The 66 foot chain was the basis of virtually all land surveying in the US until quite recently, and many property deeds are still in chains, links and poles. And if you go to Home Depot you might notice that a lot fencing is sold in 330 foot (i.e. 5 chain) rolls. Here in (basically) the original 13 colonies, we don’t use the public land system, so I get to deal with all of these units, literally on a daily basis! I LOVE MY JOB!!! Nowadays, though, we use feet and decimal feet rather than inches.

And for a number of years, until about 1999, the Federal Highway Administration mandated the metric system be used for any projects that used federal monies. That means that I get to deal with that despicable system as well – reading highway plans.

As far as I can tell (which, admittedly isn’t very far), modern mathematicians are more or less in the same boat as modern physicists — they quite literally don’t know what they’re talking about. That is to say, they are very capable of using mathematical models, etc. to achieve useful results, but they basically prescind from the ontological question of what, exactly, it is they’re talking about. The absolute best they can manage is a pragmatic (and Pragmatic) appeal to use, where that encompasses not only something like engineering, but also use in the sense of “useful result.” That’s precisely why they must have recourse to mathematics, because they can’t say what it is they’re doing. Now the question of the relationship of their models (which are by definition mathematically convenient simplifications) to the world remains very vague, to the point that, frankly, both the scientists and the philosophers of science should be ashamed. This is exactly what Husserl was talking about in The Crisis of the European Sciences and if anything the crisis is even more acute today than in the 1920’s when Husserl began to notice how the new Quantum physics was, well, crazy.

The constructivist impulse as I’m referring it here goes far beyond those modern philosophers of mathematics. We live in a constructivist age which was birthed in the corruption of first philosophy at the start of the modern age. Kant represented this constructivism taken to its most sublime pitch, but even in the so-called realism of contemporary analytic philosophy the game has already been given away in the acceptance of the basic assumptions of the modern project and the demand for epistemological grounding. What, then, is Aristotle’s or Thomas’ epistemology? When you get right down to it, the question is almost non-sensical. If you demand an answer you get something on the order of the soul’s touching the world.

But as to whether such things are ontologically untenable – I don’t know, right off, how to sort that issue out. Aristotle also seems to think that there are only as mnay numbers as there are objects in the world – but that seems plain wrong to me, not from a constructivist perspective, but from a realist (with respect to mathematical objects) perspective. Perhaps you can say more, though, about what you take the pre-modern ontological grounding of such objects to be.

As far as the modern discussion goes, if we’re to believe Stewart Shapiro, most mathematicians are realists with respect to mathematical objects, i.e. they exist independently of the mind. Some would call these folks platonists. That’s where my sympathies are. But those who endorse this view have the epistemological question to answer: if these objects are mind independent, how do we know them?

Proper modern day constructivists think that mathematical objects are not mind independent – which makes the epistemological question easy, but (perhaps) the consensus among minds/cultures/diachronically, and the strong intuition (among some) that such simply cannot be the case hard to explain/answer.

There is actually an interesting issue here, though not what you were referring to I think. This turns on the question of what a unit is, the ontology of unit-ness and the relation of the unit qua our understanding via the logos to the unity of being and in turn its relationship to the being of beings.

Aristotle, for instance, insisted that 1 was not a number and had serious doubts about 2. Ratios of your sort could be embraced within analogies to other ratios 1:3::2:6 and so forth. However, irrational numbers like pi were, for the Greeks, ontologically untenable. Which is part of the reason they worked so hard to rid their geometry of them. The modern embrace of such things beginning with the development of analytic geometry in the 16th century is at the heart of the modern constructivism that is the essence of modernism.

as an actual scientist, I can say that people who need numerical accuracy use whatever system works and is most convenient. Hence, people who work with electrons set the mass of the electron to … 1 unit. Likewise, many cosmologists work with units where the speed of light is 1. Why can’t humans work with units that are connatural their own scale, and use fractional divisions when they are the most appropriate?

Most important to me is the Fahrenheit temperature scale. I suspect this provided the denouement of the metric conversion in medicine. About 40 years ago as I was fresh out of medical school, some large hospitals were using Centigrade for fever. It floundered for nearly ten years before it was virtually abandoned. For humans a very few degrees F. make a lot of difference in comfort and in illness, the Centigrade scale obscures this into fractions of a degree. So the flip side of 1 cup of flour is a full degree of fever, F-wise means a lot more than 0.5 C.

Clara helped me further understand why the great metric march failed in the USA.

In science and much of engineering, other systems are used, but pounds of weight, cups of flour, miles per hour, the English system will probably reign for much, much longer in the USA.

You are right that cooking is the most human of activities using weights and measures. I cherish my old cookbooks and am glad that US publishers never have given in to metrics.

It’s just too bad the food companies are not better at resisting. Wine should come in ounces, not liters or grams or whatever.

Vive le Roi! Et L’ancien Régime!

Pax Christi.

Land in the U.S. is described in sections, half sections, quarter sections, quarter-quarters, etc. in the lands surveyed first in the old Northwest Territory. Kinda sounds metric to me. And that was just before the French Revolution. Maybe we should bring back roods and perches.