Not directly related to anything about starfleet, I wanted to write my feelings about this phenomenon too.
It's about seeing numbers and sequences like 11:11 (although not limited to 11:11, can be lots of similar sequences) much more often than it would normally be expected.
(At least, for myself) such sequences are most easily seen on clocks. It is like magic, you want to learn the time and BOOM! It is 11:11! (or a similar interesting sequence; 3:33, 11:01 etc.) It is like someone put so much effort into this to make sure you see that number on time.
Reminds me of this sudden irresistably-powerful urge to look at sky to see starships. You just HAVE TO look at it. I still wonder not "why", but "how" this happens.
Inner openness to higher frequencies - flowing with soul purpose - brings us into a more conscious, aware alignment with the flow of Divine Order, in my experience, which expresses through the universal coding of number and geometric sequences at the 'building blocks of Life level'.
I also love the way soul alignment reflects into physical so precisely in so many ways, and enjoy the number sequences and how the 'gateways' of 11:11 (and 12:12 etc) 'pop up' along the way. :)
I came to your page and saw this subject about 11:11 after I have seen it just about 20 minutes ago...I was feeling a pressure in my left ear and I know that it means someone is trying to get my attention...I looked at my computers time and there it was 11:11...I smile it happen almost every day...No coincidences...All happens for a purpose...