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Lorentz and rotational symmetries from many interweaving grids

I noticed that Wolfram said in the live-streams that you need to have random connections as opposed to a grid-like structure in order to achieve the Euclidean non-Manhattan distances. But I think actually you could instead just use a very large number of interweaving grids that are connected to each other in such a way that they each represent different angles of rotation while maintaining the same scale, which can actually be achieved by simple local rules on graphs. The easiest case is a 2D Euclidean space. The following drawing shows an example of how you could connect two grids such that they have the same scale: example of how to connect two grids If you now keep on adding a very large number of rotated grids at positive and negative angles that are irrational numbers with relation to pi, then the graph can approximate a 2D Euclidean space on the large scale. You can easily make a similar analogous construction to obtain a 2D Minkowski space-time with the Lorentz symmetries. Note that this leads to a density of nodes that could be an astronomical number per plank cube, while the length of the edges could just be the plank length itself. Such 2D spaces that already contain rotational and Lorentz symmetries could then be used as building blocks to generate a 4D space time, but this would be more complicated and I would not be surprised if quantum phenomena emerge from these complications.

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It is not obvious to me how you would connect grids like that. (So far i failed to construct grids but that's a different problem). You have nothing in which you can measure an angle, so you can't identify which nodes of different grids should be unified. There are ways to approximate circles, however they are really polygons, so couldn't construct irrational rotations. Furthermore you are only constructing the topology of circle and not a circle. I feel you assume the points are located in an Linear Algebra when they are only located in a Topology

No, I assume that the nodes are only located in a topology that is connected according to simple rules, while the Euclidean space with its angles emerges from the graph at a large scale. Rather than grids coming together from random directions, Imagine instead first one grid and then the second grid grows over it according to a simple rule with a default inclination. So one grid is the parent of the other grid and then you keep on adding further grids until you get a tree of grids all pointing in many different directions which leads to the rotational symmetry of euclidean space if you measure graph distances on the large scale. The drawing is just the simplest example where alpha is not irrational wrt pi, but if you change the x:y ratio from 1:2 to some other ratio e.g. 2:3, you'll get an irrational angle wrt to pi.

Do you recall in which live stream he said this?

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