10:09

In most department store catalogs, you'll see all their wristwatches set to this time. The reason is simple and obvious: the hour and minute hands are symmetric across the center of the watch face, nearly 120° from the center axis and from each other. (Remember that the hour hand moves forward a fraction of a tic for every tic the minute hand moves forward; this is why 10:09 is symmetric and 10:10 is not.) In this position, the hands will also neatly frame the brand name, typically displayed on the watch face just above where the hands pivot.

If you were to assume an ideal watch face where the watch tics had infinite precision, you might find the moment of "perfect symmetricity" in the following manner:

50+(x/60) = 60-x
    (since the hour hand is positioned at 50+x/60 minutes at x minutes after 10)
x+(x/60) = 10
60x+x = 600
x = 600/61
x = 9.8361 (approximately)
x = 9' 50.16" (to the nearest hundredth of a second)

...but in real life, the hour hand typically tics forward only when the minute hand sweeps through a full 60 seconds. So instead of rounding up to ten minutes, you must round down to nine.

The odd thing is that this practice is also carried out with digital watches, even though the above aesthetic reasons are moot. Tradition is a hard thing to buck, it seems.

There actually is a reason for showing digital watches at 10:09 (or, more often, 10:08): it shows that the LCD are functioning properly, and that the watch can show all four digits necessary, without resorting to an illogical time.

The numbers in an LCD are usually set up like so:

 _
|_|
|_|

The numbers that show the most sections are (in decreasing order) 8, 0,9, and 6. Since one would want to show as many lit sections as possible, the logic would follow:

Minute: Ones digit: can be any number. 8 or 9 is good. 0 might make the watch appear broken (see below)

Minute: Tens digit: can't be higher than 5. 0 is therefore the best choice.

Hour: Ones digit: Can be any number, but only 10, 11, and 12 are two-digit numbers, so the logical choice is 0.

Hour: Tens digit: Needs to be a one to show that the display is working.

Therefore, in a non-military time digital watch, 10:09 is a functional choice. The fact that it agrees with the best display on an analog watch is just coincidence.

Really.

Why, you can even see the "10:09 effect" in an old The Far Side cartoon. The cartoon I speak of shows a man slumped dead over a table. The room he's in is almost over-flowing with bullet-hole filled broken clocks — all of which are stopped at 10:09 (or there abouts — after all, this is one of Mr. Larson's cartoons, not a technical illustration of the SR-71). A police detective is looking around the room as he says to his partners:

"We've got the murder weapon and the motive... now if we can just establish time-of-death."

(I miss The Far Side...)