Post #119

Some notes on visualization of the graphs Stephen Wolfram, creator of Wolfram language, recently made a post Finally We May Have a Path to the Fundamental Theory of Physics… and It’s Beautiful, where he discusses possible origins of how the universe operates. I think the crux of his idea is that if you consider interactions between objects as a graph and then say how from some interactions appear new interactions you can get beautifully looking graphs that look like some 3D shapes which can represent our universe in the limit and therefore you can analyze properties of these graphs such as diameter or curvature to find equivalent notions in physics. I won't speculate whether this post is theoretically-sound or not, let physicists debate, in the end any new theory should predict new facts which we need to wait, but one thing that is noticeable is that graphs that are drawn by Wolfram are beautiful. If you try to draw some big graphs you find that it very hard to draw it so that it does not look like a mess, but here you get pretty-looking networks that indeed remind you some known 3D shapes. Wolfram language has many layouts to draw graphs, which results in different images of the graph. From the shapes of the graphs in the post, it seems that he used SpectralEmbedding or SpringElectricalEmbedding layout. Daniel Spielman, professor at Yale and twice Turing award winner, has a nice popsci video where he discusses how these drawings are related to spectral graph theory and the conditions on the adjacency matrix to have a nice drawing. So maybe next time you will use some of these layouts to impress reviewers of your paper.