If people were logical instead of historical, I suppose so. Since monetary divisions were originally based on weights of precious metals I assume the answer could be found there, but I don't know. (The 12 suggests troy weights, other than that I don't know). There were ha'pennies and farthings (fourthings?) though.

For measurements of length and mass, doubles/halves and their multiples worked well in a low-tech environment, I guess.

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For engineering/machining drawings, decimals and fractions play a role in determining what the tolerance is when not directly specified for a dimension. Usually there's a tolerance block on the drawing that states something like

_____

UOS

All dimensions are in inches.

3 place decimal ± 0.001
2 place decimal ± 0.005
1 place decimal ± 0.01
Fraction ± 1/64
Angular = ± 0^o30'
_____

Of course, tolerance blocks are a cop out since they're applied in blanket fashion to many different features, each of which very probably needs a looser or tighter tolerance. But that might involve actual design engineering work.

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I've been puzzled by the avoirdupois system for a long time. I've wondered if maybe whoever invented it had 6 fingers & toes.

Think of it this way. You're in the process of becoming 'sophisticated' & need a way to count more than 'one or many.' Surely you'd come up with a system based on 10's? Or 5's perhaps? There you are with 5 fingers & toes - what would be more natural than to start counting in groups of 5's?

And in fact, that is what happened - our number system is base 10 & that works out well.

So why on Earth would measurements be based in 6's & 12's? It's awkward to say the least to try to use such a system while simultaneously running with a base 10 number system.

360º in a circle, 60', 60" - why? Why not something that makes sense in 10's?

If you try tracing it back, it goes a long way. There's guesses that we use 360º because it matches the days in the year - no it doesn't! And to do it that way, the ancients would need to know the Earth travels in a circle.

So it's another of those 'this doesn't fit' puzzles.

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I like base 16.

Like the QWERTY keyboard?

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The division of a circle by degrees has worked out just fine for the convenience of carpenters, architechts and engineers as well as artists
for quite some thousands of years The simple functions of a circle as it is described , could not be simpler or better. Field geometry reveals much.
And the twelve comes from the twelve points of the compass. A nod to
astronomy.
The more you try to out-smart the ancients, the more you come to respect their elegant simplicity.
Best regards, Dan

If you accept devision by 2 as the source of the 2s, 4s, 8s, and such, then the source of the 6s and 12s and 60s is pretty simple: division by 3 is also a pretty basic kind of division to want to do.

But if you do divisions with higher numbers , using a calculator is the easiest thing to do .

Other than the minor nitpick that the Earth doesn't travel in a circle, I don't think you would have to know anything about orbits. You would merely have to observe that the seasons repeat themselves in a roughly 360 day cycle. Or that the day becomes long and then short again on the same cycle.

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360 is also divisible by every number 1-10 with the exception of 7, making it easy to divide a circle up into some number of zones without resorting to partial degrees.

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I would expect it to be be remnant from the babylonean base 60 floating point numbers.

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Nah... there's basic engineering behind that. QWERTY was designed to slow typists down so the typewriters didn't get jammed up.

Long before electronic keyboards, before even electric typewriters, the old mechanical actions relies on a lever action to get the letter or number to strike a ribbon, behind which is the paper. Typing too fast would cause the levers to jam together.
While I agree about respect for the ancients, the fact that since we began the 360º trip we have learned to use it doesn't lessen the puzzle of how we came up with it.

And points of a compass are 4, 8 or 16, not 12. So that doesn't explain things either.

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Except it's a very poor approximation. Using 360 means you have continuous adjustments to make, year in year out. If they were smart enough to note the cycle, they'd be smart enough to note that it's 365, even if they didn't at first notice the fraction by which the year exceeds 365 days.

Ascribing inventions to the ancients doesn't work unless you also admit they are as intelligent as we are. They wouldn't mandate a measure that simply doesn't work. if the discrepancy was across many years, maybe, but this is one they'd notice in the first couple of years.

And there is evidence they knew more than just the basics of Earth's movements.

For the others who tried to address this question, it does no good to look at us now & say that this is how things are because it works well. It works well because we have adapted to it over thousands of years.

But I grew up in an avoirdupois world that converted to metric when i was in my teens - metric makes so much more sense it is a little amazing anything else could have been used. Metrics measures things on base 10, the same system as we use for numbers. No awkward conversions required.

The question remains - we have counted in base 10 for as long as we have records, but for some reason we have only recently begun to measure in 10's. Why?

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Don't forget 12. 360 is divisible by every number 1-12 with the exception of 7 and 11. 12 is divisible by the first four numbers (1, 2, 3, 4) and 6. But 60, the Babylonian base, is divisible by the first six numbers--that divisibility by low integers cannot be ignored in the success of those two numbers.

Very true, but the problem is... first you have to have the knowledge that such a property is needed.

Try to picture it - early on, at a time lost in history (because all the records seem to indicate that the 360º system as well as the other odd measurements were in place from the beginning) someone came up with a non-metric system that used all kinds of odd numbers to make up measurements rather than making them from the natural base 10 system.

Why would they do that? Wouldn't it seem to be more natural, in such an early environment, presumably before a need for complex codes & engineering techniques, to come up with something which would be easily divisible by 10's & 5's? 500º divided into 100' would give higher accuracy than 360º & 60' & given the level of technology, it's feasible at least they would have had no way to measure more accurately than 100º & 100'

Instead we have the weirdness of 6's & 12's, as well as a few other oddnesses. It is strange.

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This is a modern myth. The speed it takes to get the hammers to bind is much lower than a normal typing speed, so you'd need to hold yourself back no matter what keyboard layout you were using. QWERTY just simply doesn't and can't do the job people say it's supposed to do. Not only that, but before the keyboard was standardized, there were public typing speed competitions put on by the makers of competing keyboards and typewriters, and QWERTY didn't produce particularly slow results. Also, you can see some of how the keyboard's form was determined by looking at it. It's just too much of a coincidence for D, F, G, H, J, K, and L to be right in a row with E and I right above D and J so it's practically the alphabetical order for 9 letters in a row, especially with M and N in order going away from L right blow that and O and P mirroring them right above. If it had been designed for some unrelated goal such as maximizing or minimizing speed, then it wouldn't have so much influence from alphabetical order.

Not a myth. I've used an old typewriter, one made in the very early 1900's & it had none of the smoothness of later manual models. The keystroke was very long, pressure required was quite high, & if I ignored actual accuracy & just pressed keys as fast as I could, it jammed regularly - I got in trouble for doing it.

Later models could also jam if one mis-keyed slightly & had 2 keys move together. Use of a recent (post 1960) manual typewriter doesn't convey what it was really like trying to use an original technology one. The sticking keys was a reality in the early models.

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We haven't counted in base 10 for as long as we have records. Some cultures have used base 12. (I don't know of any other used bases but can't eliminate them.) Our own did at one time, which is why 11 and 12 have unique names instead of "oneteen" and "twoteen".

And measurements have simply been based on "natural" amounts. A cubit was the distance from fingertip to elbow on an average adult, a hand was the width of an average adult's hand, a mile (short for mile passus) was a thousand paces (2 steps per pace, 5 feet per pace, 5000 feet total, originally), a cup was just the amount you could put in a normal cup, a pound was the weight of a normal brick or tile or such, and so on. Ratios between one natural measurement like that and another don't lend themselves to a decimal system any more than the number of days in a year or a lunar orbit, or the number of lunar orbits in a year, does.

I didn't say it wasn't an actual problem. I'm talking about a matter of what the limiting factors are in which situations, and the ones you've just described only make the keyboard layout even more irrelevant for the mechanical problem. People can learn to press keys very rapidly in any layout, so any difference in how rapidly between different layouts can only show up in the high speed range. That can only be the limiting factor when typewriter mechanics are not. You're talking about things that would force people to stick to lower speeds than that no matter what kind of arrangement the buttons were in, which would make THOSE issues, not button arrangement, the limiting factor at those lower speeds.

Just think about how fast you or someone else you've seen can type on a modern electronic keyboard without the issue you described. They're doing that with a QWERTY keyboard. If the mechanical issues force a typist to go slower than that, then QWERTY arrangement was not slowing them down enough for the old mechanical devices; the machinery, not the button arrangement, was the limiting factor. The button arrangement could have, and today does, allow for faster speeds than the old machines did, so the button arrangement simply does not slow people down enough to be a solution for the mechanical issues.