One example of a total ordering ≤ is the “hotness” scale from 1–10.
Because of the widespread disagreement about the meaning of the numbers, the only thing one can infer based on a man’s rating of a woman is that she is more attractive than those who score below her.
The Hotness Scale derives, I think, from a need to explain one’s tastes to peers and hear them justified.
It typically surfaces in sleepover conversations like this:
- Chris (secretly likes Kelly Russell): Who do you think is hotter: Liz Jones, or Kelly Russell?
- Dave: Are you kidding?! Liz Jones is waaaay hotter.
- Chris: Oh, yeah. I mean, obviously. I was just checking. I just meant, you know, that I think Kelly Russell is like maybe a 7.
- Dave: Are you crazy?! She’s like a 2.
- Chris: Come on, 2 is like people who have skin grafts. 2 is people who were burned in fires.
- Dave: Whatever. Maybe.
(sheepish retreat to celebrity hotness)
But man, Jane March is the hottest woman on the planet.
- Chris: No way, Jenny McCarthy is hotter.
I’m a little embarrassed to admit (though I’ll still admit it) that when my best friend and I started using the hotness scale, we scored girls in different categories, like
- I forget what else
- overall score
Yeah, we were really cool. (Also we were really twelve.)
Fast forward to college. We guys were joking about using the ten-point scale, which by then was passé (although I did once use the phrase “a Bloomington 6 is a hometown 9”). We were trying to answer, what is the difference between a 6 and a 7 anyway? And is the distance between 6 and 7 greater or less than the distance between a 9 and a 10?
Everybody had taken calculus by this point so statements involving derivatives were bandied about (even though none of us meant to use real numbers … it was calculus as metaphor).
One guy proposed that each number should correspond to a decile —
- 1 to the ugliest decile,
- 10 to the hottest decile,
- and so on.
Someone else said that one’s initial reaction put a girl either in
- the >4 (most of the time) or
- <5 — but that since no one would ever hit on someone in the latter category,
- in fact 1≈2≈3≈4.
Another said that he never assigned a 10 to anybody because that would mean he had met his wife. Um, yeah … we were still super cool.
Also contentious was whether each of us accepted the truth of whatever our own numerical ranking was. All I know is that whatever I said my score was, I secretly hoped it was 2 points higher.
There was a lot of inconsistency to the scores, which is why I’m bringing this up under the topic of ≤ rank without distance measure. Although I would wager that transitivity is violated, so perhaps this scale does not have a rational basis.
PEOPLE CAN BE ATTRACTIVE IN DIFFERENT WAYS
As I’m writing all of this I desperately want to jump ahead to partial orderings. But I haven’t defined them yet and I refuse to link to Wikipedia, so I’ll have to put that topic off.
Suffice to say that attraction is a perfect jumping-off point for one further generalization I want to make in order to get mathematics into bed with human experience.
Not everyone can be ranked side-by-side against everyone else. People can be attractive for different reasons (multiple >'s) and some people you just aren't comparable. All of these reasons and more are great justifications for switching to posets.
I’d be interested to hear other interpretations of the hotness scale, or other scales of attractiveness, and how they evolved over time. What measure, if any, do you give guys when you’re in your 30’s or 40’s?
PS When I was 24, my girlfriend told me that “24 is a very hot age”. Ha ha.
PPS Tim Ferriss claims to be able to quantify the difference between a 6 and a 9. Tell that to Jimi Hendrix.