<div dir="ltr">Jon,<div><br></div><div>I see Alexander's horned sphere is defined in a problem in Spivak's book on differential geometry. I'm glad you mentioned it.</div><div><br></div><div>Frank</div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Sat, Jun 6, 2020 at 9:24 AM Steve Smith <<a href="mailto:sasmyth@swcp.com">sasmyth@swcp.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<div>
<p>Jon -</p>
<p>Bombastic free-for-all is an apt description. <br>
</p>
<p>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.</p>
<p>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.</p>
<p>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.<br>
</p>
<p>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".</p>
<p>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. <br>
</p>
<p>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.</p>
<p>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". <br>
</p>
<p>We ARE the proverbial "Blind Men and the Elephant". Our
meta-trickster made this observation weeks ago:<br>
</p>
<p> <a href="http://friam-comic.blogspot.com/2020/05/the-elephant-in-room.html" target="_blank">http://friam-comic.blogspot.com/2020/05/the-elephant-in-room.html</a></p>
<p>- Steve<br>
</p>
<div>On 6/5/20 11:13 PM, Jon Zingale wrote:<br>
</div>
<blockquote type="cite">
<div dir="ltr">
<div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small;color:rgb(51,51,51)">I
was hoping you would sketch out more of your objection<br>
to my claim that the Alexander horned sphere provides an<br>
example of a fractal space whose topology is given simply<br>
as a sphere. In speech, I can feel pressured to make the<br>
best of the few words I have room to express and sometimes<br>
at the expense of accuracy. Analysis of the Alexander horned<br>
sphere (and the space it encloses) is a bit more nuanced<br>
than I let on, the details of which may be helpful for our<br>
discussion of clouds. OTOH, Friam discussions are sometimes<br>
nothing short of a bombastic free-for-all where injecting<br>
aporia or the occasional first order footnote is about<br>
<i>as good as one can hope for</i>. If it turns out to help
our<br>
discussion here, I will dust off my copy of <i>Hocking &
Young</i>.<br>
<br>
</div>
<div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small;color:rgb(51,51,51)">Yes,
a discussion of limit points would be necessary for<br>
investigating the topology of this pathological object.<br>
Analysis of its interior and exterior yield very different<br>
results, while the ball is simply connected its boundary<br>
is not. Somehow, this off-the-top-of-my-head example<br>
seemed to be relevant enough to Nick's itch that I hoped<br>
it would slow things down.<br>
</div>
<div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small;color:rgb(51,51,51)"><br>
</div>
<div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small;color:rgb(51,51,51)">Nick,
Steve, Frank, et al.</div>
<div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small;color:rgb(51,51,51)"><br>
</div>
<div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small;color:rgb(51,51,51)">Before
we dive into Mandelbrot thumping, or some other</div>
<div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small;color:rgb(51,51,51)">obnoxious
witch hunt of popular mathematics, what exactly</div>
<div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small;color:rgb(51,51,51)">is
our goal? I don't mind beginning with Nick's definition of</div>
<div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small;color:rgb(51,51,51)">a
cloud, but only if that means we work to prove what is</div>
<div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small;color:rgb(51,51,51)">and
what is not an entailing theorem. Further, I will hope</div>
<div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small;color:rgb(51,51,51)">that
we <i>do not</i> confuse these theorems for truths about</div>
<div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small;color:rgb(51,51,51)">our
material world. I maintain that any definition we start</div>
<div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small;color:rgb(51,51,51)">with
will have <i>some</i> domain of applicability, but we are</div>
<div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small;color:rgb(51,51,51)">far
too along in our understanding of rhetoric (as a culture)</div>
<div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small;color:rgb(51,51,51)">to
waste time building strawmen. Granted this, if Nick wants</div>
<div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small;color:rgb(51,51,51)">to
use <i>shrouds</i> as a way of talking about <a href="https://en.wikipedia.org/wiki/Darboux_integral" target="_blank">Darboux sums</a></div>
<div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small;color:rgb(51,51,51)">converging
to Riemann Integrals, say, well fine. I am not</div>
<div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small;color:rgb(51,51,51)">entirely
sure there is any particular reason we need to</div>
<div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small;color:rgb(51,51,51)">dive
into an analytic hole, but hey. Nick, if there is a</div>
<div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small;color:rgb(51,51,51)">question
underlying all of this demand for technology,</div>
<div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small;color:rgb(51,51,51)">please
state it. EricC, however, helped me to feel justified</div>
<div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small;color:rgb(51,51,51)">in
claiming that asking <i>what is a cloud, really</i> is not a</div>
<div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small;color:rgb(51,51,51)">productive
question.</div>
<div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small;color:rgb(51,51,51)"><br>
</div>
<div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small;color:rgb(51,51,51)">Jon</div>
<div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small;color:rgb(51,51,51)"><br>
</div>
</div>
<br>
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</blockquote></div><br clear="all"><div><br></div>-- <br><div dir="ltr" class="gmail_signature">Frank Wimberly<br>140 Calle Ojo Feliz<br>Santa Fe, NM 87505<br>505 670-9918</div>