gas Exchange in the Lung

Testing the No-Hair Theorem with Observations of Black Holes in the Electromagnetic Spectrum

About The Possible Role Of Hydrocarbon Lakes In The Origin Of Titan's Noble Gas Atmospheric Depletion

Distinguishing Left- And Right-Handed Molecules By Two-Step Coherent Pulses



Read more: http://feeds.technologyreview.com/click.phdo?i=d2761e00622842cf2323a4613f887444

 
The Mathematical Secret of Viking Jewellery PDF Print E-mail

A long-standing puzzle over the craftsmanship behind Viking bracelets and necklaces has finally been solved--mathematically

The beautiful bracelets and necklaces made by Viking artisans leave archaeologists with something of a conundrum. These objects are made from rods of gold and silver which have twisted together into double helices. The puzzle is the regularity of these helices, which are remarkably similar in jewellery found in places as diverse as Ireland, Scotland, the Orkney Islands and Scandinavia.

How could craftsmen have achieved this regularity in such disparate places?

The answer comes today thanks to the work of Kasper Olsen and Jakob Bohr at the Technical University of Denmark. They point out that two wires become maximally twisted when no more rotations can be added with deforming the double helix. They go on to demonstrate the properties of maximally twisted wires. (We looked at a similar but more detailed argument about the properties of old rope a few weeks back.)

Olsen and Bohr then measured the properties of helices in Viking jewellery are twisted. It should come as no surprise to find that Viking jewellery is maximally twisted, which neatly explains why it all looks so similar. "Maximally rotated geometry is universal and therefore independent of the skills of the craftsman," say Olsen and Bohr.

Problem solved.

Ref: arxiv.org/abs/1008.4306: Hidden Beauty in Twisted Viking Neck Rings



Read more: http://feeds.technologyreview.com/click.phdo?i=e8ebc043534a4bd37fa85ccfd42b6a98

 
The Mathematical Secret of Viking Jewelry PDF Print E-mail

A long-standing puzzle over the craftsmanship behind Viking bracelets and necklaces has finally been solved--mathematically.

The beautiful bracelets and necklaces made by Viking artisans leave archaeologists with something of a conundrum. These objects are made from rods of gold and silver which have twisted together into double helices. The puzzle is the regularity of these helices, which are remarkably similar in jewelry found in places as diverse as Ireland, Scotland, the Orkney Islands and Scandinavia.

How could craftsmen have achieved this regularity in such disparate places?

The answer comes today thanks to the work of Kasper Olsen and Jakob Bohr at the Technical University of Denmark. They point out that two wires become maximally twisted when no more rotations can be added with deforming the double helix. They go on to demonstrate the properties of maximally twisted wires. (We looked at a similar but more detailed argument about the properties of old rope a few weeks back.)

Olsen and Bohr then measured the properties of helices in Viking jewelry are twisted. It should come as no surprise to find that Viking jewelry is maximally twisted, which neatly explains why it all looks so similar. "Maximally rotated geometry is universal and therefore independent of the skills of the craftsman," say Olsen and Bohr.

Problem solved.

Ref: arxiv.org/abs/1008.4306: Hidden Beauty in Twisted Viking Neck Rings



Read more: http://feeds.technologyreview.com/click.phdo?i=e8ebc043534a4bd37fa85ccfd42b6a98

 
Fine Structure Constant Varies With Direction in Space, Says New Data PDF Print E-mail

A spatial variation in the fine structure constant has profound implications for cosmology

Over the years, many physicists have wondered whether the fundamental constants of nature might have been different when the universe was younger. If so, the evidence ought to be out there in the cosmos where we can see distant things exactly as they were in the past.

One thing that ought to be obvious is whether a number known as the fine structure constant was different. The fine structure constant determines how strongly atoms hold onto their electrons and so is an important factor in the frequencies at which atoms absorb light.

If the fine structure were different earlier in the universe, we ought to be able to see the evidence in the way distant gas clouds absorb light on its way here from even more distant objects such as quasars.

As it turns out, exactly this kind of evidence has emerged in the last ten years or so from studies of absorption spectra carried out with the Keck telescope in Hawaii. These indicate that the fine structure constant must have been smaller when the universe was younger. It's fair to say, however, that this evidence is controversial--other studies have not always corroborated the result.

That debate looks set to pale into insignificance compared to new claims being made about the fine structure constant. Today, John Webb at the University of South Wales, one of the leading proponents of the varying constant idea, and a few cobbers say they have new evidence from the Very Large Telescope in Chile that the fine structure constant was different when the universe was younger.

But get this. While data from the Keck telescope indicate the fine structure constant was once smaller, the data from the Very Large Telescope indicates the opposite, that the fine structure constant was once larger. That's significant because Keck looks out into the northern hemsiphere, while the VLT looks south

This means that in one direction, the fine structure constant was once smaller and in exactly the opposite direction, it was once bigger. And here we are in the middle, where the constant as it is (about 1/137.03599...)

That's a mind blowing result. One of the biggest conundrums that cosmologists face is explaining why the fundamental constants of nature seem fine tuned for life. If the fine structure constant were very different, stars and atoms wouldn't form and the universe as we know it couldn't exist. No theory explains why it takes the value it does which leaves scientists at a loss.

The implication from Webb and co's data is that the fine structure constant is continuously varying throughout space and is merely fine-tuned for life in this corner of the cosmos: the universe's habitable zone. Elsewhere, presumably well beyond the universe we can see, this constant is entirely different.

That's likely to put the cat among the pigeons. Webb is no stranger to controversy--he has had to fight tooth and nail to have his data and ideas accepted. But this time round, with such a radical new data on the table, the debate is likely to be fiercer still.

So sit back and enjoy the show.

Refs:

arxiv.org/abs/1008.3907: Evidence For Spatial Variation Of The fiFine Structure Constant

arxiv.org/abs/1008.3957: Manifestations Of A Spatial Variation Of Fundamental Constants On Atomic Clocks, Oklo,

Meteorites, And Cosmological Phenomena



Read more: http://feeds.technologyreview.com/click.phdo?i=96f99c9fa596f8e80e8914cbf6c64010

 
«StartPrev12345NextEnd»

Page 2 of 5