Four Dimensions

Picking up where we last left off, our dilemma of the three and four continues into the realm of mathematics. Preston Harold explains:

In the mathematician’s view, the physicist deals with four continua, or – more precisely – with four dimensions. In geometry, four dimensions would mean that one has four independent directions. For example, this could be seen by drawing four lines through a given point, all perpendicular to the others. In this narrow sense the universe has only three dimensions. The mathematicians extended the concept of dimensions to any situation where events can be described by independent coordinates, and where certain simple laws hold. In this broader sense Einstein found it convenient to use four independent coordinates, with time playing the role of a fourth dimension. In pure mathematics, as well as in its applications to physics, it is often convenient to use many more dimensions, even infinitely many.

8-cell-simple

But the idea of wholeness, or of continua itself, as one dimension greater than any number of dimensions has not broken through the tetragrammaton – through the confines of four. For example, Einstein speaks of the “bold” interpretation of the modern quantum theory associated with de Broglie, Schrodinger, Dirac, and Born – he says their interpretation “is logically unobjectionable and has important successes to its credit. Unfortunately, however, it compels one to use a continuum the number of whose dimensions is not that ascribed to space by physics hitherto (four) but rises indefinitely with the number of the particles constituting the system under consideration.”

For how long does the number not ascribed to space rise? Is it infinite? Jesus will have something to teach us here but before we get to him, we will detour into the world of music.

Until next time, peace.

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