> I hate thought experiments. But I need this one. See:
Book Chapter3: Actual Causes and Thought Experiments By Clark Glymour , Frank Wimberly MIT Press 2007 --- Frank C. Wimberly 140 Calle Ojo Feliz, Santa Fe, NM 87505 505 670-9918 Santa Fe, NM On Tue, Aug 20, 2024, 2:53 PM Santafe <desm...@santafe.edu> wrote: > 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/ >
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