Hellooo! I de-lurked during the survey and gradually started rambling at everyone but I never did one of these welcome posts!
My exposure to rationality started with idea that your brain can have bugs, which I had to confront when I was youngish because (as I randomly mentioned) I have a phobia that started pretty early. By then I had fairly accurate mental models of my parents to know that they wouldn’t be very helpful/accommodating, so I just developed a bunch of workarounds and didn’t start telling people about it until way later. The experience helped me reason about a lot of these blue-killing robot types of situations, and get used to handling involuntary or emotional responses in a goal-optimizing way. As a result, I’m interested in cognitive biases, neurodiversity and braaains, as well as how to explain and teach useful life skills to my tiny brother so that he doesn’t have to learn them the hard way.
My undergrad degree is in CS/Math, I’m currently a CS grad student (though I don’t know if I’m sticking around) and I’m noticing that I have a weird gap in my understanding of AI-related discussions, so I’ll probably start asking more questions about it. I regret to admit I’ve been avoiding probability because I was bad at it, but I’m slowly coming around to the idea that it’s important and I need to just suck it up and learn. Also, a lot of sciencey people whine about this, but I think AP Lit (and similar classes) helped me think better; it taught me to read the question carefully, read the text closely, pay attention to detail and collect evidence! But it has possibly made me way too sensitive to word choice; I apologize for comments saying “you could have used this other word but you didn’t, so clearly this means something!” when the other word has never crossed your mind.
I started reading the site so long ago that I can’t actually remember how I found it. One of the things I appreciate the most about the community is the way people immediately isolate problems, suggest solutions and then evaluate results, which is awesome! and also not an attitude I’m used to seeing a lot. I also appreciate having a common vocabulary to discuss biases, distortions, and factors that lead to disagreements. There were a lot of concepts I wanted to bring up with people that I didn’t have a concise word for in the past.
I regret to admit I’ve been avoiding probability because I was bad at it, but I’m slowly coming around to the idea that it’s important and I need to just suck it up and learn.
Fortunately, it’s also very easy to get a basic grip on it. Multiplication, addition, and a few simple formulae can lead to some very interesting results.
A probability is always written as a number between 0 and 1, where 1 is absolute certainty and 0 cannot happen in any circumstances at all, no matter how unlikely. A one in five chace is equal to a probablity of 1⁄5, or 0.2. The probability that event E, with probability P, is false is 1-P. The chances of independent events E and F, with probabilities P and Q, occurring in succession is P*Q. (This leads to an interesting result if you try to work out the odds of at least two people in a crowd sharing a birthday)
Probability theory also involves a certain amount of counting. For example; what are the chances of rolling a seven with two ordinary, six-sided dice? (Assuming that the dice are fair, and not weighted).
Each dice has a one-in-six chance of showing any particular number. For a given pair of numbers, that’s 1/6*1/6=1/36. And, indeed, if you list the results you’ll find that there are 36 pairs of numbers that could turn up: (1, 1), (1, 2), (2, 1), (1, 3)… and so on. But there’s more than one pair of numbers that adds up to 7; (2, 5) and (1, 6), for example.
So what are the odds of rolling a 7 with a pair of dice?
Yeah, it’s the counting problems that I’ve been avoiding! Because there are some that seem like you’ve done them correctly and someone else does it differently and gets a different answer and they still can’t point out what you did wrong so you never quite learn what not to do. And then conditional probabilities turn into a huge mess because you forget what’s given and what isn’t and how to use it togetherrrr.
I hope it’s a sixth, but at least this question is small enough to write out all the combinations if you really have to. It’s the straight flushes and things that are murder.
Yeah, it’s the counting problems that I’ve been avoiding!
Ah, I see. You’ll be glad to know that there are often ways to shortcut the counting process. The specifics often depend on the problem at hand, but there are a few general principles that can be applied; if you give an example, I’ll have a try at solving it.
In fact, many if not most concepts in probability theory deal with various ways of avoiding the counting process. It gets way too expensive when you start handling billions of combinations, and downright impossible when you deal with continuous values.
I will try to hunt one down! It’s usually the problems where you have to choose a lot of independent attributes but also be careful not to double-count.
Also, when someone explains it, it’s clear to see why their way is right (or sounds right), but it’s not clear why your way is wrong.
Yes, I notice that people are in general either bad at giving or reluctant to give this kind of feedback. I think I’m okay at this, so I’d be happy to do this by PM for a few problems if you think that would help.
Hellooo! I de-lurked during the survey and gradually started rambling at everyone but I never did one of these welcome posts!
My exposure to rationality started with idea that your brain can have bugs, which I had to confront when I was youngish because (as I randomly mentioned) I have a phobia that started pretty early. By then I had fairly accurate mental models of my parents to know that they wouldn’t be very helpful/accommodating, so I just developed a bunch of workarounds and didn’t start telling people about it until way later. The experience helped me reason about a lot of these blue-killing robot types of situations, and get used to handling involuntary or emotional responses in a goal-optimizing way. As a result, I’m interested in cognitive biases, neurodiversity and braaains, as well as how to explain and teach useful life skills to my tiny brother so that he doesn’t have to learn them the hard way.
My undergrad degree is in CS/Math, I’m currently a CS grad student (though I don’t know if I’m sticking around) and I’m noticing that I have a weird gap in my understanding of AI-related discussions, so I’ll probably start asking more questions about it. I regret to admit I’ve been avoiding probability because I was bad at it, but I’m slowly coming around to the idea that it’s important and I need to just suck it up and learn. Also, a lot of sciencey people whine about this, but I think AP Lit (and similar classes) helped me think better; it taught me to read the question carefully, read the text closely, pay attention to detail and collect evidence! But it has possibly made me way too sensitive to word choice; I apologize for comments saying “you could have used this other word but you didn’t, so clearly this means something!” when the other word has never crossed your mind.
I started reading the site so long ago that I can’t actually remember how I found it. One of the things I appreciate the most about the community is the way people immediately isolate problems, suggest solutions and then evaluate results, which is awesome! and also not an attitude I’m used to seeing a lot. I also appreciate having a common vocabulary to discuss biases, distortions, and factors that lead to disagreements. There were a lot of concepts I wanted to bring up with people that I didn’t have a concise word for in the past.
Fortunately, it’s also very easy to get a basic grip on it. Multiplication, addition, and a few simple formulae can lead to some very interesting results.
A probability is always written as a number between 0 and 1, where 1 is absolute certainty and 0 cannot happen in any circumstances at all, no matter how unlikely. A one in five chace is equal to a probablity of 1⁄5, or 0.2. The probability that event E, with probability P, is false is 1-P. The chances of independent events E and F, with probabilities P and Q, occurring in succession is P*Q. (This leads to an interesting result if you try to work out the odds of at least two people in a crowd sharing a birthday)
Probability theory also involves a certain amount of counting. For example; what are the chances of rolling a seven with two ordinary, six-sided dice? (Assuming that the dice are fair, and not weighted).
Each dice has a one-in-six chance of showing any particular number. For a given pair of numbers, that’s 1/6*1/6=1/36. And, indeed, if you list the results you’ll find that there are 36 pairs of numbers that could turn up: (1, 1), (1, 2), (2, 1), (1, 3)… and so on. But there’s more than one pair of numbers that adds up to 7; (2, 5) and (1, 6), for example.
So what are the odds of rolling a 7 with a pair of dice?
Yeah, it’s the counting problems that I’ve been avoiding! Because there are some that seem like you’ve done them correctly and someone else does it differently and gets a different answer and they still can’t point out what you did wrong so you never quite learn what not to do. And then conditional probabilities turn into a huge mess because you forget what’s given and what isn’t and how to use it togetherrrr.
I hope it’s a sixth, but at least this question is small enough to write out all the combinations if you really have to. It’s the straight flushes and things that are murder.
Ah, I see. You’ll be glad to know that there are often ways to shortcut the counting process. The specifics often depend on the problem at hand, but there are a few general principles that can be applied; if you give an example, I’ll have a try at solving it.
It is, indeed.
In fact, many if not most concepts in probability theory deal with various ways of avoiding the counting process. It gets way too expensive when you start handling billions of combinations, and downright impossible when you deal with continuous values.
asdfjkl; I wrote out all the pairs. -_- Can’t trust these problems otherwise! Grumble.
“You are never too cool to draw a picture” —or make a list or a chart. This particular problem is well served by a six-by-six grid.
Dice are okay; it’s the problems with cards that get toooo huge. :)
Can you give an example?
I will try to hunt one down! It’s usually the problems where you have to choose a lot of independent attributes but also be careful not to double-count.
Also, when someone explains it, it’s clear to see why their way is right (or sounds right), but it’s not clear why your way is wrong.
Yes, I notice that people are in general either bad at giving or reluctant to give this kind of feedback. I think I’m okay at this, so I’d be happy to do this by PM for a few problems if you think that would help.