Comment on ?The biological foundation of space and the evolution of spatial dimension? by Berkowitz and Tschirgi

Abstract

only if a and a do not coexist ‘at the same place’ or ‘at the same time’. As Berkowitz & Tschirgi (1988) point out-and, before them but more obliquely, Kant-dimensionality depends a priori on the circuitry available to organisms for the resolution of superpositions. The subjective effect of this limitation cannot be transcended-we normally invoke additional dimensions in mathematical models and have devised the mathematics needed to handle them, but there is no way in which we can draw a fourth orthogonal. The reason for this lies almost certainly where Berkowitz & Tschirgi place it-in our processing mechanism, not in the fact that Nature is like that. Their paper suggests physical reasons why organisms should have evolved three-space perception, but it can be extended with interesting consequences if we include the fourth term in the human experiential transform of x’ + y2 + Z’ t’, namely elapsing time. This imaginary dimension, which is orthogonal to x, y, z in the same sense that the i axis is ‘orthogonal’ to the real-number line, can be endowed with a phylogeny exactly as can chirality. Wholly instinctual organisms (those with a read-only programme) can be regarded as achronic, though they may be seen by us as exhibiting sequential behaviour: the biological counterpart of ‘flowing time’ is presumably learning, the process by which prior experience modifies subsequent behaviour. The quantity t as experienced by organisms is something quite distinct from 1 as a component of space-time and is so recognized by physics: the ‘flow of time’, which is the most strongly a priori intuition in the experience of higher organisms must be replaced, as Davies (1974) points out, where it belongs, in the human brain: space-time exists en bloc, but we invincibly experience it, in de Broglie’s image, as successive slices (de Broglie, 1959) there being no way in which space-time can be consistently sliced so that the ‘news’ of spatially-separated observers can be sequentially ordered. This truism-nicely expressed in the slogan John Wheeler saw chalked on a wall in Berkeley, ‘Time is Nature’s way of ensuring that everything doesn’t happen together’,