The way the question is almost always worded (including in this case), there is at the very least a strong implication that you're talking to a random person who is telling you about his kids, in which case the sex of the other child is independent of the sex of the child he's telling you about.
You have to jump through verbal hoops to actually state the situation unambiguously in the way the usual answer assumes. Someone has to go out and specifically select a person who has at least one child of a particular, predetermined sex, and introduce that person to you. Once you add all that detail to the question it's pretty clear something is going on, which takes all the fun out of it for people who like silly puzzles, but does turn it into a meaningful lesson about selection bias.
"You're on the Jay Leno show. Jay sent a flunky out to randomly choose a guy who had two children, at least one of which was a boy. Jay then asks you: what is the probability the guy's other child is a boy?"
You have managed to describe precisely the unlikely situation where the non-intuitive answer is correct.
same-gender, both male: 50% different-gender: 50%
boy first: 25%
girl first: 25%
You'll note the girl, girl families will show up in neither result set. So they can do nothing to skew the numbers.
The results of both queries will, predictably, be 50/50 male and female.
By selecting only pairs where at least one child is male you've discarded all the girl/girl families. So the ratio of girls to boys in your new set won't be 50/50, will it? By not selecting girl/girl families you have indeed skewed the numbers. By making selections and imposing criteria you've screwed up the sex distribution in your set.
You've also made the dangerous mistake of stating absolutely what the result of an experiment will be without actually trying it.
I flip a coin twice and record the answer. I repeat this many times. I discard all the pairs where both coins came up tails. I then select a pair where at least one toss came up heads. What is the probability that the other is also heads?
The selection criteria screw up the probabilities. If instead I flip a coin, see that it comes up heads, and ask what the probability of it coming up heads again is, the answer is 50%.
You're absolutely correct IF you assume that the man is just describing one of his children. That is the logical interpretation of the problem. However, if someone went out and specifically selected a family with at least one boy, the probability of the other child being a girl is not 50% - the population in question has been artificially depleted of girls because the criteria excluded all two-girl families.
Very enlightening. Perhaps you'd like to actually provide some reasoning for your position?
An FFT or compression algorithm is a set of instructions for carrying out a particular computation. It's no more an abstract idea in the way the court used the term than the method for refining aluminum ore.
No, given algorithm/method patents you can't patent pi. Pi isn't a method, nor an algorithm. You might be able to patent a method for estimating pi (which in my view should be patentable if it is novel and non-obvious), but you couldn't patent pi.
Go ahead. Refute me by explaining in detail how pi would be patentable if the FFT was patentable.
The fast Fourier transform. Or a compression algorithm. Both are examples of things that are not machines, do not transform matter, yet are not abstract ideas.
How about the recipe for Cocoa Cola? That would be written. Also, instructions for the Bayer process for refining aluminum are written. Actually, ALL patents are written!
"Software patents" is just a misleading short hand. Nobody actually patents software, they patent the methods, ideas and algorithms that are implemented in the software. By the same token, the actual written recipe for Coca Cola would not be patented, rather the process for and idea to combine those ingredients in a particular manner would be patented.
Well, SCOTUS, besides being an acronym that requires explanation, at least acknowledges that there are places outside the United States that may have their own supreme courts. I'd suggest "US supreme court" myself. Agreed that "the Supreme's" is both grammatically incorrect and stupid though.
It sounds like the court said the existing requirements are fine, if they're properly applied. In other words, properly apply the existing standards, dumbasses.
I have yet to see a bad software patent that isn't either an abstract idea, obvious, or invalidated by prior art. On the other hand, most Slashdotter's proposals for patent reform throw out good patents too. My usual test is this: supposing the fast Fourier transform hadn't been invented, would it be patentable?
That may be what you were trying to say, but it's not what you said. I see how you might interpret your statement your way, but the way I read it is equally valid. It's too vague.
"What you wrote is exactly what you can't say."
No, read it again:
"based on this experiment there is a 97.5%* chance that the true ratio between neutrinos and antineutrinos is greater than 1." That's the same as what you were trying to say. The true mean (the actual ratio) lies within the confidence interval (greater than one... okay, there's a little subtlety about the top range, more in a minute) 97.5% of the time. I did not say anything about any effect that is already observed. The statement is about the experiment, not the results. The statement is equivalent to your "Then, using this method, the actual result is in the predicted set 95% of the time."
"Also, you are confused about the interpretation of one versus two tailed tests."
No, I'm not. I'm assuming they used a two-tailed test. Note that where my statement differs from yours is in the upper end of the confidence interval. I'm interested in whether the asymmetry is different than zero, not if it lies between 0 X Y where Y is the upper threshold. Thus, there's an extra 2.5% at the top where the true value is more extreme than the prediction - the region of the distribution that is greater than zero has an area of 97.5%, not 95%. In your statement this part is neglected, even though it would be every bit as interesting as a true value lying within the CI.
My statement is about the experiment, not the measured effects. The experiment has no preference for an asymmetry one way or the other. I stated it that way to match Gumbi's post, where he asserted that there is a 95% probability that the experiment would show a positive ratio, given the null hypothesis. That's not true. Since we're dealing dealing with counts the actual probabilities are something less than 50% neutino > anti, something less than 50% anti > neutrino and the remainder the probability of getting equal counts.
For a statement about the actual outcome of the experiment you could say something like "based on this experiment there is a 97.5%* chance that the true ratio between neutrinos and antineutrinos is greater than 1", which would be the usual confidence interval interpretation.
* assuming their test was a two tailed test (which it probably was) and that their p-value was derived from a normally distributed test statistic.
You gave a misleading confidence interval interpretation. Your statement disregards the magnitude of the observed effect.
It's likely wrong too - the correct statement is almost certainly something more like "An experiment conducted this way would find more muon antineutrinos than muon neutrinos disappear X% of the time, more muon neutrinos than antineutrinos disappear Y% of the time and the observed numbers are equal Z% of the time," where X+Y+Z = 100, X = Y and X,Y >> Z. X = 95 is not a solution to that system.
You replied to me, and I replied to you. You said this:
"Only the google-specific applications (Maps, gmail, gtalk, google market, facebook, google voice ) are not open source. Many of them can be replaced with alternatives if one wants to release a system without paying to google: e.g. SlideMe market, one of many different e-mail/gps apps, etc."
This statement is not true. The baseband is not open source. The baseband is what makes a phone a phone, and is responsible for many or most of the restrictions that phones come with. We're not talking about hardware - we're talking about software, which interfaces with common, off the the shelf hardware, and is specifically designed to restrict use. But sure, I guess you can run Google's phone OS freely if you want - just not on a phone.
I'm not a free software zealot. I think proprietary software is important, and is a valid choice for someone choosing how to release his or her work. I do think the free software movement is making a mistake vehemently attacking all things proprietary on the desktop while there aren't even any open source alternatives for phones and proprietary software is actually being used there to restrict people's freedom.
As for the iPhone, Apple doesn't seriously try to block jailbreaking. Sometimes a method stops working because they patched a vulnerability, but a jailbreak is frequently available for a new version as soon as it is released. Baseband updates usually take weeks or months. The developers of Pwnage tool recommend always installing updates through their software so you can update the OS, pre-jailbroken, and not the baseband. Apple hasn't even changed the well-known root password since one of the first updates!
If you want to build a fully open phone, you need open baseband. Otherwise you dont have a phone. Many would say it's the most important part, since it's the baseband code that, for example, locks the phone to a particular carrier. In particular, people who like to compare the iPhone to android constantly confuse jail breaking, which is something Apple doesn't really interfere with much and is just like rooting, with unlocking, Which Apple does regularly interfere with, just like every other carrier/manufacturer.
So yes, there are NO open source phones. The most important part is missing.
If the N900, or any Maemo phone got sold widely by a major carrier it would be locked down so the carrier is root and you're not. Same as Android. Same as iPhone OS.
Most people do own their propane tanks. The ones who don't pay extra for them over the long term by swapping them.
If you don't own the battery, who do you think is going to pay for the wear and tear on it? That's right, you are, just in small chunks every time you swap one. It doesn't solve the problem, it shuffles it off somewhere else.
Three years of driving the Leaf costs you $1000/year PLUS whatever you have to pay for electricity/gas. Driving your current car costs you $1000/year in gas. When the three years is up, presumably your current car will still be worth something, while the Leaf probably won't be, assuming the batteries actually die at 8 years.
Slashdot Mirror
The way the question is almost always worded (including in this case), there is at the very least a strong implication that you're talking to a random person who is telling you about his kids, in which case the sex of the other child is independent of the sex of the child he's telling you about.
You have to jump through verbal hoops to actually state the situation unambiguously in the way the usual answer assumes. Someone has to go out and specifically select a person who has at least one child of a particular, predetermined sex, and introduce that person to you. Once you add all that detail to the question it's pretty clear something is going on, which takes all the fun out of it for people who like silly puzzles, but does turn it into a meaningful lesson about selection bias.
You have to get clearer than that.
"You're on the Jay Leno show. Jay sent a flunky out to randomly choose a guy who had two children, at least one of which was a boy. Jay then asks you: what is the probability the guy's other child is a boy?"
The selection step is critical to the problem.
You have managed to describe precisely the unlikely situation where the non-intuitive answer is correct.
By selecting only pairs where at least one child is male you've discarded all the girl/girl families. So the ratio of girls to boys in your new set won't be 50/50, will it? By not selecting girl/girl families you have indeed skewed the numbers. By making selections and imposing criteria you've screwed up the sex distribution in your set.
You've also made the dangerous mistake of stating absolutely what the result of an experiment will be without actually trying it.
Close. The situation with coins is this:
I flip a coin twice and record the answer. I repeat this many times. I discard all the pairs where both coins came up tails. I then select a pair where at least one toss came up heads. What is the probability that the other is also heads?
The selection criteria screw up the probabilities. If instead I flip a coin, see that it comes up heads, and ask what the probability of it coming up heads again is, the answer is 50%.
Failed to read the article, hey?
You're absolutely correct IF you assume that the man is just describing one of his children. That is the logical interpretation of the problem. However, if someone went out and specifically selected a family with at least one boy, the probability of the other child being a girl is not 50% - the population in question has been artificially depleted of girls because the criteria excluded all two-girl families.
That's a favourite trick of the Nostradamus crowd too - they typically contain something that we can interpret as....
Very enlightening. Perhaps you'd like to actually provide some reasoning for your position?
An FFT or compression algorithm is a set of instructions for carrying out a particular computation. It's no more an abstract idea in the way the court used the term than the method for refining aluminum ore.
Everything is a simple set of algorithms.
No, given algorithm/method patents you can't patent pi. Pi isn't a method, nor an algorithm. You might be able to patent a method for estimating pi (which in my view should be patentable if it is novel and non-obvious), but you couldn't patent pi.
Go ahead. Refute me by explaining in detail how pi would be patentable if the FFT was patentable.
The fast Fourier transform. Or a compression algorithm. Both are examples of things that are not machines, do not transform matter, yet are not abstract ideas.
How about the recipe for Cocoa Cola? That would be written. Also, instructions for the Bayer process for refining aluminum are written. Actually, ALL patents are written!
"Software patents" is just a misleading short hand. Nobody actually patents software, they patent the methods, ideas and algorithms that are implemented in the software. By the same token, the actual written recipe for Coca Cola would not be patented, rather the process for and idea to combine those ingredients in a particular manner would be patented.
Well, SCOTUS, besides being an acronym that requires explanation, at least acknowledges that there are places outside the United States that may have their own supreme courts. I'd suggest "US supreme court" myself. Agreed that "the Supreme's" is both grammatically incorrect and stupid though.
It's not superfluous, it's wrong. It indicates that whatever we're talking about belongs to Supreme, whoever that is.
Slashdot. We don't actually know, and we don't care. We'll just fake it.
Yeah, I know, it's not as catchy as yours.
It sounds like the court said the existing requirements are fine, if they're properly applied. In other words, properly apply the existing standards, dumbasses.
I have yet to see a bad software patent that isn't either an abstract idea, obvious, or invalidated by prior art. On the other hand, most Slashdotter's proposals for patent reform throw out good patents too. My usual test is this: supposing the fast Fourier transform hadn't been invented, would it be patentable?
That may be what you were trying to say, but it's not what you said. I see how you might interpret your statement your way, but the way I read it is equally valid. It's too vague.
"What you wrote is exactly what you can't say."
No, read it again:
"based on this experiment there is a 97.5%* chance that the true ratio between neutrinos and antineutrinos is greater than 1." That's the same as what you were trying to say. The true mean (the actual ratio) lies within the confidence interval (greater than one... okay, there's a little subtlety about the top range, more in a minute) 97.5% of the time. I did not say anything about any effect that is already observed. The statement is about the experiment, not the results. The statement is equivalent to your "Then, using this method, the actual result is in the predicted set 95% of the time."
"Also, you are confused about the interpretation of one versus two tailed tests."
No, I'm not. I'm assuming they used a two-tailed test. Note that where my statement differs from yours is in the upper end of the confidence interval. I'm interested in whether the asymmetry is different than zero, not if it lies between 0 X Y where Y is the upper threshold. Thus, there's an extra 2.5% at the top where the true value is more extreme than the prediction - the region of the distribution that is greater than zero has an area of 97.5%, not 95%. In your statement this part is neglected, even though it would be every bit as interesting as a true value lying within the CI.
My statement is about the experiment, not the measured effects. The experiment has no preference for an asymmetry one way or the other. I stated it that way to match Gumbi's post, where he asserted that there is a 95% probability that the experiment would show a positive ratio, given the null hypothesis. That's not true. Since we're dealing dealing with counts the actual probabilities are something less than 50% neutino > anti, something less than 50% anti > neutrino and the remainder the probability of getting equal counts.
For a statement about the actual outcome of the experiment you could say something like "based on this experiment there is a 97.5%* chance that the true ratio between neutrinos and antineutrinos is greater than 1", which would be the usual confidence interval interpretation.
* assuming their test was a two tailed test (which it probably was) and that their p-value was derived from a normally distributed test statistic.
May change. A good amount of physics respects some or all of the subsymmetries as well.
You gave a misleading confidence interval interpretation. Your statement disregards the magnitude of the observed effect.
It's likely wrong too - the correct statement is almost certainly something more like "An experiment conducted this way would find more muon antineutrinos than muon neutrinos disappear X% of the time, more muon neutrinos than antineutrinos disappear Y% of the time and the observed numbers are equal Z% of the time," where X+Y+Z = 100, X = Y and X,Y >> Z. X = 95 is not a solution to that system.
You replied to me, and I replied to you. You said this:
"Only the google-specific applications (Maps, gmail, gtalk, google market, facebook, google voice ) are not open source. Many of them can be replaced with alternatives if one wants to release a system without paying to google: e.g. SlideMe market, one of many different e-mail/gps apps, etc."
This statement is not true. The baseband is not open source. The baseband is what makes a phone a phone, and is responsible for many or most of the restrictions that phones come with. We're not talking about hardware - we're talking about software, which interfaces with common, off the the shelf hardware, and is specifically designed to restrict use. But sure, I guess you can run Google's phone OS freely if you want - just not on a phone.
I'm not a free software zealot. I think proprietary software is important, and is a valid choice for someone choosing how to release his or her work. I do think the free software movement is making a mistake vehemently attacking all things proprietary on the desktop while there aren't even any open source alternatives for phones and proprietary software is actually being used there to restrict people's freedom.
As for the iPhone, Apple doesn't seriously try to block jailbreaking. Sometimes a method stops working because they patched a vulnerability, but a jailbreak is frequently available for a new version as soon as it is released. Baseband updates usually take weeks or months. The developers of Pwnage tool recommend always installing updates through their software so you can update the OS, pre-jailbroken, and not the baseband. Apple hasn't even changed the well-known root password since one of the first updates!
If you want to build a fully open phone, you need open baseband. Otherwise you dont have a phone. Many would say it's the most important part, since it's the baseband code that, for example, locks the phone to a particular carrier. In particular, people who like to compare the iPhone to android constantly confuse jail breaking, which is something Apple doesn't really interfere with much and is just like rooting, with unlocking, Which Apple does regularly interfere with, just like every other carrier/manufacturer.
So yes, there are NO open source phones. The most important part is missing.
And the baseband code. You can't build a fully working system from the open source components. The most important bit is completely closed.
Same as Android, same as iPhone OS.
If the N900, or any Maemo phone got sold widely by a major carrier it would be locked down so the carrier is root and you're not. Same as Android. Same as iPhone OS.
B-b-but Google was supposed to be different!
Most people do own their propane tanks. The ones who don't pay extra for them over the long term by swapping them.
If you don't own the battery, who do you think is going to pay for the wear and tear on it? That's right, you are, just in small chunks every time you swap one. It doesn't solve the problem, it shuffles it off somewhere else.
Uh, you missed a couple of somethings.
Three years of driving the Leaf costs you $1000/year PLUS whatever you have to pay for electricity/gas. Driving your current car costs you $1000/year in gas. When the three years is up, presumably your current car will still be worth something, while the Leaf probably won't be, assuming the batteries actually die at 8 years.