Hey boss, we seem to be all out of 3.31mm^2 romex, all I got left is 2.08mm^2. And why did you mention cross-sectional area? Why not radius? or diameter? Or better yet, circumference? I'll take awg12 and awg14 please.
There's nothing more natural about an inch than a centimeter, and nice, round, easy-to-remember numbers can be had on both scales for "natural", commonly found distances. Ditto for pounds and kilograms, Celsius and Fahrenheit, acre and hectare etc.
Objectively, metric wins because it uses the same decimal scale as our number system, and because the units are designed to establish the most straightforward relations between different quantities.
Yes, using 12 for a base has some advantages due to more divisors, but not being consistent with decimal wipes them all out (and traditional units don't consistently use 12, either - consider units of volume, for example). In an ideal world, we'd have 6 fingers on each hand, and use base-12 everywhere; alas...
Recently I was building a roof with an old, very experienced builder. Turns out that on construction sites, nails and planks are always discussed in inches, even when they're actually metric. So a 60mm nail would be "a two point fiver" ("kakspuokki" or such in Finnish).
Note the inconsistency in 1/4".
What's the purpose of having mm^2? You can't measure it any easier (how the heck are you gonna measure area without calipers? you're gonna need a gauge with holes in it to identify wires), nor is it easier to express the number easily.
For manufacturing purposes, expressing the radius or diameter might be good, but for using them, the AWG number is really nice and streamlined.
This doesn't really preclude a logarithmic scale, but it should be the kind that's easy to convert (i.e. increasing numbers denote increasing area). Looking at AWG, it could actually even be decimal, like dB. Consider: 17 gauge is almost exactly 1 mm^2 in area, so if we pick exactly mm^2 as 1 on our hypothetical scale, then 10 would be 10mm - close to 7 gauge, and -10 would be 0.1mm - close to 27 gauge. And there are plenty of industries that already know how to work with dB scale, and use the shortcuts that it offers.
By the way, while looking up related things, I've discovered the existence of a weird unit called "circular mil" (basically, cross-section of a wire 1 mil in diameter) that is, apparently, already used in US for wires that are out of bounds on AWG gauge scale. Which seems to indicate that cross-section area is, indeed, the preferred metric.
And when I say natural, I don't mean elegant. They often tend to be thoroughly arbitrary. But they match the needs, which is usually reasonably pragmatic. For example, 360 degrees is ideal for simple in-head directional geometry, but radians are by far simpler in algebra or very precise measurements (because Pi can often be neatly factored out).
Once you start using enough decimal points, all units are lousy. I remember using angstroms in astronomy because it fit better into the optics theory and the distances are already absurd it didn't matter. So you may as well use the units that are convenient, and just get good swapping.
(PS: glass sheets are sold by the square foot, but in thicknesses measured in millimeters. Turns out to be pretty convenient that way.)
Another thing I've encountered: in South India, there is a measure of distance & time called a "nazhika". It is 24 minutes. 2 1/2 nazhika is one hour, 60 nazhikas make a day. A nazhika is also roughly the time taken for a normal person to walk 1 mile. Hence a nazhika is also used as approximately one mile. Seems a bit weird until you remember that light-years involve the same identification of time and distance.
Non-metric units like these and others ("foot") have probably very good reasons behind them, and they could be used by people in their day-to-day activities while not carrying measuring instruments with them. Metric System is more systematic, but people "lose touch" with intuitions of quantity.
The Sumerians did, in fact, periodically insert intercalary months in order to offset the difference, which suggests that this is in part close approximation and on the other part nice for application.
Of course, at some point it becomes a huge pain and you buckle down and choose something just as arbitrary but easier to handle. And that's why we don't count angles in the milliseconds since 1970. Or days in a year; though we do sometimes measure 3D angles in solid minutes, which seems like a metaphor taken too far :)
Even in metric-using countries, nobody uses it for time.
For actual applications of spherical trig though degree, minute, second makes a lot of sense, primarily because the earth rotates about one arc second every 4 minutes, and if you know this then you can do manual navigation via the stars and many other things.
However for many things I do use metric time, just not for the human aspect of it. For example, for one customer (admittedly in the sciences), we had to help them estimate how much hardware they needed for additional load. So you do the work in seconds because at that point the math is easiest, and convert to ratios following.
Of course for practical use using SI second wouldn't be very good solution. Traditionally second is derived from the length of day, and I think that would make sense for metric time too. 1 milliday would be somewhat close to 1 minute and 50 millidays (or maybe half deciday) would be close to one hour. Of course the name probably should be something else than "day" to reduce confusion.
So I could be working something like 16 decidays next week.
The number of sides depends on the divisiblity of 360 by the number of angles so:
3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 30, and so forth.
For angle measurement where you want a closed geometry figure at the end, degrees are extremely elegant, and 360 is 2^3x3^2x5
You'd also lose the small-angle approximations sin(theta)=tan(theta)=theta which in my field are used extensively to convert nonlinear to linear equations.
Nonetheless, your proposed unit already exists and is called tau. Or write it as 2pi if you want to be more easily understood.
I've sometimes heard the same remark about temperatures: jeez, how do you guys manage to work with something as unintuitive as degrees celcius? But really, you just get used to whatever it is you're using.
If you're going to knock the other way, wouldn't t be far to at least check what that it is rather than making something up as a strawman?
Responding to commenter e2e8: Using 2mm, 3mm, etc. would be substantially less functional.
Once you have a log scale, it hardly matters whether you measure diameter or area, that’s just a constant factor.
In the ideal case, the log scale would have a slightly easier to compute definition for the dilation at each step than the 39th root of 92 (~1.1229).
Perhaps they could use the 6th root of 2 instead (~1.1224). Then every 6 steps you’d get a factor of two. Size 0 could be defined as 1mm diameter (or size 0 could be 1 millimeter squared cross sectional area, with 3rd root of 2 as the step each time).
In practice if you’re wiring a house, it doesn’t much matter.
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One of the reasons the metric system built on a base ten number system is so frustrating for practical purposes is that powers of ten are entirely arbitrary and indivisible, and tenth roots of ten or numbers expressed in terms of natural logarithms are even worse. We’d be much better off with a general-purpose base twelve number system, plus log scales uniformly designed around the twelfth root of 2. [Western music scale, ISO paper sizes, etc. would fit right in.]
For an exponential scale you can just pick some reasonably evenly-spaced round numbers and repeat them at different factors of 10: 1, 2, 5, 10, 20, 50, ...
Anyway, neither way here is right or wrong. One optimizes for uniformity of scaling, the other optimizes for intelligibility with a base ten number system.
However, using something like the E12 series would work pretty well.