This thread is for discussing some of the entries in the LessWrong Wiki (http://lesswrong.com/). Some of the entries are fairly wordy and confusing, so why not talk them through?
Ah, thanks, LMNO.
So I've started reading it, and I read the Intuitive Explanation of Bayes Theorem. (http://yudkowsky.net/rational/bayes)
Maybe not that intuitive since I still don't really understand what Bayesian reasoning entails.
Here's the really, really easy version.
Moe: I believe, based upon the knowledge I currently have, that there's a 30% chance it will rain today.
Larry: Have you looked out the window?
Moe: No.
Larry: There are thunderclouds in the sky.
Moe: Updating my knowledge base, I now believe there is a 90% chance of rain.
There you go. Based upon incoming knowledge, adjust your predictions. The rest is math.
Quote from: LMNO, PhD (life continues) on August 27, 2013, 04:48:18 PM
Here's the really, really easy version.
Moe: I believe, based upon the knowledge I currently have, that there's a 30% chance it will rain today.
Larry: Have you looked out the window?
Moe: No.
Larry: There are thunderclouds in the sky.
Moe: Updating my knowledge base, I now believe there is a 90% chance of rain.
There you go. Based upon incoming knowledge, adjust your predictions. The rest is math.
Ok. I was getting lost in the breast cancer example, and trying to follow along with the math there, and not seeing exactly what they were trying to say. I'm making an attempt to read one article a day, or at least every other day, so I'll probably have quite a bit to ask about.
Oho! The breast cancer bit is kind of awesome, but it really deals with a deeper issue, which is that most people have no idea how to deal with probabilities.
If something has a 0.01% chance of killing you, and I tell you that plucking your pubic hair out one by one will cut that probability in half, would you reach for the tweezers?
Quote from: LMNO, PhD (life continues) on August 27, 2013, 04:57:09 PM
Oho! The breast cancer bit is kind of awesome, but it really deals with a deeper issue, which is that most people have no idea how to deal with probabilities.
If something has a 0.01% chance of killing you, and I tell you that plucking your pubic hair out one by one will cut that probability in half, would you reach for the tweezers?
No. The chances of me dying are already pretty slim, and reducing that by half by that method doesn't sound very pleasant for such a marginal benefit.
And all the breast cancer example is showing is, it's often really, really hard to make that calculation when dealing with multiple probabilities.
Quote from: LMNO, PhD (life continues) on August 27, 2013, 05:12:03 PM
And all the breast cancer example is showing is, it's often really, really hard to make that calculation when dealing with multiple probabilities.
Ah, gotcha. I think the multiple probabilities is where I got lost.
So why do people get really excited over it?
Quote from: LMNO, PhD (life continues) on August 27, 2013, 04:48:18 PM
Here's the really, really easy version.
Moe: I believe, based upon the knowledge I currently have, that there's a 30% chance it will rain today.
Larry: Have you looked out the window?
Moe: No.
Larry: There are thunderclouds in the sky.
Moe: Updating my knowledge base, I now believe there is a 90% chance of rain.
There you go. Based upon incoming knowledge, adjust your predictions. The rest is math.
That is a really good explanation.
I love the lesswrong wiki. Conjunction fallacy made my head hurt until I realized I was reading their explanation backwards. Then it made a lot of sense.
For the rest of the board: The problem given is this:
1% of women at age forty who participate in routine screening have breast cancer. 80% of women with breast cancer will get positive mammographies. 9.6% of women without breast cancer will also get positive mammographies. A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer?
What often gets lost is your "prior", or the knowledge you start with. In this example,
only 100 out of 10,000 women have cancer.
-> 80 of them will have a positive test
-> 20 will have a negative test
9,900 do not have cancer
-> 8,950 will have a negative test
-> 950 will have a positive test
So, how many people have a positive result? 80+950 = 1030. And, 80 out of 1030 positive results is 80/1030 = 7.8%
So if you give a test to 10,000 women, and you get 1030 positive tests, only 80 of those women have cancer.
A woman with a positive test has a 7.8% chance of having cancer.
The point being, a lot of people look at the "80% chance of detecting breast cancer" and stop there. You need to be aware of all the other probabilities involved in order to get the correct answer.
Please note these numbers are made up; Elizer used breast cancer as an example so people would pay attention.
So, the main, MAIN point is: Your "prior probability" was that 1% of women who get screened have breast cancer. That's the "reality". The box is opened, they either do or don't.
The probabilities of the test are "conditional probabilities". You can have a test that is correct 90% of the time, or a test that's correct 10% of the time. That doesn't change the prior probability that 1% of the women have cancer; it just changes what you can guess about a person if they have a positive test. That final guess is known as the "revised" or "posterior" probability.
The problem being is that most people think: "I got a positive test, so there's an 80% chance I have cancer!"
That's why people get so excited when they're shown Bayes. It allows for correct thinking.
Quote from: LMNO, PhD (life continues) on August 27, 2013, 06:05:55 PM
So, the main, MAIN point is: Your "prior probability" was that 1% of women who get screened have breast cancer. That's the "reality". The box is opened, they either do or don't.
The probabilities of the test are "conditional probabilities". You can have a test that is correct 90% of the time, or a test that's correct 10% of the time. That doesn't change the prior probability that 1% of the women have cancer; it just changes what you can guess about a person if they have a positive test. That final guess is known as the "revised" or "posterior" probability.
The problem being is that most people think: "I got a positive test, so there's an 80% chance I have cancer!"
That's why people get so excited when they're shown Bayes. It allows for correct thinking.
Gotcha.
Also, I was thinking the opposite. The woman still has a 1% chance of breast cancer, because I figured I was being tricked somehow.
She had a 1% chance. Now that she's got a positive test result, she now has a 7.8% chance.
Quote from: LMNO, PhD (life continues) on August 27, 2013, 06:32:52 PM
She had a 1% chance. Now that she's got a positive test result, she now has a 7.8% chance.
I got that part after it was explained.
That does seem counterintuitive though.
Which is part of the beauty of Bayes. It's not that you should go through life doing weird math. It's showing that the Intuitive answer is often wrong, and you have think things through (i.e. be rational) when making tough decisions.
I really liked my stats classes (as tedious as they were) for helping me to look at probability differently.
Thanks for starting this thread, LMNO.
I've found there's a great deal of variability in article /quality/ on LW. On one hand, you have Yudkowsky, and on the other you have things that feel a bit like philosophy amateur hour, or super far out ramblings on singularity related topics, or a combination of the two. When I first got interested in Less Wrong through the sequences, I was a little carried away with it, and I can see how easy it would be to dive into a cult-like mentality surrounding those ideas. Like how many Scientologists get started appreciating the benefits and are able to stomach the Xenu conspiracy when they finally learn about it. Replace Xenu with the singularity/cryopreservation/uploading-your-brain transhumanism and it can be much the same. Except, well, the Singularity Institute doesn't steal your money.
What I'm saying, I guess, is that I was a little taken in by the grandeur of the sequences and went a little overboard. I'm finding it really important to step back after reading and question in big black letters "IS THIS BULLSHIT?" Some of it isn't. Other parts may be (YMMV).
=
Just wanted to point out: In the most HPMOR chapter, Yudkowsky had a couple fiction recommendations at the end. One of them was this manga Murasakiiro no Qualia, which includes such topics as: a girl who sees everyone as robots, philosophical zombies, qualia, ethics, and probably more. I'm only halfway through.
The scanlation is here (Read right to left): http://www.mangahere.com/manga/murasakiiro_no_qualia/c001/
That sounds cool. Thanks, Kai!
Quote from: Cain on August 28, 2013, 10:22:34 AM
Yes. The majority of the sequences seem pretty useful, well thought and structured in such a way as to be easy to apply...but some of the general blog entries are of widely variable quality. When I see the names of certain members, I generally skip their pieces (or at least I used to, when I read the blog regularly) because I found them either flawed, or self-centered, or to be reiterating information stated more eloquently elsewhere.
Has anyone looked at the Wiki in depth, and have any opinions on it? I have only browsed it so far, and don't really have a strong impression either way.
I agree with you, it's hit-or-miss. Some people are obviously trying to be TSGITR, and some are honestly interested in the work. And some are simply bad writers. I also started reading it as revelation, and have toned it down considerably since.
Funnily enough, that's pretty much what I did with RAW, as well. Luckily, the cycle time on this was much faster.
Quote from: Cain on August 28, 2013, 10:22:34 AM
Has anyone looked at the Wiki in depth, and have any opinions on it? I have only browsed it so far, and don't really have a strong impression either way.
Seems like a dictionary to less wrong terminology. What it's useful for is finding posts on a particular topic, say, free will or Bayes Theorem. But it also makes the whole thing feel like a cult, with its own special language that is more than a bit exclusionary.
Crapulism (noun): The process whereby a thing that had some inherent budding merit is driven down in quality by low-quality intermediaries, inadvisable practices or a willful effort launched in a bid to keep a lesser being from appearing to be outclassed, whether true or not.
Quote from: The Good Reverend Roger on August 30, 2013, 08:22:05 PM
Crapulism (noun): The process whereby a thing that had some inherent budding merit is driven down in quality by low-quality intermediaries, inadvisable practices or a willful effort launched in a bid to keep a lesser being from appearing to be outclassed, whether true or not.
That might explain it.
Quote from: Kai on August 30, 2013, 08:33:46 PM
Quote from: The Good Reverend Roger on August 30, 2013, 08:22:05 PM
Crapulism (noun): The process whereby a thing that had some inherent budding merit is driven down in quality by low-quality intermediaries, inadvisable practices or a willful effort launched in a bid to keep a lesser being from appearing to be outclassed, whether true or not.
That might explain it.
Well, something like LW, you have two choices...Keep the content quality high, and become covered in dust as the site sinks into the depths of the internet, or crank out content whether or not you have any, and pretty soon it's a bunch of guys telling you why THEY are smart and YOU are NOT.
Reminds me of the "Black Iron Escapees" on TDS/Facebook.
Quote from: The Good Reverend Roger on August 30, 2013, 08:36:26 PM
Quote from: Kai on August 30, 2013, 08:33:46 PM
Quote from: The Good Reverend Roger on August 30, 2013, 08:22:05 PM
Crapulism (noun): The process whereby a thing that had some inherent budding merit is driven down in quality by low-quality intermediaries, inadvisable practices or a willful effort launched in a bid to keep a lesser being from appearing to be outclassed, whether true or not.
That might explain it.
Well, something like LW, you have two choices...Keep the content quality high, and become covered in dust as the site sinks into the depths of the internet, or crank out content whether or not you have any, and pretty soon it's a bunch of guys telling you why THEY are smart and YOU are NOT.
Reminds me of the "Black Iron Escapees" on TDS/Facebook.
Yeah. Without the constant content, Less Wrong would be dead. Even if the innovators are spitting out good stuff as often as they can, innovators don't tend to stay in one place. So, Yudkowsky finishes his sequence on free will, he's not talking about it anymore. But since these other people in the community are adopters, not innovators, they can't help but rehash what he's already done. Is there a necessary trade off to keep a community going? It feels like some of this applies to PD as well.
Quote from: Kai on August 30, 2013, 08:48:19 PM
It feels like some of this applies to PD as well.
Hey, thanks. Thanks a fucking lot.
Sorry we don't live up to your expectations.
Quote from: The Good Reverend Roger on August 30, 2013, 08:57:07 PM
Quote from: Kai on August 30, 2013, 08:48:19 PM
It feels like some of this applies to PD as well.
Hey, thanks. Thanks a fucking lot.
Sorry we don't live up to your expectations.
No, that's not what I meant. I meant that in every community there are a small number of innovators and a much larger number of adopters. This isn't necessarily a bad thing (see question about requirements of a community). Hell, I'm an adopter, not an innovator, so why would I insult myself by saying that was a bad thing? It doesn't mean we have crapulism.
Quote from: Kai on August 30, 2013, 09:06:30 PM
Quote from: The Good Reverend Roger on August 30, 2013, 08:57:07 PM
Quote from: Kai on August 30, 2013, 08:48:19 PM
It feels like some of this applies to PD as well.
Hey, thanks. Thanks a fucking lot.
Sorry we don't live up to your expectations.
No, that's not what I meant. I meant that in every community there are a small number of innovators and a much larger number of adopters. This isn't necessarily a bad thing (see question about requirements of a community). Hell, I'm an adopter, not an innovator, so why would I insult myself by saying that was a bad thing? It doesn't mean we have crapulism.
Okay, my bad.
Here we have a dozen posters and 4 times that many people who sit and stare at the screen, congratulating themselves for being too smart to watch TV.
Different folks for different folks, I guess.
Quote from: The Good Reverend Roger on August 30, 2013, 09:08:20 PM
Quote from: Kai on August 30, 2013, 09:06:30 PM
Quote from: The Good Reverend Roger on August 30, 2013, 08:57:07 PM
Quote from: Kai on August 30, 2013, 08:48:19 PM
It feels like some of this applies to PD as well.
Hey, thanks. Thanks a fucking lot.
Sorry we don't live up to your expectations.
No, that's not what I meant. I meant that in every community there are a small number of innovators and a much larger number of adopters. This isn't necessarily a bad thing (see question about requirements of a community). Hell, I'm an adopter, not an innovator, so why would I insult myself by saying that was a bad thing? It doesn't mean we have crapulism.
Okay, my bad.
Here we have a dozen posters and 4 times that many people who sit and stare at the screen, congratulating themselves for being too smart to watch TV.
Different folks for different folks, I guess.
I really don't want to turn this into a thread about 'what's wrong with PD'. But if I had to sum up why I "sit and stare at the screen", it's because you "dozen posters" have a whole lot of Holy
TM, and I'm just sitting here wondering how the hell I could ever collaborate at your level, not wanting to fuck up the process.
Quote from: Kai on August 30, 2013, 09:18:32 PM
Quote from: The Good Reverend Roger on August 30, 2013, 09:08:20 PM
Quote from: Kai on August 30, 2013, 09:06:30 PM
Quote from: The Good Reverend Roger on August 30, 2013, 08:57:07 PM
Quote from: Kai on August 30, 2013, 08:48:19 PM
It feels like some of this applies to PD as well.
Hey, thanks. Thanks a fucking lot.
Sorry we don't live up to your expectations.
No, that's not what I meant. I meant that in every community there are a small number of innovators and a much larger number of adopters. This isn't necessarily a bad thing (see question about requirements of a community). Hell, I'm an adopter, not an innovator, so why would I insult myself by saying that was a bad thing? It doesn't mean we have crapulism.
Okay, my bad.
Here we have a dozen posters and 4 times that many people who sit and stare at the screen, congratulating themselves for being too smart to watch TV.
Different folks for different folks, I guess.
I really don't want to turn this into a thread about 'what's wrong with PD'. But if I had to sum up why I "sit and stare at the screen", it's because you "dozen posters" have a whole lot of HolyTM, and I'm just sitting here wondering how the hell I could ever collaborate at your level, not wanting to fuck up the process.
Thing is, this ain't a competition. It's Discordia. It's for everyone.
And as far as the Holy™ goes, I recently went back and read my 2003/2004 stuff, and cringed. You learn to Holy™ by doing it.
Or you can just shoot the breeze.
But for God's sake, let's not let this shit turn into television or a blog or something.
Here's the thing; my Discordia isn't for everybody, but I try to live my Discordia by the same philosophy Mama from Here Comes Honey Boo Boo lives her life; big, loud, kind of nasty, and don't give a fuck.
This is my Discordia: http://www.youtube.com/watch?v=4hXjFLd1RYg
As a relative newcomer to PD.com I will say it can be a little intimidating to post. They always warn you that with discordians you won't be the weirdest person in the room but no one ever points out that you won't be the smartest person in the room. A lot of folks here are smart. Like, really smart, I still have to look up words all the time here and I consider myself pretty well read and learned. Also a lot of folks on here have been talking to each other for a long while. Their maps have been traced out, concepts have been agreed upon (or at least defined in terms of conversation) Catching up on all that takes some time and is a lot of work (good awesome work, but effort nonetheless) The old threads in these forums are a library unto themselves in many ways.
That said, after getting over the, whoa you guys are smart and I've never even heard of a reality tunnel before, I find this place to be a great place to discuss ideas. As long as you're honest, can back up an argument, and recognize when you're A)possibly wrong or B)too ignorant on the subject to continue the conversation, then it's a fairly open place. Sure, sometimes eldritch abominations will ambush you, hold you down and shit in your soul, but you'll have that here. Discordia wasn't meant to be safe. It's a place where everything gets poked with a stick.
Back on topic though, I really really dig the lesswrong movement. Especially the statistics stuff as it's easy to be swayed by statistics that sound good or plausible. An example from a book I just read was a court case where a man was on trial for murdering his spouse who he had previously abused. The defense provided a statistic that showed that of all cases of abused women in a marriage, only 2 percent were murdered by their spouse. 2 percent sounds kind of low but this is not actually relevant. The relevant stat isn't the percentage of battered women who went on to be murdered by their spouses but the percentage of battered women
Who were also murdered who were killed by their spouses. This percentage is 90 percent and is the exact opposite of what the defense were trying to show.
The classic girl named Florida problem still makes my head hurt though:
QuoteThe Girl Named Florida problem is usually preceded by an easier problem that goes as follows:
Suppose you know that a family with two children has at least one girl. What is the probability that this family has two girls?
Now for the Girl Named Florida problem:
Suppose you know that a family with two children has at least one girl named Florida. What is the probability that this family has two girls?
On the face of it, roughly 50% for both cases. It sounds the same as the "coin flip came up heads ten times" problem.
Am I missing something? Wouldn't be the first time.
It's 25% when you have no information, then it's 50% because you've already confirmed one.
(25% because you could have M|F, F|M, M|M, or F|F)
Wait, what?
Each occurrence has no bearing on the previous. Every pregnancy is a coin flip, with no bearing on any other.
Hmm now I see what you might be saying. I gotta think about this.
Oh, ok. It's not, "what's the chance of the second child being a girl," it's "what's the chance of the total combination"?
In that case, it is the end result. So you HAVE TO UPDATE YOUR PRIORS. Also, figure out what the question is actually asking.
Quote from: LMNO, PhD (life continues) on September 02, 2013, 03:22:40 AM
Oh, ok. It's not, "what's the chance of the second child being a girl," it's "what's the chance of the total combination"?
In that case, it is the end result. So you HAVE TO UPDATE YOUR PRIORS. Also, figure out what the question is actually asking.
As in, the order of birth matters? It's not just the combination, but the order?
No it's about the sum.
If the question is, "what's the chance this kid is a girl?" Then it's 50%.
If the question is, "if the first kid is a girl, what's the chance of two girls?" Then it's 25%.
I know, it doesn't feel right. But it's looking at the narrative, not the circumstance.
Quote from: LMNO, PhD (life continues) on September 02, 2013, 03:47:19 AM
No it's about the sum.
If the question is, "what's the chance this kid is a girl?" Then it's 50%.
If the question is, "if the first kid is a girl, what's the chance of two girls?" Then it's 25%.
I know, it doesn't feel right. But it's looking at the narrative, not the circumstance.
That makes sense. I guess the problem wasn't worded very well. I was wondering how I had so much trouble with that and none at all with the battered wife murder example.
The more I live, the more the case is, "in life, the question is rarely worded very well."
An argument can be made that this is a common downfall of purely rationalist thinkers.
Quote from: LMNO, PhD (life continues) on September 02, 2013, 03:47:19 AM
No it's about the sum.
If the question is, "what's the chance this kid is a girl?" Then it's 50%.
If the question is, "if the first kid is a girl, what's the chance of two girls?" Then it's 25%.
I know, it doesn't feel right. But it's looking at the narrative, not the circumstance.
If the first kid is a girl, you have a 50% chance of two girls, because you already have one there and it's just a coin flip for the second. If you don't know either gender, you're doing two coin flips and it's 25%
Damn. I got it wrong again. This shit is hard.
Ok, so the questions are:
If it's predicting one kid at a time, it's 50%.
If it's predicting two kids at a time, it's 25%.
If you know the gender of one, it's the same as predicting one kid.
I think I'm getting the hang of this.
Male -> Male + Male
/
Male -> Coin Flip
/ \
Coin Flip Female -> Male + Female
\ Male -> Female + Male
\ /
Female -> Coin Flip
\
Female -> Female + Female
I made a chart!
Quote from: Kai on August 30, 2013, 08:48:19 PM
Even if the innovators are spitting out good stuff as often as they can, innovators don't tend to stay in one place.
Speaking of this, have you tried picking a few innovators you like and see where they went?
Many of lesswrong's top contributors have their own blogs, for example. Check their user pages.
I, for one, enjoy reading Gwern's site (http://www.gwern.net/), Katja Grace's blog (http://meteuphoric.wordpress.com/) and Yvain's blog (http://slatestarcodex.com/).
The way I understand it, this is the solution (though the second one still seems weird to me)
Suppose you know that a family with two children has at least one girl. What is the probability that this family has two girls?
The possiblities are:
Boy-Girl
Girl-Boy
Girl-Girl
So the probability is 1 in 3.
Say you know a family has two children, and further that at least one of them is a girl named Florida. What is the probability that they have two girls?
Here we have:
Boy-Girl (Florida)
Girl (Florida)-Boy
Girl (Not Florida)-Girl (Florida)
Girl (Florida)-Girl (Not Florida)
Girl (Florida)-Girl (Florida)
Here we get 3/5 which is a 60 percent chance. Although they seem to take out the Florida Florida scenario (which kinda feels like cheating) and get a 50 percent chance. This still feels odd.
That's the Monty Hall problem. It's also covered in the sequences.
Quote from: LMNO, PhD (life continues) on September 02, 2013, 04:09:52 PM
That's the Monty Hall problem. It's also covered in the sequences.
Yes. That's another good one. I like hearing the stories of when Marilyn vos Savant answered the Monty Hall problem in her column and had hundreds of PhD's in statistics and engineering write in to tell her she was wrong. Funny stuff and also another really good example of where intuition can fall short.
Quote from: McGrupp on September 02, 2013, 03:07:13 PM
The way I understand it, this is the solution (though the second one still seems weird to me)
Suppose you know that a family with two children has at least one girl. What is the probability that this family has two girls?
The possiblities are:
Boy-Girl
Girl-Boy
Girl-Girl
So the probability is 1 in 3.
Say you know a family has two children, and further that at least one of them is a girl named Florida. What is the probability that they have two girls?
Here we have:
Boy-Girl (Florida)
Girl (Florida)-Boy
Girl (Not Florida)-Girl (Florida)
Girl (Florida)-Girl (Not Florida)
Girl (Florida)-Girl (Florida)
Here we get 3/5 which is a 60 percent chance. Although they seem to take out the Florida Florida scenario (which kinda feels like cheating) and get a 50 percent chance. This still feels odd.
It's not 1 in 3, it's 1 in 4. Just because you don't care about the birth order doesn't mean you get to collapse two potential outcomes into one.
Quote from: McGrupp on September 01, 2013, 10:03:36 PM
As a relative newcomer to PD.com I will say it can be a little intimidating to post. They always warn you that with discordians you won't be the weirdest person in the room but no one ever points out that you won't be the smartest person in the room.
Or how horrible the notion of being the smartest guy in the room can be.
Quote from: Queen Gogira Pennyworth, BSW on September 03, 2013, 01:22:06 AM
Quote from: McGrupp on September 02, 2013, 03:07:13 PM
The way I understand it, this is the solution (though the second one still seems weird to me)
Suppose you know that a family with two children has at least one girl. What is the probability that this family has two girls?
The possiblities are:
Boy-Girl
Girl-Boy
Girl-Girl
So the probability is 1 in 3.
Say you know a family has two children, and further that at least one of them is a girl named Florida. What is the probability that they have two girls?
Here we have:
Boy-Girl (Florida)
Girl (Florida)-Boy
Girl (Not Florida)-Girl (Florida)
Girl (Florida)-Girl (Not Florida)
Girl (Florida)-Girl (Florida)
Here we get 3/5 which is a 60 percent chance. Although they seem to take out the Florida Florida scenario (which kinda feels like cheating) and get a 50 percent chance. This still feels odd.
It's not 1 in 3, it's 1 in 4. Just because you don't care about the birth order doesn't mean you get to collapse two potential outcomes into one.
Yeah, it seems that the birth order is an irrelevant factor. You want to know the odds of one kid being something, not a specific kid.
But even then, gender is determined by sperm, and the likelihood of one particular gendered sperm out of millions to get to fertilize the egg makes the math a bit unwieldy. I get that it's mostly a coin toss, but that's only because out of millions of sperm cells, the lottery winner can't be predicted on just that. What I mean is you have to factor in the amount of sperm that even get to the egg. Not all of them get there, and the gender distribution of those isn't necessarily 50/50. Or am I overthinking this?
You're over thinking this, in that the question is a hypothetical.
However, this is a great example of Bayes, in that you use the above probabilities until you encounter SPECIFIC FACTS about the genetic makeup if the parents, at which time you add them to your priors and then slide the probability up or down. Although, given what we've just covered, the sliding would most likely be in the tenths of a percent rather than anything significant.
Quote from: LMNO, PhD (life continues) on September 03, 2013, 04:16:07 AM
You're over thinking this, in that the question is a hypothetical.
However, this is a great example of Bayes, in that you use the above probabilities until you encounter SPECIFIC FACTS about the genetic makeup if the parents, at which time you add them to your priors and then slide the probability up or down. Although, given what we've just covered, the sliding would most likely be in the tenths of a percent rather than anything significant.
So, I'm thinking about this in a Bayesian way, but for an irrelevant example, yes?
Quote from: McGrupp on September 01, 2013, 10:03:36 PMThe Girl Named Florida problem is usually preceded by an easier problem that goes as follows:
Suppose you know that a family with two children has at least one girl. What is the probability that this family has two girls?
Now for the Girl Named Florida problem:
Suppose you know that a family with two children has at least one girl named Florida. What is the probability that this family has two girls?
How are the probabilities for these two scenarios different? Is it a trick question? All it's asking is what the probability of the other child being a girl is in both cases.
...
I have been reading that wrong this entire time.
<appropriate "I'm an idiot" emote here>
Quote from: Queen Gogira Pennyworth, BSW on September 03, 2013, 04:58:37 AM
...
I have been reading that wrong this entire time.
<appropriate "I'm an idiot" emote here>
How so? It still seems like probability is birth order, which is irrelevant, unless I'm missing something too.
Quote from: McGrupp on September 01, 2013, 10:03:36 PM
QuoteThe Girl Named Florida problem is usually preceded by an easier problem that goes as follows:
Suppose you know that a family with two children has at least one girl. What is the probability that this family has two girls?
Now for the Girl Named Florida problem:
Suppose you know that a family with two children has at least one girl named Florida. What is the probability that this family has two girls?
Bolded the part I read past
over and over again.
Quote from: Queen Gogira Pennyworth, BSW on September 03, 2013, 05:04:15 AM
Quote from: McGrupp on September 01, 2013, 10:03:36 PM
QuoteThe Girl Named Florida problem is usually preceded by an easier problem that goes as follows:
Suppose you know that a family with two children has at least one girl. What is the probability that this family has two girls?
Now for the Girl Named Florida problem:
Suppose you know that a family with two children has at least one girl named Florida. What is the probability that this family has two girls?
Bolded the part I read past over and over again.
I'm still missing it. I thought that at least one girl was a given. The probability of the gender of the second child is independent of that. Are we talking about the at least one girl problem or the girl named Florida problem?
Quote from: Kim Jong Jesus on September 03, 2013, 05:13:22 AM
Quote from: Queen Gogira Pennyworth, BSW on September 03, 2013, 05:04:15 AM
Quote from: McGrupp on September 01, 2013, 10:03:36 PM
QuoteThe Girl Named Florida problem is usually preceded by an easier problem that goes as follows:
Suppose you know that a family with two children has at least one girl. What is the probability that this family has two girls?
Now for the Girl Named Florida problem:
Suppose you know that a family with two children has at least one girl named Florida. What is the probability that this family has two girls?
Bolded the part I read past over and over again.
I'm still missing it. I thought that at least one girl was a given. The probability of the gender of the second child is independent of that. Are we talking about the at least one girl problem or the girl named Florida problem?
Both problems appear to be the same question. They are identical. The name of the "at least one girl" is irrelevant. The only difference between the two questions are the two words "named Florida".
Quote from: Surprise Happy Endings Whether You Want Them Or Not on September 03, 2013, 06:25:22 AM
Quote from: Kim Jong Jesus on September 03, 2013, 05:13:22 AM
Quote from: Queen Gogira Pennyworth, BSW on September 03, 2013, 05:04:15 AM
Quote from: McGrupp on September 01, 2013, 10:03:36 PM
QuoteThe Girl Named Florida problem is usually preceded by an easier problem that goes as follows:
Suppose you know that a family with two children has at least one girl. What is the probability that this family has two girls?
Now for the Girl Named Florida problem:
Suppose you know that a family with two children has at least one girl named Florida. What is the probability that this family has two girls?
Bolded the part I read past over and over again.
I'm still missing it. I thought that at least one girl was a given. The probability of the gender of the second child is independent of that. Are we talking about the at least one girl problem or the girl named Florida problem?
Both problems appear to be the same question. They are identical. The name of the "at least one girl" is irrelevant. The only difference between the two questions are the two words "named Florida".
Fair. I'm still not getting it though. Family has two kids. At least one of them is a girl. That means that the options are:
1 girl, 1 boy
2 girls
We already know that the family has one girl, so the probability is the gender of the second child only, no? I'm missing Gogira's revelation entirely. Since the one child being a girl is part of the priors, that brings the probability of to girls up to 50%, not 25% or 60%?
Quote from: Surprise Happy Endings Whether You Want Them Or Not on September 03, 2013, 06:25:22 AM
Quote from: Kim Jong Jesus on September 03, 2013, 05:13:22 AM
Quote from: Queen Gogira Pennyworth, BSW on September 03, 2013, 05:04:15 AM
Quote from: McGrupp on September 01, 2013, 10:03:36 PM
QuoteThe Girl Named Florida problem is usually preceded by an easier problem that goes as follows:
Suppose you know that a family with two children has at least one girl. What is the probability that this family has two girls?
Now for the Girl Named Florida problem:
Suppose you know that a family with two children has at least one girl named Florida. What is the probability that this family has two girls?
Bolded the part I read past over and over again.
I'm still missing it. I thought that at least one girl was a given. The probability of the gender of the second child is independent of that. Are we talking about the at least one girl problem or the girl named Florida problem?
Both problems appear to be the same question. They are identical. The name of the "at least one girl" is irrelevant. The only difference between the two questions are the two words "named Florida".
Thanks Nigel, I couldn't figure out any difference between the two questions when I read this thread yesterday and my brain started leaking out of my ear.
Yeah, I screwed up and thought that the
Quote from: Kim Jong Jesus on September 03, 2013, 06:36:50 AM
Quote from: Surprise Happy Endings Whether You Want Them Or Not on September 03, 2013, 06:25:22 AM
Quote from: Kim Jong Jesus on September 03, 2013, 05:13:22 AM
Quote from: Queen Gogira Pennyworth, BSW on September 03, 2013, 05:04:15 AM
Quote from: McGrupp on September 01, 2013, 10:03:36 PM
QuoteThe Girl Named Florida problem is usually preceded by an easier problem that goes as follows:
Suppose you know that a family with two children has at least one girl. What is the probability that this family has two girls?
Now for the Girl Named Florida problem:
Suppose you know that a family with two children has at least one girl named Florida. What is the probability that this family has two girls?
Bolded the part I read past over and over again.
I'm still missing it. I thought that at least one girl was a given. The probability of the gender of the second child is independent of that. Are we talking about the at least one girl problem or the girl named Florida problem?
Both problems appear to be the same question. They are identical. The name of the "at least one girl" is irrelevant. The only difference between the two questions are the two words "named Florida".
Fair. I'm still not getting it though. Family has two kids. At least one of them is a girl. That means that the options are:
1 girl, 1 boy
2 girls
We already know that the family has one girl, so the probability is the gender of the second child only, no? I'm missing Gogira's revelation entirely. Since the one child being a girl is part of the priors, that brings the probability of to girls up to 50%, not 25% or 60%?
All of them are 50% because there's no difference between the two sentences as far as the genders are concerned. I screwed up and read the first sentence without the "one of them is a girl" part, which would make it "one family has two kids and you have no information about either gender." Because I am a moron.
Hrmmm... so I googled this and there seems to be all sorts of debate.
So far I am most swayed by the 50% argument. However, I did find an argument for WHY the name Florida would change the probabilities. Florida is an uncommon name. Therefore there is a higher probability of a girl being named Florida if there are two girls, rather that one.
That is Boy/Girl(Florida) or Girl(Florida)/Boy are supposedly less likely than Girl/Girl (Florida) or Girl(Florida)/Girl.
I don't know if I agree with that, but it at least provides some rationale for the additional piece of data.
ETA:
Another argument:
For the first question we have the options:
Boy/Girl, Girl/Girl, Girl/Boy
So 1/3 chance that the second child is a girl.
For the second question we have the following options:
Boy/Girl named Florida, Girl Named Florida/Boy, Girl/Girl Named Florida, Girl Named Florida/Girl.
So 2/4 (1/2) chance that the second child is a girl.
Though that seems kinda shady to me since Girl/Girl is just being counted twice.
Quote from: Bebek Sincap Ratatosk on September 03, 2013, 11:59:01 AM
Hrmmm... so I googled this and there seems to be all sorts of debate.
So far I am most swayed by the 50% argument. However, I did find an argument for WHY the name Florida would change the probabilities. Florida is an uncommon name. Therefore there is a higher probability of a girl being named Florida if there are two girls, rather that one.
That is Boy/Girl(Florida) or Girl(Florida)/Boy are supposedly less likely than Girl/Girl (Florida) or Girl(Florida)/Girl.
I don't know if I agree with that, but it at least provides some rationale for the additional piece of data.
ETA:
Another argument:
For the first question we have the options:
Boy/Girl, Girl/Girl, Girl/Boy
So 1/3 chance that the second child is a girl.
For the second question we have the following options:
Boy/Girl named Florida, Girl Named Florida/Boy, Girl/Girl Named Florida, Girl Named Florida/Girl.
So 2/4 (1/2) chance that the second child is a girl.
Though that seems kinda shady to me since Girl/Girl is just being counted twice.
That logic is erroneous because the fact that the girl is named Florida is given. The commonness or uncommonness of the name has zero bearing.
Quote from: Bebek Sincap Ratatosk on September 03, 2013, 11:59:01 AM
Hrmmm... so I googled this and there seems to be all sorts of debate.
So far I am most swayed by the 50% argument. However, I did find an argument for WHY the name Florida would change the probabilities. Florida is an uncommon name. Therefore there is a higher probability of a girl being named Florida if there are two girls, rather that one.
That is Boy/Girl(Florida) or Girl(Florida)/Boy are supposedly less likely than Girl/Girl (Florida) or Girl(Florida)/Girl.
I don't know if I agree with that, but it at least provides some rationale for the additional piece of data.
ETA:
Another argument:
For the first question we have the options:
Boy/Girl, Girl/Girl, Girl/Boy
So 1/3 chance that the second child is a girl.
For the second question we have the following options:
Boy/Girl named Florida, Girl Named Florida/Boy, Girl/Girl Named Florida, Girl Named Florida/Girl.
So 2/4 (1/2) chance that the second child is a girl.
Though that seems kinda shady to me since Girl/Girl is just being counted twice.
So is Girl/Boy in the 1/3 chance. The position of the girl has no bearing. They're not asking that. Girl/Boy is the same as Boy/Girl.
Quote from: Queen Gogira Pennyworth, BSW on September 03, 2013, 11:04:37 AM
Yeah, I screwed up and thought that the Quote from: Kim Jong Jesus on September 03, 2013, 06:36:50 AM
Quote from: Surprise Happy Endings Whether You Want Them Or Not on September 03, 2013, 06:25:22 AM
Quote from: Kim Jong Jesus on September 03, 2013, 05:13:22 AM
Quote from: Queen Gogira Pennyworth, BSW on September 03, 2013, 05:04:15 AM
Quote from: McGrupp on September 01, 2013, 10:03:36 PM
QuoteThe Girl Named Florida problem is usually preceded by an easier problem that goes as follows:
Suppose you know that a family with two children has at least one girl. What is the probability that this family has two girls?
Now for the Girl Named Florida problem:
Suppose you know that a family with two children has at least one girl named Florida. What is the probability that this family has two girls?
Bolded the part I read past over and over again.
I'm still missing it. I thought that at least one girl was a given. The probability of the gender of the second child is independent of that. Are we talking about the at least one girl problem or the girl named Florida problem?
Both problems appear to be the same question. They are identical. The name of the "at least one girl" is irrelevant. The only difference between the two questions are the two words "named Florida".
Fair. I'm still not getting it though. Family has two kids. At least one of them is a girl. That means that the options are:
1 girl, 1 boy
2 girls
We already know that the family has one girl, so the probability is the gender of the second child only, no? I'm missing Gogira's revelation entirely. Since the one child being a girl is part of the priors, that brings the probability of to girls up to 50%, not 25% or 60%?
All of them are 50% because there's no difference between the two sentences as far as the genders are concerned. I screwed up and read the first sentence without the "one of them is a girl" part, which would make it "one family has two kids and you have no information about either gender." Because I am a moron.
Gotcha. I was confused as to where you were coming from and thought that I was wrong about the 50%
Reframe: Coin flips.
Round 1:
Heads 1/2
Tails 1/2
Round 2
Heads Heads 1/4
Heads Tails 1/4
Tails Heads 1/4
Tails Tails 1/4
But in this case, the order doesn't matter.
So,
Heads Heads 1/4
[Hails Teads] 2/4
Tails Tails 1/4
So the chance of two girls is 25%?
... Did I totally get a different answer here? Goddammit.
Quote from: Surprise Happy Endings Whether You Want Them Or Not on September 03, 2013, 04:12:29 PM
Quote from: Bebek Sincap Ratatosk on September 03, 2013, 11:59:01 AM
Hrmmm... so I googled this and there seems to be all sorts of debate.
So far I am most swayed by the 50% argument. However, I did find an argument for WHY the name Florida would change the probabilities. Florida is an uncommon name. Therefore there is a higher probability of a girl being named Florida if there are two girls, rather that one.
That is Boy/Girl(Florida) or Girl(Florida)/Boy are supposedly less likely than Girl/Girl (Florida) or Girl(Florida)/Girl.
I don't know if I agree with that, but it at least provides some rationale for the additional piece of data.
ETA:
Another argument:
For the first question we have the options:
Boy/Girl, Girl/Girl, Girl/Boy
So 1/3 chance that the second child is a girl.
For the second question we have the following options:
Boy/Girl named Florida, Girl Named Florida/Boy, Girl/Girl Named Florida, Girl Named Florida/Girl.
So 2/4 (1/2) chance that the second child is a girl.
Though that seems kinda shady to me since Girl/Girl is just being counted twice.
That logic is erroneous because the fact that the girl is named Florida is given. The commonness or uncommonness of the name has zero bearing.
That's what I thought as well, however it seems to be a popular argument on the many blogs where this problem is discussed. In fact at this site: http://bblais.blogspot.co.uk/2010/01/there-once-was-girl-named-florida-aka.html (http://bblais.blogspot.co.uk/2010/01/there-once-was-girl-named-florida-aka.html)Someone actually wrote a simulation and a formal analysis on the point.
I don't know enough to say that I agree, only that it seems pretty damn weird :lulz:
Both questions, as they are worded, are "what is the probability that the other child is a girl?"
Quote from: Bebek Sincap Ratatosk on September 03, 2013, 04:42:02 PM
Quote from: Surprise Happy Endings Whether You Want Them Or Not on September 03, 2013, 04:12:29 PM
Quote from: Bebek Sincap Ratatosk on September 03, 2013, 11:59:01 AM
Hrmmm... so I googled this and there seems to be all sorts of debate.
So far I am most swayed by the 50% argument. However, I did find an argument for WHY the name Florida would change the probabilities. Florida is an uncommon name. Therefore there is a higher probability of a girl being named Florida if there are two girls, rather that one.
That is Boy/Girl(Florida) or Girl(Florida)/Boy are supposedly less likely than Girl/Girl (Florida) or Girl(Florida)/Girl.
I don't know if I agree with that, but it at least provides some rationale for the additional piece of data.
ETA:
Another argument:
For the first question we have the options:
Boy/Girl, Girl/Girl, Girl/Boy
So 1/3 chance that the second child is a girl.
For the second question we have the following options:
Boy/Girl named Florida, Girl Named Florida/Boy, Girl/Girl Named Florida, Girl Named Florida/Girl.
So 2/4 (1/2) chance that the second child is a girl.
Though that seems kinda shady to me since Girl/Girl is just being counted twice.
That logic is erroneous because the fact that the girl is named Florida is given. The commonness or uncommonness of the name has zero bearing.
That's what I thought as well, however it seems to be a popular argument on the many blogs where this problem is discussed. In fact at this site: http://bblais.blogspot.co.uk/2010/01/there-once-was-girl-named-florida-aka.html (http://bblais.blogspot.co.uk/2010/01/there-once-was-girl-named-florida-aka.html)Someone actually wrote a simulation and a formal analysis on the point.
I don't know enough to say that I agree, only that it seems pretty damn weird :lulz:
It may be a common argument, but it's a stupid one because
he is answering a different question.
Quote from: LMNO, PhD (life continues) on September 03, 2013, 04:41:46 PM
Reframe: Coin flips.
Round 1:
Heads 1/2
Tails 1/2
Round 2
Heads Heads 1/4
Heads Tails 1/4
Tails Heads 1/4
Tails Tails 1/4
But in this case, the order doesn't matter.
So,
Heads Heads 1/4
[Hails Teads] 2/4
Tails Tails 1/4
So the chance of two girls is 25%?
... Did I totally get a different answer here? Goddammit.
You got the right math for the wrong problem, I missed a key phrase in the question and I think I've hopelessly confused the thread :oops:
Let me put it this way: Once you have a given, the probability of the given is 100%. It is no longer a factor in the calculation for the probability of the not-given.
Quote from: Surprise Happy Endings Whether You Want Them Or Not on September 03, 2013, 04:44:28 PM
Both questions, as they are worded, are "what is the probability that the other child is a girl?"
Yes, and when you're given the information that one of them is a girl, the question moves from "what are the chances that a child is born a girl," and becomes "What are the chances that two children are both born girls?"
Or, in other words, you're asked about two coin flips, not just one.
If I flip a coin four times, the sequence of flips has 1/16 chance of happening. But if I ask what the chances of
any given flip, then it's 1/2.
And if I ask the odds of the
total amount of heads v tails, that's another probability entirely.
For the record, that is the kind of question that is given in statistics classes to train students to disregard extraneous data. As this thread illustrates perfectly, one of the challenges in statistics is to answer the question that is actually being posed and not the question that you think is being posed.
Quote from: LMNO, PhD (life continues) on September 03, 2013, 04:52:33 PM
Quote from: Surprise Happy Endings Whether You Want Them Or Not on September 03, 2013, 04:44:28 PM
Both questions, as they are worded, are "what is the probability that the other child is a girl?"
Yes, and when you're given the information that one of them is a girl, the question moves from "what are the chances that a child is born a girl," and becomes "What are the chances that two children are both born girls?"
Or, in other words, you're asked about two coin flips, not just one.
If I flip a coin four times, the sequence of flips has 1/16 chance of happening. But if I ask what the chances of any given flip, then it's 1/2.
And if I ask the odds of the total amount of heads v tails, that's another probability entirely.
No, you have it backward. The first coin has already been flipped, there is no remaining probability for the first coin.
Look at it this way: You have flipped a coin, and it came up heads. What is the probability that it came up tails?
http://www.awfulfinance.com/a-girl-named-florida/ (http://www.awfulfinance.com/a-girl-named-florida/)
This actually pulls some specifics from the book where the problem is found:
QuoteAlthough the statement of the problem says that one child is a girl, it doesn't say which one, and that changes things...The new information – one of the children is a girl – means that we are eliminating from consideration the possibility that both children are boys....That leaves only 3 outcomes in the sample space: (girl, boy), (boy, girl), and (girl, girl).
QuoteThe variant is this: in a family with two children, what are the chances, if one of the children is a girl named Florida, that both children are girls?...I picked (Florida) rather carefully, because part of the riddle is the question, what, if anything, about the name Florida affects the odds?...are the chances of two girls still 1 in 3?...The fact that one of the girls is named Florida changes the chances to 1 in 2.
There are some interesting charts and then a comment that:
QuoteThe answer isn't 50%, it's 49.9999875%
*twitch*
Note: my viewpoint on this has been changing, so each subsequent post may not be fully in line with the previous.Quote from: Surprise Happy Endings Whether You Want Them Or Not on September 03, 2013, 04:56:50 PM
For the record, that is the kind of question that is given in statistics classes to train students to disregard extraneous data. As this thread illustrates perfectly, one of the challenges in statistics is to answer the question that is actually being posed and not the question that you think is being posed.
I see what you're saying, and I think I am ignoring extraneous data?
Pardon if I keep doing it as coin flips.
Situation: two flips.
Probability of both flips being tails: 1/4
Known: One flip is tails.
Probability of both flips being tails: still 1/4.
The question being asked is the probability of two tails. Telling me that one of the flips is tails changes nothing, as that's what I'm looking for.
Also, I'm sorry if I keep pushing the "wrong" answer. Please don't get frustrated with me.
Quote from: Bebek Sincap Ratatosk on September 03, 2013, 05:03:49 PM
http://www.awfulfinance.com/a-girl-named-florida/ (http://www.awfulfinance.com/a-girl-named-florida/)
This actually pulls some specifics from the book where the problem is found:
QuoteAlthough the statement of the problem says that one child is a girl, it doesn't say which one, and that changes things...The new information – one of the children is a girl – means that we are eliminating from consideration the possibility that both children are boys....That leaves only 3 outcomes in the sample space: (girl, boy), (boy, girl), and (girl, girl).
The position is irrelevant though. It doesn't say what's the likelihood that the youngest one is a girl. It says what's the likelihood that they are both girls.
QuoteQuoteThe variant is this: in a family with two children, what are the chances, if one of the children is a girl named Florida, that both children are girls?...I picked (Florida) rather carefully, because part of the riddle is the question, what, if anything, about the name Florida affects the odds?...are the chances of two girls still 1 in 3?...The fact that one of the girls is named Florida changes the chances to 1 in 2.
There are some interesting charts and then a comment that:
QuoteThe answer isn't 50%, it's 49.9999875%
*twitch*
49.9999875% is more or less the same as 50%
I'd like to hear more on the explanation that the name of the girl affects the odds of the sex of the other child. It sounds like they're inserting an otherwise meaningless cultural bias and insisting that it has statistical meaning.
Quote from: LMNO, PhD (life continues) on September 03, 2013, 05:07:51 PM
Note: my viewpoint on this has been changing, so each subsequent post may not be fully in line with the previous.
Quote from: Surprise Happy Endings Whether You Want Them Or Not on September 03, 2013, 04:56:50 PM
For the record, that is the kind of question that is given in statistics classes to train students to disregard extraneous data. As this thread illustrates perfectly, one of the challenges in statistics is to answer the question that is actually being posed and not the question that you think is being posed.
I see what you're saying, and I think I am ignoring extraneous data?
Pardon if I keep doing it as coin flips.
Situation: two flips.
Probability of both flips being tails: 1/4
Known: One flip is tails.
Probability of both flips being tails: still 1/4.
The question being asked is the probability of two tails. Telling me that one of the flips is tails changes nothing, as that's what I'm looking for.
You can't do probability on an event that has already happened, so if one of the flips has already been performed and we know the outcome of that flip, and both flips are independent of one another (which they have to be for this example, otherwise we would be performing a much more complex ANOVA calculation) we can only calculate the odds of the remaining flip.
Quote from: Surprise Happy Endings Whether You Want Them Or Not on September 03, 2013, 05:13:01 PM
Quote from: LMNO, PhD (life continues) on September 03, 2013, 05:07:51 PM
Note: my viewpoint on this has been changing, so each subsequent post may not be fully in line with the previous.
Quote from: Surprise Happy Endings Whether You Want Them Or Not on September 03, 2013, 04:56:50 PM
For the record, that is the kind of question that is given in statistics classes to train students to disregard extraneous data. As this thread illustrates perfectly, one of the challenges in statistics is to answer the question that is actually being posed and not the question that you think is being posed.
I see what you're saying, and I think I am ignoring extraneous data?
Pardon if I keep doing it as coin flips.
Situation: two flips.
Probability of both flips being tails: 1/4
Known: One flip is tails.
Probability of both flips being tails: still 1/4.
The question being asked is the probability of two tails. Telling me that one of the flips is tails changes nothing, as that's what I'm looking for.
You can't do probability on an event that has already happened, so if one of the flips has already been performed and we know the outcome of that flip, and both flips are independent of one another (which they have to be for this example, otherwise we would be performing a much more complex ANOVA calculation) we can only calculate the odds of the remaining flip.
Let's put it this way-
Moe: I think there's 25% chance that two girls are standing outside.
Larry: Have you looked outside?
Moe: No.
LArry: There's two people, and at least on of them is a girl.
Moe: There's a 50% chance that two girls are standing outside.
Once again, think of a fair coin that you have just flipped, and it came up heads. What is the chance that it came up tails? None, because it came up heads.
When you have not yet flipped the coin, it has a 50% chance of coming up heads. So does the second coin. To determine the probability that both will come up heads, you can multiply .50 x .50 and find that the probability is .25, right?
Once it has been flipped, there is no more probability, or, you could state it as the probability that it came up heads is 100%.
The second coin flip still has a 50% probability of coming up heads. 1 x .50 = .50. The probability that both coins will be heads, once the first coin has been flipped and came up heads, is 50%, the same as the probability for a single coin flip.
Quote from: Bebek Sincap Ratatosk on September 03, 2013, 05:03:49 PM
http://www.awfulfinance.com/a-girl-named-florida/ (http://www.awfulfinance.com/a-girl-named-florida/)
This actually pulls some specifics from the book where the problem is found:
QuoteAlthough the statement of the problem says that one child is a girl, it doesn't say which one, and that changes things...The new information – one of the children is a girl – means that we are eliminating from consideration the possibility that both children are boys....That leaves only 3 outcomes in the sample space: (girl, boy), (boy, girl), and (girl, girl).
QuoteThe variant is this: in a family with two children, what are the chances, if one of the children is a girl named Florida, that both children are girls?...I picked (Florida) rather carefully, because part of the riddle is the question, what, if anything, about the name Florida affects the odds?...are the chances of two girls still 1 in 3?...The fact that one of the girls is named Florida changes the chances to 1 in 2.
There are some interesting charts and then a comment that:
QuoteThe answer isn't 50%, it's 49.9999875%
*twitch*
I might argue that the author of that book isn't doing statistics, he's doing economics. :lulz:
Quote from: Surprise Happy Endings Whether You Want Them Or Not on September 03, 2013, 05:19:28 PM
Once again, think of a fair coin that you have just flipped, and it came up heads. What is the chance that it came up tails? None, because it came up heads.
When you have not yet flipped the coin, it has a 50% chance of coming up heads. So does the second coin. To determine the probability that both will come up heads, you can multiply .50 x .50 and find that the probability is .25, right?
Once it has been flipped, there is no more probability, or, you could state it as the probability that it came up heads is 100%.
The second coin flip still has a 50% probability of coming up heads. 1 x .50 = .50. The probability that both coins will be heads, once the first coin has been flipped and came up heads, is 50%, the same as the probability for a single coin flip.
This is reminding me of the time that my stats professor said he doesn't usually play the lottery because, statistically, there's no point, but when he feels like it, he'll go up and say loudly enough for the other numbers players to hear that he's playing 0000, just to piss them off. Each ball has 10% chance of coming up a 0, and on the off chance that 0000 does come up, he'll have been the only spag to play that number.
Quote from: Kim Jong Jesus on September 03, 2013, 05:26:16 PM
Quote from: Surprise Happy Endings Whether You Want Them Or Not on September 03, 2013, 05:19:28 PM
Once again, think of a fair coin that you have just flipped, and it came up heads. What is the chance that it came up tails? None, because it came up heads.
When you have not yet flipped the coin, it has a 50% chance of coming up heads. So does the second coin. To determine the probability that both will come up heads, you can multiply .50 x .50 and find that the probability is .25, right?
Once it has been flipped, there is no more probability, or, you could state it as the probability that it came up heads is 100%.
The second coin flip still has a 50% probability of coming up heads. 1 x .50 = .50. The probability that both coins will be heads, once the first coin has been flipped and came up heads, is 50%, the same as the probability for a single coin flip.
This is reminding me of the time that my stats professor said he doesn't usually play the lottery because, statistically, there's no point, but when he feels like it, he'll go up and say loudly enough for the other numbers players to hear that he's playing 0000, just to piss them off. Each ball has 10% chance of coming up a 0, and on the off chance that 0000 does come up, he'll have been the only spag to play that number.
:lulz: :lulz: :lulz:
I hear there's 50% chance that there's a million dollars in the house next door. However, there is a 50% chance that there is no house next door.
Well, then let's build one!
(Not to detract...I just wanted to have this thread pop up in my new replies.)
LMNO, this way of thinking about it might also be helpful:
A family has two children, and at least one of the children is a boy. What are the chances that both children are girls?
Quote from: Surprise Happy Endings Whether You Want Them Or Not on September 03, 2013, 05:28:02 PM
Quote from: Kim Jong Jesus on September 03, 2013, 05:26:16 PM
Quote from: Surprise Happy Endings Whether You Want Them Or Not on September 03, 2013, 05:19:28 PM
Once again, think of a fair coin that you have just flipped, and it came up heads. What is the chance that it came up tails? None, because it came up heads.
When you have not yet flipped the coin, it has a 50% chance of coming up heads. So does the second coin. To determine the probability that both will come up heads, you can multiply .50 x .50 and find that the probability is .25, right?
Once it has been flipped, there is no more probability, or, you could state it as the probability that it came up heads is 100%.
The second coin flip still has a 50% probability of coming up heads. 1 x .50 = .50. The probability that both coins will be heads, once the first coin has been flipped and came up heads, is 50%, the same as the probability for a single coin flip.
This is reminding me of the time that my stats professor said he doesn't usually play the lottery because, statistically, there's no point, but when he feels like it, he'll go up and say loudly enough for the other numbers players to hear that he's playing 0000, just to piss them off. Each ball has 10% chance of coming up a 0, and on the off chance that 0000 does come up, he'll have been the only spag to play that number.
:lulz: :lulz: :lulz:
That was my reaction, too. I like the idea of a mathematician trolling gamblers.
The conversation here is almost exactly like the conversation in my head when I was trying to figure out the problem. Still makes my head hurt.
My understanding is that the name Florida is meant to be misleading. It could be replaced with Susan, or anything. I think it's just important that we know some type of specific information about one of the girls, I think.
but I'm still missing something.
Quote from: Bebek Sincap Ratatosk on September 03, 2013, 05:03:49 PM
That leaves only 3 outcomes in the sample space: (girl, boy), (boy, girl), and (girl, girl).
I have to take issue with this, because as LG pointed out earlier there are 4 outcomes: (girl, boy), (boy, girl), (girl, girl) and (girl, girl). Just because (girl, girl) and (girl, girl) look identical doesn't mean you can discount one.
You could also look at it as a 25% chance for each (boy, girl) and (girl, boy) and a 50% chance of (girl, girl), though. But you can pretty safely dismiss the bloggers who are looking at it as somehow indicating that there is only a 1/3 chance of (girl, girl) because they clearly have no idea what they're talking about from the word go, so any further analysis from them is a waste of time.
Quote from: McGrupp on September 03, 2013, 05:36:45 PM
The conversation here is almost exactly like the conversation in my head when I was trying to figure out the problem. Still makes my head hurt.
My understanding is that the name Florida is meant to be misleading. It could be replaced with Susan, or anything. I think it's just important that we know some type of specific information about one of the girls, I think.
but I'm still missing something.
It sounds like, from the excerpt that Rat posted, the original author of the question was using the name Florida to trigger some kind of discussion of the theoretical economics of the name; it doesn't appear to be a book about statistics, but a book about randomness, and so the question is not meant to be answered literally from a statistical perspective.
Ok, I think I'm getting on board, but...
Quote from: Surprise Happy Endings Whether You Want Them Or Not on September 03, 2013, 05:19:28 PM
Once again, think of a fair coin that you have just flipped, and it came up heads. What is the chance that it came up tails? None, because it came up heads.
When you have not yet flipped the coin, it has a 50% chance of coming up heads. So does the second coin. To determine the probability that both will come up heads, you can multiply .50 x .50 and find that the probability is .25, right?
Once it has been flipped, there is no more probability, or, you could state it as the probability that it came up heads is 100%.
The second coin flip still has a 50% probability of coming up heads. 1 x .50 = .50. The probability that both coins will be heads, once the first coin has been flipped and came up heads, is 50%, the same as the probability for a single coin flip.
So, if we real-timed this..
I happen to have a coin.
Before I flip it, what's the probability it will turn up heads twice? 25%.
I flip the coin once, and don't tell you what it was. Before I flip the second one, what's the probability it will turn up heads twice? 25%.
I flip the coin a second time, and don't tell you what either coin is. What's the probability it will turn up heads twice? 25%.
I turn over one of the coins. It's heads. What's the probability it will turn up heads twice?
...oh.
OH.I turn over one of the coins. It's heads. What's the probability the other one is heads? 50%
And if I ask you what were the chances both of them would have come up heads... would you say 25%?
YOU GOT IT!
But the question asked isn't the one you answered. You answered the one I read (where we didn't know the gender of either kid at first). But yay for wrapping your head around a super useful concept for future things!
Quote from: Queen Gogira Pennyworth, BSW on September 03, 2013, 05:53:44 PM
YOU GOT IT!
But the question asked isn't the one you answered. You answered the one I read (where we didn't know the gender of either kid at first). But yay for wrapping your head around a super useful concept for future things!
Wait, what?
QuoteThe Girl Named Florida problem is usually preceded by an easier problem that goes as follows:
Suppose you know that a family with two children has at least one girl. What is the probability that this family has two girls?
Now for the Girl Named Florida problem:
Suppose you know that a family with two children has at least one girl named Florida. What is the probability that this family has two girls?
2 girls = two coin flips.
girl = heads
1 gender known = 1 flip known.
Probability of 2 girls = probability of two heads.
As per the above, 50%.
What am I missing
now?
Quote from: LMNO, PhD (life continues) on September 03, 2013, 05:49:14 PM
Ok, I think I'm getting on board, but...Quote from: Surprise Happy Endings Whether You Want Them Or Not on September 03, 2013, 05:19:28 PM
Once again, think of a fair coin that you have just flipped, and it came up heads. What is the chance that it came up tails? None, because it came up heads.
When you have not yet flipped the coin, it has a 50% chance of coming up heads. So does the second coin. To determine the probability that both will come up heads, you can multiply .50 x .50 and find that the probability is .25, right?
Once it has been flipped, there is no more probability, or, you could state it as the probability that it came up heads is 100%.
The second coin flip still has a 50% probability of coming up heads. 1 x .50 = .50. The probability that both coins will be heads, once the first coin has been flipped and came up heads, is 50%, the same as the probability for a single coin flip.
So, if we real-timed this..
I happen to have a coin. Before I flip it, what's the probability it will turn up heads twice? 25%.
I flip the coin once, and don't tell you what it was. Before I flip the second one, what's the probability it will turn up heads twice? 25%.
I flip the coin a second time, and don't tell you what either coin is. What's the probability it will turn up heads twice? 25%.
I turn over one of the coins. It's heads. What's the probability it will turn up heads twice?
...oh.
OH.
I turn over one of the coins. It's heads. What's the probability the other one is heads? 50%
And if I ask you what were the chances both of them would have come up heads... would you say 25%?
Yes.
The key is in the word "probability". Probability collapses into reality the moment a potential becomes an actual.
As long as you're saying it's 50% either way, nothing.
Quote from: Queen Gogira Pennyworth, BSW on September 03, 2013, 05:53:44 PM
YOU GOT IT!
But the question asked isn't the one you answered. You answered the one I read (where we didn't know the gender of either kid at first). But yay for wrapping your head around a super useful concept for future things!
No, he got it. Right here:
Quote from: LMNO, PhD (life continues) on September 03, 2013, 05:49:14 PM
OH.
I turn over one of the coins. It's heads. What's the probability the other one is heads? 50%
You could even look at it from an IRL POV:
"Hi, Betty! It's me. How's little Sheila doing? That's great. What? You're pregnant again? Great news! Do you know if it's a girl or a boy? Not yet? Well, it could go either way, right? fifty-fifty."
"Betty, it's me again! How's baby Janice? Wonderful news! I know, two girls, isn't that something? 1 in 4 chance, like they say..."
Quote from: McGrupp on September 02, 2013, 03:07:13 PM
Say you know a family has two children, and further that at least one of them is a girl named Florida. What is the probability that they have two girls?
Here we have:
Boy-Girl (Florida)
Girl (Florida)-Boy
Girl (Not Florida)-Girl (Florida)
Girl (Florida)-Girl (Not Florida)
Girl (Florida)-Girl (Florida)
Here we get 3/5 which is a 60 percent chance. Although they seem to take out the Florida Florida scenario (which kinda feels like cheating) and get a 50 percent chance. This still feels odd.
I know this is yesterday's post but I wanted to revisit it to point out that the name of the other girl isn't part of the question, so the fifth possibility you included there is invalid, as is designating one of the girls "Not Florida". Other than that you were on the right track in recognizing that there are two (girl, girl) possibilities; there are (girl, Florida) and (Florida, girl). The second girl, if she exists, could be named Florida or not be named Florida.
Quote from: LMNO, PhD (life continues) on September 03, 2013, 06:09:29 PM
You could even look at it from an IRL POV:
"Hi, Betty! It's me. How's little Sheila doing? That's great. What? You're pregnant again? Great news! Do you know if it's a girl or a boy? Not yet? Well, it could go either way, right? fifty-fifty."
"Betty, it's me again! How's baby Janice? Wonderful news! I know, two girls, isn't that something? 1 in 4 chance, like they say..."
Yes, exactly.
Quote from: LMNO, PhD (life continues) on September 03, 2013, 05:49:14 PM
I flip the coin a second time, and don't tell you what either coin is. What's the probability it will turn up heads twice? 25%.
I turn over one of the coins. It's heads. What's the probability it will turn up heads twice?
...oh.
OH.
I turn over one of the coins. It's heads. What's the probability the other one is heads? 50%
Now you know how Vegas makes money.
Quote from: Surprise Happy Endings Whether You Want Them Or Not on September 03, 2013, 05:41:35 PM
Quote from: McGrupp on September 03, 2013, 05:36:45 PM
The conversation here is almost exactly like the conversation in my head when I was trying to figure out the problem. Still makes my head hurt.
My understanding is that the name Florida is meant to be misleading. It could be replaced with Susan, or anything. I think it's just important that we know some type of specific information about one of the girls, I think.
but I'm still missing something.
It sounds like, from the excerpt that Rat posted, the original author of the question was using the name Florida to trigger some kind of discussion of the theoretical economics of the name; it doesn't appear to be a book about statistics, but a book about randomness, and so the question is not meant to be answered literally from a statistical perspective.
Somehow this makes the problem even more interesting in some discordian koan way ;)
Quote from: Bebek Sincap Ratatosk on September 03, 2013, 07:07:21 PM
Quote from: Surprise Happy Endings Whether You Want Them Or Not on September 03, 2013, 05:41:35 PM
Quote from: McGrupp on September 03, 2013, 05:36:45 PM
The conversation here is almost exactly like the conversation in my head when I was trying to figure out the problem. Still makes my head hurt.
My understanding is that the name Florida is meant to be misleading. It could be replaced with Susan, or anything. I think it's just important that we know some type of specific information about one of the girls, I think.
but I'm still missing something.
It sounds like, from the excerpt that Rat posted, the original author of the question was using the name Florida to trigger some kind of discussion of the theoretical economics of the name; it doesn't appear to be a book about statistics, but a book about randomness, and so the question is not meant to be answered literally from a statistical perspective.
Somehow this makes the problem even more interesting in some discordian koan way ;)
Koans are for people who can't think without them.
TGRR,
Doesn't think, EITHER way. :whack:
Quote from: LMNO, PhD (life continues) on September 03, 2013, 05:49:14 PM
Ok, I think I'm getting on board, but...Quote from: Surprise Happy Endings Whether You Want Them Or Not on September 03, 2013, 05:19:28 PM
Once again, think of a fair coin that you have just flipped, and it came up heads. What is the chance that it came up tails? None, because it came up heads.
When you have not yet flipped the coin, it has a 50% chance of coming up heads. So does the second coin. To determine the probability that both will come up heads, you can multiply .50 x .50 and find that the probability is .25, right?
Once it has been flipped, there is no more probability, or, you could state it as the probability that it came up heads is 100%.
The second coin flip still has a 50% probability of coming up heads. 1 x .50 = .50. The probability that both coins will be heads, once the first coin has been flipped and came up heads, is 50%, the same as the probability for a single coin flip.
So, if we real-timed this..
I happen to have a coin. Before I flip it, what's the probability it will turn up heads twice? 25%.
I flip the coin once, and don't tell you what it was. Before I flip the second one, what's the probability it will turn up heads twice? 25%.
I flip the coin a second time, and don't tell you what either coin is. What's the probability it will turn up heads twice? 25%.
I turn over one of the coins. It's heads. What's the probability it will turn up heads twice?
...oh.
OH.
I turn over one of the coins. It's heads. What's the probability the other one is heads? 50%
And if I ask you what were the chances both of them would have come up heads... would you say 25%?
This post is /directly relevant/. http://lesswrong.com/lw/oj/probability_is_in_the_mind/
QuoteProbabilities express uncertainty, and it is only agents who can be uncertain. A blank map does not correspond to a blank territory. Ignorance is in the mind.
Quote from: Kai on September 03, 2013, 11:12:36 PM
Quote from: LMNO, PhD (life continues) on September 03, 2013, 05:49:14 PM
Ok, I think I'm getting on board, but...Quote from: Surprise Happy Endings Whether You Want Them Or Not on September 03, 2013, 05:19:28 PM
Once again, think of a fair coin that you have just flipped, and it came up heads. What is the chance that it came up tails? None, because it came up heads.
When you have not yet flipped the coin, it has a 50% chance of coming up heads. So does the second coin. To determine the probability that both will come up heads, you can multiply .50 x .50 and find that the probability is .25, right?
Once it has been flipped, there is no more probability, or, you could state it as the probability that it came up heads is 100%.
The second coin flip still has a 50% probability of coming up heads. 1 x .50 = .50. The probability that both coins will be heads, once the first coin has been flipped and came up heads, is 50%, the same as the probability for a single coin flip.
So, if we real-timed this..
I happen to have a coin. Before I flip it, what's the probability it will turn up heads twice? 25%.
I flip the coin once, and don't tell you what it was. Before I flip the second one, what's the probability it will turn up heads twice? 25%.
I flip the coin a second time, and don't tell you what either coin is. What's the probability it will turn up heads twice? 25%.
I turn over one of the coins. It's heads. What's the probability it will turn up heads twice?
...oh.
OH.
I turn over one of the coins. It's heads. What's the probability the other one is heads? 50%
And if I ask you what were the chances both of them would have come up heads... would you say 25%?
This post is /directly relevant/. http://lesswrong.com/lw/oj/probability_is_in_the_mind/
QuoteProbabilities express uncertainty, and it is only agents who can be uncertain. A blank map does not correspond to a blank territory. Ignorance is in the mind.
That post was awesome and I actually understood it!
Sorry to resurrect an old thread, but I just found this, and there is a critical point missing.
Quote from: LMNO, PhD (life continues) on September 03, 2013, 05:49:14 PM
So, if we real-timed this..
I happen to have a coin. Before I flip it, what's the probability it will turn up heads twice? 25%.
I flip the coin once, and don't tell you what it was. Before I flip the second one, what's the probability it will turn up heads twice? 25%.
I flip the coin a second time, and don't tell you what either coin is. What's the probability it will turn up heads twice? 25%.
I turn over one of the coins. It's heads. What's the probability it will turn up heads twice?
...oh.
OH.
I turn over one of the coins. It's heads. What's the probability the other one is heads? 50%
And if I ask you what were the chances both of them would have come up heads... would you say 25%?
Let's try it a different way:
- I happen to have two coins. Before I flip either, what's the probability they will turn up the same way? 50%.
- I flip one coin and keep it hidden under a cup. Before I flip the second one, what's the probability it will turn up the same way as they first? 50%.
- I flip the second coin, keeping it hidden as well. What's the probability they turned up the same way? 50%.
- I let you pick a cup, and I reveal its coin. It's heads. What's the probability the other is heads?
This is also 50%. If that isn't obvious from the progression, consider what you would have said if it had come up tails. The answer can't be different, so call it X for both questions. And if it is X for both questions, it is X if I just ask you to pick a cup and don't reveal its coin. And that's the same as the previous question.
The temptation to give a different answer is a paradox; and it even has a name. It is known as Bertrand's Box Paradox. The need to get the same answer, when the question is about symmetric options like heads or tails, forces the answer to be the same as when nothing was revealed.
- Suppose, instead if you picking a cup, you ask me if either is heads. I look at both, and reveal one, showing that it is heads. What's the probability the other came up the same way?
If both had been tails, originally a 25% chance, I couldn't have done this. Of the remaining 75%, 25% has two heads and 50% has a heads and a tails. So the answer is 25%/75%, or 33%.
Bertrand's Box Paradox doesn't apply, because the possible answers to your question aren't symmetric. The probability of two of the same result must be 100% if I can't reveal a heads.
- Suppose, instead of letting you pick anything, I look under both cups and show that one is a heads. What's the probability the other is heads?
This can't be answered without more information. If I decided to show a random coin (say, the left cup), the answer is 50% just like when you picked a cup. If I decided to show a heads if I could, the answer is 33%. And if I decided to show a tails if I could, but found I couldn't so I showed you a heads, the answer is 100%.
So the question is ambiguous. But if you had to pick one of those answers as "best," which would you pick? Can you apply Bertrand's Box Paradox?
The Florida question is essentially the same. The question is ambiguous, but maybe a "best" answer is possible. And it isn't the one usually given.
Quote from: Kai on September 03, 2013, 11:12:36 PM
Quote from: LMNO, PhD (life continues) on September 03, 2013, 05:49:14 PM
Ok, I think I'm getting on board, but...Quote from: Surprise Happy Endings Whether You Want Them Or Not on September 03, 2013, 05:19:28 PM
Once again, think of a fair coin that you have just flipped, and it came up heads. What is the chance that it came up tails? None, because it came up heads.
When you have not yet flipped the coin, it has a 50% chance of coming up heads. So does the second coin. To determine the probability that both will come up heads, you can multiply .50 x .50 and find that the probability is .25, right?
Once it has been flipped, there is no more probability, or, you could state it as the probability that it came up heads is 100%.
The second coin flip still has a 50% probability of coming up heads. 1 x .50 = .50. The probability that both coins will be heads, once the first coin has been flipped and came up heads, is 50%, the same as the probability for a single coin flip.
So, if we real-timed this..
I happen to have a coin. Before I flip it, what's the probability it will turn up heads twice? 25%.
I flip the coin once, and don't tell you what it was. Before I flip the second one, what's the probability it will turn up heads twice? 25%.
I flip the coin a second time, and don't tell you what either coin is. What's the probability it will turn up heads twice? 25%.
I turn over one of the coins. It's heads. What's the probability it will turn up heads twice?
...oh.
OH.
I turn over one of the coins. It's heads. What's the probability the other one is heads? 50%
And if I ask you what were the chances both of them would have come up heads... would you say 25%?
This post is /directly relevant/. http://lesswrong.com/lw/oj/probability_is_in_the_mind/
QuoteProbabilities express uncertainty, and it is only agents who can be uncertain. A blank map does not correspond to a blank territory. Ignorance is in the mind.
I'm having trouble understanding that.
That may be because I am trying to be a probabilist.
Is probabilism inherently solipsistic?
If that is true, then why did I not notice that?
Quote from: jeffjo on July 12, 2014, 02:39:44 PM
I happen to have two coins. Before I flip either, what's the probability they will turn up the same way? 50%.
wat
Quote from: Pæs on July 13, 2014, 11:46:11 PM
Quote from: jeffjo on July 12, 2014, 02:39:44 PM
I happen to have two coins. Before I flip either, what's the probability they will turn up the same way? 50%.
wat
Probability they will both flip to heads is .50 x .50. Probability they will both flip to tails is also .50 x .50. Each probability is .25, both probabilities combined is .50.
Essentially you have four conditions:
1. Coin A is heads and coin B is tails .25
2. Coin A is tails and coin B is heads .25
3. Coin A is heads and coin B is heads. .25
4. Coin A is tails and coin B is tails. .25
So you end up with 50% probability of one of each, and 50% probability of two of one.
Quote from: The Right Reverend Nigel on July 15, 2014, 05:44:39 AM
Quote from: Pæs on July 13, 2014, 11:46:11 PM
Quote from: jeffjo on July 12, 2014, 02:39:44 PM
I happen to have two coins. Before I flip either, what's the probability they will turn up the same way? 50%.
wat
Probability they will both flip to heads is .50 x .50. Probability they will both flip to tails is also .50 x .50. Each probability is .25, both probabilities combined is .50.
Essentially you have four conditions:
1. Coin A is heads and coin B is tails .25
2. Coin A is tails and coin B is heads .25
3. Coin A is heads and coin B is heads. .25
4. Coin A is tails and coin B is tails. .25
So you end up with 50% probability of one of each, and 50% probability of two of one.
Oh, the SAME WAY. Reading comprehension issue, don't mind me.
Happens to the best! :lol:
Brainfart: The difference between interchangable and identical becomes important when you deal with quantums: There are no mecha-gazillion protons in the universe, there is only one and it has mecha-gazillion instances of existence.
A proton ain't nothing but an instance of a probabilistic interaction.
Incidentally, the same occurs with theoretical coin-flips. :horrormirth:
What the hell are you talking about? Wait. Is this that "there is only one quanta" bullshit? Feynman was stoned out of his gourd when he came up with that one.
Quote from: LMNO, PhD (life continues) on July 24, 2014, 01:56:15 PM
What the hell are you talking about? Wait. Is this that "there is only one quanta" bullshit? Feynman was stoned out of his gourd when he came up with that one.
I have not read what Feynman said about it, but I don't think that is what i mean.
I mean that things on the level that quantum mechanics deals with are definitively identical, not just interchangable. You can't 'exchange' one electron for another, it is a meaningless concept.
Not so in tires, you can replace one tire with another and the car still works despite having one of its parts changed. The tire has been changed.
With electrons there is no slight difference in functionality, there is no change
at all. And I mean that in the absolute way, I'm not just saying that there is no detectable change.
Electrons (and their siblings) don't exist outside of their context: They are patterns of interaction, nothing more. Being patterns they are pure abstraction, unlike the objects on the scale we are used to think on.
Argh. Again, I can't tell if i am communicating effectively.