The Notion Of A "Rolled Up" Space Dimension Through Systemic Functional Linguistics

Davies & Gribbin (1992: 244-5):

The idea that space may have more than three dimensions actually has a long history. Shortly after the general theory of relativity was developed, when only two fundamental forces (gravity and electromagnetism) were properly recognised, a German mathematician called Theodor Kaluza found a way to describe electromagnetism in terms of geometry, just as Einstein had described gravity in terms of geometry. The electromagnetic field, Kaluza pointed out, could be regarded as a kind of space warp, but not a warp in the ordinary three-dimensional space of our perceptions. Instead, Kaluza's space warp lay in a hypothetical fourth dimension of space, that, for some reason, we do not see in daily life. … 

Kaluza's theory was taken up by a Swedish physicist, Oskar Klein, who found a way to explain why we do not notice the fourth dimension of space. Klein argued that this is because the extra space dimension is "rolled up." Just as a hosepipe looks like a one-dimensional line from a distance, but is in reality a cylinder, so four-dimensional space could be wrapped into a hypertube (Figure 40). What we previously thought of as structureless points in three-dimensional space are, Klein asserted, really tiny circles in the fourth dimension.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the notion of a 'rolled up' space dimension derives from confusing dimension with trajectory. (The curved shape of a hose-pipe is not a curved dimension; what is curved is the trajectory of any body traversing its surface.) When Einstein described gravity as the curvature of space-time, the curvature he actually described was the curvature of the path of a photon in the vicinity of a massive body, not a curvature of space. 

According to the General Theory of Relativity, gravity is the increasing contraction of space intervals with increasing proximity to a centre of mass. Because space intervals are shorter in the direction of the centre of mass, relative to space intervals in other directions, the shortest path that a passing body takes unless acted upon by another force, the geodesic, is curved in the direction of the centre of the massive body.

This confusion of dimension with trajectory invalidates not only the Kaluza-Klein theory, but all versions of String Theory that depend on the notion of a curved dimension.