Friday, January 8, 2021

Groups Act

Filed under: General — m759 @ 2:08 PM

“Somehow, a message had been lost on me. Groups act .
The elements of a group do not have to just sit there,
abstract and implacable; they can do  things, they can
‘produce changes.’ In particular, groups arise
naturally as the symmetries of a set with structure.”

— Thomas W. Tucker, review of Lyndon’s Groups and Geometry
in The American Mathematical Monthly , Vol. 94, No. 4
(April 1987), pp. 392-394.

“The concept of group actions is very useful in the study of
isomorphisms of combinatorial structures.”

— Olli Pottonen, “Classification of Steiner Quadruple Systems
(Master’s thesis, Helsinki, 2005, p. 48).

“In a sense, we would see that change arises from
the structure of the object.”

— Nima Arkani-Hamed, quoted in “A  Jewel at the Heart of
Quantum Physics
,” by Natalie Wolchover, Quanta Magazine ,
Sept. 17, 2013.

See as well “Change Arises” in this  journal.

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