Tuesday, September 11, 2007

Numbers game

Readers are invited to guess the meaning of the following set of numbers (note: the order in which the numbers are presented is not germane to their meaning overall):

94, 61, 80, 89, 84, 88, 82, 81, 89, 68, 47, 88, 85, 59, 87, 84, 92, 97, 80, 95, 75, 85, 93, 79, 81, 58, 76, 85, 79, 89, 88, 80, 72, 92, 88, 80, 90, 66, 89, 85, 56, 87, 76, 50, 52, 63, 90, 91, 65, 91

Obviously, this particular set of numbers does not obey Benford's Law. At least not when expressed in base 10. But perhaps there is some base in which they would more closely approximate the behavior it predicts? (This is just idle speculation on my part)

And you thought my geekitude was confined to matters pertaining to grammar and syntax. Wrong. My geekitude knows no bounds.


Jared said...

Naturally, they don't correspond to Benford's law or Meineiki's theorum either, for that matter. And I suspect they are a little esoteric for Carl's conundrum or Patterson's puzzle. Could they have something to do with Peterson's paradox?

gaelstat said...

Well, in the absence of further answers to my little question, I will go ahead and reveal that the numbers in question represent the age-at-death of everyone listed in the death notices on the necrologia page of last Tuesday's El Pais. Interestingly, most of the younger deaths were among women.

And a little reflection suggests that my earlier speculations about Benford's law were idiotic - the range of these numbers is not wide enough to expect it to hold, in base 10 or any other base.

Benford's law predicts the distribution of the first, and subsequent digits within a collection of numbers. It predicts, that digits are not, as one might naively expect, uniformly distributed, or even close to it. Lower digits predominate, thus explaining the empiricial observation that the earlier pages of log tables tended to be grubbier and more dog-eared than later pages. In the days when people still used log tables, that is. Another version of the law, known as Zipf's law, is used to describe such phenomena as the distribution of hits to internet web sites.

Diabetic butterflies salivate over grandiloquent funeral pyres.

Anonymous said...

The plain people of Ireland: BUTTERFLIES? Are you gone mad altogether?

gaelstat said...

Oops, sorry! I felt sure nobody would still be reading at that point.

Kitty said...

Well written article.