Halfs are easy enough in either. Quarters are hard in metric as 4 is not a factor of 10. Which is why imperial systems are often base 12 (gives you 3 and 4 as a factor). circles are base 360 so that you get factors form 2 all the way to 12.

How much this matters is open to debate, but base 10 is clearly a terrible thing in this. It might be a good compromise, but I am not sure.

Yeah, I meant repeated halving or doubling. So for example if you start with 1, and keep dividing by 2, in base 10 you get 1, 0.5, 0.25, 0.125, 0.0625, 0.03125, etc. In base 8, 1, 0.4, 0.2, 0.1, 0.04, 0.02, 0.01, 0.004, etc. Much simpler.

Obviously multiplying and dividing by 5 and 10 are more natural in a base 10 system, but dividing things in halves, quarters, etc. (or multiplying by powers of two) are a much more common operation. (We only think of 10s as round numbers because of the base-10 decimal system.)

12 is useful in that it has so many different factors, but it misses all the benefits of being a power of 2, so I feel 8 is superior. Hexadecimal also has benefits, but my feeling is that 16 symbols would be too many for everyday use. Difficult to count on fingers and such. 8 really seems ideal to me. In fact, I've mused in the past that it's kind of a shame - you can imagine a world where people ignored their thumbs when finger counting and just lucked into a base-8 system thousands of years ago. (Although of course in that case we wouldn't call it base-8, it'd be base-10!)

> I've mused in the past that it's kind of a shame - you can imagine a world where people ignored their thumbs when finger counting and just lucked into a base-8 system thousands of years ago.

What a fascinating hypothetical!

But to the main topic - sorry to be dense about it, but I'm actually just not used to the imperial system. Which parts of it are easy to manipulate in this way? I know there are 12 inches in a foot but that's the only "easy" conversion I remember off the top of my head.

The metric system, since it's all based around base-10 counting, tends to operate in decimals. So you wouldn't normally talk about for example a quarter cm; rather you'd have 25mm. In the imperial system working in fractions is much more common, so you have quarter inches, eighth inches, etc. Halving is more intuitive using fractions since it amounts to multiplying the denominator, rather than dividing.

Anyway, I'm not really arguing for the imperial system, just saying that aside from legacy use, that's the one advantage I see for it vs metric. But a metric system based on base-eight... that would be beautiful.

Oh interesting, you're saying it's not about the specific conversion factors, but rather the idea that people tend to subdivide units into halves/quarters/etc in imperial, whereas they don't in metric.

I just meant in imperial, it's common to use fractional measurements. IE 1/16", or 1/4 cup or whatever. Doubling or halving those fractions, especially repeatedly, is simpler than with metric measurements. IE taking 1/4 of 25mm.