When the ensemble of cesium beam and hydrogen maser atomic clocks strike 11:11 today at Boulder's National Institute of Standards and Technology nothing will happen. Never mind the fact that the numbers are both binary and identical and that the square of any cluster of 1's is going to be palindromic as well. 11 x 11 = 121 and 121 x 121 = 14641 [edit.comm.: first draft of the post had a typo here, omitting the 2 in both instances of 121].
Pop culture is considerably less oblivious. Tumblr microblogs are reveling in the fact that we're also on the 11th Doctor Who and Spinal Tap fans are observing Nigel Tufnel day in honor of the legendary fake popstar's legendary fictitious amp.
A group of British explorers are launching a reenactment of the Scott / Admunson race to the pole today to raise funds for the British Royal Legion today in honor of Veterans day which is observed on November 11th because on the eleventh hour of the eleventh day of the eleventh month of the year 1918, the ceasefire between The Allied Nations and Germany went into effect. Granted, "The War to End All Wars" officially ended on June 28, 1919 with the signing of the Treaty of Versailles but consistency makes for good symbolism. Scientific?
Palindromes and symmetry have a decided emotional resonance. A surge of weddings are scheduled for today because the symbolic symmetry corresponds to the two individuals taking the vows of matrimony. A spike in the number of births and of deaths would not be surprising. Science?
I read Stephen Jay Gould's "Questioning the Millennium" in 1999 while writing and rehearsing my first New York full length solo performance, GreenlandY2K. Gould's observations about numerological coincidences gave context and ground to the story I was creating about the millennium, the Y2K bug and a doomed expedition to the North Pole coinciding at the stroke of midnight.
"Numerological coincidences remain fascinating precisely because they can boast no general or cosmic meaning whatsoever," Gould explains in I Have Landed: the End of a Beginning in Natural History. The "eerie fascination" many people have with "coincidence and numerology" Gould attributes to the fact that people have "so thoroughly misunderstood probability." He cites famous historical coincidences --Thomas Jefferson and John Adams both died on the 4th of July; Charles Darwin and Abraham Lincoln were both born on February 12, 1809-- as examples and points out that, by ordinary rules of probability, both coincidences are unremarkable. In Questioning the Millennium, Gould details how the 1,000 AD Gregorian miscalculation continues to skew our calendars because you actually start counting at one, not zero.
As the national standard for frequency, time interval, and time-of-day and a vital contributor to time and frequency standards throughout the world, it is not NIST's place to acknowledge anything exceptional about 11/11/11. Will NIST's employees be as irreverent about the coincidence as the institution they work for or will they gather round the clocks? A surge in attention, interest and activity would not be inconsistent with the principles of probability, or the principles of human nature.