Here is a quick, painless introduction to the kind of symmetry that you probably learned in school. In that lesson, we learn that there are different kinds of symmetry: Rotational Translational Mirror and so on. What this video (and your teacher) did not explain was what symmetry is in general.  If you learned about symmetry in University Math, your idea was  expanded a bit  to come closer to what symmetry is  in general . The first step is to think of symmetry as a set of transformations (rotate, move, flip) rather than a property of whatever it is that is being transformed. And that's just the start. For example, in physics, you learned the Lorentz Transformation  is a symmetry group in the "real world" that leaves the laws of physics unchanged. Newton's laws are not symmetric in this sense but with a bit of tweaking (Special Relativity) they can be fixed. In  physics , the Lorentz transformation (or transformations) are  coordinate tr...

I am particularly attracted to the idea of the "fractal", which is a scale-independent repetition of a theme. Nature seems to "discover" a few patterns then use them in endless patterns and variations. This is one of the building blocks of what is taking shape as a "theory of mind". To build a "super mind", it would make sense to design the largest scale of this mind in the cloud to tap the computational power of millions of volunteer machines (as in the cloud project to classify galaxies). However, perhaps this as already been done. At least to serve in my "thought experiment", Google may be enough. The "theme" that has me fascinated is the mapping of one brain state into another, using something similar to the Shrodinger Wave Equation. That equation describes the state of the universe in the "next instant" as a function of the state of the universe in the "previous instant". The mental equivalent would be...