Complex plane as a connection between differentiation and integration

The coefficients in a Taylor series may be calculated by differentiation, while those in a Fourier Series may be calculated by integration. Since these two types of series are really the same in the complex plane, this suggests that there exists some hidden connection between differentiation and integration that the only complex number can reveal.

— Visual Complex Analysis p.79, by Tristan Needham

2009.12.31 Thursday ACHK

Twistor string theory

In 2003, Edward Witten proposed to marry twistor and string theory by embedding the topological B model of string theory in twistor space. His objective was to model certain Yang-Mills amplitudes. The resulting model has come to be known as twistor string theory.

Witten (2004) built on this insight to propose a way to do string theory in twistor space, whose dimensionality is necessarily the same as that of 3+1 Minkowski spacetime. Hence twistor string theory is a possible way to eliminate the need for more than 3 spatial dimensions when doing (super)string theory.

— Wikipedia on Twistor theory

2009.12.30 Wednesday ACHK

PLT Scheme

There is also PLT Scheme, which uses an incompatible branch of wxWindows (version 1), created in 1995. The toolkit is deeply integrated with the language run-time (garbage collection, resource administration) unlike in other languages, which simply provide a library binding.

— Wikipedia on wxWidgets

2009.12.29 Tuesday ACHK