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Clearly, the analogies above are not the one I wrote about.
... As a special case, it follows that the instant distance
between the edges of a longitudinally moving rod (DEFINED as its length in the new RF)
Now, John wondered why I do not use the same logics to prove
that, say, an x-projection of a rod in a 2-D space (x, y) is equal to the actual length of the
rod.
This is equivalent to demanding that I use the logics leading to the result "six" = "half a
dozen" to prove the result "six" = "quarter of a dozen". The only possible way to justify such a
demand can be that, in John's view, the purely spatial system (x, y) is TOTALLY analogous to the
spacetime system (x, ct). Such analogy, if taken to this extreme, is false.