Saturday, December 29, 2012
Asylum Walk (2)
Richard Dedekind, who died 92 years ago on this date, originated his “Dedekind Cut” as a means of avoiding the gaps, or discontinuities, implied by a number line continuum composed of discrete numbers. At any point on the continuum where a rational number does not occur, the mathematician creates an irrational number, thus ensuring continuity. For example, √2 is that point on the number line between, to its left, all numbers whose squares are less than 2 and, to its right, all numbers whose squares are greater than 2.
Is our sense of “now” a kind of Dedekind Cut? Behind it, to its left, lie all events, including mental states, that have occurred (“the past”); to its right, ahead, lie all events that will occur (“the future”).
In mathematics, an irrational number cannot be expressed as an integer (a whole) nor as the quotient of two integers (a fraction). Likewise, “now,” though it permits of feelings of wholeness, does not comprehend any whole or ratio of wholes. It is flux and partialness and the perception of flux and partialness. It both moves and does not move along the time continuum. Perceived as a still point, it yet consists of ceaseless movement. At every instant, consciousness is constructing and becoming the future, and constructing and becoming the past, advancing and building and revising in both directions, left and right, without pause—yet it does so from a point of notional and experiential stability that it calls, irrationally and necessarily, “now.”
“Now” is a moving Dedekind Cut.