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The fate of the primal scene:
There may be an actual sensory experience. This would correspond to the lowest-level hypotheses of empirically verifiable fact.
The scene assumes the character of a hieroglyph or an ideogram.
The ideogram becomes (a) formularized, or (b) abstract. If abstracted, then it becomes a figure constructed out of the ‘elements’ (of Euclidean geometry).
An intermediate phase derived from another context – the invention of Cartesian co-ordinates.
The further abstraction of the scientific deductive system that is Euclidean geometry, to produce the algebraic calculus representing the scientific deductive system that is Euclidean geometry. Thus is established algebraic geometry.
Further calculi.
Now the algebraic calculus has to be returned to the lowest-level hypotheses of empirically verifiable data; it can then find its ‘realization’ in ‘space’ from which Euclidean geometry supposedly springs. But in fact the calculi that have been produced are many and diverse, including those of non-Euclidean geometry. Some of these calculi are applicable to study of astronomical space. But in so far as inappropriate calculi may be used, they tend to betray their origin, and the space that is explored by virtue of these calculi is given characteristics that are markedly reminiscent of the empirical data from which the calculi were originally derived. Are these characteristics then actual characteristics of space? Are there actualities or realities
corresponding to the ideas of reality that the calculi have enabled the astronomer to achieve? Or are the ideas only reflecting the origin of the calculi and the scientific deductive system, Euclidean geometry – namely the space of the primitive individual from which the scientific process sprang?
Unfortunately astronomy is based on data derived from one sense, sight, so ‘common sense’ may be hard to achieve. Furthermore, the actual elaboration of calculi, in the way I have described it, is a kind of