[If you've stumbled upon this page from
a search engine, please see Digital
Clock coincidences first, for context.
Meanwhile, welcome to some analysis by a friend
of mine, I hand over to Q-bit...
- JE]
About a year ago Eadon and several others were quipping, as I recall anyhow, about "coincidence" on the ICC server. During the course of the conversation I volunteered to analyze the states of a digital clock to see how many of them were "striking" or "coincidental." I have quoted the two preceding words because their meaning is far from clear. As I recall, the flavor of the conversation was to determine the probability of looking at a digital clock and seeing a pattern that was somehow specially ordered, and therefore noteworthy to the mind of an individual seeking coincidence. The problem with this idea is that individual experience and individual perception could make any digital pattern interesting or synchronistic.
In any case, Jim and I informally settled, if memory serves, on symmetrical, repeated, and "counting" (see below) digit patterns as the definition of "synchronistic." A simple counting problem resulted, and the analysis follows.
Assume a standard digital clock that shows civilian time. It has a total of 12 x 60 states (multiply that number by 2 if you consider AM/PM to be a parameter).
1) There are 8 ways to have repeated digits (time separator omitted): 111,222,333...1212.
2) There are 9 ways to have a string symmetrical about 1: 111, 212, 313...919. We can have strings symmetrical about the numbers 1 through 5, so there are 9 x 5 = 45 such symmetrical strings + 3 special ones (1001, 1111, 1221). But we have to subtract the monotone sequences since we already counted them in step 1. That gives 48 - 6 = 42 striking strings from this step.
3) There are also a handful of "counting" sequences of natural number order: 123, 1234, 234, 345, 456,1011,1112,1213--8 in total.
So the chances of looking at a digital clock
and seeing a symmetrical or repeated pattern
of digits, assuming that you take a significant
random sample of looks, is, by my estimate,
(42 + 8 + 8) / (12 x 60) = 58 / (12 x 60) =
5/72 = .08055555... =~ 8%.
[Thanks Q-bit. If any mathematicians would
like to add their analysis on digital
clock coincidences, or related subjects,
please let
me know.
Jim E]
What do you think?
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