TITLE: Cardinality -- or Absolute Value? AUTHOR: Eugene Wallingford DATE: December 01, 2005 7:39 PM DESC: An unexpected ambiguity opens one idea to another interpretation. ----- BODY: My friend Kris Anderson sent e-mail in response to my entry on I = k|P|. Here's part of what he said:
So then, I got to thinking about the variable "|P|" in your equation. Absolute value? As I thought about it, Aerosmith's "Dream On" started playing in my head... "Live and learn from fools and from sages..." 'Fools' represent negative values and 'Sages' represent positive values. And since the lesson one can learn from either is of equal value, that's why 'P' must be '|P|'. Very cool.
As I told him, Now that is cool. When I wrote my message, by |P| I meant the cardinality of the set P. Kris took P to mean not a set but the value of some interaction, either positive or negative. The ambiguous |P| then can indicate that we learn something of value from both positive influences and negative influences, like positive and negative examples in induction. I think that I'll stick with my original intention and leave credit for this re-interpretation to Kris. And who knew that anyone would read my entry and make a connection to Aerosmith? Different people, different familiar ideas, different connections. That reminds of something Ward Cunningham said at OOPSLA 2005. I learn so much from other folks reading what I write -- yet another example of the point of the article. -----