World Cup 2010 prediction — here comes the science

(drumroll …)

And sophisticated analysis of Netherlands’ and Spain’s tactics predict a Spanish win this Sunday at Soccer City Stadium.

From the link:

Mathematicians and football supporters Dr Javier López Peña and Dr Hugo Touchette from Queen Mary, University of London have collected ball passing data from all of the FIFA World Cup games and analysed it to reveal the nations’ different styles of play.

Using the mathematical technique called Graph Theory, they have revealed the gaping holes in England’s tactics against Germany game and made predictions about the Netherlands-Spain final that could rival the psychic octopus.

For each national side, Drs López Peña and Touchette have drawn up a ‘network’ of passes between players throughout the tournament and analysed how these networks compare between teams. Dr Touchette explains: “Each player in the network is given a score called centrality which measures how vital they are to the network. The higher the centrality score, the bigger the impact if that player wasn’t there. This method is most commonly used to make computer networks more robust, but it can also be used to plan football strategy.”

Multiple choice theories of everything

Back in January I blogged about “the most beautiful structure in mathematics,” the basis of a physics theory-of-everything proposed by Garrett Lisi, That theory is part of an article on “Knowing the mind of God” at NewScientist outlining seven different theories of everything.

From the last link, more on Lisi’s concept”

E8

In 2007 the physicist (and sometime surfer) Garrett Lisi made headlines with a possible theory of everything.

The fuss was triggered by a paper discussing E8, a complex eight-dimensional mathematical pattern with 248 points. Lisi showed that the various fundamental particles and forces known to physics could be placed on the points of the E8 pattern, and that many of their interactions then emerged naturally.

Some physicists heavily criticised the paper, while others gave it a cautious welcome. In late 2008, Lisi was given a grant to continue his studies of E8.

And here’s the article’s synopsis of string theory, one of the better known ideas out there:

String theory

This is probably the best known theory of everything, and the most heavily studied. It suggests that the fundamental particles we observe are not actually particles at all, but tiny strings that only “look” like particles to scientific instruments because they are so small.

What’s more, the mathematics of string theory also rely on extra spatial dimensions, which humans could not experience directly.

These are radical suggestions, but many theorists find the string approach elegant and have proposed numerous variations on the basic theme that seem to solve assorted cosmological conundrums. However, they have two major challenges to overcome if they are to persuade the rest of the scientific community that string theory is the best candidate for a ToE.

First, string theorists have so far struggled to make new predictions that can be tested. So string theory remains just that: a theory.

Secondly, there are just too many variants of the theory, any one of which could be correct – and little to choose between them. To resolve this, some physicists have proposed a more general framework called M-theory, which unifies many string theories.

But this has its own problems. Depending how you set it up, M-theory can describe any of 10⁵⁰⁰ universes. Some physicists argue that this is evidence that there are multiple universes, but others think it just means the theory is untestable.

Get a free online education with Khan Academy

I came across this post at Metamodern discussing a very interesting, and utile, online resource — Khan Academy. If you’re looking for short, to-the-point online lessons (more than 1000) on mathematics ranging from basic arithmetic and algebra to differential equations, physics, chemistry, biology and finance, this is a great resource.

From the first link:

I got a pointer to a free, online educational resource today.

It deserves more attention.

The eyeballs of a few million students might be a good start. Students in elementary school, grad school, rural Africa… places like that.

It consists of 1000+ brief lectures on YouTube.

It centers on math, but goes beyond.

” … perhaps the most beautiful structure in mathematics.”

Via KurzweilAI.net — Do hit the “Read Original Article” link for this entire interesting intersection of mathematics, string theory and practical physics.

Most beautiful math structure appears in lab for first time

New Scientist Physics & Math, Jan. 7, 2010 A complex form of mathematical symmetry linked to string theory has been glimpsed in the real world for the firsttime, in laboratory experiments on exotic crystals. The structure is also the basis for another proposed theory of everything advanced in 2007 by surfer-physicist Garrett Lisi, who refers to E8 as “perhaps the most beautiful structure in mathematics“. Read Original Article>>

From the New Scientist link:

Radu Coldea of the University of Oxford and his colleagues chilled a crystal made of cobalt and niobium to 0.04 °C above absolute zero. Atoms in the crystal are arranged in long, parallel chains. Because of a quantum property called spin, electrons attached to the atom chains act like tiny bar magnets, each of which can only point up or down.

Strange things occurred when the experimenters applied a powerful 5.5-Tesla magnetic field perpendicular to the direction of these electron “magnets”. Patterns appeared spontaneously in the electron spins in the chains – in a simplified example with three electrons, the spins could read up-up-down or down-up-down, among other possibilities. Each distinct pattern has a different energy associated with it.

The ratio of these different energy levels showed that the electron spins were ordering themselves according to mathematical relationships in E8 symmetry.

Happy Pi day!

No not this sort of pie —

This sort of pi —

3.14159265358979323846264338327950288419716939937510
  58209749445923078164062862089986280348253421170679
  82148086513282306647093844609550582231725359408128
  48111745028410270193852110555964462294895493038196
  44288109756659334461284756482337867831652712019091
  45648566923460348610454326648213393607260249141273
  72458700660631558817488152092096282925409171536436
  78925903600113305305488204665213841469519415116094
  33057270365759591953092186117381932611793105118548
  07446237996274956735188575272489122793818301194912
  98336733624406566430860213949463952247371907021798
  60943702770539217176293176752384674818467669405132
  00056812714526356082778577134275778960917363717872
  14684409012249534301465495853710507922796892589235
  42019956112129021960864034418159813629774771309960
  51870721134999999837297804995105973173281609631859
  50244594553469083026425223082533446850352619311881
  71010003137838752886587533208381420617177669147303
  59825349042875546873115956286388235378759375195778
  18577805321712268066130019278766111959092164201989

For anyone terminally confused at this point, here's the Wikipedia page for pi.

Okay -- couldn't leave this crazy video off this post ...

Invisibility cloak, part six

I’ve done plenty of blogging on cloak of invisibility tech, and here’s the latest news from PhysOrg.

From the second link:

A paper published in the March 2009 issue of SIAM Review, “Cloaking Devices, Electromagnetic Wormholes, and Transformation Optics,” presents an overview of the theoretical developments in cloaking from a mathematical perspective.

One method involves light waves bending around a region or object and emerging on the other side as if the waves had passed through empty space, creating an “invisible” region which is cloaked. For this to happen, however, the object or region has to be concealed using a cloaking device, which must be undetectable to electromagnetic waves. Manmade devices called metamaterials use structures having cellular architectures designed to create combinations of material parameters not available in nature.

Mathematics is essential in designing the parameters needed to create metamaterials and to show that the material ensures invisibility. The mathematics comes primarily from the field of partial differential equations, in particular from the study of equations for electromagnetic waves described by the Scottish mathematician and physicist James Maxwell in the 1860s.

One of the “wrinkles” in the mathematical model of cloaking is that the transformations that define the required material parameters have singularities, that is, points at which the transformations fail to exist or fail to have properties such as smoothness or boundness that are required to demonstrate cloaking. However, the singularities are removable; that is, the transformations can be redefined over the singularities to obtain the desired results.