Monday, August 16, 2021

The Space of Possibilities

Filed under: General — Tags: , — m759 @ 3:57 AM

The title is from "Federico Ardila on Math, Music and
the Space of Possibilities
," a podcast from Steven Strogatz's
Quanta Magazine  series. The transcript is dated March 29, 2021.

Ardila: … in a nutshell, what combinatorics is about is just
the study of possibilities and how do you organize them,
given that there’s too many of them to list them.

Strogatz:  So, I love it. Combinatorics is not just
the art of the possible, but the enumeration of the possible,
the counting of the possible and the organizing of the possible.

Strogatz:  It’s such a poetic image, actually: the space of possibilities.

This  journal on the podcast date, March 29, 2021 —

A more precise approach to the space of possibilities:

Wednesday, May 26, 2021

Heavy Metaphor

Filed under: General — Tags: , — m759 @ 9:51 PM

Earlier posts that are also tagged "Points Omega" suggest some 
context for a May 19 New Republic  illustration.

      x -1/x

  See as well
"Flowers and Brown."

Monday, October 26, 2020


Filed under: General — Tags: , — m759 @ 11:37 AM

These news items suggest a review —

The above “Pynchon’s Paranoid History” page number  appeared
in this  journal on Groundhog Day, 2015 —

David Justice on a Zeta-related theory —

Friday, May 26, 2017

Night at the Museum

Filed under: General — Tags: — m759 @ 10:05 PM

In memory of an author who reportedly 
died on Wednesday, May 24.

Monday, February 2, 2015

Spielraum as Ω

Filed under: General,Geometry — Tags: , — m759 @ 6:29 PM

From "Origins of the Logical Theory of Probability: von Kries, Wittgenstein, Waismann," by Michael Heidelberger —

"Von Kries calls a range of objective possibilities of a hypothesis or event (under given laws) its Spielraum   (literally: play space), which can mean ‘room to move’, ‘leeway’, ‘latitude of choice’, ‘degree of freedom’ or ‘free play’ and ‘clearance’ – or even ‘scope’. John Maynard Keynes translated it as ‘field’, but the term ‘range’ has generally been adopted in English. Von Kries now holds that if numerical probability were to make any sense at all it must be through this concept of the Spielraum  . Von Kries’s theory is therefore called a ‘Spielraum  theory’ or ‘range theory of probability’."

— International Studies in the Philosophy of Science , Volume 15, Issue 2, 2001, pp. 177-188

See also the tag Points Omega
(Scroll down to January 11-12, 2015.)

Related material:

"Now, for example, in how far are
the six sides of a symmetric die
'equally possible' upon throwing?"

— From "The Natural-Range Conception
     of Probability," by Dr. Jacob Rosenthal,
     page 73 in Time, Chance, and
     Reduction: Philosophical Aspects of
Mechanics , ed. by 
     Gerhard Ernst and Andreas Hüttemann, 
     Cambridge U. Press, 2010, pp. 71-90

Monday, January 12, 2015

Points Omega*

Filed under: General,Geometry — Tags: , — m759 @ 12:00 PM

The previous post displayed a set of
24 unit-square “points” within a rectangular array.
These are the points of the
Miracle Octad Generator  of R. T. Curtis.

The array was labeled  Ω
because that is the usual designation for
a set acted upon by a group:

* The title is an allusion to Point Omega , a novel by
Don DeLillo published on Groundhog Day 2010.
See “Point Omega” in this journal.

Sunday, January 11, 2015

Real Beyond Artifice

Filed under: General,Geometry — Tags: , , , — m759 @ 7:20 PM

A professor at Harvard has written about
“the urge to seize and display something
real beyond artifice.”

He reportedly died on January 3, 2015.

An image from this journal on that date:

Another Gitterkrieg  image:

 The 24-set   Ω  of  R. T. Curtis

Click on the images for related material.

Sunday, May 23, 2010

Annals of Conceptual Art

Filed under: General — Tags: , — m759 @ 2:02 AM

Josefine Lyche's
  "Theme and Variations" (Oslo, 2009)


Some images in reply—

  Frame Tale

Image by R. T. Curtis from 'Further Elementary Techniques...'

Click on images for further details.

"In the name of the former
and of the latter
and of their holocaust.

Finnegans Wake

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