You’re interested in is Bayesian inference.
You’re right.
Quoth Jragon:
7 and base 10 just don’t agree. Everybody has trouble with the 7 times tables. In any base, the factors of the base have nice times tables, and the factors of the base minus one have nice times tables, and everything that’s a product of those has nice times tables. 7 is the only number less than 10 that doesn’t meet any of those criteria, so it doesn’t have a nice times table.
Right, and the reason why statistics doesn’t tell you the answer to the question you’re asking is because you don’t have enough information. Suppose you find that there was only a 1 in 1000 chance to get the sequence you got from a fair coin. OK, but how common are trick coins? If only 1 in a million coins is unfair, then even with your flukish result, you probably still had a fair coin. If, however, fair coins and unfair coins are equally common, then you could probably safely conclude that your coin is unfair. You need to have that initial estimate of the probability, called a prior, to answer that question.
Right, that I get; I understand that to satisfy my tastes I have to switch to Bayesian statistics and drown in the problem of the priors. What I don’t get is what frequentist statisticians think they’re doing; clearly, they don’t regard their own work as deeply mistaken, which leads me to believe that probably it isn’t. But what’s it doing, then?
This is a massive subject, and one that my favorite quantitative methods teacher called “theological”. The wiki entry is a decent start.
Thank you for the Lockhart article. I was somewhat “math phobic” growing up: although I did well enough with the advanced/AP sequence, I did it despite autonomic unpleasantness (terrible anxiety, sweaty palms, accelerated heartbeat, etc) and thus very inconsistent test results. I did not truly discover mathematics until, of all places, grad school. I lament the lost time and have tried since then to make up for it. There is so much now that interests me, but picking up standard textbooks on my own has met with extremely limited success.
I think I must be the one crazy person who was an indifferent equation solver at best (I can hardly help misplacing signs and other unforced errors), but good lord, I could spend hours tinkering with a proof or struggling to express a real-world process into game theoretical mathematics. I could spend my life doing that.
Hm… one other thing that I don’t know, I suppose, is what the connection is supposed to be between “frequentist” and “Bayesian” statistics and frequentist and Bayesian interpretations of probability, respectively. (Is there a connection?) Well, maybe this thread isn’t the place for getting the full lesson; I should perhaps start another…
I like to think I’ve got a pretty decent vocabulary, but for some reason I cannot remember the definition of the word “tautology.” People explain it to me, I look it up in the dictionary, I get it…until next time I encounter it and then I’ve forgotten it again.
I used to be this way with “aggregate,” too, but I’ve got that one down. I keep hoping I’ll have another epiphany. It’s embarrassing.
Please do. Although my job description says “statistician”, I am definitely not a capital-S statistician. I might have something to contribute, but even more to learn.
It might help to think about it this way. The part of the word “tauta” means “all” or “every”. If you can remember that, you can probably remember what a tautology means in formal logic.
Volts. WTF are they, and what makes them all that different from an amp? And how do watts figure into all this.
Also, to the OP: push the back of your hand against the bottom of your chin gently, and say the word out loud. The number of times your chin bobs down is the number of syllables.
Calculus is pretty much where my brain called it quits. I got to the point where I could push my way through it by rote memorization and brute effort but it never really sunk in.
Infinity.
One of the simplest ways to look at electricity is to compare it to water. Volts are like water pressure. Amps are like the amount of water passing a given point. Watts are kind of a combination of the two.
Watts measure electrical power. Power is the rate of energy flow per unit time.
To get the same number of watts, you can have a few amps and many volts, which is like a thin stream of water jetting out of a narrow hole at high pressure. Or, you can have many amps and a few volts, which is like a wide and deep river flowing slowly past under low pressure. In both cases, the same amount of energy is being transferred (the same volume of water is being transferred each second).
Multiplying double digit numbers by other double digit numbers in my head. I write 'em down everytime.
When you say product you actually mean factor, right? I ask because beyond that, this is the most fascinating piece of math knowledge I’ve gotten in a really long time. I’ve always had trouble with my 7 times tables, to the point that I only know 6x7 because it’s 7 times 7 minus 7 (It’s easy for me to remember the squares.)
And on the subject of math, I still don’t know how I got a C in calculus. I know that the derivation of x to third power is 3 times x to the second, and beyond that I know nothing about calculus at all.
I will second that, didn’t get a B+ though; got a C and ran away as quickly as possible and never looked back.
I’d rather remain ignorant and just say you can’t take the square root of a negative number!
Science is a breeze for me, as is math. But I utterly (and embarrassingly!) fail at languages other than English and Latin (and 2yrs of Latin were the hardest courses I’ve taken). For some reason, even trying to learn Romance languages is an effort in futility. That and getting “its” and “it’s” straight. No matter how often I hear what the difference is, 5 minutes later, I’ll end up guessing.
The only science-related subject I’ve ever had trouble with is electricity. I’ve gone through all of the helpful analogies, but I just cannot make my brain work it out. I had an entire semester of it in college, and the only way I passed was by just plugging in equations without understanding them. It was miserable.
Frustrating.
If you’re still wondering, I could try explaining, but it might be too confusing. So I’m abstaining and refraining from elaborating on verbal noun-ing.
I never learned to factor. I remember quite clearly not paying attention that day in Algebra II. I made a 5 on the AP Calculus exam doing six times the work because I had to fake backwards from what the calculator said to pretend I could factor.
I was such a freaking dumbass. If I had gone to my teacher over lunch, like, ONCE, I’d have learned how. And I’m sure she knew, too.
Not that it matters now, as I don’t remember a single thing about calculus except how points are awarded on the AP exam.
It’s in calculus (which I was never good at) where these things start showing their usefulness. You can use them to figure out how long it’ll take to fill or empty your swimming pool (god, why do I still remember that test question?) or whether the building or bridge you designed is going to collapse under its own weight.
Try saying “Hah” and “Hi” very slowly. “Hi” starts as “hah” but then glides into a different sound – haaaaaaaaeeeeeeeeee. You should be able to feel your tongue move as you stop saying “ha” and start saying “eeeee.”