Physical Space Vs The Mathematical Notion Of Number Viewed Through Systemic Functional Linguistics

 Penrose (2004: 58):

By the 19th and 20th centuries, however, the view had emerged that the mathematical notion of number should stand separately from the nature of physical space. Since mathematically consistent geometries other than that of Euclid had been shown to exist, this rendered it inappropriate to insist that the mathematical notion of ‘geometry’ should be necessarily extracted from the supposed nature of ‘actual’ physical space. 

Moreover, it could be very difficult, if not impossible, to ascertain the detailed nature of this supposed underlying ‘Platonic physical geometry’ in terms of the behaviour of imperfect physical objects. In order to know the nature of the numbers according to which ‘geometrical distance’ is to be defined, for example, it would be necessary to know what happens both at indefinitely tiny and indefinitely large distances. Even today, these questions are without clearcut resolution. Thus, it was far more appropriate to develop the nature of number in a way that does not directly refer to physical measures.

 

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From the perspective of Systemic Functional Linguistic Theory, the view that 'the mathematical notion of number should stand separately from the nature of physical space' was a recognition that mathematical notions and physical space are of different orders of experience.