Patterns in the years

Some applied numerology. . .

For reasons we needn’t go into, one of our consultants recently wrote the year 2016 in binary.  We were all taught in school how to do this kind of thing, even before the digital revolution made binary arithmetic of some practical importance.  His answer was a bit surprising: 11,111,100,000.  He wondered about other “left-justified” binary years, and made up a table, going from the year 1024 (10,000,000,000) to 2048 (100,000,000,000); they are 1024 (Knut of Denmark is King of England), 1536 (Charles V is Holy Roman Emperor), 1792 (the French Revolution), 1920 (Prohibition in the US), 1984, 2016, 2032, 2040, 2044, 2046, 2047, 2048.

They crowd together closely toward the end, as smaller place-value numbers are added.  It’s only in the twentieth century that a lifetime could encompass as many as two; but someone born in the last quarter of that century could hope to see eight.  Even in our familiar decimal years he noticed another pattern: both 1991 and 2002 are “palindromic” years, reading identically forward and backward.  Generally they come at intervals of 110 years, so people can expect a single palindrome at most, but we’ve seen two.  These seem to be special times.

Of course there’s no actual meaning in these patterns of numbers.  The accidents of left-justification and palindromes have little mathematical importance, and certainly point to nothing unusual in human lives around these years.  From a scientific point of view the fact that we count in base 10 and can convert to base 2 is not important; the patterns would dissolve in any other base.  And from a scientific and even historical point of view the starting-year for our count is rather arbitrary.

But it’s human to be impressed with patterns of numbers, to celebrate decade-years and century-years.  It’s also human to try to predict events by seeing patterns.  There are many people trying to work out who will win the World Series or the election based on patterns of the past, with various levels of seriousness.  (Earnest belief in one’s system, however, probably means descent into paradoxer status.)

With all that said, it’s tempting to dismiss the anxiety around the year 2000 as more numerology.  But in that case there was a real possibility of something unusual happening.  The reasoning went something like this: much of the technology of the time was running on computer programs, some of them written many years before.  When they were written there was no thought that they’d be around so long, but it turned out in many cases it was easier to use what you had then to start over.  Suppose your program only used the last two digits of the year, plausible if you’re in 1981 and need to get something running quickly.  Then on January 1, 2000 it might decide that the year was actually 1900, or even 0, throwing off lots of calculations: negative numbers appearing where they shouldn’t, crashing processes.  And some computer languages use “0” to mean “false” or “stop,” so everything might grind to a halt.

Well, in the event nothing happened.  But now consider that all numbers, even years, are stored by computers in binary.  Up until now you’ve only needed 11 binary digits to do this,  In 2048 you’ll need twelve.  Need we fear the “year 2048 bug?”