### Any sufficiently simple explanation is indistinguishable from magic

Take for example the mystical belief that the number 11 or 11:11 is somehow significant. Uri Geller goes on about this on his web site. To quote from Geller's web site (and you'll find other similar thinking on many 11:11 web sites):

String theory is said to be the theory of everything. It is a way of describing every force and matter regardless of how large or small or weak or strong it is. There are a few eleven's that have been found in string theory.

I find this to be interesting since this theory is supposed to explain the universe! The first eleven that was noticed is that string theory has to have 11 parallel universes (discussed in the beginning of the "11.11" article) and without including these universes, the theory does not work.

The second is that Brian Greene has 11 letters in his name. For those of you who do not know, he is a physicist as well as the author of The Elegant Universe, which is a book explaining string theory. (His book was later made into a mini series that he hosted.) Another interesting find is that Isaac Newton (who's ideas kicked off string theory many years later) has 11 letters in his name as well as John Schwarz. Schwarz was one of the two men who worked out the anomalies in the theory. Plus, 1 person + 1 person = 2 people = equality.

Also, the two one's next to each other is 11. The two men had to find the same number (496) on both sides of the equation in order for the anomalies to be worked out, so theequation had to have equality! There were two matching sides to the equation as wellbecause they ultimately got 496 on both sides. So, the 1 + 1 = 2 = equality applies for the equation as well.

I added a little bold type there because it amused me; pity that Mr Geller didn't look up the definition of equation before writing that line.

But key to this whole belief is that the number 11 keeps turning up at random. When I first read about this I looked up at the clock and it was 11:43. Whoa! Spooky!

But then I remembered Benford's Law. Benford's Law is essentially that in lots of real-life data the leading digit is 1 with a probability of about 30% (instead of the 10% you'd expect if the first digit was random from 0 through 9) and hence numbers beginning with 1 occur more often than numbers starting with any other digit.

A simple illustration is my clock experience. What's the probability that if you look at a clock at random that the first digit is a 1? Well it's more likely than any other number.

For a clock showing 12 hour time it cycles through: 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11. A simple count will show you that the number 1 is the first digit for 8 out of the 24 hours and that all the other digits occur 2 times in 24 hours. So what's the probability that if I glance at a clock at random I'll see a 1 at the beginning? 8/24 or 1/3 of the time... which is Benford's Law.

Now, Benford's Law isn't restricted to time. It occurs all over the place (Wikipedia lists: electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and mathematical constants) and so if you walk through life looking at random numbers you'll see numbers starting with a 1 more often than any other number. In 1988 a mathematician named Ted Hill showed why this is the case for many real-world systems.

But, what about 11? I hear you ask. Well if the first digit is more likely to be 1 than any other than it's clear that you are more likely to see numbers in the range 10 through 19 more than other two digit numbers, but a more interesting offshoot of Benford's Law is explained here.

Essentially as you walk through the digits of a number you are more likely to see a 1 than another digit, but that effect diminishes the longer the number gets. The probability that the the second digit is a 1 is about 11% (instead of the expected 10%) and given that the probability that the first digit is a 1 is 30% you are bound to come across 11 more frequently than you'd expect (if numbers were random).

So, it's no surprise that we see lots of 11s, and hence there's a simple explanation for all those 11s. Either that or I've been missing the call of the 11:11 Spirit Guardians all these years:

These 11:11 Wake-Up Calls on your digital clocks, mobile phones, VCR’s and microwaves are the "trademark" prompts of a group of just 1,111 fun-loving Spirit Guardians, or Angels. Once they have your attention, they will use other digits, like 12:34, or 2:22 to remind you of their presence. Invisible to our eyes, they are very real.

Labels: mathematics, pseudo-randomness