1. I think people do realize this by themselves. Just eavesdrop on any online chat room or the text messages of a typical 10 year old. But this is beside the point. I think you're fixating on compression algorithms being very strong nowadays. No one is disagreeing with you on that.
I think the actual point is that at some point we have to admit that compression can only reach a certain level of effectiveness if the compressor can evaluate and exploit the information content of the text. Compressors work by eliminating redundancy from the representation of the knowledge. Essentially, a compressor is trying to capture the heart of the matter. I think this is exactly what a human does when he or she reads text. This is why compression is interesting to AI.
2. I totally agree with you up until your assertion that it makes the contest weak. I think the contest is testing exactly the goal you state. It asks to losslessly compress (a proxy for) human knowledge. I think it has to be a proxy (because knowledge representation is a different and arguably more slippery AI subtopic), and I think it has to be lossless (to protect the experiment from the debate over what text/information is acceptable to lose on the grounds of irrelevance). I'm not sure how to set up a different experiment that would test your goal in reasonable isolation and still be scientifically rigorous.
3. I think your elision of my sentence changed its meaning (bad compression/decompression?:) ). I never claimed the Turing Test should be to ask the subject to compress a sentence. I said it should be able to extract the knowledge from it. If it can compress the sentence as well as a human, then it is as efficient at cutting to the heart of the information in the sentence.
first point: "If its so easy to put the vowels back in, (a) good statistical compressor will use very little space for them." That's probably true. In fact, I'd consider such an algorithm fairly intelligent. That might be what the Hutter prize winning algorithm does. I think what you're saying here is that most things humans can do to improve compression algorithms are already being done in the best algorithms. I have a feeling you're right, which probably is why compressors are approaching researchers' best guess at the average human level of compression of English.
second point, regarding ambiguity: First of all, I said *most* vowels, not all. The human has to intelligently decide which ones. Also, if your text can't be unambiguously recovered, then you can't claim to have losslessly compressed it. That's like me compressing the same sentence to 1 bit and declaring that I have the most efficient compression algorithm possible. That's why when we talk about compression algorithms, we also talk about decompression algorithms. The human shouldn't remove vowels in such a way as to make the text unrecoverable. I think you understand the difference, since you engineered your vowel-less sentence to be as confusing as possible.
third point: I'm not exactly sure what you mean by "proxies" in this context. I think you are claiming that I am using language as a proxy for intelligence. Rest assured, I am not. Like I've been saying all along, having language faculties is necessary, *but not sufficient* for intelligence. This is exactly the distinction that everyone seems to be missing: no one (who has a clue) is saying "it compresses/understands language, so presto, it's intelligent." The claim is "we are one step closer to having a machine that passes the Turing Test, since one can no longer stump the machine on the basis of its ability to capture the information in an English sentence."
This being said, I think that *compression* and intelligence are highly related. Fundamentally, there is only so far you can go in compressing a blob of text without actually understanding the underlying information. For example, we both used 'gd' in our sentences; and we both without skipping a beat interpreted it as "good" rather than "god", "goad", "gad", etc. Sure, a statistical compressor could've chosen "good" and been right most of the time. But hypothetically you could have meant "god" if we were having a religious debate. This kind of technique relies on intelligence, and allows us to "compress" pretty well. The assertion is that when we pass Shannon's estimate, we probably have an algorithm that is just starting to exploit these kinds of techniques, and that's exciting. At least to me.
Thanks for the lively debate... it's nice to exercise some logical chops again.
Beating gzip is easily. As you point out, English is extremely redundant and thus inefficient in its usage of bits. Try removing most vowels from some English text: Stdis hv shwn tht ppl cn rd ths knd f txt lmst effrtlsly. My compression/decompression works by reading all of wikipedia, removing most of the vowels, then running it through the gzip algorithm (executed on paper, of course!). To decompress, execute gunzip (on paper), and then have a literate human being put the vowels back in. Sure it's going to be insanely slow, but speed of computation better not be the interesting part of intelligence; otherwise computers are already much more intelligent than we are. Also, I should be forgiven for not knowing the gzip algorithm. Even computers have to be "told" the algorithm.
This sort of technique can be used for just about any compression algorithm. The example I gave simply isolates one way in which gzip is unintelligent... it doesn't "get the point" about English. I'm going to assert that one can call compression good enough to be intelligent when an intelligent person can't (non-negligibly) improve its compression ratio on some arbitrary and information rich English text. And I think the compression ratio on such an intelligent compression algo will be (somewhere near) Shannon's number. That is to say, it will "get the point" about English as well as an intelligent human. In this light, compression is a proxy for understanding human languages, which is absolutely crucial to human intelligence.
Fair enough. I suppose a Turing Test subject asked to compress some data better be able to respond like a human would: either by compressing it on par with Shannon's estimate or by having a convincing reason why it can't (while still claiming to be human).
This is the beauty of the Turing Test... it cleverly avoids the trap of defining intelligence by simply stating that artificial intelligence should be practically indistinguishable from natural (human) intelligence. This means the test subject is allowed some realistic intellectual weakness. In fact, the lack of it might mark a subject as non-human!
I should have said something like "so logically it's harder to call something UNintelligent if it's at least this good at compression." Alternatively, it would have been acceptable to say "we can't call anything as intelligent as most humans unless it's at least this good at compression."
It is not equivalent, so I'm not surprised you didn't get it. As far as I know, the reasoning goes as follows: Shannon estimated that each character contains 1.something bits of information. Shannon was an intelligent human being. So if a program reaches this limit, it is as smart as Shannon. I don't know where you got that idea... but trust me, no computer scientist or mathematician would ever present such an illogical argument. It's kind of like saying "Dan thinks elephants have trunks. Dan is smart. So if an elephant has a trunk, it's as smart as Dan."
And yes, that's absolute bollocks. Worse, it's absolutely spurious: there's a good chance you made it up to sound smart.
A reasonable explanation is in order. No one said that compression to 1.x bits per character is sufficient to call something intelligent. They just claim that this is the best that humans can do, so logically we can't call anything as intelligent as a human unless it's at least this good at compression.
People are (incorrectly) presenting the link between compression and AI as: "If it can compress as well or better than Shannon's estimate, then it is intelligent." In fact, only the converse is true: "If it is intelligent, it can compress as well or better than Shannon's estimate." This is interesting, because the contrapositive of the latter ("If it cannot compress as well or better than Shannon's estimate, it is not intelligent") is a negative test of intelligence.
Recall the Turing Test of Intelligence: a human "decider" sits at a terminal and chats with whatever is on the other end. On the other end is the subject; randomly either a computer or a human. After some fixed amount of time, the decider is asked whether he was chatting with a human being. This test is run lots of times, for lots of deciders and lots of subjects. If the decider answers yes for the computer at least as often as he answers yes for the human, then the computer can be regarded to be intelligent. A compression algorithm that beats the human threshold would imply that one gap between humans and computers has been closed, since the decider can no longer simply test to see if the subject can compress stuff. But there are billion other tests a decider could employ that AIs still can't do... so AI is still 10 years off, just like it's been for 50 years now.
However keep in mind that you aren't "copying by listening." You are describing (at best only partially) how the music was created in the first place. It's not the music any more than instructions to knit a hat is the hat.
The band Nine Inch Nails has intentionally 'leaked' songs via USB keys hidden at restrooms during their current European tour. Excuse me guys, I gotta go take a 'leak'.
"Jeez I love these people that cry racist at every turn." Ok O'Reilly Factor.
Napster (and their copycats) made a living off this behavior. Were they raided by the SWAT team? No, they were sued. And they were making WAY more money. Face it: this is not an issue of degree. This is an entirely different attack strategy, where the only difference seems to be the perpetrator. I'm not saying it's definitely racist, but I'd like to see an explanation of why the SWAT team, why now.
I can't help but see some sort of prejudice, probably racial, in this. Think about the differences between the way the RIAA prosecutes their agenda when it comes to college students vs. "urban" hip-hop musicians. College students (or their parents) are hit with a civil lawsuit and settle out of court. This DJ has his place raided (by the SWAT TEAM?!?) and stuff confiscated and gets held on a 100k bail bond. I can't tell from the picture if this guy is black, white, latino, or whatever, but hip-hop has been a mostly african-american, urban phenomenon. Everyone knows the statistics on the ethnicities of college students. C'mon, slashdot, do these draconian measures smack of racism?
1. Absolutely, assuming both languages are Turing Complete 2. How in general? If you mean "for all turing machine programs" or something, then yes, there is a reduction to the halting problem (though not the one given above, that's just terrible). But if you mean "all programs that can run on my T-42 IBM laptop", then no. This is because there are a finite number of states that my laptop can be in, and therefore the set of all programs that can run on it is NOT Turing complete. So there IS in fact a program that can determine whether a certain program that I'm about to run on my machine will halt on a given input. The program is simple: you count the total number of states the machine could enter, and then you run the program on a machine simulator for exactly that many "cycles." If it hasn't halted by then, it won't. Proof by counting: if you continue to run the program, then there is some state you have entered twice, meaning there is a loop which will cause the program to run forever. 3. True.
Right, impeachment is so radioactive it's never used to enforce the president's faithful execution of his duties. Impeachment is only used to neuter a popular president because he had extramarital sex and lied about it.
Actually, the article didn't quote any study at all. It hand-wavingly declared such and such a study said thus and so, and provided a link to make it look authentic. Try clicking the link. It goes to Fox's search page, where none of the results point to a UN study. Frankly, it seems a little underhanded to present a link this way as if it's a citation.
It goes on to remind us that California just passed a very strict emissions bill (like what you're calling for) that the auto companies are trying to fight in court. IN COURT! So turn about is fair play.
I was especially interested to read this: in NY state, in a similar case, utility companies (the defendant) argued successfully that the attorneys-general were attempting to resolve a political issue in the courts; the judge threw out the case saying it is an issue for the legislature to resolve. The auto industries guys point to that case as a suggestion of how the current California lawsuit will go. But the brilliant part is that now if the auto companies successfully argue that this is a political, not legal, issue that should be dealt with by the legislature, they'll look a little silly trying to block the recent emissions law (passed by... oh, the legislature).
Obviously California has no hope of winning this suit. But that's not the point. It's simply a tactic to get the auto companies to drop their attempts to block the recent emissions law.
Taking lots of measurements at lots of different places does not eliminate error, but it reduces its likelihood. This is the essence of statistics. Basically it comes down to this: as you sum up all the measurements to take the average, the errors should cancel eachother out. Here's a thought experiment... you wish to measure your own weight, and you have a scale. However, the scale reports your weight +/- 1 kg. In fact, it flips a coin. If heads, add a kg, if tails, subtract a kg. If you do this measurement once, you will have the result to accuracy of +/- 1 kg. If you do it a million times and average the result, you will also have a result of accuracy +/- 1 kg. However, consider the likelihood of your result being 1 kg too much in both cases. In the first case, to be off by 1 kg, the scale must have flipped heads. So 1 in 2 times, 50-50 odds. In the second case, the scale would have had to flip heads one million times in a row. So that's 1 in 2^1000000. Pretty unlikely. In fact, the most likely result is that you get your weight exactly, and most of the time you'll get it within a few grams of the actual amount. And notice in this example the original scale COULDN'T actually give you your real weight... it was always off by 1 kg. (This actually works for all error distributions... and in fact I picked the one that causes uncertainty to dissappear least quickly.)
If you want to know the average weight of all people on the planet, it works in much the same way... only now, consider there to be a "true" average... the average you would have if you actually measured everone's weight with an honest scale and averaged it. We expect that to first order approximation, it is equally likely that any one person has weight above or below that average. So we start picking people randomly and measuring their weight with our original coin flipping scale. I've already shown you how the coin-flipping scale will have its error reduced to extraordinarily unlikely, so let's ignore it (since we're adding it up in exactly the same way as before). So say we actually weigh a few hundred people. Since we're picking randomly, we expect to pick approximately as many heavier than avg people as lighter than avg people. So with more and more measurements, we should expect the likelihood of being much too high to decrease (the same with much to low). If we only picked NFL linemen, then we're extraordinarily unlucky. It's possible, but unlikely. Again, this holds regardless of the distribution of individual measurements.
By the way, whenever you see a margin for error, you should also look for a measurement of probability that the measurement is within this margin for error. I don't know for sure, but the reason these studies probably omit the margin for error on aggrigates is because significant error is so unlikely that it isn't worth considering. Yes, it would be nicer for the papers to state that. But simply put, for a hundred measurements of temperature (with 100% probability of being accurate to +/-.7 and worst-case distribution) to yield a measurement that is off by +.7, each and every measurement would have to have been off by the full +.7. That's like flipping heads one hundred times in a row. Unlikely.
Man, is it warm out here?
Re:There's a gene that confers some resistance...
on
Humanity Gene Found?
·
· Score: 1
Many people are stricken with HIV or AIDS before they have children. Yes, they CAN breed, but many just don't on account of their disease. As far as evolution goes, same diff: fewer offspring from people without resistance.
Also, if I understand the way HIV is passed, the offspring of people infected with HIV are at least somewhat more likely to have HIV. Children are unlikely to themselves have children unless they have some amount of resistance (either natural or artificial) to HIV; and in children the disease has longer to take its toll (or at least make itself known) before reproduction can begin.
Bottom line: humans can/will acquire resistance to the disease. On the other hand, I'm pretty sure we shouldn't be waiting for humans to evolve in order to combat the disease. I'm just saying from an evolutionary perspective, it will happen or we'll die out.
Slashdot Mirror
The slides are dated 2008. Was there any follow up? Were these experiments repeated and/or confirmed anywhere else?
...am, please shut up. You're making us all dumber.
:|
That's a kickass compressor.
Way to go! First "I for one!"
"Umm, let's see." You're going to hell :)
:) ). I never claimed the Turing Test should be to ask the subject to compress a sentence. I said it should be able to extract the knowledge from it. If it can compress the sentence as well as a human, then it is as efficient at cutting to the heart of the information in the sentence.
1. I think people do realize this by themselves. Just eavesdrop on any online chat room or the text messages of a typical 10 year old. But this is beside the point. I think you're fixating on compression algorithms being very strong nowadays. No one is disagreeing with you on that.
I think the actual point is that at some point we have to admit that compression can only reach a certain level of effectiveness if the compressor can evaluate and exploit the information content of the text. Compressors work by eliminating redundancy from the representation of the knowledge. Essentially, a compressor is trying to capture the heart of the matter. I think this is exactly what a human does when he or she reads text. This is why compression is interesting to AI.
2. I totally agree with you up until your assertion that it makes the contest weak. I think the contest is testing exactly the goal you state. It asks to losslessly compress (a proxy for) human knowledge. I think it has to be a proxy (because knowledge representation is a different and arguably more slippery AI subtopic), and I think it has to be lossless (to protect the experiment from the debate over what text/information is acceptable to lose on the grounds of irrelevance). I'm not sure how to set up a different experiment that would test your goal in reasonable isolation and still be scientifically rigorous.
3. I think your elision of my sentence changed its meaning (bad compression/decompression?
4. That's pretty cool. I want it.
first point: "If its so easy to put the vowels back in, (a) good statistical compressor will use very little space for them." That's probably true. In fact, I'd consider such an algorithm fairly intelligent. That might be what the Hutter prize winning algorithm does. I think what you're saying here is that most things humans can do to improve compression algorithms are already being done in the best algorithms. I have a feeling you're right, which probably is why compressors are approaching researchers' best guess at the average human level of compression of English.
second point, regarding ambiguity: First of all, I said *most* vowels, not all. The human has to intelligently decide which ones. Also, if your text can't be unambiguously recovered, then you can't claim to have losslessly compressed it. That's like me compressing the same sentence to 1 bit and declaring that I have the most efficient compression algorithm possible. That's why when we talk about compression algorithms, we also talk about decompression algorithms. The human shouldn't remove vowels in such a way as to make the text unrecoverable. I think you understand the difference, since you engineered your vowel-less sentence to be as confusing as possible.
third point: I'm not exactly sure what you mean by "proxies" in this context. I think you are claiming that I am using language as a proxy for intelligence. Rest assured, I am not. Like I've been saying all along, having language faculties is necessary, *but not sufficient* for intelligence. This is exactly the distinction that everyone seems to be missing: no one (who has a clue) is saying "it compresses/understands language, so presto, it's intelligent." The claim is "we are one step closer to having a machine that passes the Turing Test, since one can no longer stump the machine on the basis of its ability to capture the information in an English sentence."
This being said, I think that *compression* and intelligence are highly related. Fundamentally, there is only so far you can go in compressing a blob of text without actually understanding the underlying information. For example, we both used 'gd' in our sentences; and we both without skipping a beat interpreted it as "good" rather than "god", "goad", "gad", etc. Sure, a statistical compressor could've chosen "good" and been right most of the time. But hypothetically you could have meant "god" if we were having a religious debate. This kind of technique relies on intelligence, and allows us to "compress" pretty well. The assertion is that when we pass Shannon's estimate, we probably have an algorithm that is just starting to exploit these kinds of techniques, and that's exciting. At least to me.
Thanks for the lively debate... it's nice to exercise some logical chops again.
Beating gzip is easily. As you point out, English is extremely redundant and thus inefficient in its usage of bits. Try removing most vowels from some English text: Stdis hv shwn tht ppl cn rd ths knd f txt lmst effrtlsly. My compression/decompression works by reading all of wikipedia, removing most of the vowels, then running it through the gzip algorithm (executed on paper, of course!). To decompress, execute gunzip (on paper), and then have a literate human being put the vowels back in. Sure it's going to be insanely slow, but speed of computation better not be the interesting part of intelligence; otherwise computers are already much more intelligent than we are. Also, I should be forgiven for not knowing the gzip algorithm. Even computers have to be "told" the algorithm.
This sort of technique can be used for just about any compression algorithm. The example I gave simply isolates one way in which gzip is unintelligent... it doesn't "get the point" about English. I'm going to assert that one can call compression good enough to be intelligent when an intelligent person can't (non-negligibly) improve its compression ratio on some arbitrary and information rich English text. And I think the compression ratio on such an intelligent compression algo will be (somewhere near) Shannon's number. That is to say, it will "get the point" about English as well as an intelligent human. In this light, compression is a proxy for understanding human languages, which is absolutely crucial to human intelligence.
Fair enough. I suppose a Turing Test subject asked to compress some data better be able to respond like a human would: either by compressing it on par with Shannon's estimate or by having a convincing reason why it can't (while still claiming to be human).
This is the beauty of the Turing Test... it cleverly avoids the trap of defining intelligence by simply stating that artificial intelligence should be practically indistinguishable from natural (human) intelligence. This means the test subject is allowed some realistic intellectual weakness. In fact, the lack of it might mark a subject as non-human!
I should have said something like "so logically it's harder to call something UNintelligent if it's at least this good at compression." Alternatively, it would have been acceptable to say "we can't call anything as intelligent as most humans unless it's at least this good at compression."
A reasonable explanation is in order. No one said that compression to 1.x bits per character is sufficient to call something intelligent. They just claim that this is the best that humans can do, so logically we can't call anything as intelligent as a human unless it's at least this good at compression.
People are (incorrectly) presenting the link between compression and AI as: "If it can compress as well or better than Shannon's estimate, then it is intelligent." In fact, only the converse is true: "If it is intelligent, it can compress as well or better than Shannon's estimate." This is interesting, because the contrapositive of the latter ("If it cannot compress as well or better than Shannon's estimate, it is not intelligent") is a negative test of intelligence.
Recall the Turing Test of Intelligence: a human "decider" sits at a terminal and chats with whatever is on the other end. On the other end is the subject; randomly either a computer or a human. After some fixed amount of time, the decider is asked whether he was chatting with a human being. This test is run lots of times, for lots of deciders and lots of subjects. If the decider answers yes for the computer at least as often as he answers yes for the human, then the computer can be regarded to be intelligent. A compression algorithm that beats the human threshold would imply that one gap between humans and computers has been closed, since the decider can no longer simply test to see if the subject can compress stuff. But there are billion other tests a decider could employ that AIs still can't do... so AI is still 10 years off, just like it's been for 50 years now.
On your first point, me too.
However keep in mind that you aren't "copying by listening." You are describing (at best only partially) how the music was created in the first place. It's not the music any more than instructions to knit a hat is the hat.
I'm not that impressed when we talk about how expensive a laptop is on account of its rare diamond!
The first time I read that headline, I parsed it as:
65% of Americans Spend More Time With Their PC Than Their SO's do.
And thought "duh!"
Or you could just drop some other bits at random. After all, you don't need an exact copy of the original... just something that can't be traced.
"Jeez I love these people that cry racist at every turn." Ok O'Reilly Factor.
Napster (and their copycats) made a living off this behavior. Were they raided by the SWAT team? No, they were sued. And they were making WAY more money. Face it: this is not an issue of degree. This is an entirely different attack strategy, where the only difference seems to be the perpetrator. I'm not saying it's definitely racist, but I'd like to see an explanation of why the SWAT team, why now.
I can't help but see some sort of prejudice, probably racial, in this. Think about the differences between the way the RIAA prosecutes their agenda when it comes to college students vs. "urban" hip-hop musicians. College students (or their parents) are hit with a civil lawsuit and settle out of court. This DJ has his place raided (by the SWAT TEAM?!?) and stuff confiscated and gets held on a 100k bail bond. I can't tell from the picture if this guy is black, white, latino, or whatever, but hip-hop has been a mostly african-american, urban phenomenon. Everyone knows the statistics on the ethnicities of college students. C'mon, slashdot, do these draconian measures smack of racism?
Intractible is WAY better than unsolvable. I wasn't saying it was easy. Just that it's possible.
1. Absolutely, assuming both languages are Turing Complete
2. How in general? If you mean "for all turing machine programs" or something, then yes, there is a reduction to the halting problem (though not the one given above, that's just terrible). But if you mean "all programs that can run on my T-42 IBM laptop", then no. This is because there are a finite number of states that my laptop can be in, and therefore the set of all programs that can run on it is NOT Turing complete. So there IS in fact a program that can determine whether a certain program that I'm about to run on my machine will halt on a given input. The program is simple: you count the total number of states the machine could enter, and then you run the program on a machine simulator for exactly that many "cycles." If it hasn't halted by then, it won't. Proof by counting: if you continue to run the program, then there is some state you have entered twice, meaning there is a loop which will cause the program to run forever.
3. True.
That quote still seems to be good for auto +5!
Right, impeachment is so radioactive it's never used to enforce the president's faithful execution of his duties. Impeachment is only used to neuter a popular president because he had extramarital sex and lied about it.
Actually, the article didn't quote any study at all. It hand-wavingly declared such and such a study said thus and so, and provided a link to make it look authentic. Try clicking the link. It goes to Fox's search page, where none of the results point to a UN study. Frankly, it seems a little underhanded to present a link this way as if it's a citation.
Right, I get you... tempt the virus with food, and then shoot it.
Good luck in the pandemic, man.
RT(rest of the)FA.
It goes on to remind us that California just passed a very strict emissions bill (like what you're calling for) that the auto companies are trying to fight in court. IN COURT! So turn about is fair play.
I was especially interested to read this: in NY state, in a similar case, utility companies (the defendant) argued successfully that the attorneys-general were attempting to resolve a political issue in the courts; the judge threw out the case saying it is an issue for the legislature to resolve. The auto industries guys point to that case as a suggestion of how the current California lawsuit will go. But the brilliant part is that now if the auto companies successfully argue that this is a political, not legal, issue that should be dealt with by the legislature, they'll look a little silly trying to block the recent emissions law (passed by... oh, the legislature).
Obviously California has no hope of winning this suit. But that's not the point. It's simply a tactic to get the auto companies to drop their attempts to block the recent emissions law.
Taking lots of measurements at lots of different places does not eliminate error, but it reduces its likelihood. This is the essence of statistics. Basically it comes down to this: as you sum up all the measurements to take the average, the errors should cancel eachother out. Here's a thought experiment... you wish to measure your own weight, and you have a scale. However, the scale reports your weight +/- 1 kg. In fact, it flips a coin. If heads, add a kg, if tails, subtract a kg. If you do this measurement once, you will have the result to accuracy of +/- 1 kg. If you do it a million times and average the result, you will also have a result of accuracy +/- 1 kg. However, consider the likelihood of your result being 1 kg too much in both cases. In the first case, to be off by 1 kg, the scale must have flipped heads. So 1 in 2 times, 50-50 odds. In the second case, the scale would have had to flip heads one million times in a row. So that's 1 in 2^1000000. Pretty unlikely. In fact, the most likely result is that you get your weight exactly, and most of the time you'll get it within a few grams of the actual amount. And notice in this example the original scale COULDN'T actually give you your real weight... it was always off by 1 kg. (This actually works for all error distributions... and in fact I picked the one that causes uncertainty to dissappear least quickly.)
.7 and worst-case distribution) to yield a measurement that is off by +.7, each and every measurement would have to have been off by the full +.7. That's like flipping heads one hundred times in a row. Unlikely.
If you want to know the average weight of all people on the planet, it works in much the same way... only now, consider there to be a "true" average... the average you would have if you actually measured everone's weight with an honest scale and averaged it. We expect that to first order approximation, it is equally likely that any one person has weight above or below that average. So we start picking people randomly and measuring their weight with our original coin flipping scale. I've already shown you how the coin-flipping scale will have its error reduced to extraordinarily unlikely, so let's ignore it (since we're adding it up in exactly the same way as before). So say we actually weigh a few hundred people. Since we're picking randomly, we expect to pick approximately as many heavier than avg people as lighter than avg people. So with more and more measurements, we should expect the likelihood of being much too high to decrease (the same with much to low). If we only picked NFL linemen, then we're extraordinarily unlucky. It's possible, but unlikely. Again, this holds regardless of the distribution of individual measurements.
By the way, whenever you see a margin for error, you should also look for a measurement of probability that the measurement is within this margin for error. I don't know for sure, but the reason these studies probably omit the margin for error on aggrigates is because significant error is so unlikely that it isn't worth considering. Yes, it would be nicer for the papers to state that. But simply put, for a hundred measurements of temperature (with 100% probability of being accurate to +/-
Man, is it warm out here?
Many people are stricken with HIV or AIDS before they have children. Yes, they CAN breed, but many just don't on account of their disease. As far as evolution goes, same diff: fewer offspring from people without resistance.
Also, if I understand the way HIV is passed, the offspring of people infected with HIV are at least somewhat more likely to have HIV. Children are unlikely to themselves have children unless they have some amount of resistance (either natural or artificial) to HIV; and in children the disease has longer to take its toll (or at least make itself known) before reproduction can begin.
Bottom line: humans can/will acquire resistance to the disease. On the other hand, I'm pretty sure we shouldn't be waiting for humans to evolve in order to combat the disease. I'm just saying from an evolutionary perspective, it will happen or we'll die out.