An eternity of infinities (via) [more inside]
posted by kliuless on Feb 2, 2013 - 23 comments

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]
posted by kliuless on Dec 1, 2012 - 19 comments

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]
posted by kliuless on Jul 21, 2012 - 78 comments

The trend of mathematics and physics towards unification provides the physicist with a powerful new method of research into the foundations of his subject, a method which has not yet been applied successfully, but which I feel confident will prove its value in the future. The method is to begin by choosing that branch of mathematics which one thinks will form the basis of the new theory. One should be influenced very much in this choice by considerations of mathematical beauty. [1939] [more inside]
posted by smcg on Apr 28, 2012 - 8 comments

Mark Taylor. Reform the PhD system or close it down. Nature 472, 261 (2011) [more inside]
posted by jeffburdges on Apr 26, 2011 - 54 comments

A brief tour of the mysteriously universal laws of mathematics and nature. [more inside]
posted by kliuless on Oct 24, 2010 - 33 comments

Nature by Numbers is a new animated short film by Cristóbal Vila (previously) inspired by some mathematical constructs found in nature. (via)
posted by gruchall on Mar 23, 2010 - 7 comments

Hunting the Hidden Dimension. You may be familiar with fractals, but in this PBS Nova episode, divided online into 5 parts, fractals go beyond the impossible zoom of the Mandelbrot set. Scientists are using fractals to describe complex natural occurrences, like lava, capillaries, and rain forests. In part 5, scientists measure one tree in the rain forests, and the distribution of small and large branches mirror the distribution of small and large trees. Fractals, it seems, are nature.
posted by plexi on Nov 2, 2008 - 43 comments