It is indeed true, despite how familiar such frameworks can become throughout life, that not only the words for units of measurement are arbitrary human constructs, but also the habit of using one set of units over another. Yes, though logical truths about them are no such thing (one gallon is by logical necessity one gallon, and 10 sets of 10 centimeters is one meter), units of measurement for spatial distance, weight, and size are happenstance in their cultural prominence. Distance, weight, and size are objective qualities of physical environments and objects. The inability to ultimately know a great many things about items in the external world beyond subjective perceptions of them does not mean that whatever physical things exist do not really have a certain size, weight, and so on. They would have such characteristics, whatever the particulars.
The vast majority of the countries in the world, more than 190, are reported to use the metric system for standardized weights and measures, rather than the imperial system stubbornly held onto by the United States, a holdover from British influence at the time of the country's founding. Based on multiples of 10, the metric assortment of measures is rather simple; 10 centimeters is a decimeter, 100 centimeters is a meter (and 10 decimeters), 1,000 meters is a kilometer, and so on with similar conversions. Some people in America, accustomed to something else because of their intra-cultural experiences despite it in actuality being random, might balk at the idea of ever adopting the metric system, perhaps out of nationalistic motivations (desiring to be set apart from other countries without any reason beyond tradition, whim, or feeling). While the acceptance of the metric system is also a cultural construct--it could have been the case that a system based on multiples of 9 or 13 was popularized, however less simplistic and accessible this would be--some systems are more arbitrary than others.
The imperial system is objectively more complicated than the metric system, and needlessly so, but it is not irrational itself; there is no contradiction between the various units of the imperial system, and nothing about this system contradicts logical axioms, other necessary truths, or the observed features of the natural world. What is irrational is a person or country holding onto an especially arbitrary set of units for the mere sake of tradition or a nationalistic pride (nationalism already being philosophically erroneous on its own). Yes, a foot containing 12 inches, a yard containing three feet, and a mile containing 1760 yards is far more randomly complicated than consistent multiples of 10, but there is nothing conceptually false about such relationships.
At this point in history, it would be even more difficult to shift the societal direction of the United States than before, in the sense that there are even more years of custom behind the imperial system's enduring use. It is nonetheless utterly inconvenient for international interactions to have a small handful of countries that do not use the same units of weight and measures as the rest. The foremost issues concerning units like those of the metric or imperial systems, nevertheless, are those of logical necessity regarding concepts, the ultimately arbitrary adoption of some units over others, and the difference between units themselves (either the objective concepts that transcend concrete examples or the linguistic symbols assigned to those concepts) and what they are measuring.
Units are not primarily a matter of science, after all, although of course scientific matters of length and weight in the physical world are intimately related. They are a matter of logical necessity and the consequential relationship between ideas, which do not and cannot change with shifts in the words or mathematical symbols affiliated with units, or with alterations to scientific or broader cultural consensus. They can only be discovered and not invented--or at least the concepts and logically necessary truths about them, such as numeric relations and the fact that they, as with all other things, are governed by logical axioms. Whether one given word or another will be used to speak or write of them or whether one set of units will take predominance in one region or another is a separate subject.
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