Second inadequate reply, to Glen, unhappily similar to the first to Jon: > On Aug 19, 2024, at 23:37, glen <geprope...@gmail.com> wrote:
> There's so much I'd like to say in response to 3 things: 1) to formalize and > fail is human, 2) necessary (□) vs possible (◇) languages, and 3) principle > vs generic/privied models. But I'm incompetent to say them. > > So instead, I'd like to ask whether we (y'all) think a perfectly rigid > paddle, embedded in a perfectly rigid solid, with a continual twisting force > on the handle, exhibits "degenerative" symmetry? Of course, such things don't > exist; and I hate thought experiments. But I need this one. I got lost here because I don’t know what “degenerative” symmetry is meant to refer to. In context of your next para, I see a contrast between discrete symmetries, such as the rotations that would preserve a crystalline unit cell, versus continuous symmetries, which I need as a formal model to derive restoring forces. Is “degenerative” somehow another term for the continuous ones? The question when a continuum model can be seen as a limit of discrete models on finer and finer grains, and when one needs it to be an independent construct, is interesting. It feels like it goes back to the Eleatics. I have often thought that Zeno’s paradoxes nicely illustrate the things you can’t do if you have a mechanics that mathematizes only positions. Hamilton sweeps those limitations away by making momentum an independent coordinate in a phase space, and in that way granting it status as an independent property of objects from their positions (in classical mechanics). All the consequences of Noether’s theorem, conservations, restoring forces, etc., are formulated in terms of these independent and dual properties. With the advent of quantum mechanics, their independence becomes even more foundational to the picture of what exists, as a system in a momentum eigenstate is really in a completely distinct state from one in a position eigenstate. The two are differentiated in something like the way traveling waves and standing waves are differentiated in various wave mechanicses. > Similarly, if the paddle+solid could only be in 1 of 2 states, rotation 0° > and rotation 180°, and would move instantly (1/∞) from one to the other, with > `NaN` force at every other angle and 100% force at the 2 angles. This seems > like symmetry as well, but not degenerative. And we could go on to add more > states to the symmetry (3, 4, ...) to get groups all the way up to ∞, > somewhere in between where the embedding material becomes liquid, then gas, > etc. and the "symmetry" is better expressed as a cycle/circle. But I'm not > actually asking questions about 1D symmetry groups. My question is more > banal, or tacit, or targeted to those who think with their bodies. When all > the other non-Arthur peasants try to pull Excalibur out of the stone, my > guess is they're not thinking it exhibits degenerative symmetry. And that > implies that normal language is not possible. It's impoverished, for this > concept. Math-like languages are necessary in the sea of all possible > languages. The would-be King *must* use math to describe the degenerative > symmetry. (Missed opportunity in Python's Holy Grail, if you ask me. "I > didn't vote for you!”) Here I end with the same one I ended the reply to Jon: I strongly bet that much of what people think they believe for “Natural” reasons are actually learned beliefs through formal systems. I don’t think farmers before Newton had a Cartesian and Newtonian concept of space x time, or that they would have been bothered by Einstein. I don’t think they would have cared about Einstein any more than they cared about Newton. They had some ontology of “things", and the “places” that things *occupy*. And probably an ontology of keeping appointments, which in a more formal world might entail something analogous to a “theory of mind” construction about what other people are doing somewhere else “at the same time” as you are doing your thing here. But my default assumption would be that any of this only ever took on the rigidities of a Cartesian system after the lived practice of Newtonian mechanics had started to make some of its rigid entailments part of routine experience. Then it became a struggle to let that go when Minkowskian geometry required something different. I don’t mean to be perverse and excessive in denying the implications of folk physics: Probably, had farmers been dragged through it (strongly against their will), they would have found QM’s notion that what we _should_ call a _thing_ can be characterized by “being at” multiple “places” more difficult than Newton’s “thing at a single place”. But I’m not sure how much trouble it would have been. Considering the worldviews people are proud to claim they hold in various religious and superstitious traditions, the things asked from modern physics seem relatively benign as imaginative lifts. Would be nice to have something substantive to say about any of this, that would deserve to last. But I don’t think I do. Eric -. --- - / ...- .- .-.. .. -.. / -- --- .-. ... . / -.-. --- -.. . FRIAM Applied Complexity Group listserv Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom https://bit.ly/virtualfriam to (un)subscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ archives: 5/2017 thru present https://redfish.com/pipermail/friam_redfish.com/ 1/2003 thru 6/2021 http://friam.383.s1.nabble.com/
