I was noticing that a clock was about to enter an "opposition" (with the minute and hour hands pointing in exactly opposite directions) and it occurred to me that there was something strange about how 6 o'clock and 12 o'clock are not reciprocal. This had always bugged me on some level, and I am not sure why, so I made a chart of oppositions to discover if something expected or unexpected would appear.
What I found was the (probably obvious) fact that the clock only makes 11, rather than 12, oppositions each 12 hours. As a result, a 24 hour day will only have 22 hand oppositions.
This is because, simply explained (though it's easier to see the visual) the minute hand must always advance a little further to reach the next opposition, as the hour hand slowly moves around to its "starting place" (from the time we've begun measuring).
As such, by the time we arrive at 5 o'clock from having left 6 o'clock (11 hours previously), the minute hand will be too far from its 4th hour opposition (which occurs around 4:55) and the hour hand not yet close enough to opposition to stay within the 5-minute area occupied by the 5th hour.
There is no 5th hour opposition for the hour and minute hand.
Similarly, if we measure alignments rather than oppositions, there will also be 11 alignments, with the most obvious being 12 o'clock. And, like the pattern mentioned above, there will be no alignment in the 11th hour.
What this "means" on a mathematical, cosmic or practical level I do not know. But I suppose for those that hadn't heard of this phenomenon, it could lead to a semi-interesting bar room discussion or gamble.
If you would like to learn and understand more practical and cosmic "puzzles" like this, I highly suggest studying the TYCHOS model (www.tychos.info) because it serves as a fascinating geometrical explanation for observations made of the planets and stars.