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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