Still, I have to face the fact that if I want to major in, say, applied math, chances are I might be lonely or below-average or both.
As long as you know your own skills, there is no need to use your gender as a predictor. We use the worse information only in the absence of better information; because the worse information can be still better than nothing. We don’t need to predict the information we already have.
When we already know that e.g. “this woman has IQ 150”, or “this woman has won a mathematical olympiad” there is no need to mix general male and female IQ or math curves into the equation. (That’s only what you do when you see a random woman and you have no other information.)
If there are hundred green balls in the basket and one red ball, it makes sense to predict that a randomly picked ball will be almost surely green. But once you have randomly picked a ball and it happened to be red… then it no longer makes sense to worry that this specific ball might still be green somehow. It’s not; end of story.
If you had no experience with math yet, then I’d say that based on your gender, your chances to be a math genius are small. But that’s not the situation; you already had some math experience. So make your guesses based on that experience. Your gender is already included in the probability of you having that specific experience. Don’t count it twice!
If you had no experience with math yet, then I’d say that based on your gender, your chances to be a math genius are small.
To be perfectly accurate, any person’s chances of being a math genius are going to be small anyway, regardless of that person’s gender. There are very few geniuses in the world.
As long as you know your own skills, there is no need to use your gender as a predictor. We use the worse information only in the absence of better information; because the worse information can be still better than nothing. We don’t need to predict the information we already have.
When we already know that e.g. “this woman has IQ 150”, or “this woman has won a mathematical olympiad” there is no need to mix general male and female IQ or math curves into the equation. (That’s only what you do when you see a random woman and you have no other information.)
If there are hundred green balls in the basket and one red ball, it makes sense to predict that a randomly picked ball will be almost surely green. But once you have randomly picked a ball and it happened to be red… then it no longer makes sense to worry that this specific ball might still be green somehow. It’s not; end of story.
If you had no experience with math yet, then I’d say that based on your gender, your chances to be a math genius are small. But that’s not the situation; you already had some math experience. So make your guesses based on that experience. Your gender is already included in the probability of you having that specific experience. Don’t count it twice!
To be perfectly accurate, any person’s chances of being a math genius are going to be small anyway, regardless of that person’s gender. There are very few geniuses in the world.
What’s true of one apple isn’t true of every apple.