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17 posts tagged with physics *and* maths.

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## So, the unknowable kicks in

Logic hacking - "Writing shorter and shorter computer programs for which it's unknowable whether these programs run forever, or stop... the winner of the Busy Beaver Game for N-state Turing machines becomes unknowable using ordinary math - somewhere between N = 5 and N = 1919." [more inside]

## Famous Fluid Equations Are Incomplete

The Singular Mind of Terry Tao - "Imagine, he said, that someone awfully clever could construct a machine out of pure water. It would be built not of rods and gears but from a pattern of interacting currents." (via) [more inside]

## √2N

At the Far Ends of a New Universal Law

The law appeared in full form two decades later, when the mathematicians Craig Tracy and Harold Widom proved that the critical point in the kind of model May used was the peak of a statistical distribution. Then, in 1999, Jinho Baik, Percy Deift and Kurt Johansson discovered that the same statistical distribution also describes variations in sequences of shuffled integers — a completely unrelated mathematical abstraction. Soon the distribution appeared in models of the wriggling perimeter of a bacterial colony and other kinds of random growth. Before long, it was showing up all over physics and mathematics. “The big question was why,” said Satya Majumdar, a statistical physicist at the University of Paris-Sud. “Why does it pop up everywhere?”

## 21st Century Wiener

Norbert Wiener: The Eccentric Genius Whose Time May Have Finally Come (Again) - "The most direct reason for Wiener's fall to relative obscurity was the breakthrough of a young mathematician and engineer named Claude Shannon." [more inside]

## there is no soundtrack

Finite time blowup for an averaged three-dimensional Navier-Stokes equation - "[Terence Tao] has shown that in an alternative abstract universe closely related to the one described by the Navier-Stokes equations, it is possible for a body of fluid to form a sort of computer, which can build a self-replicating fluid robot that, like the Cat in the Hat, keeps transferring its energy to smaller and smaller copies of itself until the fluid 'blows up.' " [1,2,3] (previously)

## John Baez on the maths of connecting everyone (and everything) on earth

Network Theory Overview - "The idea: nature and the world of human technology are full of networks! People like to draw diagrams of networks. Mathematical physicists know that in principle these diagrams can be understood using category theory. But why should physicists have all the fun? This is the century of

*understanding living systems and adapting to life on a finite planet*. Math isn't the main thing we need, but it's got to be part of the solution... so one thing we should do is develop a unified and powerful theory of networks." (via ;)## binding the andat

Closing in on the twin prime conjecture (Quanta) - "Just months after Zhang announced his result, Maynard has presented an independent proof that pushes the gap down to 600. A new Polymath project is in the planning stages, to try to combine the collaboration's techniques with Maynard's approach to push this bound even lower." [more inside]

## This looks legit

Eric Weinstein has a PhD in mathematical physics from Harvard, but has spent most of the last 10 years outside academia working as an economic consultant for a New York hedge fund. Now he apparently has a new theory of everything that claims to be able to explain quantum gravity, dark matter and dark energy. Actual details have not yet been provided and some physicists are dismissive. But his work has received enthusiastic endorsement from Oxford's Simonyi Professor of Public Understanding Marcus du Sautoy, with whom he has been discussing the theory over the last two years. [more inside]

## the power and beauty of mathematics

## direct realism

The Nature of Computation - Intellects Vast and Warm and Sympathetic: "I hand you a network or graph, and ask whether there is a path through the network that crosses each edge exactly once, returning to its starting point. (That is, I ask whether there is a 'Eulerian' cycle.) Then I hand you another network, and ask whether there is a path which visits each node exactly once. (That is, I ask whether there is a 'Hamiltonian' cycle.) How hard is it to answer me?" (via) [more inside]

## noncommutative balls in boxes

Morton and Vicary on the Categorified Heisenberg Algebra - "In quantum mechanics, position times momentum does not equal momentum times position! This sounds weird, but it's connected to a very simple fact. Suppose you have a box with some balls in it, and you have the magical ability to create and annihilate balls. Then there's one more way to create a ball and then annihilate one, than to annihilate one and then create one. Huh? Yes: if there are, say, 3 balls in the box to start with, there are 4 balls you can choose to annihilate after you've created one but only 3 before you create one..." [more inside]

## from complexity, universality

## Symmetry. Shakespeare. Islamic medicine. Creative writing challenges.

Symmetry. Shakespeare. Islamic medicine. Creative writing challenges. Four podcast series from University of Warwick.

## Science

Free Science and Video Lectures Online A nice blog collecting science videos. The most recent post on Cognitive Computing, Consciousness, Science Philosophy and Mind Video Lectures has some hum-dingers.

## Math You Don't Know, and Math You Didn't Know You Didn't Know.

Jim Loy's Mathematics Page is (among other things) a collection of interesting theorems (like Napoleon's Triangle theorem), thoughtful discussions of both simple and complex math, and geometric constructions (my personal favorite); the latter of which contains surprisingly-complex discussions on the trisection of angles, or the drawing of regular pentagons.

Similarly enthralling are the pages on Billiards (and the physics of), Astronomy (and the savants of), and Physics (and the Phlogiston Theory of), all of which are rife with illustrations and diagrams. See the homepage for much more.

If you like your geometric constructions big, try Zef Damen's Crop Circle Reconstructions.

Similarly enthralling are the pages on Billiards (and the physics of), Astronomy (and the savants of), and Physics (and the Phlogiston Theory of), all of which are rife with illustrations and diagrams. See the homepage for much more.

If you like your geometric constructions big, try Zef Damen's Crop Circle Reconstructions.

## Java applets to help visualize various concepts in math, physics, and engineering

## Yo, books!

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