In “The Road to Reality”*, Sir Roger Penrose defines three ‘worlds’ as mathematical, physical and mental and describes the mysterious and complex connections betwixt. Diagrammatically, the triangular image comprises three spheres, each connected to its clockwise neighbour by a conic section that is narrow on the originating sphere but wide enough to encompass the destination sphere entirely. Somewhat like an ouroboros made of three segments.

 

3 ‘worlds’ and their connections. (After Penrose, 2004)

 

 

Physical reason (the nature of reality) is embraced by the world of mathematics. The procedures, functions and attributes of mathematics are contained in well-defined groups: the rotational symmetry group, O(3), for example. The claim by Paul J. Steinhardt & Neil Turok (1998) that all physics in the observable universe (OU) – the 10-brane on which we live - is solvable using the mathematics of Special Unitary group in eleven dimensions, SU(11), is as revolutionary as Newton, Planck and Einstein were on first appearance. To reach this conclusion after such a brief interlude since human language developed is truly remarkable. These are the most interesting of times – to a physicist, at least.

 

The progression to SU(11) is via the realisation of Unitary group in three dimensions, U(3), as, positive (it goes forward in time) definite: U(3) contains the hyper-complex numbers of quaternion analysis and in the early 21^st century AD, Hamilton’s 19^th century graffiti, on Brougham Bridge, Dublin has been modernised, thrice.

 

 

The mathematics of General Relativity theory in four, continuous and possibly infinite, dimensions (3 of space and 1 of time), GR(4), is under constant scrutiny (Gravity Probe ‘B’, NASA’s Cassini Mission &c) and discrepancies between GR(4) and reality are coming to notice as time passes. It seems that the space-time of GR(4) is stable only if there are no massive objects embedded within. The black-hole singularity otherwise implied leads to absurd results in the behaviour of time. Stephen Hawking’s 2005 bet-loss to Kip Thorne is because of a result from SU(11) showing that information isn’t ‘lost’ beyond a gravitational event horizon but is returned to the same universe “in an exquisitely scrambled state”.

 

The observed acceleration in the expansion of the OU requires a non-zero cosmological constant that is difficult to give physical meaning to without recourse to a 4^th space dimension.

 

* Oxford University Press, 2004.