Wanted to come back to this post to share a few additional …
Wanted to come back to this post to share a few additional pieces of content that I think are interesting to consider in this context.
Recently, I noticed a paper which argued that rotations in physical space for dynamic systems can return to their origin by doubling the walk and uniformly scaling all rotation angles. I believe this is connected to the argument that all motion is vector reflection which I included in the sub comments of this original post. You can read this new paper here:
Walks in Rotation Spaces Return Home when Doubled and Scaled
https://arxiv.org/abs/2502.14367
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John Baez talks about many of these topics in the video I shared in this thread. You can see it here: https://app.treechat.com/p/060591cb-14f9-492b-96bd-ee44b129b7a4
He talks about the "Clifford Algebras" which describe something called the Double Cover of the Orthogonal Group.. and they represent a capacity to use matrices to produce algebras that allow for this kind of manipulation. https://en.wikipedia.org/wiki/Spin_group
I think that computer graphics famously use this kind of math to make very easily manipulatable 3d graphics such as avatars for video games or 3d structures inside the game that need to move and pivot while retaining their orthogonality such as moving towards a tree while also spinning and looking up.. Using this kind of vector relationships for the object allows for all three actions being produced simultaneously to produce a visualization that matches what our own eye would see if we were doing the same but in the physical world instead of a virtual one. In other words, this Clifford algebra, the spin groups, the vectors, the matrices, etc. help produce a visually consistent experience between physical and virtual worlds. This allows for the virtual world to be experienced in some ways as an extension of the physical world, and in some ways helps us to accept the world as "real" or "authentic."
Recently, Dr. Michael Levin was on the Lex Fridman podcast, and I think he made some interesting and unique claims about consciousness and interfaces... I think it's highly worth checking out his entire video. I'll leave it here for your review if you find time to do so:
https://www.youtube.com/watch?v=Qp0rCU49lMs
One of the ideas that I've been considering has to do with this concept of boundaries and connecting them to this idea of multi-scale competency architecture which is being described by Dr Michael Levin.. and combining these ideas with this concept of motion being hyperplane reflection...
So I guess if I can create an analogy, we could imagine a system of coordinated symbol-logic... imagine it is the logical boundary of a rational young adult... the arrival at the boundary such as 2+2 = 4 affords a reflection opportunity. On the one hand, a "katoptron" reflection of the individual... depending on the individual, this reflection can either be integrated or it's discarded.
This relates somewhat to Dr. Levin's competency archiecture model... for example, a non-rational being may encounter the rationality boundary, and discard or otherwise reject its reflection in the same way that as young children, we often reject hard truths about the world because we are not yet mature enough to acknowledge and embrace them.
This is related to ergodicity. Thermodynamic states also return (arbitrarily close) to their starting position.