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Gödel’s incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems for mathematics. The theorems, proven by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The two results are widely interpreted as showing that Hilbert’s program to find a complete and consistent set of axioms for all of mathematics is impossible, thus giving a negative answer to Hilbert’s second problem.

The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an “effective procedure” (essentially, a computer program) is capable of proving all facts about the natural numbers. For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem shows that if such a system is also capable of proving certain basic facts about the natural numbers, then one particular arithmetic truth the system cannot prove is the consistency of the system itself.

-Wikipedia

melisaki:

EastEnd girl dancing the Lambeth Walk

photo by Bill Brandt, sometime in the ’30s

(via endlessforms)

melisaki:

Cabbage Leaf

photo by Edward Weston, 1931

(via endlessforms)

"…by its self-sufficient presence the work of art is similar rather to the mere thing which has taken shape by itself without being constrained to serve a purpose."

Martin Heidegger
Der Ursprung des Kunstwerkes (The Origin of the Work of Art), 1950
based on lectures in 1935, 1936

"What seems natural to us is probably just something familiar in a long tradition that has forgotten the unfamiliar source from which it arose."

Martin Heidegger
Der Ursprung des Kunstwerkes (The Origin of the Work of Art), 1950
based on lectures in 1935, 1936

surrealism:

Orgiastic Melody by Reuben Mednikoff, 1937.

There’s a lot going on here. There is a great article by Caherine Milner describing Mednikoff and his “wife”, Grace Pailthorpe. Suffusive to say, these two where true surrealists.

(via 50watts)

art-documents:

Marcel Marien, L‘Introuvable, 1937, Coll. Sylvio Perlstein, Antwerp

Virginia Woolf, The Waves, published 1931. First Edition dust jacket by Vanessa Bell.

Image via { Encyclopedia Britannica }