Even though the (untwisted) Whitehead doubling operation kills all known abelian invariants of knots (and makes them topologically slice), we show that it does not kill the rational function that equals to the 2-loop part of the Kontsevich integral.

We show that finite-dimensional Lie algebras over a field of characteristic zero such that the second cohomology group in every finite-dimensional module vanishes, are, essentially, semisimple.

We investigate the Whiteheadness of Borel abelian groups (א1-free, without loss of generality as otherwise this is trivial). We show that CH (and even WCH) implies any such abelian group is free, and always א2-free. 1998 Mathematics Subject Classification 03C60, 03E15, 20K20.

As a consequence of identifying the principle described in the title, we prove that for any uncountable cardinal λ, if there is a λ-free Whitehead group of cardinality λ which is not free, then there are many “nice” Whitehead groups of cardinality λ which are not free.

Kenneth M. Anderson, Richard N. Taylor* and E. James Whitehead Jr.** Department of Information and Computer Science University of California, Irvine Irvine, CA 92697-3425, USA Email: [email protected], Tel: +1.714.824.2776, Kenneth M. Anderson home page *Email: [email protected], Tel: +1.714.824.6429, Richard N. Taylor home page **Email: [email protected], Tel: +1.714.824.4121, E. James White...

This article develops a philosophy of the humanities by reading C.P. Snow’s famous thesis of “the two cultures” through the early work of Alfred North Whitehead. I argue that, whereas Snow refers to Whitehead’s Science and the Modern World, he ultimately paves the way for a reductive interpretation of humanities scholarship, which is a move that can be repaired by delving into Snow’s own refere...