Jon, I see Alexander's horned sphere is defined in a problem in Spivak's book on differential geometry. I'm glad you mentioned it.
Frank On Sat, Jun 6, 2020 at 9:24 AM Steve Smith <[email protected]> wrote: > Jon - > > Bombastic free-for-all is an apt description. > > I think "what is a cloud" came up when I used my own "watching a cloud > evolve" as an example of how one might begin to develop an intuition for > higher-dimensional objects/phenomena through the limits of our visual > system. This was for Dave's question about trying to develop an intuition > for the 4-polytopes he thinks he observes/perceives/experiences in his > dreams/visions. > > I tossed in another extra degree of freedom in the discussion by > introducing SimTable's aspirations to use the often-widely-visible skyscape > of clouds and even more directly interestingly, smoke plumes for the > primary purpose of calibrating multiple cameras whose view frustums might > include the same clouds. This augments capturing or pre-stating the > camera extrinsics (location/pose) and intrinsics (focal length/FOV, etc.) > and the use of landscape features (skyline, etc.) for tweaking > calibration. Smoke plumes, of course, have more direct utility to the > problem at hand, of estimating and locating wildfire as it evolves. > > The first observation about clouds is very intuitional and perhaps > whimsical... maybe I really can't intuit anything about the distribution > of atmospheric conditions by observing the evolution of a cloud... and the > second is very practical and any mathematical abstractions obtained for > that purpose are only as meaningful as they are useful. I appreciate > your offering of the _Alexander Horned Sphere_ in that spirit. > > Clouds are interesting "alternative" objects to say mountains or buildings > because of there ephemerality and ambiguity of boundary, etc. This > tangent may be of interest to those considering "what means object". > > Over my shoulder in many of our zoom calls, sits a hand-painted and framed > phrase by the hand (and mind?) of Thich Naht Hahn which states "A Cloud > Never Dies". This use of the term "Cloud" references (for me) all of the > observations above and many more. Thus the explosion of threads when > things like this are discussed on FriAM. > > Some of us are primarily an analytical bunch, wanting to dissect things > down until we feel we understand (apprehend) the parts directly and then by > extension, possibly understand the original whole in that way. Of course, > the theme that brought this group together is bigger than that. Systems > Thinking, Complexity, Synthesis, Emergence, Exaptation, Spandrels, > Attractors, etc. are all complementary to the traditions of Analytical > Thinking, yet compatible. > > So, on this list, I really have no other goal perhaps than to put "yet > more perspectives on the table" on the off chance that someone will > recognize one of them and provide some parallax that is useful (or > interesting) to me. Well, that and to _scratch the itches_ that sometimes > spontaneously jump up under the casts that others try to put around what > they see to be a broken limb, thinking that reducing the degrees of freedom > is the best way to "put it right". > > We ARE the proverbial "Blind Men and the Elephant". Our meta-trickster > made this observation weeks ago: > > http://friam-comic.blogspot.com/2020/05/the-elephant-in-room.html > > - Steve > On 6/5/20 11:13 PM, Jon Zingale wrote: > > I was hoping you would sketch out more of your objection > to my claim that the Alexander horned sphere provides an > example of a fractal space whose topology is given simply > as a sphere. In speech, I can feel pressured to make the > best of the few words I have room to express and sometimes > at the expense of accuracy. Analysis of the Alexander horned > sphere (and the space it encloses) is a bit more nuanced > than I let on, the details of which may be helpful for our > discussion of clouds. OTOH, Friam discussions are sometimes > nothing short of a bombastic free-for-all where injecting > aporia or the occasional first order footnote is about > *as good as one can hope for*. If it turns out to help our > discussion here, I will dust off my copy of *Hocking & Young*. > > Yes, a discussion of limit points would be necessary for > investigating the topology of this pathological object. > Analysis of its interior and exterior yield very different > results, while the ball is simply connected its boundary > is not. Somehow, this off-the-top-of-my-head example > seemed to be relevant enough to Nick's itch that I hoped > it would slow things down. > > Nick, Steve, Frank, et al. > > Before we dive into Mandelbrot thumping, or some other > obnoxious witch hunt of popular mathematics, what exactly > is our goal? I don't mind beginning with Nick's definition of > a cloud, but only if that means we work to prove what is > and what is not an entailing theorem. Further, I will hope > that we *do not* confuse these theorems for truths about > our material world. I maintain that any definition we start > with will have *some* domain of applicability, but we are > far too along in our understanding of rhetoric (as a culture) > to waste time building strawmen. Granted this, if Nick wants > to use *shrouds* as a way of talking about Darboux sums > <https://en.wikipedia.org/wiki/Darboux_integral> > converging to Riemann Integrals, say, well fine. I am not > entirely sure there is any particular reason we need to > dive into an analytic hole, but hey. Nick, if there is a > question underlying all of this demand for technology, > please state it. EricC, however, helped me to feel justified > in claiming that asking *what is a cloud, really* is not a > productive question. > > Jon > > > - .... . -..-. . ...- --- .-.. ..- - .. --- -. -..-. .-- .. .-.. .-.. -..-. > -... . -..-. .-.. .. ...- . -..-. ... - .-. . .- -- . -.. > FRIAM Applied Complexity Group listserv > Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam > un/subscribe <http://bit.ly/virtualfriamun/subscribe> > http://redfish.com/mailman/listinfo/friam_redfish.com > archives: http://friam.471366.n2.nabble.com/ > FRIAM-COMIC http://friam-comic.blogspot.com/ > > - .... . -..-. . ...- --- .-.. ..- - .. --- -. -..-. .-- .. .-.. .-.. > -..-. -... . -..-. .-.. .. ...- . -..-. ... - .-. . .- -- . -.. > 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-comic.blogspot.com/ > -- Frank Wimberly 140 Calle Ojo Feliz Santa Fe, NM 87505 505 670-9918
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