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Monday, June 20, 2011

The Search for Invariants

Filed under: General,Geometry — m759 @ 9:29 AM

The title of a recent contribution to a London art-related "Piracy Project" begins with the phrase "The Search for Invariants."

A search for that phrase  elsewhere yields a notable 1944* paper by Ernst Cassirer, "The Concept of Group and the Theory of Perception."

Page 20: "It is a process of objectification, the characteristic nature
and tendency of which finds expression in the formation of invariants."

Cassirer's concepts seem related to Weyl's famous remark that

“Objectivity means invariance with respect to the group of automorphisms.”
Symmetry  (Princeton University Press, 1952, page 132)

See also this journal on June 23, 2010— "Group Theory and Philosophy"— as well as some Math Forum remarks on Cassirer and Weyl.

Update of 6 to 7:50 PM June 20, 2011—

Weyl's 1952 remark seems to echo remarks in 1910 and 1921 by Cassirer.
See Cassirer in 1910 and 1921 on Objectivity.

Another source on Cassirer, invariance, and objectivity—

The conclusion of Maja Lovrenov's 
"The Role of Invariance in Cassirer’s Interpretation of the Theory of Relativity"—

"… physical theories prove to be theories of invariants
with regard to certain groups of transformations and
it is exactly the invariance that secures the objectivity
of a physical theory."

— SYNTHESIS PHILOSOPHICA 42 (2/2006), pp. 233–241

A search in Weyl's Symmetry  for any reference to Ernst Cassirer yields no results.

* Published in French in 1938.

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