Higher-Dimensional Spacetime Viewed Through Systemic Functional Linguistics [2]

Penrose (2004: 881):

Before we dismiss this idea as a total fantasy we must recall the ingenious scheme, put forward in 1919 by the (at that time) little-known Polish mathematician Theodor Kaluza, and then further taken up by that same Swedish mathematical physicist Oskar Klein. Provided that the extra dimensions (in excess of 4, that is) are taken as small dimensions, in some appropriate sense, then we might not be directly aware of them. What does ‘small’ mean in this context? 

Recall the ‘hosepipe’ analogy of Fig. 15.1. When looked at from a great distance, the hosepipe appears to be 1-dimensional, but if we examine it more closely, we find a 2-dimensional surface. 

The idea is that some being, inhabiting the hosepipe universe, would not ‘know’ that the extra dimension wrapping around the pipe is actually ‘there’, provided that the physical dimensions of that being are much larger than the circumference of the hosepipe. Similar remarks would apply to a higher-dimensional ‘hosepipe universe’ of 4 + d dimensions, where d of the dimensions are ‘small’ and not directly perceived by a much larger being inhabiting this universe, who perceives only the 4 ‘large’ dimensions; see Fig. 31.3.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the hosepipe analogy confuses phenomena in spacetime with the spacetime in which phenomena are located. A 2-dimensional surface is a thing which extends in two spatial dimensions. A 3-dimensional hosepipe is a thing which extends in three spatial dimensions. The trajectory around the circumference of the hosepipe is here misconstrued as a spatial dimension.