ON SPACE AND MEASUREMENT


When we speak of the calculatable separation between one end of a board and the other, we call it Distance. It is only when we try to measure across a gas or liquid, especially when the measurement exceeds the limits of a hand-held line or similar measuring device, that we start to think of what lies between our manned measurement points as Space. To speak of the space between the two ends of a board would be misleading, since it would imply that the board was discontinuous. Similarly if we speak of the space between the earth and the moon as being a certain number of miles, we imply that we are dealing with three things: Earth, inter-space, and Moon, which is contrary to our usual notions, which assign reality by common consent to mass-endowed objects. The vacuum-like "space" between earth and moon is real enough, but it is somehow of a different nature.

Measurement of the seas has always been a problem for cartographers, the vast liquids expanses cannot be measured in the same incremental ways as land, and in the days before men began to chart the sea floor, the oceans were only spaces between land-points. This arises from their liquid nature, which suggests to men a continuum which on the one hand can be seen as a single phenomenon, but which on the other hand can be infinitely divided. This certainly has something to do with our finite human experience, which prepares us better for dealing with incremental calculations based on "fixed points" in a solid and mass-ful field.

In the l8th century the problems which arose in navigation were finally seen as revolving about the need for a stable micro-experience, which was seen as a reliable second of time on a clock. The perfection of reliable clockworks made calculation of the liquid ocean-medium understandable and feasible, the small-end finite moment was set at one second of time. Without this the seas would have continued to be unmeasurable and because of this, in part, unthinkable.

In this century "Space" has become a common kind of reality, although much clearer on the linguistic than on the philosophical level. We may even go so far as to consider space the natural matrix of large distances, in which measurable points are scattered with great infrequency. The universe might appear to be something like this, in terms of our present astronomical knowledge. But this thinking is deceptive, it merely reverses the usual process of measurement, and treats the measurement-number, in situations of great distance, as the reality factor, whereas we know that all out concepts of astronomical distance are based on light and radiofrequency emission from very finite, distant points. It is a little like looking at one of those black and white psychological test drawings which you can read either way; but at the moment when you "switch" your perception, you reverse all the data one hundred percent. It is easy to do this in large space considerations, and see the universe as mostly space with a few dots of stuff floating around in it, or bits of stuff just floating around, highly isolated from each other.

Leibniz' concept of space as infinitely divisible, yet consisting of a web of contiguous "cells", points to something which we can see in a very different way. We know that we cannot measure the Atlantic ocean by the number of waves rising at a given moment, we need a stable measuring modulus, which in this century we can specify as a thousandth or a millionth of a second. If we seek for a minimum module for performing very large calculation in "real space", we find the minimum-modulus which we can count on is related to the speed of light. This is a universal phenomenon and it is stable, so we can dimensionalize space realiably by measuring distances through space by the minimal time-unit correlated with any energy signal. If we want a simple, earthly parallel, we might consider electromagnetic or light energy as being our measuring tape, while the ticking of micro-seconds will be the intervals marked on the tape.

In rephrased Leibnizian terms, real space will be a continuum of contiguous, momentarily scanned individual Angstrom unit lengths, which correspond to Leibniz' "cells". These have finite size by definition, and therefore a finite space, which has a start and a terminus, would be a finite sum of such unit lengths, while a "space" without a finite terminus would be an infinite series of such lengths. In considering "space" we should probably make a distinction between two different concepts which are unfortunately housed under the umbrella of the one word Space. If we define alpha-space as space between two conceivable termini, then this space will be a continuum consisting of a series of micro time-space units, and hence it is finite and potentially measurable. But if we are speaking of beta-space, which has at least one terminus undefined, then we are dealing with a continuum consisting of micro time-space units which are infinite in series, and hence unmeasurable. "Real" space would be measurable space, not actually more real because it is measurable, but different in kind from the unmeasurable "ideal" space which falls into a different category in human consciousness.

The oceans were the same before we learned to measure them by time plotted against celestial markers, the previously unreal and unthinkable oceans were not actually changed because we made them more real to ourselves. Micro time-space units can be thought of as extending out in every direction, whether they have a photon beam to accompany them, and whether they collide with an object or not. Ideal time in an ideal space is the invention of our minds, which want to remain open to the vast world of the unknown, possibly with a simple faith that someday it can all be understood. Knowing anything at all about the unknowable is what has always attracted philosophical and scientific minds, which are on the other hand constantly cautioned by Heracleitos' warning that "Nature loves to hide itself". The large number of things that we have been able to know about fairly accurately gives us at times the illusory thought that everything is discoverable and understandable. When ideas about space verge into the "ideal", where thought alone can operate, we know we are again working with the unknowable, travelling on a healthy voyage away from the finite and the measurable, and on into the uncharted seas of the unimaginable. It is probably in this direction, the quadrant of what we do not know, that the greatest and most important truths lie.

William Harris
Prof. Em. Middlebury College
www.middlebury.edu/~harris