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The Detection of Absolutes (2) 
in which we try by experiment to test an hypothesis ... 

RecapIt is shown here that neither translational nor rotational measure can be had from elementary geometry, and that in fact no kind of measure can be had.So, acting on the very common supposition that Nature and Geometry bind seamlessly to each other, we may turn to Nature to see how She copes. In Nature, we observe perspective, which entails special, socalled “ideal”, points at infinity – the points in which certain coplanar lines, which are ‘special’ by way of being parallel, appear to meet. But ‘special’ qualites are adventitious and extraneous, because
This specialisation grafts equality
on to projective intervals to confer on them an entirely nonnative and quite extraordinary property – namely, size. It recasts a simple count of sizeless intervals as a sum of units. The supposition is that if the real invariants, X and Y, are both placed at ∞, ↑ a Simple Count of Sizeless Intervals ↑ is converted to ↓a “Sum of Equal Units”, ↓ But this is wholly empirical, and the ‘supposition’ is an hypothesis that must be tested. 
If ...
as is hypothesised here, and recapped on the left, actually find (i.e., detect) these elements in their natural places ...
... and establish their existence as
natural objects.^{[ * ]}
Find and mark these pairs.
We see that in order to locate the pairs of parallels, we would –
However, there is nothing in the photograph (which, do please note, is our sole and only source of objective information) that allows us to locate its infinity, so the attempt to locate the photographed parallels must always fail.
Find and mark the circles.
We see that to find the embedded circles, we have, in addition to locating the photographic infinity, to find those conics for which the radii are constant, because every conic has a pole cum centre, corresponding to the line at infinity as its polar, whether or not the conic is a circle. The detection of circles requires more than detection of poles/centres. The photograph offers nothing to help us do this, so attempts to locate circles must also always fail. 

So, because the absolute, natural infinite defies detection, the hypothesis is untestable. we must conclude that there is no geometric way to detect or establish absolute, isotropic equality.

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