Measurement and Ordinal Numbers

A Ratio and a Measurement are each a kind of comparison, and are perhaps intuitable as such.  But the significant difference between the two is that the terms of a Measurement are ordered, while those of a Ratio are not.  For, in the former, one term is the measurer and the other is the measured, whereas in a Ratio, both terms are Numbers.  Now, the Measurer-Measured relation is ordered because the former is prior to the latter in some respect, e. g. a timer precedes the timed.  But, being ordered means that one term is First, and the other is Second.  In other words, Measurement is based on what can be called Ordinal Numerology, in distinction from the Cardinal Numerology of Pythagoreanism.  But Ordinal Numerology cannot be reduced to Cardinal Numerology.  For, since the Cardinal Numbers, according to Pythagoreanism, are each a self-subsistent entity, they are also independent of one another.  But Ordinal Numbers are mutually implicative.  So, to the contrary, Cardinal Numbers are perhaps abstracted from Ordinal Numbers. In any case, even if it is not Man who is the measure of things, Protagoreanism presents a radical alternative to Pythagoreanism simply by virtue of introducing Measurement as its fundamental concept.