Isotropy
Thursday, September 16, 2004
A Special Day
Today I turn 33. As they say in Mexico, "la edad de Cristo".
Today is also Rosh Hashanah, starting the year 5765.
The High Holy Days are a time for re-evaluating your life. I'm not Jewish, but this is a pensive-making coincidence if there ever was one.
May the Lord mark you down for a good year....
Friday, September 03, 2004
It's for Science...Really
I love sites like What's Better? and Hot or Not?. Recently I found Pick the Hottie, a perfect combination of the two: the front page presents two pictures, and asks you to click the more-attractive person. Each "hottie" has his/her own page, showing their win-loss record and photos of recent competitors ("see who I've lost to"). Here's an example. The nice thing about this is you two different pieces of information: the lifetime win-ratio, and a sample of recent wins and losses. That means you can find plenty of plainer Janes that at least one visitor liked better than sexy Susan.
Okay, so the science bit: find the hottest Hottie (without cheating by looking at the Top Ten list). For a lot of search problems, we can only do head-to-head comparisons of candidates. We can't figure out the best solution from scratch, and we can't try every possible candidate (so many candidates...so little time....) We can only search through examples that we actually have, and hope we find the best one. This is called "heuristic search". One technique in heuristic search is "hill climbing" - you look at head-to-head comparisons between some candidates and your current "best girl". If any are better, pick the best new candidate. Repeat. The nice thing about this technique is that you're situation can only improve or stay the same - you'll never make a choice that leaves you worse off.
The problem with hill climbing is beautifully illustrated by "Pick the Hottie" - you want to find the best-looking person on the site? You can look at the Top 10 list, of course, but try this: start with anybody on the site, and hill climb - look at who they lost to recently, then pick the hottest hottie that beat them. Look at who they lost to, and pick the hottest...etc. You'll reach a "local" maximum - a hottie that hasn't recently lost to anybody with a higher score. You will very, very rarely reach the very top, though. There aren't enough direct recent comparisons between the top scorers to produce an increasing-only path from, say, the 50th-hottest picture to the 1st.
