Friday, November 8, 2019


Filed under: General — Tags: — m759 @ 7:12 AM

The terms glitch  and cross-carrier  in the previous post
suggest a review


Gerard Manley Hopkins in 1888


For some backstory, see GlitchGerard Manley HopkinsInscape
particularly the post A Balliol Star.

Monday, July 22, 2019

The Four Diamonds Meet the Five Red Herrings

Filed under: General — Tags: — m759 @ 11:34 AM

Lord Peter Wimsey (Balliol 1912) on the Balliol-Trinity rivalry at Oxford:

See also Balliol College in the post subtitled Spidey Goes to Church.

Monday, April 8, 2013

Star Wars

Filed under: General — m759 @ 11:01 AM

See searches in this journal for Balliol and for Star Quality.

Related material:

Above: A Google image search for Göpel tetrads  today. Click to enlarge.

Wednesday, January 30, 2013

Abstract Possibility

Filed under: General — m759 @ 1:01 PM

Today's NY Times  "Stone Links" to philosophy include
a link to a review of a collection of Hilary Putnam's papers.

Related material, from Putnam's "What is Mathematical
" (Historia Mathematica  2 (1975): 529-543)—

"In this paper I argue that mathematics should be interpreted realistically – that is, that mathematics makes assertions that are objectively true or false, independently of the human mind, and that something answers to such mathematical notions as ‘set’ and ‘function’. This is not to say that reality is somehow bifurcated – that there is one reality of material things, and then, over and above it, a second reality of ‘mathematical things’. A set of objects, for example, depends for its existence on those objects: if they are destroyed, then there is no longer such a set. (Of course, we may say that the set exists ‘tenselessly’, but we may also say the objects exist ‘tenselessly’: this is just to say that in pure mathematics we can sometimes ignore the important difference between ‘exists now’ and ‘did exist, exists now, or will exist’.) Not only are the ‘objects’ of pure mathematics conditional upon material objects; they are, in a sense, merely abstract possibilities. Studying how mathematical objects behave might better be described as studying what structures are abstractly possible and what structures are not abstractly possible."

See also Wittgenstein's Diamond and Plato's Diamond.

Saturday, December 22, 2012

Web Links:

Filed under: General,Geometry — m759 @ 5:01 PM

Spidey Goes to Church

More realistically

  1. "Nick Bostrom is a Swedish philosopher at 
    St. Cross College, University of Oxford…."
  2. "The early location of St Cross was on a site in
    St Cross Road, immediately south of St Cross Church."
  3. "The church building is located on St Cross Road
    just south of Holywell Manor."
  4. "Balliol College has had a presence in the area since
    the purchase by Benjamin Jowett, the Master, in the 1870s
    of the open area which is the Balliol sports ground
    'The Master's Field.' "
  5. Leaving Wikipedia, we find a Balliol field at Log24:
  6. A different view of the same field, from 1950—
  7. A view from 1974, thanks to J. J. Seidel — 
  8. Yesterday's Analogies.

Wednesday, September 19, 2012

Art Wars (continued)

Filed under: General,Geometry — m759 @ 8:00 PM

Today's previous post, "For Odin's Day," discussed 
a mathematical object, the tesseract, from a strictly
narrative point of view.

In honor of George Balanchine, Odin might yield the
floor this evening to Apollo.

From a piece in today's online New York Times  titled
"How a God Finds Art (the Abridged Version)"—

"… the newness at the heart of this story,
in which art is happening for the first time…."

Some related art

IMAGE- Figure from Plato's Meno in version by Benjamin Jowett, Master of Balliol College, Oxford

and, more recently

This more recent figure is from Ian Stewart's 1996 revision 
of a 1941 classic, What Is Mathematics? , by Richard Courant
and Herbert Robbins.

Apollo might discuss with Socrates how the confused slave boy
of Plato's Meno  would react to Stewart's remark that

"The number of copies required to double an
 object's size depends on its dimension."

Apollo might also note an application of Socrates' Meno  diagram
to the tesseract of this afternoon's Odin post


Friday, May 2, 2008

Friday May 2, 2008

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

A Balliol Star

In memory of
Graham Higman of
 Balliol College and
Magdalen College,
  Jan. 19, 1917 –
April 8, 2008

From a biography of an earlier Balliol student,
Gerard Manley Hopkins (1844-1889):

"In 1867 he won First-Class degrees in Classics
and 'Greats' (a rare 'double-first') and was
considered by Jowett to be the star of Balliol."

Gerard Manley Hopkins in 1888

Hopkins, a poet who coined the term "inscape," was a member of the Society of Jesus.

According to a biography, Higman was the founder of Oxford's Invariant Society.

From a publication of that society, The Invariant, Issue 15– undated but (according to Issue 16, of 2005) from 1996 (pdf):

Taking the square root
  of a function

 by Ian Collier

"David Singmaster once gave a talk at the Invariants and afterwards asked this question:

What is the square root of the exponential function? In other words, can you define a function such that for all xf  2(x) — that is, f (f (x)) — is equal to e  x ? He did not give the answer straight away so I attempted it…."

Another approach to the expression f(f(x)), by myself in 1982:

Inscapes II by Steven H. Cullinane: f(f(x)) and power sets

For further details,
see Inscapes.

For more about Higman, see an interview in the September 2001 newsletter of the European Mathematical Society (pdf).

"Philosophers ponder the idea
 of identity: what it is to give
 something a name on Monday
 and have it respond to 
  that name on Friday…."

Bernard Holland 

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