I noticed on his websites that he likes to write dates in a format like "2009-121" or "2006-257", i.e., year and then day of year (1..366).

I also use that concept, though I write it as XXYYY where XX is years post 2000 and YYY is the day number. For example, today is 22100.

Why do I like this? I find this is more "mentally ergonomic" to use for software tooling I have made for myself only. I usually don't care about the month or date of the month; I care about offsets (e.g. tomorrow is 22101 and ten days from now is 22110). If I'm computing an offset in my head, I don't have to account for wrap-arounds due to month (e.g. 10 days from March 25 is April 4 because March has 31 days.) The XXYYY format is about as concise as you can get (i.e., takes up minimal space on the screen) while still capturing all the information I care about. XXYYY sorts easily (though that's also true of YY.MM.DD which is my second favorite format).