My assumptions and use of probability laws are clearly stated above. Tell me where I made a mistake, otherwise just saying “you’re wrong” is not going to move things forward.
“Suppose this experiment were repeated 1,000 times. We would expect to get 500 heads and 500 tails. So Beauty would be awoken 500 times after heads on Monday, 500 times after tails on Monday, and 500 times after tails on Tuesday. In other words, only in a third of the cases would heads precede her awakening. So the right answer for her to give is 1⁄3. This is the correct answer from Beauty’s perspective.”
That gives:
P(monday and heads)=500/1500. P(monday and tails)=500/1500. P(tuesday and tails)=500/1500.
You appear to have gone wrong by giving a different answer—based on a misinterpretation of the meaning of the interview question, it appears.
So you are not willing to tell me where I made a mistake?
P(heads)=1/2, p(monday | heads)=1. Which one of these is wrong?
You’re using expected frequencies to estimate a probability, apparently. But you’re counting the wrong thing. What you are calling P(monday and heads) is not that. There is a problem with your denominator. Think about it. Your numerator has a maximum value of 1000 (if the experiment was repeated 1000 times). Your denominator has a maximum value of 2000. If the maximum possible values of the numerator and denominator do not match, there is a problem. You have an outcome-dependent denominator. Try taking expectation of that. You won’t get what you think you’ll get.
Re: “If the maximum possible values of the numerator and denominator do not match, there is a problem.
The total possible number of awakenings is 2000.
That represents all tails—e.g.:
P(monday and heads) = 0/2000;
P(monday and tails) = 1000/2000;
P(tuesday and tails) = 1000/2000;
These values add up to 1 - i.e. the total numerators add up to the commonn denominator. That is the actual constraint. The maximum possible value of the numerator in each individual fraction is permitted to be smaller than the common denominator—that is not indicative of a problem.
Oh, it is a huge problem. It proves that your ratio isn’t of the form # of events divided by # of trials. Your ratio is something else. The burden is on you to prove that it actually converges to a probability as the number of trials goes to infinity.
Using cell counts and taking a ratio leads to a probability as the number of trials goes to infinity if you have independent draws. You don’t. You have a strange dependence in there that messes things up. Standard theory doesn’t hold. Your thing there is estimating something, you just don’t know what it is
The total number of events (statements by Beauty) adds up to the total number of trials (interviews).
You should not expect the number of statements by beauty on Monday to add up to the total number of interviews alltogether. It adds up to the number of interviews on Monday. This is not very complicated.
Do you have to make a condescending remark every time you respond? You told me things that I already know, and then said “This is not very complicated.” Great, but nothing accomplished.
You are using an estimator that is valid when you have counts from independent trials. Coin flips are independent here, but interviews are not. You need to take that into account.
It is the plain truth. I don’t know why you are asking such silly questions in public. Maybe you have a weak background in this sort of maths. Or maybe you just don’t like admitting that you posted a whole bunch of inaccurate nonsense—and so keep digging yourself deeper in.
You show no sign of being able to understand your problems—so it seems to me as though there is little point in continuing to point them out. You can’t say I didn’t try to help you sort yourself out.
Well, I have a phd in biostatistics and teach Bayesian data analysis at the University of Pennsylvania, so I either have background in such matters or Penn isn’t real careful on who they hire.
The fact that I am very careful about these kinds of problems is what lead me to discover the flaw in the 1⁄3 argument—it wasn’t obvious to me at first.
Hi, Nancy! I haven’t researched this issue. I imagine the results would depend on the details of the situation, the relative status of the participants, etc. I recommend you consult a social psychologist—if you are sincerely looking for answers.
Uh—improving neq1′s state of knowledge was not the intended purpose of that post.
I have already written literally dozens of posts attempting to improving the state of knowledge of other participants on this thread. That post was publicly explaining why I am now likely to stop—just so there is no subsequent confusion about the issue.
Right—but I call a spade a spade, don’t beat about the bush, say what I think—etc.
Insulating others from what I think in order to protect their egos is not my style. If I did that people would always be wondering if I meant what I said—or whether I was shielding them from my true opinions in order to protect their egos. In the long run, it is best to just speak the truth, as I see it, IMO. At least then, others know where I stand.
There are a lot of approaches one can take when interacting with other people. Your approach leads me to not want to make your acquaintance. The same isn’t true for most of the other people here, even the ones who disagree with me.
In the spirit of experimentation, I’m going to try giving up being oblique.
My primary motivation is not to do you a favor. My purpose is also not to protect neq1.
It is to convey that the purpose of this website is to work on thinking clearly, to some extent to further the creation of FAI, and also to improve skills at living. There’s also a little pleasant socializing.
However, insulting people (or having an atmosphere where insults are accepted) does not further any of the purposes of the site.
I believe that people generally think less well when they’ve been insulted. Also, I’ve been online for a long time. Insults are pretty much similar to each other—in other words, they’re noise, not signal so far as anything about the world generally is concerned.. They’re signal about emotional state and/or attempted dominance, but (as should be clear from the conversation so far), not a terribly clear signal.
What’s worse, insults are likely to lead to more insults.
I’m not a moderator, but I’m asking you not to dump hostility here.
Nancy, your beliefs about the average effect of insults on people do not seem to me to be a good reason to avoid bluntly telling people when they are behaving badly. IMO, you are not properly considering the positive effects of pointing out such bad behaviour. If someone behaves badly, and you don’t tell them, they don’t learn. Others might think their behaviour is acceptable. Still others might think you approve of their behaviour—and so on. It is not as though I had not tried all manner of rational argument first. Yes, people might be insulted or offended by someone else pointing out what is going on—if it reflects badly on them, but that is—ultimately—their business.
Not especially—and certainly not from my point of view. Alas, I found responding to your comments to be a waste of my time and energy. Especially so with your “oblique” comments. So, overall, I would rather you had not bothered commenting in the first place.
In the spirit of experimentation, I’m going to try giving up being oblique.
My primary motivation is not to do you a favor. My purpose is also not to protect neq1.
It is to convey that the purpose of this website is to work on thinking clearly, to some extent to further the creation of FAI, and also to improve skills at living. There’s also a little pleasant socializing.
However, insulting people (or having an atmosphere where insults are accepted) does not further any of the purposes of the site.
I believe that people generally think less well when they’ve been insulted. Also, I’ve been online for a long time. Insults are pretty much similar to each other—in other words, they’re noise, not signal so far as anything about the world generally is concerned.. They’re signal about emotional state and/or attempted dominance, but (as should be clear from the conversation so far), not a terribly clear signal.
What’s worse, insults are likely to lead to more insults.
I’m not a moderator, but I’m asking you not to dump hostility here.
In the spirit of experimentation, I’m going to try giving up being oblique.
My primary motivation is not to do you a favor. My purpose is also not to protect neq1.
It is to convey that the purpose of this website is to work on thinking clearly, to some extent to further the creation of FAI, and also to improve skills at living. There’s also a little pleasant socializing.
However, insulting people (or having an atmosphere where insults are accepted) does not further any of the purposes of the site.
I believe that people generally think less well when they’ve been insulted. Also, I’ve been online for a long time. Insults are pretty much similar to each other—in other words, they’re noise, not signal so far as anything about the world generally is concerned.. They’re signal about emotional state and/or attempted dominance, but (as should be clear from the conversation so far), not a terribly clear signal.
What’s worse, insults are likely to lead to more insults.
I’m not a moderator, but I’m asking you not to dump hostility here.
In the spirit of experimentation, I’m going to try giving up being oblique.
My primary motivation is not to do you a favor. My purpose is also not to protect neq1.
It is to convey that the purpose of this website is to work on thinking clearly, to some extent to further the creation of FAI, and also to improve skills at living. There’s also a little pleasant socializing.
However, insulting people (or having an atmosphere where insults are accepted) does not further any of the purposes of the site.
I believe that people generally think less well when they’ve been insulted. Also, I’ve been online for a long time. Insults are pretty much similar to each other—in other words, they’re noise, not signal so far as anything about the world generally is concerned.. They’re signal about emotional state and/or attempted dominance, but (as should be clear from the conversation so far), not a terribly clear signal.
What’s worse, insults are likely to lead to more insults.
I’m not a moderator, but I’m asking you not to dump hostility here.
But there are probably an infinite number of propositions that you actually believe, and even an infinite number of relevant propositions that you actually believe. You choose which things that you think to actually say (I’m just assuming that everything you think ‘out loud’ doesn’t get posted to Less Wrong, since I assume you have more thoughts than I’ve observed comments from you). As long as you’re leaving out an infinite amount of information, you might as well also leave out insulting language.
I said he was asking “silly questions”. However, that is true—and was not “insulting language”. If you think I was using “insulting language”, you will have to be more specific about what you mean.
As to the possibility of you making a more general point, IMO, systematically not speaking truths that might cause offense would have bad results—especially for truth-seekers:
“Unfortunately some people take offense more easily than others. Also, some people are offended by true statements.”
It is the same with pressuring other people to not speak truths that might cause offense. That too, would have—and has had—seriously unpleasant long-term effects.
That was implied information: “it seems to me as though there is little point in continuing to point them out. You can’t say I didn’t try to help you sort yourself out.”
“Likely to stop” is a probabalistic statement. I am still likely to stop posting on this thread soon. I have done my bit to promote the correct answer to this problem. A top level post explains the correct answer in some detail. I feel as though my work here is done.
Were someone else exhibiting similar posting behavior, would you draw the same conclusion? You may sincerely desire to terminate your conversation with neq1, but you appear to cesire* to continue it.
* A “cesire” is a motivator to action that works like a desire even when accompanied by a conflicting desire—much like an alief can induce emotional reactions in the same way as beliefs even in the presence of a contrary belief.
The conclusion that you feel your work is done. Such a state removes the desire to continue responding to neq1, and—as such a desire is the only apparent reason to respond to neq1 - leads to a cessation of posts in the associated thread(s). This has not occurred.
I haven’t argued about the topic of this post for a little while now—and certainly not since writing “I feel as though my work here is done”.
Rather I am here defending my reputation against assaults from people who don’t like my posting style—and seem keen to let everyone else know of their disapproval. I’ll probably give up with that too, soon enough.
Were someone else exhibiting similar posting behavior, would you draw the same conclusion? You may sincerely desire to terminate your conversation with neq1, but you appear to cesire* to continue it.
* A “cesire” is a motivator to action that works like a desire even when accompanied by a conflicting desire—much like an alief can induce emotional reactions in the same way as beliefs even in the presence of a contrary belief.
Actually, I have supplied my real name (in a previous post I linked to my blog, which has my name). I’m confident my colleagues would be in agreement with me.
My assumptions and use of probability laws are clearly stated above. Tell me where I made a mistake, otherwise just saying “you’re wrong” is not going to move things forward.
Well, the correct sum is this one:
“Suppose this experiment were repeated 1,000 times. We would expect to get 500 heads and 500 tails. So Beauty would be awoken 500 times after heads on Monday, 500 times after tails on Monday, and 500 times after tails on Tuesday. In other words, only in a third of the cases would heads precede her awakening. So the right answer for her to give is 1⁄3. This is the correct answer from Beauty’s perspective.”
That gives:
P(monday and heads)=500/1500. P(monday and tails)=500/1500. P(tuesday and tails)=500/1500.
You appear to have gone wrong by giving a different answer—based on a misinterpretation of the meaning of the interview question, it appears.
So you are not willing to tell me where I made a mistake?
P(heads)=1/2, p(monday | heads)=1. Which one of these is wrong?
You’re using expected frequencies to estimate a probability, apparently. But you’re counting the wrong thing. What you are calling P(monday and heads) is not that. There is a problem with your denominator. Think about it. Your numerator has a maximum value of 1000 (if the experiment was repeated 1000 times). Your denominator has a maximum value of 2000. If the maximum possible values of the numerator and denominator do not match, there is a problem. You have an outcome-dependent denominator. Try taking expectation of that. You won’t get what you think you’ll get.
Re: “If the maximum possible values of the numerator and denominator do not match, there is a problem.
The total possible number of awakenings is 2000.
That represents all tails—e.g.:
P(monday and heads) = 0/2000; P(monday and tails) = 1000/2000; P(tuesday and tails) = 1000/2000;
These values add up to 1 - i.e. the total numerators add up to the commonn denominator. That is the actual constraint. The maximum possible value of the numerator in each individual fraction is permitted to be smaller than the common denominator—that is not indicative of a problem.
Oh, it is a huge problem. It proves that your ratio isn’t of the form # of events divided by # of trials. Your ratio is something else. The burden is on you to prove that it actually converges to a probability as the number of trials goes to infinity.
Using cell counts and taking a ratio leads to a probability as the number of trials goes to infinity if you have independent draws. You don’t. You have a strange dependence in there that messes things up. Standard theory doesn’t hold. Your thing there is estimating something, you just don’t know what it is
The total number of events (statements by Beauty) adds up to the total number of trials (interviews).
You should not expect the number of statements by beauty on Monday to add up to the total number of interviews alltogether. It adds up to the number of interviews on Monday. This is not very complicated.
Do you have to make a condescending remark every time you respond? You told me things that I already know, and then said “This is not very complicated.” Great, but nothing accomplished.
You are using an estimator that is valid when you have counts from independent trials. Coin flips are independent here, but interviews are not. You need to take that into account.
It is the plain truth. I don’t know why you are asking such silly questions in public. Maybe you have a weak background in this sort of maths. Or maybe you just don’t like admitting that you posted a whole bunch of inaccurate nonsense—and so keep digging yourself deeper in.
You show no sign of being able to understand your problems—so it seems to me as though there is little point in continuing to point them out. You can’t say I didn’t try to help you sort yourself out.
Well, I have a phd in biostatistics and teach Bayesian data analysis at the University of Pennsylvania, so I either have background in such matters or Penn isn’t real careful on who they hire.
The fact that I am very careful about these kinds of problems is what lead me to discover the flaw in the 1⁄3 argument—it wasn’t obvious to me at first.
If true, a good job you haven’t supplied your real name, then—or your friends and colleagues might come across this thread.
Do you find that people generally think more clearly after they’ve been insulted?
Do you find that you think more clearly after you’ve been insulted?
Hi, Nancy! I haven’t researched this issue. I imagine the results would depend on the details of the situation, the relative status of the participants, etc. I recommend you consult a social psychologist—if you are sincerely looking for answers.
NancyLebovitz was being oblique. I believe her point was that your remarks were not useful for the purpose of improving neq1′s state of knowledge.
I would add that they were also not useful for the purpose of entertaining the lurkers, if the downvotes are anything to go by.
Uh—improving neq1′s state of knowledge was not the intended purpose of that post.
I have already written literally dozens of posts attempting to improving the state of knowledge of other participants on this thread. That post was publicly explaining why I am now likely to stop—just so there is no subsequent confusion about the issue.
I think
would have gone over better.
Right—but I call a spade a spade, don’t beat about the bush, say what I think—etc.
Insulating others from what I think in order to protect their egos is not my style. If I did that people would always be wondering if I meant what I said—or whether I was shielding them from my true opinions in order to protect their egos. In the long run, it is best to just speak the truth, as I see it, IMO. At least then, others know where I stand.
There are a lot of approaches one can take when interacting with other people. Your approach leads me to not want to make your acquaintance. The same isn’t true for most of the other people here, even the ones who disagree with me.
In that case, I would recommend you shut up as soon as possible. If, as you said,
then stop wasting your time.
Thanks for your proposal about how to optimise my time management.
I think you are best leaving that issue to me, though—I have more relevant information about the topic than you do.
In the spirit of experimentation, I’m going to try giving up being oblique.
My primary motivation is not to do you a favor. My purpose is also not to protect neq1.
It is to convey that the purpose of this website is to work on thinking clearly, to some extent to further the creation of FAI, and also to improve skills at living. There’s also a little pleasant socializing.
However, insulting people (or having an atmosphere where insults are accepted) does not further any of the purposes of the site.
I believe that people generally think less well when they’ve been insulted. Also, I’ve been online for a long time. Insults are pretty much similar to each other—in other words, they’re noise, not signal so far as anything about the world generally is concerned.. They’re signal about emotional state and/or attempted dominance, but (as should be clear from the conversation so far), not a terribly clear signal.
What’s worse, insults are likely to lead to more insults.
I’m not a moderator, but I’m asking you not to dump hostility here.
Nancy, your beliefs about the average effect of insults on people do not seem to me to be a good reason to avoid bluntly telling people when they are behaving badly. IMO, you are not properly considering the positive effects of pointing out such bad behaviour. If someone behaves badly, and you don’t tell them, they don’t learn. Others might think their behaviour is acceptable. Still others might think you approve of their behaviour—and so on. It is not as though I had not tried all manner of rational argument first. Yes, people might be insulted or offended by someone else pointing out what is going on—if it reflects badly on them, but that is—ultimately—their business.
I’ve told you rather bluntly that I don’t approve of your behavior, though I think I’ve managed to avoid insulting your intelligence or character.
Do you think the world is a better place as a result?
Not especially—and certainly not from my point of view. Alas, I found responding to your comments to be a waste of my time and energy. Especially so with your “oblique” comments. So, overall, I would rather you had not bothered commenting in the first place.
I apologize.
In the spirit of experimentation, I’m going to try giving up being oblique.
My primary motivation is not to do you a favor. My purpose is also not to protect neq1.
It is to convey that the purpose of this website is to work on thinking clearly, to some extent to further the creation of FAI, and also to improve skills at living. There’s also a little pleasant socializing.
However, insulting people (or having an atmosphere where insults are accepted) does not further any of the purposes of the site.
I believe that people generally think less well when they’ve been insulted. Also, I’ve been online for a long time. Insults are pretty much similar to each other—in other words, they’re noise, not signal so far as anything about the world generally is concerned.. They’re signal about emotional state and/or attempted dominance, but (as should be clear from the conversation so far), not a terribly clear signal.
What’s worse, insults are likely to lead to more insults.
I’m not a moderator, but I’m asking you not to dump hostility here.
In the spirit of experimentation, I’m going to try giving up being oblique.
My primary motivation is not to do you a favor. My purpose is also not to protect neq1.
It is to convey that the purpose of this website is to work on thinking clearly, to some extent to further the creation of FAI, and also to improve skills at living. There’s also a little pleasant socializing.
However, insulting people (or having an atmosphere where insults are accepted) does not further any of the purposes of the site.
I believe that people generally think less well when they’ve been insulted. Also, I’ve been online for a long time. Insults are pretty much similar to each other—in other words, they’re noise, not signal so far as anything about the world generally is concerned.. They’re signal about emotional state and/or attempted dominance, but (as should be clear from the conversation so far), not a terribly clear signal.
What’s worse, insults are likely to lead to more insults.
I’m not a moderator, but I’m asking you not to dump hostility here.
In the spirit of experimentation, I’m going to try giving up being oblique.
My primary motivation is not to do you a favor. My purpose is also not to protect neq1.
It is to convey that the purpose of this website is to work on thinking clearly, to some extent to further the creation of FAI, and also to improve skills at living. There’s also a little pleasant socializing.
However, insulting people (or having an atmosphere where insults are accepted) does not further any of the purposes of the site.
I believe that people generally think less well when they’ve been insulted. Also, I’ve been online for a long time. Insults are pretty much similar to each other—in other words, they’re noise, not signal so far as anything about the world generally is concerned.. They’re signal about emotional state and/or attempted dominance, but (as should be clear from the conversation so far), not a terribly clear signal.
What’s worse, insults are likely to lead to more insults.
I’m not a moderator, but I’m asking you not to dump hostility here.
But there are probably an infinite number of propositions that you actually believe, and even an infinite number of relevant propositions that you actually believe. You choose which things that you think to actually say (I’m just assuming that everything you think ‘out loud’ doesn’t get posted to Less Wrong, since I assume you have more thoughts than I’ve observed comments from you). As long as you’re leaving out an infinite amount of information, you might as well also leave out insulting language.
I said he was asking “silly questions”. However, that is true—and was not “insulting language”. If you think I was using “insulting language”, you will have to be more specific about what you mean.
As to the possibility of you making a more general point, IMO, systematically not speaking truths that might cause offense would have bad results—especially for truth-seekers:
“Unfortunately some people take offense more easily than others. Also, some people are offended by true statements.”
http://timtyler.org/political_correctness/
It is the same with pressuring other people to not speak truths that might cause offense. That too, would have—and has had—seriously unpleasant long-term effects.
You didn’t mention that you were likely to stop posting in the thread.
That was implied information: “it seems to me as though there is little point in continuing to point them out. You can’t say I didn’t try to help you sort yourself out.”
Your continued involvement in the conversation was stronger information.
“Likely to stop” is a probabalistic statement. I am still likely to stop posting on this thread soon. I have done my bit to promote the correct answer to this problem. A top level post explains the correct answer in some detail. I feel as though my work here is done.
Were someone else exhibiting similar posting behavior, would you draw the same conclusion? You may sincerely desire to terminate your conversation with neq1, but you appear to cesire* to continue it.
* A “cesire” is a motivator to action that works like a desire even when accompanied by a conflicting desire—much like an alief can induce emotional reactions in the same way as beliefs even in the presence of a contrary belief.
Your question seems vague: Similar posting behavior to what posting behaviour? - and by whom? Would I draw the same conclusion—as which conclusion?
The conclusion that you feel your work is done. Such a state removes the desire to continue responding to neq1, and—as such a desire is the only apparent reason to respond to neq1 - leads to a cessation of posts in the associated thread(s). This has not occurred.
I haven’t argued about the topic of this post for a little while now—and certainly not since writing “I feel as though my work here is done”.
Rather I am here defending my reputation against assaults from people who don’t like my posting style—and seem keen to let everyone else know of their disapproval. I’ll probably give up with that too, soon enough.
Were someone else exhibiting similar posting behavior, would you draw the same conclusion? You may sincerely desire to terminate your conversation with neq1, but you appear to cesire* to continue it.
* A “cesire” is a motivator to action that works like a desire even when accompanied by a conflicting desire—much like an alief can induce emotional reactions in the same way as beliefs even in the presence of a contrary belief.
Actually, I have supplied my real name (in a previous post I linked to my blog, which has my name). I’m confident my colleagues would be in agreement with me.