Matrices that have no inverse are called "singular". Would that word work in this context?
The treatment of fibers, bundles, connections, etc. that I am familiar with is in Baez's book Gauge Theory, Knots and Gravity. Frank On Wed, May 20, 2020 at 9:40 AM uǝlƃ ☣ <geprope...@gmail.com> wrote: > > On 5/19/20 4:55 PM, Jon Zingale wrote: > > Doing so could be one meaningful way to interpret /tracing a thought/. > > Yes. While I don't fully grok the expansions from fibers to bundles/sheaf, > what it evokes in my head seems coherent. > > > With regards to the discussion about our holographic surface, I could > use more > > clarification on the lossy/lossless property. I assume we agree that > sorting is > > not dual to shuffling. For instance, defining the type of a shuffling > algorithm > > does not require Ord < > http://zvon.org/other/haskell/Outputprelude/Ord_c.html> to be a class > constraint, where it /is/ required for sorting. > > I think whether shuffle is yet another ordering depends on what we mean by > "random". But I don't want to devolve into metaphysical conversations about > free will and whatnot. So, if we assume shuffle is ordered, just ordered > mysteriously, then we can talk about loss sans metaphysics. > > > If we are claiming that the information found on our holographic surface > is > > complete, I would like to think we are claiming it to be lossless‡. At > the end > > of the day, it may be the case that we will never know the ontological > status of > > information reversibility through a black hole. Am I wrong about this? > If our > > holographic surface isn't reversible, is hashing perhaps a better > analogy? > > To do complete justice to the steelman of the EricC/Nick claim, I think we > do have to assert no loss. And invertibility of the transform(s) is the > right way to think. But I *also* think, if we tried hard enough, we could > get EricC/Nick to admit to some loss with the caveat that what's lost in > that lossy transform is *irrelevant* somehow (EricC's use of "invalid" and > yammerings about Wittgenstein >8^D). And since my point isn't to > inadvertently create a *strawman* of their claim by making the steelman too > ... well, steely, I'd like to allow for a lossy transform as well as a > lossless transform. And, by extension, I'd like to allow both invertible > and uninvertible transforms. > > That may well be important if the steelman turns out to be nothing *more* > than metaphor. If all I'm doing is laying out a metaphor for privacy, then > I'll lose interest pretty quick because what I'm *trying* to do is classify > privacy. I want string comprehension to be in the same class as > behaviorism. I don't want to draw super-flawed analogies between them. > > But the distinction ([non]invertibility) might very well help evaluate the > believability of the steelman. > > > If in the limit of behavioral investigation we find no more semantic > ambiguity than > > the semantic ambiguities we experience when attempting to understand an > others > > language, [...] > > I don't think it is. I think there is a no-go lurking that is associated > by EricS's recent mention of the student laughing because the insight was > "at his elbow". And it's (somehow) associated with Necker cubes, paradigm > shifts, and even a "loss of innocence" you see in people who've become > cynical, the difference between work and play, "flow", etc. It's related > (somehow) to the opportunity costs of using decoder X instead of decoder Y. > As SteveS pointed out, one's participation in the landscape *changes* the > landscape. > > This is fundamental to the steelman we're building. It's not merely > epiphenomenal. By decoding the surface of the ... [ahem] ... "patient", you > are *manipulating* the patient. You can see this directly in your worry > about [ab]using Frank as our privacy touchstone. > > I wanted to set the stage for this in the formulation of 1st order privacy > (by obscurity) by laying out the thing to decode side-by-side with the > decoder, evoking a UTM where the tape contains both the computation and the > description of the machine that can do the computation ... but I thought > that would interfere with my main targets EricC and Nick. If they reject > the steelman, then this becomes a tangent project of numbers, groups, and > codes ... which is cool, but not what I intended [†]. > > [†] I'd love to sit in on a read of Gentry's paper, though it'd all be > over my head. > > > -- > ☣ uǝlƃ > > -- --- .-. . .-.. --- -.-. -.- ... -..-. .- .-. . -..-. - .... . -..-. . > ... ... . -. - .. .- .-.. -..-. .-- --- .-. -.- . .-. ... > FRIAM Applied Complexity Group listserv > Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam > un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com > archives: http://friam.471366.n2.nabble.com/ > FRIAM-COMIC <http://friam.471366.n2.nabble.com/FRIAM-COMIC> > http://friam-comic.blogspot.com/ > -- Frank Wimberly 140 Calle Ojo Feliz Santa Fe, NM 87505 505 670-9918
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