Just plain day number as the calendar is worse than weeks imo. We want to optimise for the common case, and wanting to know the day of week and number of weeks from today is much more common than day of year.

For example, “our next meeting is w48.3” is much more understandable than “day 339”.

It's indeed harder to compute the time difference, but maybe it's also an indication that mental calculation should be practiced more.

I don't see how. You are making assumptions and claims for others with no support. To me that week.day number looks more complicated and less meaningful than plain days.

Perhaps weeks seems to make sense since we sometimes use them for offsets and ranges, like "this project will take 6 weeks" and figuring out how many days that is is inconvenient. But if we were using days then we simply wouldn't use groups of 30 or 7 for things like that, we would use groups and multiples of 10 or 5. We'd probably end up using kilodays and millidays too instead of years or minutes, and years would be arbitrary, but 51.9something weeks is already arbitrary anyways.

And as that # of weeks example just showed, .day is ambiguous with decimal fractions of a unit.

All in all I see no special obvious rightness here. It's kinda crap actually.

Mr. I-Can't-Recognize-A-Joke here to explain in painful detail why your proposal won't work...

>Or 365.25 one-day months.

or 365.2425 one day months and no squabbles every 400 years. (we will however be squabbling the entire rest of the time)

If you put Christmas in month 0.24 I'm sold.