I was reflecting on this, and considering how statistics might look to a pure mathematician:
"Probability distribution, I know. Real number, I know. But what is this 'rolling a die'/'sampling' that you are speaking about?"
Honest answer: Everybody knows what it means (come on man, it's a die!), but nobody knows what it means mathematically. It has to do with how we interpret/model the data that we see that comes to us from experiments, and the most philosophically defensible way to give these models meaning involves subjective probability.
"Ah so you belong to that minority sect of Bayesians?"
Well, if you don't like Bayesianism you can give meaning to sampling a random variable X=X(\omega) by treating the "sampled value" x as a peculiar notation for X(\omega), and if you consider many such random variables, the things we do with x often correspond to theorems for which you could prove that a result happens with high probability using the random variables.
"Hmm. So what's an experiment?"
Sigh.
I was reflecting on this, and considering how statistics might look to a pure mathematician: "Probability distribution, I know. Real number, I know. But what is this 'rolling a die'/'sampling' that you are speaking about?"
Reflecting some more here (I hope this schizophrenic little monologue doesn't bother anyone), I notice that none of this would trouble a pure computer scientist / reductionist:
"Probability? Yeah, well, I've got pseudo-random number generators. Are they 'random'? No, of course not, there's a seed that maintains the state,...
In response to falenas108's "Ask an X" thread. I have a PhD in experimental particle physics; I'm currently working as a postdoc at the University of Cincinnati. Ask me anything, as the saying goes.
This is an experiment. There's nothing I like better than talking about what I do; but I usually find that even quite well-informed people don't know enough to ask questions sufficiently specific that I can answer any better than the next guy. What goes through most people's heads when they hear "particle physics" is, judging by experience, string theory. Well, I dunno nuffin' about string theory - at least not any more than the average layman who has read Brian Greene's book. (Admittedly, neither do string theorists.) I'm equally ignorant about quantum gravity, dark energy, quantum computing, and the Higgs boson - in other words, the big theory stuff that shows up in popular-science articles. For that sort of thing you want a theorist, and not just any theorist at that, but one who works specifically on that problem. On the other hand I'm reasonably well informed about production, decay, and mixing of the charm quark and charmed mesons, but who has heard of that? (Well, now you have.) I know a little about CP violation, a bit about detectors, something about reconstructing and simulating events, a fair amount about how we extract signal from background, and quite a lot about fitting distributions in multiple dimensions.