Comments on: Common Sense: Blinded by Math http://regex.info/blog/2009-01-03/1090 Not a photo blog. A personal blog with photos. Wed, 23 May 2012 12:55:23 +0000 hourly 1 http://wordpress.org/?v=3.3.2 By: JeffJ http://regex.info/blog/2009-01-03/1090#comment-33764 JeffJ Sat, 10 Jan 2009 15:47:59 +0000 http://regex.info/blog/2009-01-03/1090#comment-33764 My initial reaction when I first saw Jeff Atwood's original post is still the interpretation that I think makes the most sense in this case. That is, JeffA took a problem that is intrinsically confusing for many people, and he intentionally worded his version of the question such that there exists three valid interpretation of his ambiguously-worded question. If the ambiguity was intentional, then JeffA was exceptionally clever at driving traffic to his (often interesting, sometimes controversial) blog. As your 9th commenter points out, the 3rd interpretation is that we were already told that the subject has exactly one girl. JeffreyF's math is correct. Still, my preferred answer remains: 100%. Why? JeffA is an adept computer programmer, is competent at english, and I suspect he knew a priori that his wording was ambiguous. I look forward the next "stack overflow" podcast to see if Jeff and Joel discuss this question. My initial reaction when I first saw Jeff Atwood’s original post is still the interpretation that I think makes the most sense in this case. That is, JeffA took a problem that is intrinsically confusing for many people, and he intentionally worded his version of the question such that there exists three valid interpretation of his ambiguously-worded question. If the ambiguity was intentional, then JeffA was exceptionally clever at driving traffic to his (often interesting, sometimes controversial) blog. As your 9th commenter points out, the 3rd interpretation is that we were already told that the subject has exactly one girl.

JeffreyF’s math is correct. Still, my preferred answer remains: 100%. Why? JeffA is an adept computer programmer, is competent at english, and I suspect he knew a priori that his wording was ambiguous. I look forward the next “stack overflow” podcast to see if Jeff and Joel discuss this question.

]]> By: Herve http://regex.info/blog/2009-01-03/1090#comment-33762 Herve Sat, 10 Jan 2009 15:00:38 +0000 http://regex.info/blog/2009-01-03/1090#comment-33762 Hello Here is an other example of the way our mind works: One flow is intuitive and fast (sometimes right , sometimes wrong) The other is analytical and slow (and sometimes right or wrong) Here is the problem: I just purchased an envelope and a stamp for $1.10 The envelope costs $1 more than the stamp What is the cost of the stamp??? Quickly you will answer : obvious $1 for the envelope and $0.1 for the stamp , this adds to $1.10 But if you now substract , you'll find a $0.9 difference, not a $1 as asked !!!! I let you compute the correct answer When intuition and analytics are in conflict, there is a little voice in our brain which tells us "it looks that way, but it's wrong" This little voice has been experimentally measured (like in the envelope problem) and tells the truth in 95% of cases . So follow your little inner voice when it tells you "something is incoherent here" Hello
Here is an other example of the way our mind works:
One flow is intuitive and fast (sometimes right , sometimes wrong)
The other is analytical and slow (and sometimes right or wrong)

Here is the problem:
I just purchased an envelope and a stamp for $1.10
The envelope costs $1 more than the stamp
What is the cost of the stamp???

Quickly you will answer : obvious $1 for the envelope and $0.1 for the stamp , this adds to $1.10

But if you now substract , you’ll find a $0.9 difference, not a $1 as asked !!!!

I let you compute the correct answer

When intuition and analytics are in conflict, there is a little voice in our brain which tells us “it looks that way, but it’s wrong” This little voice has been experimentally measured (like in the envelope problem) and tells the truth in 95% of cases . So follow your little inner voice when it tells you “something is incoherent here”

]]> By: Andre http://regex.info/blog/2009-01-03/1090#comment-33741 Andre Fri, 09 Jan 2009 00:40:13 +0000 http://regex.info/blog/2009-01-03/1090#comment-33741 A little late to the conversation, but may be adding another perspective. What most people seemed to be struggling with is that by randomly identifying the girl on the swing to be his/her daughter, one explicitly breaks the symmetry in the "girl then girl" pairing of the answer space. More precisely, the answer space should include "girl-on-swing then girl-not-on-swing" and "girl-not-on-swing then girl-on-swing" in addition to "boy-not-on-swing then girl-on-swing" and "girl-on-swing then boy-not-on-swing". Consequently, the kid who is not sitting on the swing has a 50% chance of being a boy. In general, we don't know which girl of the (girl, girl) pair is randomly named as being his/her daughter by the parent. The Monty Hall problem is different in that the revealation of the game show host depends on the prior pick of the game show contestant. A little late to the conversation, but may be adding another perspective.

What most people seemed to be struggling with is that by randomly identifying the girl on the swing to be his/her daughter, one explicitly breaks the symmetry in the “girl then girl” pairing of the answer space.

More precisely, the answer space should include “girl-on-swing then girl-not-on-swing” and “girl-not-on-swing then girl-on-swing” in addition to “boy-not-on-swing then girl-on-swing” and “girl-on-swing then boy-not-on-swing”.

Consequently, the kid who is not sitting on the swing has a 50% chance of being a boy.

In general, we don’t know which girl of the (girl, girl) pair is randomly named as being his/her daughter by the parent.

The Monty Hall problem is different in that the revealation of the game show host depends on the prior pick of the game show contestant.

]]> By: Grandma Friedl http://regex.info/blog/2009-01-03/1090#comment-33626 Grandma Friedl Wed, 07 Jan 2009 22:05:31 +0000 http://regex.info/blog/2009-01-03/1090#comment-33626 Hmmm, I'm beginning to think my number one son and your oldest brother Steve is going to be proven correct in his prediction of the number of comments this is likely to "engender." (Sorry. Couldn't resist.) Hmmm, I’m beginning to think my number one son and your oldest brother Steve is going to be proven correct in his prediction of the number of comments this is likely to “engender.” (Sorry. Couldn’t resist.)

]]> By: Alex http://regex.info/blog/2009-01-03/1090#comment-33609 Alex Wed, 07 Jan 2009 19:05:40 +0000 http://regex.info/blog/2009-01-03/1090#comment-33609 My point was that the interpretation of the probability is down to the model you choose. > The question has nothing to do with ordering True but the interpretation of it and modelling it via mathematical representation - has everything todo with it. > in this context, boy/girl is indistinguishable in every respect from girl/boy Depends on the model, if you choose to introduce some "ordering" (relation) in a pair such as "older than", then (boy, girl) is not the same as (girl, boy). <span class='jfriedl'>I really am missing your point, because if you "choose to introduce some ordering" to the question, you're then answering a different question. —Jeffrey</span> > This one-of-each set is not, however, equal in probability to the other sets (two boys, two girls) It is if there is no "ordering" to the pair. My point was that the interpretation of the probability is down to the model you choose.

> The question has nothing to do with ordering

True but the interpretation of it and modelling it via mathematical representation – has everything todo with it.

> in this context, boy/girl is indistinguishable in every respect from girl/boy

Depends on the model, if you choose to introduce some “ordering” (relation) in a pair such as “older than”, then (boy, girl) is not the same as (girl, boy).

I really am missing your point, because if you “choose to introduce some ordering” to the question, you’re then answering a different question. —Jeffrey

> This one-of-each set is not, however, equal in probability to the other sets (two boys, two girls)

It is if there is no “ordering” to the pair.

]]> By: Alex http://regex.info/blog/2009-01-03/1090#comment-33601 Alex Wed, 07 Jan 2009 16:59:10 +0000 http://regex.info/blog/2009-01-03/1090#comment-33601 To me, from mathematical prospective, it all boils down to how to build your model of what being stated. The groups of objects (children pairs in this case) are represented as a set. The probability is then chosen amongst number of distinct sets. But this sets can be an ordinary unordered or partially ordered. In the former case the set (boy, girl) and (girl, boy) is one and the same and you can't count it twice - hence in this model you will only have 3 possible pairs. In the latter case when we introduce some partial ordering to the set (by age, by eye colour or something else) we end up with (boy, girl) and (girl, boy) being distinct and will have 4 total pairs to shoose from. I am not saying that one of them is right and one is wrong - it all depends how you choose your mathematical model. But in a simple case when there is nothing known apart from the kids gender/sex/whatever - the former model where (boy, girl) and (girl, boy) are one and the same seems to be the closes match. Adding partial ordering by age may as well be replaced by anything else similar(like ordering by height, weight etc - I don't see why age should be preferred to anything else and used at all ;-) <span class='jfriedl'>I'm not sure what you indend your point to be in the context of my post. The question has nothing to do with ordering, so there are only three types of sets under consideration, and in this context, boy/girl is indistinguishable in every respect from girl/boy. This one-of-each set is <i>not</i>, however, equal in <i>probability</i> to the other sets (two boys, two girls), and that inequality among the three members of the set is important to understanding both the question and its answers. —Jeffrey</span> To me, from mathematical prospective, it all boils down to how to build your model of what being stated. The groups of objects (children pairs in this case) are represented as a set. The probability is then chosen amongst number of distinct sets. But this sets can be an ordinary unordered or partially ordered. In the former case the set (boy, girl) and (girl, boy) is one and the same and you can’t count it twice – hence in this model you will only have 3 possible pairs. In the latter case when we introduce some partial ordering to the set (by age, by eye colour or something else) we end up with (boy, girl) and (girl, boy) being distinct and will have 4 total pairs to shoose from.

I am not saying that one of them is right and one is wrong – it all depends how you choose your mathematical model. But in a simple case when there is nothing known apart from the kids gender/sex/whatever – the former model where (boy, girl) and (girl, boy) are one and the same seems to be the closes match. Adding partial ordering by age may as well be replaced by anything else similar(like ordering by height, weight etc – I don’t see why age should be preferred to anything else and used at all ;-)

I’m not sure what you indend your point to be in the context of my post. The question has nothing to do with ordering, so there are only three types of sets under consideration, and in this context, boy/girl is indistinguishable in every respect from girl/boy. This one-of-each set is not, however, equal in probability to the other sets (two boys, two girls), and that inequality among the three members of the set is important to understanding both the question and its answers. —Jeffrey

]]> By: Peter http://regex.info/blog/2009-01-03/1090#comment-33567 Peter Wed, 07 Jan 2009 09:35:46 +0000 http://regex.info/blog/2009-01-03/1090#comment-33567 Well, I *am* older than you! Fowler's Modern English Usage says: "gender (n.) is a grammatical term only. To talk of persons or creatures of the masculine or feminine gender, meaning of the male or female sex, is either a jocularity (permissible or not according to context) or a blunder." Your esteemed compatriot, Bill Bryson, says "Gender, originally strictly a grammatical term, became in the nineteenth century a euphemism for the convenience of those who found 'sex' too disturbing a word to utter. Its use today in that sense is disdained by most authorities as old-fashioned and over-delicate.". But I guess it is not for me to comment on anyone else's use of English, sorry - mine is flakey enough at times! <span class='jfriedl'>Maybe it's my midwestern American upbringing, but I find no need to borrow from the noun "sex" (making babies) to describe the one-or-the-other result one gets from it. I also don't use the word "flip" to describe the obverse/reverse nature of the side of a coin, but maybe Bill Bryson does :-) —Jeffrey</span> Well, I *am* older than you!

Fowler’s Modern English Usage says: “gender (n.) is a grammatical term only. To talk of persons or creatures of the masculine or feminine gender, meaning of the male or female sex, is either a jocularity (permissible or not according to context) or a blunder.”

Your esteemed compatriot, Bill Bryson, says “Gender, originally strictly a grammatical term, became in the nineteenth century a euphemism for the convenience of those who found ‘sex’ too disturbing a word to utter. Its use today in that sense is disdained by most authorities as old-fashioned and over-delicate.”.

But I guess it is not for me to comment on anyone else’s use of English, sorry – mine is flakey enough at times!

Maybe it’s my midwestern American upbringing, but I find no need to borrow from the noun “sex” (making babies) to describe the one-or-the-other result one gets from it. I also don’t use the word “flip” to describe the obverse/reverse nature of the side of a coin, but maybe Bill Bryson does :-) —Jeffrey

]]> By: Leo Butler http://regex.info/blog/2009-01-03/1090#comment-33532 Leo Butler Wed, 07 Jan 2009 00:39:14 +0000 http://regex.info/blog/2009-01-03/1090#comment-33532 Took me a while to wrap my head around this. That was up until a friend whom I was discussing it with said, "It's easier to think of it like this: suppose you have 1000 doors to choose from. You pick one, and then they'll eliminate 998 other doors. It's the same problem, just much more obvious that you clearly picked the wrong one 999 times out of a 1000 (on average)." That did it for me. Having three and eliminating one is just the extreme case of this. <div class='jfriedl'><p>The "this" you're speaking of here is the Monty Hall problem, mentioned in the first comment. Indeed, that's a good way to think of it, but you have to remember the important point is that when "they" eliminate 998 other doors, it's done with the knowledge of which door holds the prize, and the intent to not reveal the prize. (If they eliminate 998 doors randomly, they'll reveal the prize 99.8% of the time, but because they know where the prize is and choose not to reveal it, they end up revealing it the desired 0% of the time.)</p><p>None of this is directly related to the two-kids problem discussed in the post, though. —Jeffrey</p></div> Took me a while to wrap my head around this. That was up until a friend whom I was discussing it with said, “It’s easier to think of it like this: suppose you have 1000 doors to choose from. You pick one, and then they’ll eliminate 998 other doors. It’s the same problem, just much more obvious that you clearly picked the wrong one 999 times out of a 1000 (on average).”

That did it for me. Having three and eliminating one is just the extreme case of this.

The “this” you’re speaking of here is the Monty Hall problem, mentioned in the first comment. Indeed, that’s a good way to think of it, but you have to remember the important point is that when “they” eliminate 998 other doors, it’s done with the knowledge of which door holds the prize, and the intent to not reveal the prize. (If they eliminate 998 doors randomly, they’ll reveal the prize 99.8% of the time, but because they know where the prize is and choose not to reveal it, they end up revealing it the desired 0% of the time.)

None of this is directly related to the two-kids problem discussed in the post, though. —Jeffrey

]]> By: Grandma Friedl http://regex.info/blog/2009-01-03/1090#comment-33461 Grandma Friedl Mon, 05 Jan 2009 21:57:49 +0000 http://regex.info/blog/2009-01-03/1090#comment-33461 Some people have WAY too much time on their hands! Some people have WAY too much time on their hands!

]]> By: Gregg http://regex.info/blog/2009-01-03/1090#comment-33454 Gregg Mon, 05 Jan 2009 16:29:52 +0000 http://regex.info/blog/2009-01-03/1090#comment-33454 Yep. You're right. It's more about the inadequacies and imprecision of language and the near infinite, subtly different, potential interpretations of any statement by a diverse population. Despite (or maybe because of) the verbosity, I still do not get what you're trying to present as the problem space at its most basic level which would lead one to believe you're incapable of presenting it or that I am incapable of grasping it. The truth I believe, as is often the case, somewhere in between. The result, again, as is often the case, simply one of failed communication between two people. Either that or I can't has got the cheezbergr upstairs to rekin it. Which I'm perfectly willing to accept as truth. Not knowing something is bad. Not knowing what you don't know is worse. There's allot I know I don't know and I know I don't know allot of what I don't know. Every day I get a glimpse into what I don't know. And it is humbling. This is another instance. It is a valuable new data point I shall keep and <i>try</i> to reference in the future when trying to present ideas and I find myself failing. Sorry for the long post. :-( I shall enter "Shut the H... up mode" now. Yep. You’re right. It’s more about the inadequacies and imprecision of language and the near infinite, subtly different, potential interpretations of any statement by a diverse population.
Despite (or maybe because of) the verbosity, I still do not get what you’re trying to present as the problem space at its most basic level which would lead one to believe you’re incapable of presenting it or that I am incapable of grasping it. The truth I believe, as is often the case, somewhere in between. The result, again, as is often the case, simply one of failed communication between two people.

Either that or I can’t has got the cheezbergr upstairs to rekin it. Which I’m perfectly willing to accept as truth. Not knowing something is bad. Not knowing what you don’t know is worse. There’s allot I know I don’t know and I know I don’t know allot of what I don’t know. Every day I get a glimpse into what I don’t know. And it is humbling. This is another instance. It is a valuable new data point I shall keep and try to reference in the future when trying to present ideas and I find myself failing.

Sorry for the long post. :-( I shall enter “Shut the H… up mode” now.

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