M-theory is not yet complete; however it can be applied in many situations (usually by exploiting string theoretic dualities [clarification needed]). The theory of electromagnetism was also in such a state in the mid-19th century; there were separate theories for electricity and magnetism and, although they were known to be related, the exact relationship was not clear until James Clerk Maxwell published his equations, in his 1864 paper A Dynamical Theory of the Electromagnetic Field. Witten has suggested that a general formulation of M-theory will probably require the development of new mathematical language.

— Wikipedia on M-theory

2010.05.05 Wednesday ACHK

In physics, the AdS/CFT correspondence (anti-de-Sitter space/conformal field theory correspondence), sometimes called the Maldacena duality, is the conjectured equivalence between a string theory defined on one space, and a quantum field theory without gravity defined on the conformal boundary of this space, whose dimension is lower by one or more.

— Wikipedia on AdS/CFT correspondence

2010.05.04 Tuesday ACHK

Physicists learned rather unexpectedly, beginning in the early 1970s, that the problem of quantum gravity could be overcome by introducing a new sort of fuzziness. One replaces “point particles” by “strings”. Of course, the point particles and strings must both be treated quantum mechanically. Quantum effects are proportional to Planck’s constant , and stringy effects are proportional to a new constant (equal to approximately ) that determines the size of strings.

— Edward Witten

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2010.05.03 Monday ACHK

The real numbers are the dependable breadwinner of the family, the complete ordered field we all rely on. The complex numbers are a slightly flashier but still respectable younger brother: not ordered, but algebraically complete. The quaternions, being noncommutative, are the eccentric cousin who is shunned at important family gatherings. But the octonions are the crazy old uncle nobody lets out of the attic: they are nonassociative.

— John Baez

2010.05.02 Sunday ACHK

Golden ratio

The number 5 is quirky and intriguing, thanks in large part to its relation with the golden ratio, the “most irrational” of irrational numbers.

— John Baez

2010.05.01 Saturday ACHK

Nature of the fractional derivative

An important point is that the fractional derivative at a point x is a local property only when a is an integer; in non-integer cases we cannot say that the fractional derivative at x of a function f depends only on the graph of f very near x, in the way that integer-power derivatives certainly do. Therefore it is expected that the theory involves some sort of boundary conditions, involving information on the function further out. To use a metaphor, the fractional derivative requires some peripheral vision.

— Wikipedia on Fractional calculus

2010.04.30 Friday ACHK