Absolutely serious. Using base 12 instead of base 10 would be a huge advantage, if only we had done it 500 years ago. To start, it would make the relationship between fractions and duodecimals much clearer and easier to learn. But it would also make pretty much every type of routine measurement task at least slightly more convenient.

Obviously it’s not feasible at this point to switch our number system, as a social/political question. It would cost trillions of dollars and require redoing our whole measurement system, rewriting all our technical books, changing all of our manufacturing standards, [edit: and retraining the whole society]. But our current systems are by no means perfect.

Within the metric system, there are inconsistencies all over the place, especially where we still accommodate important prior systems, like the calendar and time measures. Day -> Hour -> Minute -> Second and especially Day -> Week -> Month -> Year are quite annoying systems to interact with in an otherwise base 10 world.

Angle measures in terms of either 2pi or 360° -> arcminutes/arcseconds are also pretty bad, bearing little relation to the metric system.

Most of the basic metric system units would surely be chosen differently if designed from scratch knowing what we know now. We could also definitely pick better names for them than names of dead men. For one thing, derived units should have a more obvious relation to the base units, in their names. For one thing, we could finally fix the sign for the electron’s charge. Personally I’d recommend defining time using the day as a base unit, and then measuring distance with respect to the speed of light divided by 12^13, or similar (but that’s just me; perhaps a smart committee could come up with something better).

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Much of our standard mathematics notation could also be improved if we put some thought into it. Fractions are a pretty excellent notation. Positional (decimal) notation is alright, but making some kind of floating point/scientific notation more basic would improve understanding in many ways I think. Basic infix operator notation works reasonably well, though I’m not the biggest fan of the way we handle subtraction or division operators or inverses in general. I like the way we use parentheses. Our notation for exponents is okay but not great, and having two notations for the exponential function is especially confusing. Our notation for square roots, logarithms, and trigonometric functions are all absolutely awful: terribly named, symbolically heavyweight, and revealing nothing about their structural properties. The way we handle vectors and complex numbers is pretty bad (we should use so-called geometric algebra instead, and develop a good notation for it). Our common notations for derivatives are confusingly varied and overloaded, and I don’t at all like our notations for summation and integration. In general, we should measure exterior rather than interior angles, since continuing straight is most natural to define as zero angle.

At a more basic level, our languages should have a highly unique single-syllable word for each basic numeral (from 0–9 or 0–11 or whatever), combined with a highly unique and fast to write glyph for each. We should have a single syllable for making a number negative, even “minus” isn’t a good word, especially since it’s overloaded to also mean subtraction, and we should have a single-syllable word for rotating a vector through a right angle. In speaking, we should compose multi-digit numbers by just saying the digit names, or saying a bunch of numeral names then some marker word, then a numeral name for the exponent. Phrases like “fourteen thousand, seven hundred and twelve” are horribly confusing and wasteful, and do immense damage to fluency with basic arithmetic. Don’t even get me started on the way numbers are spoken in French.