at least tangentially P-related: Class of all classes

[Mark Kohut]

A-and in AtD, there is 'the map of all maps" search................

Mark Kohut <markekohut at yahoo.com> wrote:    that line with the nice ring to it reminds me, in the ring of it, of ye olde definition of God:
   
  THE CENTRE IN THE MIDST OF THE CONDITIONS
  FURTHER NOTES ON 'YOD' AS SACRED CENTRE. 
  Alain de Lille, a 12th century theologian, borrowing from the Corpus Hermeticum of the 3rd Century: 
  "God is an intelligible sphere whose centre is everywhere and whose circumference is nowhere." 
  While Giordano Bruno wrote: 
  "We can assert with certainty that the universe is all centre, or that the centre of the universe is everywhere and its circumference is nowhere." 
              Pascal used the following words: 
  "God is a circle; His centre is everywhere, His circumference is nowhere." 
  Or in another translation: 
              "Nature is an infinite sphere whose centre is everywhere, whose circumference is nowhere." 
  And in his short story: 'The Library of Babel', J.L.Borjes plays with the idea: 
  "The library is a sphere whose exact centre is in any one of the hexagons and whose circumference is inaccessible." 
  Circle and Centre, 
  "The famous saying that God is "a sphere of which the centre is everywhere and the circumference nowhere" is, in fact, first found in a pseudo-Hermetic treatise of the twelth century, and was transferred by Cusanus to the universe, as a reflection of God, in a manner which is Hermetic in spirit..This concept was basic for Bruno, for whom the innumerable worlds are all divine centres of the unbounded universe." 
  Yates, Bruno, p. 247. 
  The Liber XXIV philosophorum, published by Clemens Baeumker, Das pseudi.hermetische Buch der XXIV Meister, Beitrage zur Geschichte der Philosophie und Theologue des Mittelalters, fasc.xxv, Munster, 1928. 
  The source of Cusanus, is: De docta ignorantia, II, cap.2; cf.Koyre, op. cit., pp. 10ff. 
   
   
  

Monte Davis <monte.davis at verizon.net> wrote:
  David Payne writes:

> > the "curve which is everywhere continuous and nowhere 
> > differentiable"... Nice ring to it.
> 
> That would be the Weierstrass function, which is "a 
> pathological example of a real-valued function on the real 
> line. The function has the property that it is continuous 
> everywhere but differentiable nowhere" 
> (http://en.wikipedia.org/wiki/Weierstrass_function).

Not differentiable = crudely, not amenable to that basic operation of
calculus, deriving a graph line's slope (ratio of "rise":"run") over smaller
and smaller intervals. The most obvious bad actors would be discontinuous --
dashed or intermittent lines, which have no Y value for a given X because
the function is doing something illegal like dividing by 0.

Naturally, over-generalizing like the rest of us, mathematicians had grown
to think "continuous" and "differentiable" must go together when Weierstrass
rubbed their noses in counterexamples: functions yielding graph lines that
are *all* spikes, *all* cusps where the slope has no meaning. no matter how
small the interval. And of course, once the bad juju of the "pathological"
label wore off, people started finding such functions everywhere.

> I am pleased to learn that 
> "pathological" has a mathematical definition: "In 
> mathematics, a pathological phenomenon is one whose 
> properties are considered atypically bad or counterintuitive" 
> (http://en.wikipedia.org/wiki/Pathological_%28mathematics%29).

Likewise, Benoit Mandelbrot dwelled on some "pathological" geometric forms
(Koch snowflake, Sierpinski sponge, Peano dusts etc.) until it turned out
they were descriptive of lots of everyday phenomena. Likewise, a century of
dynamical-systems work from Poincare and Liouville through Abraham, Smale &
co. turned "chaotic" systems from rare curosities into the stuff of
turbulence, weather, solar systems over hundred-million-year spans, etc.

In retrospect, it looks like the drunk searching for his keys under the
streetlight not because he lost them there, but because that's all he can
do. Yet the circle of light *does* expand. 





    
---------------------------------
  Be a better friend, newshound, and know-it-all with Yahoo! Mobile. Try it now.

       
---------------------------------
Be a better friend, newshound, and know-it-all with Yahoo! Mobile.  Try it now.
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://waste.org/pipermail/pynchon-l/attachments/20080509/20a3bc8d/attachment-0001.html>