> Just curious — aesthetics aside what other
> advantages do you think an analog watch provides?
Think of an analogue watch as a 2d graph where one of the dimensions is t. If you have a table of numbers you can compare them by looking at all the cells or you can graph each row one a cartesian (or polar or...) plot. Both contain the same info, and the table probably has higher resolution, but which tells a more illuminating story?
On a watch face, the minute hand is the biggest win: you can see at a glance approximately what time it is / approximately how long you have / approximately how far away you are which is what you usually need. I definitely think in terms of it being about "a quarter past fourteen" or "half past seven". The digital watch has too much precision and requires too much parsing.
The hour hand gives you similar data on a larger scale, but you typically need that less. And in fact though the watch face shows 2x 12 hours, when I look at it I see the normal 24 hour clock.
The second hand is good when you're working out since as you see it sweep to its goal you might push harder to get one more rep in or whatever, but this is a less common need and in fact many analogue watches come without a second hand.
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The analogue clock face is an example of more humane design for specific problem domain, sort of the like US & Imperial unit systems. They are utterly useless for engineering (but even in engineering I use both MKS and CGS depending on the problem domain -- and its community). Miles and km / acres and hectares -- it's no big deal to me either way. But when making a staircase, cooking a meal for three people or resizing a dress pattern, the ability to use a system that naturally decomposes into rational factors is appropriate. And that's the beauty of the babylonian time system: despite the annoying (though necessary) primality of the week, there are plenty of factors available for subdividing the intervals.