A beginners guide to the galaxy

Admittedly, I have no idea about Quantum Gravity, apart that some physicists like their universe to be rather bubbly than stringy ( or just the other way around: more stringy than loopy, like Leonhard in Series 2 Episode 2 of “Big Bang Theory“).

But the caption of the above movie from the Max-Planck Institute for Gravitational Physics in Potsdam/Golm says (quote) “The following sequence visualises the quantum evolution of geometry in Loop Quantum Gravity. The colours of the faces of the tetrahedra indicate where and how much area exists at a given moment of time. The movie illustrates how these excitations of geometry change as dictated by the Quantum Einstein Equations. Technically, the faces form a complex dual to the graph of a spin network state and the colour shows the amount of spin (area) with which the edges of the graph area are charged.” (end quote).
Wow – a combination of words like evolution, network, graph, spin, state, geometry and tetrahedra in a few lines and you have my full attention! Although it was bound to appear on my radar at some point, I don’t quite see the exact connection with biomolecular networks and structures clearly – yet. Nevertheless, it’s either watching the visualisation for mere aesthetic reasons or digging deeper with the aid of “Loop and Spin Foam Quantum Gravity: A Brief Guide for Beginners” – by Hermann Nicolai, a string theorist and director of the Quantum Gravity and Unified Theories department at the MPI for Gravitational Physics / Albert Einstein Institute. The visualisation is available for download on their pages.

Actually I was looking into the topic of k-dimensional embedding (with k<=3) and drawing of arbitrary graphs when I came across all the links on quantum-physics.
I vividly remmeber a test on theoretical computer science where we had (as an exercise) to draw a 4D hypercube – points given for logically, but not necessarily geometrically correct solutions. Here is a nice 4D Hypercube Rotation / Projection

It's also very instructive to see it the other way around – these animations are do just that and take you from from 0 to 6D in under 2 minutes:

While we are into mind-twisting geometry: here's "How to Turn a Sphere Inside Out"

And some cool animations of the Klein Bottle, which is a more complex moebius strip:

A real version made of glass appears in this TED-Talk by Clifford Stoll on … everything.

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  1. #1 by cistronic on 2012/02/17 - 14:25

    Niles Johnson (Department of Mathematics, University of Georgia) visualized 7-dimensional spheres.
    Some of the structures in the end are reminiscent of higher-order chromatin organisation (nucleosome and 30nm fibres … ) – probably just a case of biased perception (“deformation prof’essionelle”) ?

    found via Schockwellenreiter

  2. #2 by cistronic on 2012/10/13 - 12:41

    Nine chapters, two hours of maths, that take you gradually up to the fourth dimension. Mathematical vertigo guaranteed! Background information on every chapter:


  1. Everything and Nothing « cistronic

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