The Lake Woebegon Effect and Counting Numbers

Mathematician Jim Propp connects the counting numbers — the concept of them, not particular, specific numbers — to the seemingly unconnected Lake Woebegon Effect. Propp’s essay appears in his Mathematical Enchantments blog:

Beneath and Beyond

… The twentieth century weekly radio show “A Prairie Home Companion” had a recurring feature called “The news from Lake Woebegone”, in which host Garrison Keillor would describe fictional happenings during the past week in his iconic, nonexistent home town of Lake Woebegone, Minnesota. Each week he’d end the news segment with the same tag-line: “And that’s the news from Lake Woebegone, where all the women are strong, all the men are good-looking, and all the children are above average.” That last line gave humorous expression to the fact that most parents think their children are objectively special, and it even gave rise to a new bit of psychological jargon. But curiously, a version of the Lake Woebegone fallacy applies to the counting numbers, not as a fallacy but as a fact – specifically, the fact that every counting number is smaller than average….

Propp then goes on to explain, clearly, why every counting number is smaller than average.