It's not a second problem, it's evaluating the other half of the problem. In probability it's often useful to split up the problem into multiple parts. So first they consider the case where the oldest is a boy born on Tuesday, then consider the case where that isn't true and therefore the youngest must be, then add all the possibilities up and eliminating duplicates.
In the first case, there's no restriction on the youngest child, so the possibility of the youngest also being a Tuesday-boy is counted there. In the second case, you've specifically disallowed the oldest to be a Tuesday-boy (or alternatively, you allow it, but since you've already counted it once in the first case, you don't count it again in the second).
I have two children, one of whom is a son born on a Tuesday. What is the probability that I have two boys?
One of whom is not "exactly one of whom", so 'one' might be opposed to 'the other' or 'two'.
Pfft.
If you accept that "one of whom is a son born on a Tuesday" might not mean "exactly one boy born on Tuesday", then you must also accept that "I have two children" might not mean "exactly two children".
In which case, the probability of having two boys could be much higher, though it depends on whether you take "two boys" to mean exactly two or at least two.:P
This is a perfect example of why trying to establish the single precise meaning of a standardly ambiguous English sentence so often fails and is almost always pointless. Because the pedantic literalism is only applied to whatever the person analyzing it wants to, because 99% of the time we don't understand language in that fashion and it takes a specific intent to break out of that natural understanding.
Further, the problem doesn't ask about any probability related to the second boy's birthday. The problem doesn't ask, e.g., What is the probability that my other child is a boy not born on Tuesday?. That makes the birth weekday completely irrelevant.
But if you say there's exactly two children, and at least one is a boy born on Tuesday, then out of the general population of such families, there are more where the second child is a girl than a boy.
The more tangents you throw at it, the closer you get to.5 (50%), while never reaching it. This is the limit, why? Because there's only two potential outcomes for the other child: boy or girl.
Though as others have pointed out, the probability of having a boy is actually slightly higher than that, around 51%. The "two outcomes equals 50% chance" only applies to the special case of each outcome having equal probability, which is why problems that are being rigorous will always say a "fair" coin or die.
I could roll a die 99 times, and get 6, the probability of getting 100 6's when I've already got 99 6's is still 1 out of 6, not 6^100.
Yes, but human biology is more complicated than a fair die roll. Specifically, some men tend to produce more sperm of one sex than another, or have more vigorous sperm of one sex than the other. Henry the VIII famously had this problem of only producing viable female sperm, and he cut his wives' heads off for it.
So there's a conditional probability based on having N children of one sex that the father has such a condition, and in that case the probability of a boy would be different. The result would like P(boy given no condition)*(1 - P(condition given one boy)) + P(boy given condition)*P(condition given one boy).
I don't have the information to actually calculate the probability. But it's not 50%, and "extraneous" information like "I've already had a boy" is not actually extraneous and not an example of the Gambler's Fallacy.
Well, the problem here is that physicists prefer to do what works and if adding in a new exotic ____ (fill in the blank) that is conveniently invisible but that we're surely going to find eventually fixes the problem, then the problem can be said to have gone away.
Er, it would be bad if they thought having a mere theoretical explanation meant the problem had 'gone away'. Instead, dark matter is one of the problems at the forefront of modern astrophysics and people are constantly trying to find ways to bring more experimental light to bear on it so we can actually figure out what is going on. People are actively looking for evidence.
In that sense it is quite inconvenient that the most likely dark matter candidates are invisible, because that makes it hard to find them and I assure you that physicists want to find them. It was hoped they'd turn out to be normal matter that was just hard to see (MACHOs), but extensive surveys of the galaxy with Hubble have put that out to pasture.
The sense of "convenient" you meant though, which is the same way it's "convenient" that a crazy guy from the future's time machine won't let him bring advanced technology through it to prove he's from the future, is completely off. Particles that have mass yet are invisible to light are already known to exist. Other theories predicted the existence of heavier versions of these particles before dark matter even entered the picture, and it's from that theory (supersymetry) that we "fill in the blank". A particle that doesn't interact electromagnetically is strongly suggested by the evidence, too, that clouds of dark matter appear to be able to pass through an entire galaxy unperturbed.
So it's hardly some "conveniently" unprovable postulate that science made up on the spot to avoid having to deal with the problem.
It's the most likely explanation for observation, and there are many people trying to find evidence for or against it. What exactly is the problem here again?
Does this all remind you of anything? Do Epicycles come to mind?
Not in the slightest, because Epicycles were a case of avoiding the simple explanation (planets travel in ellipses) because circles were more aesthetically or (weirdly) religiously pleasing, yet ended up as a complicated mess that to a modern eye is distinctly less pleasing than the simple math of Kepler's Laws.
Where is the simpler explanation that is being avoided, here? "Gravity is wrong" is not such an explanation, it's just a statement. Actually explaining what we observe without dark matter is going to result in a much more complicated theory of gravity to explain why it's seemingly coming from nowhere when it usually seems to require mass. It turns out it's rather hard to come up with an explanation that is simpler than "gravity works mostly like we think it does, and there are things that are like neutrinos but heavier".
Scientists are constantly looking for ways to simplify things, explain more with less, merge separate theories or forces into one, and so on. And they've had many successes at doing so -- electromagnetic theory, electroweak theory, and modern color theory. The latter seems complicated in that it introduces quarks in many combinations to make what were previously fundamental things like protons and neutrons. Isn't that what Occam warned us about: needlessly multiplying entities? But before quark theory, there were literally hundreds of particles known to exist and with no coherent theory to explain them. By explaining all those particles using only six sub-particles, we made a great stride.
Yet the end picture is still complex. There is a certain elegance to the laws as they exist today, even if understanding them all is tough. That elegance leads
Sounds like I wasn't exactly right, as the difference isn't just in how the muscles are coordinated, but in actual genetic differences in the tissue itself.
Chimps don't have really have any more muscle than a similarly sized person, but so much of our muscles are used to control precise movements that we lose out a lot on strength.
As I heard it, it's actually that we just don't activate as many muscle clusters simultaneously as chimps do. It's not about fine motor control when it comes to big muscles like the quadriceps or biceps, it's just that we're optimized for endurance over strength.
And when we do activate all of our muscles at once, we tend to injure ourselves because our skeletons aren't designed for it.
Of course, and you're a hack to make the "there aren't AIs randomly posting to slashdot" theory work. It's not like I can actually infer your existence or anything without the direct use of my senses.
The problem is when there's no observation to either agree or disagree with, or when the observations they're developing models for are actually wrong. That is why many of these people do what is called "theoretical physics". Of course sometimes observations are made that contradict current theoretical physical theories.
There are actually many observations that support the existence of dark matter. Which is why the statement "there is more error in WMAP than thought" is a far jump from "dark matter doesn't exist". The first evidence for dark matter was not in the CMB at all, but in the behavior of galaxies. First that the observed matter was not enough to give them the behavior observed, then in galaxy collisions where large amounts of apparent matter appeared outside the galaxies, having passed right through unslowed by the collision, and then ultimately by creating maps (and more maps) of dark matter via gravitational lensing.
Like I said, many very talented physicists have tried to make sense of the observations without resorting to dark matter, and it worked when the evidence was only in the spinning of galaxies, but at this point they have mostly admitted defeat. The idea that dark matter is only accepted because nobody wants to rethink the prevailing theory is utter nonsense.
What has happened is a theory that cannot explain observation has been given a crutch to aid it limping along for a while longer until a new hypothesis is introduced to explain the discrepancy.
But the theory works perfectly if you simply infer the existence of mass as all evidence suggests. Then there is no discrepancy. Why this is such a sin, such a hack, is beyond me. Do you think that this is just a little fudge, like the numbers are off so we push 'em this way or change this constant or the mass value of this galaxy and it works? And we're happy because that's better than admitting the theory is wrong?
That's not even close. There is no way to modify gravitational theory in any sane (as in consistent with other experiments) way and get the observed results, without there being matter out there. You'd have to explain how gravitational lensing occurs in the absence of any mass/energy and how visible masses experience accelerations towards apparently empty space. To actually get that to happen, you would basically have to have gravity working completely differently than it appears to in every other observation and experiment.
So as regards evidence, I think you need some evidence for your "gravity pulls things in random directions and causes lensing around empty space without an mass/energy there" theory. But first I think you should figure out whether this theory is even consistent with the all the non-dark-matter evidence.
I think the difference is that we know from the experience of our own senses that 9 (or 8, depending on whether or not you agree) planets do actually exist, are visible and have some demonstrable gravitational effect on our own Sun. It's not such a great leap to infer that perhaps other such bodies exist around other stars and perhaps by measuring the wobble of those stars we may be able to learn something new.
Exactly. The difference is that planets are "normal", and dark matter sounds strange and weird and therefore your gut reaction is to think they are just making things up to keep their theory working. The idea of a kind of matter that has mass, but doesn't interact with photons and is thus invisible to any sort of direct electromagnetic detection, just can't be true. Even though this very article is a
Then of course we havethe hacked dark matter née aether to make everything work out and match the theory.
Dark matter is no more a "hack" than expolanets around stars with slight wobbles are "hacks". Omigosh, you need a planet there to "match the theory"! Or is the planet a prediction based on observation and an already well-working theory? Yes, that's what it is. We use the theory of gravity to infer the existence of masses.
People have tried to modify the theory to avoid having to infer mass in places where we couldn't directly see any. It nearly worked for a while, until further evidence showed that you couldn't just adjust the magnitude of gravitational attraction and make things work (like MOND), you had to have gravity pointing in completely different directions, for different cases! We've come as close as we probably can to directly seeing the dark matter (if it's WIMPs) via gravitational lensing.
In any event, you're absolutely right that new data that shows weaknesses of existing theory is very exciting, because that's where new physics is discovered.
I'm just sayin', this is basically what's already happened to dark-matter-free theories.
Every time one of their fixes fails, and I'm tempted to say things like "those guys are idiots!", people like you come along to demonstrate what true idiocy looks like.
Heck, I had a cat who was raised like crap, neglected and mistreated by his owner and his owner's roommates. Was ridiculously skittish and neurotic (for a cat!) and definitely didn't like having his feet touched. By the time he'd been my cat for a year, I could trim his nails with no problems.
Still, I wouldn't blame anyone for putting a cat under for just about any medical procedure even if it's just attaching prosthetics to leg-posts.
I appreciated this line from the abstract: "We identify models where dark matter particles are beyond the reach of any planned direct detection experiments while being within reach of neutrino telescopes."
So they're looking to cover the space that isn't covered by projects like CDMS, which does direct detection. Which only makes sense, but it's just exciting to me to see cutting-edge science tackling problems from multiple different angles simultaneously.
One glance at the picture in the article and it's clear that what we be dealin with be a Pirate cat. And if Pirate Cat says he be bionic, he be bionic. You can tell im different, if ye don't be valuin yer pretty face. Yar har har!
Oh hey thanks for bringing that up. Mainstream processors have some BIST too, at least on the cache arrays. I didn't think of it because I was focused on detecting errors during operation.
You say they use two CPUs in lockstep, which got me thinking why not three so you can correct errors rather than just detect them? But automotives are very cost sensitive, and since a bad answer probably isn't going to make the car blow up*, and flagging an error so the 'check engine' light can be turned on and the car taken in for repair is probably good enough. Is that a good guess?
* Or blow up at the wrong time, or not at all, if we're comparing to certain military applications.:)
Perhaps the largest of those myths is "man made tools and tools made man": the idea that once tool-use, including fire, became part of proto-human life we were on a slippery evolutionary slope to big brains. Upright bipedalism in this myth is necessary to free our hands to work with and carry tools.
We happened to have a body plan that resulted in us being able to do something more useful than tell dirty jokes after run-away sexual selection blew our brain out into its current magnificent proportions. Once that entirely accidental potential was realized, about 50,000 years ago, there has likely been some evolutionary pressure toward more effective tool use and whatnot, up until the last 200 years, anyway.
Early upright bipedalism challenges all the myths, and people hate that.
Feh. Rubbish.
The only necessary role of bipedalism in the "myth" that intelligence and tool use were positively selected for in human evolution is that it provided a skeletal structure that would support a larger brain and yes using tools.
It is neither surprising nor crippling to the "myth" that bipedalism could have evolved far earlier and for other reasons. That's common with many biological traits -- they serve one purpose as they evolve, but once present have other advantages that allow other features to arise. If the only reason our two-legged gait was selected for was because it let us chase prey and run away from predators on the plains when we came down from the trees (or whatever), so what? It still freed our hands and supported our heads.
What matters is that the fossil record shows skulls of human ancestors increasing in size, indicating selection for larger brains. Archaeological records show tool use millions of years ago, not fifty thousand. Yes there was an explosion of technological and societal growth in the relatively recent past. Yet humans had clearly been heading down a path of increasing their survivability through increasing tool use and intelligence for a long time.
Why that's a myth equivalent to religion, which was a concept that came long after tool use, I don't know.
I do appreciate your hypothesis that intelligence is the result of sexual selection, and I am not about to downplay the role. But... it seems likely that doing useful things with intelligence came before dirty jokes or similar means of pleasing the opposite sex. Jokes are actually pretty advanced concepts. Abstract thinking and problem solving would have certainly had to arise first. Before that, attracting mates was more about finding food, giving the same selective pressure towards tools and intellect as the need to find food for oneself. Intelligence was a survival trait.
Though on the other hand intelligence and tool use -- at least human intelligence and tool use -- has yet to prove itself as a truly long-term survival trait. Let's see if we're around for another fifty million.
Slashdot Mirror
It's not a second problem, it's evaluating the other half of the problem. In probability it's often useful to split up the problem into multiple parts. So first they consider the case where the oldest is a boy born on Tuesday, then consider the case where that isn't true and therefore the youngest must be, then add all the possibilities up and eliminating duplicates.
In the first case, there's no restriction on the youngest child, so the possibility of the youngest also being a Tuesday-boy is counted there. In the second case, you've specifically disallowed the oldest to be a Tuesday-boy (or alternatively, you allow it, but since you've already counted it once in the first case, you don't count it again in the second).
The sum of the two is the answer.
The problem is stated thus:
I have two children, one of whom is a son born on a Tuesday. What is the probability that I have two boys?
One of whom is not "exactly one of whom", so 'one' might be opposed to 'the other' or 'two'.
Pfft.
If you accept that "one of whom is a son born on a Tuesday" might not mean "exactly one boy born on Tuesday", then you must also accept that "I have two children" might not mean "exactly two children".
In which case, the probability of having two boys could be much higher, though it depends on whether you take "two boys" to mean exactly two or at least two. :P
This is a perfect example of why trying to establish the single precise meaning of a standardly ambiguous English sentence so often fails and is almost always pointless. Because the pedantic literalism is only applied to whatever the person analyzing it wants to, because 99% of the time we don't understand language in that fashion and it takes a specific intent to break out of that natural understanding.
Further, the problem doesn't ask about any probability related to the second boy's birthday. The problem doesn't ask, e.g., What is the probability that my other child is a boy not born on Tuesday?. That makes the birth weekday completely irrelevant.
But if you say there's exactly two children, and at least one is a boy born on Tuesday, then out of the general population of such families, there are more where the second child is a girl than a boy.
It's where you plug in your AI.
with the Blackuweather airport forecast. Ollie, what's the air quality like there?
Ollie: [face covered in red welts and puffing up] It's full of bees!
I'm glad to see that ED-209 found new work as a lawyer.
The more tangents you throw at it, the closer you get to .5 (50%), while never reaching it. This is the limit, why? Because there's only two potential outcomes for the other child: boy or girl.
Though as others have pointed out, the probability of having a boy is actually slightly higher than that, around 51%. The "two outcomes equals 50% chance" only applies to the special case of each outcome having equal probability, which is why problems that are being rigorous will always say a "fair" coin or die.
I could roll a die 99 times, and get 6, the probability of getting 100 6's when I've already got 99 6's is still 1 out of 6, not 6^100.
Yes, but human biology is more complicated than a fair die roll. Specifically, some men tend to produce more sperm of one sex than another, or have more vigorous sperm of one sex than the other. Henry the VIII famously had this problem of only producing viable female sperm, and he cut his wives' heads off for it.
So there's a conditional probability based on having N children of one sex that the father has such a condition, and in that case the probability of a boy would be different. The result would like P(boy given no condition)*(1 - P(condition given one boy)) + P(boy given condition)*P(condition given one boy).
I don't have the information to actually calculate the probability. But it's not 50%, and "extraneous" information like "I've already had a boy" is not actually extraneous and not an example of the Gambler's Fallacy.
Until somebody figures out what the ????? is supposed to be between "1) Space Travel" and "3) PROFIT!", we aren't going anywhere.
I don't know, but I somehow get the impression that The Riddler is involved.
To the moon, Alice! ... is where I'm going to go!
Well, the problem here is that physicists prefer to do what works and if adding in a new exotic ____ (fill in the blank) that is conveniently invisible but that we're surely going to find eventually fixes the problem, then the problem can be said to have gone away.
Er, it would be bad if they thought having a mere theoretical explanation meant the problem had 'gone away'. Instead, dark matter is one of the problems at the forefront of modern astrophysics and people are constantly trying to find ways to bring more experimental light to bear on it so we can actually figure out what is going on. People are actively looking for evidence.
In that sense it is quite inconvenient that the most likely dark matter candidates are invisible, because that makes it hard to find them and I assure you that physicists want to find them. It was hoped they'd turn out to be normal matter that was just hard to see (MACHOs), but extensive surveys of the galaxy with Hubble have put that out to pasture.
The sense of "convenient" you meant though, which is the same way it's "convenient" that a crazy guy from the future's time machine won't let him bring advanced technology through it to prove he's from the future, is completely off. Particles that have mass yet are invisible to light are already known to exist. Other theories predicted the existence of heavier versions of these particles before dark matter even entered the picture, and it's from that theory (supersymetry) that we "fill in the blank". A particle that doesn't interact electromagnetically is strongly suggested by the evidence, too, that clouds of dark matter appear to be able to pass through an entire galaxy unperturbed.
So it's hardly some "conveniently" unprovable postulate that science made up on the spot to avoid having to deal with the problem.
It's the most likely explanation for observation, and there are many people trying to find evidence for or against it. What exactly is the problem here again?
Does this all remind you of anything? Do Epicycles come to mind?
Not in the slightest, because Epicycles were a case of avoiding the simple explanation (planets travel in ellipses) because circles were more aesthetically or (weirdly) religiously pleasing, yet ended up as a complicated mess that to a modern eye is distinctly less pleasing than the simple math of Kepler's Laws.
Where is the simpler explanation that is being avoided, here? "Gravity is wrong" is not such an explanation, it's just a statement. Actually explaining what we observe without dark matter is going to result in a much more complicated theory of gravity to explain why it's seemingly coming from nowhere when it usually seems to require mass. It turns out it's rather hard to come up with an explanation that is simpler than "gravity works mostly like we think it does, and there are things that are like neutrinos but heavier".
Scientists are constantly looking for ways to simplify things, explain more with less, merge separate theories or forces into one, and so on. And they've had many successes at doing so -- electromagnetic theory, electroweak theory, and modern color theory. The latter seems complicated in that it introduces quarks in many combinations to make what were previously fundamental things like protons and neutrons. Isn't that what Occam warned us about: needlessly multiplying entities? But before quark theory, there were literally hundreds of particles known to exist and with no coherent theory to explain them. By explaining all those particles using only six sub-particles, we made a great stride.
Yet the end picture is still complex. There is a certain elegance to the laws as they exist today, even if understanding them all is tough. That elegance leads
Sounds like I wasn't exactly right, as the difference isn't just in how the muscles are coordinated, but in actual genetic differences in the tissue itself.
Interesting.
Of course, that's it, you're just too nice a guy.
All Paladins suffer from crippling self-doubt.
Chimps don't have really have any more muscle than a similarly sized person, but so much of our muscles are used to control precise movements that we lose out a lot on strength.
As I heard it, it's actually that we just don't activate as many muscle clusters simultaneously as chimps do. It's not about fine motor control when it comes to big muscles like the quadriceps or biceps, it's just that we're optimized for endurance over strength.
And when we do activate all of our muscles at once, we tend to injure ourselves because our skeletons aren't designed for it.
Yeah, exactly. And the search for what it is or could be is where lots of new science is taking place. I don't get GP's mentality.
Of course it's a hack!
Of course, and you're a hack to make the "there aren't AIs randomly posting to slashdot" theory work. It's not like I can actually infer your existence or anything without the direct use of my senses.
The problem is when there's no observation to either agree or disagree with, or when the observations they're developing models for are actually wrong. That is why many of these people do what is called "theoretical physics". Of course sometimes observations are made that contradict current theoretical physical theories.
There are actually many observations that support the existence of dark matter. Which is why the statement "there is more error in WMAP than thought" is a far jump from "dark matter doesn't exist". The first evidence for dark matter was not in the CMB at all, but in the behavior of galaxies. First that the observed matter was not enough to give them the behavior observed, then in galaxy collisions where large amounts of apparent matter appeared outside the galaxies, having passed right through unslowed by the collision, and then ultimately by creating maps (and more maps) of dark matter via gravitational lensing.
Like I said, many very talented physicists have tried to make sense of the observations without resorting to dark matter, and it worked when the evidence was only in the spinning of galaxies, but at this point they have mostly admitted defeat. The idea that dark matter is only accepted because nobody wants to rethink the prevailing theory is utter nonsense.
What has happened is a theory that cannot explain observation has been given a crutch to aid it limping along for a while longer until a new hypothesis is introduced to explain the discrepancy.
But the theory works perfectly if you simply infer the existence of mass as all evidence suggests. Then there is no discrepancy. Why this is such a sin, such a hack, is beyond me. Do you think that this is just a little fudge, like the numbers are off so we push 'em this way or change this constant or the mass value of this galaxy and it works? And we're happy because that's better than admitting the theory is wrong?
That's not even close. There is no way to modify gravitational theory in any sane (as in consistent with other experiments) way and get the observed results, without there being matter out there. You'd have to explain how gravitational lensing occurs in the absence of any mass/energy and how visible masses experience accelerations towards apparently empty space. To actually get that to happen, you would basically have to have gravity working completely differently than it appears to in every other observation and experiment.
So as regards evidence, I think you need some evidence for your "gravity pulls things in random directions and causes lensing around empty space without an mass/energy there" theory. But first I think you should figure out whether this theory is even consistent with the all the non-dark-matter evidence.
I think the difference is that we know from the experience of our own senses that 9 (or 8, depending on whether or not you agree) planets do actually exist, are visible and have some demonstrable gravitational effect on our own Sun. It's not such a great leap to infer that perhaps other such bodies exist around other stars and perhaps by measuring the wobble of those stars we may be able to learn something new.
Exactly. The difference is that planets are "normal", and dark matter sounds strange and weird and therefore your gut reaction is to think they are just making things up to keep their theory working. The idea of a kind of matter that has mass, but doesn't interact with photons and is thus invisible to any sort of direct electromagnetic detection, just can't be true. Even though this very article is a
What makes you think Higgs is going to share his bacon with you?
Then of course we havethe hacked dark matter née aether to make everything work out and match the theory.
Dark matter is no more a "hack" than expolanets around stars with slight wobbles are "hacks". Omigosh, you need a planet there to "match the theory"! Or is the planet a prediction based on observation and an already well-working theory? Yes, that's what it is. We use the theory of gravity to infer the existence of masses.
People have tried to modify the theory to avoid having to infer mass in places where we couldn't directly see any. It nearly worked for a while, until further evidence showed that you couldn't just adjust the magnitude of gravitational attraction and make things work (like MOND), you had to have gravity pointing in completely different directions, for different cases! We've come as close as we probably can to directly seeing the dark matter (if it's WIMPs) via gravitational lensing.
In any event, you're absolutely right that new data that shows weaknesses of existing theory is very exciting, because that's where new physics is discovered.
I'm just sayin', this is basically what's already happened to dark-matter-free theories.
Every time one of their fixes fails, and I'm tempted to say things like "those guys are idiots!", people like you come along to demonstrate what true idiocy looks like.
Thanks for puttin' it in perspective.
Heck, I had a cat who was raised like crap, neglected and mistreated by his owner and his owner's roommates. Was ridiculously skittish and neurotic (for a cat!) and definitely didn't like having his feet touched. By the time he'd been my cat for a year, I could trim his nails with no problems.
Still, I wouldn't blame anyone for putting a cat under for just about any medical procedure even if it's just attaching prosthetics to leg-posts.
Fascinating, thanks for the link.
I appreciated this line from the abstract: "We identify models where dark matter particles are beyond the reach of any planned direct detection experiments while being within reach of neutrino telescopes."
So they're looking to cover the space that isn't covered by projects like CDMS, which does direct detection. Which only makes sense, but it's just exciting to me to see cutting-edge science tackling problems from multiple different angles simultaneously.
No, it plays the Meow Mix jingle. Which admittedly takes some of the drama out of it.
One glance at the picture in the article and it's clear that what we be dealin with be a Pirate cat. And if Pirate Cat says he be bionic, he be bionic. You can tell im different, if ye don't be valuin yer pretty face. Yar har har!
Oh hey thanks for bringing that up. Mainstream processors have some BIST too, at least on the cache arrays. I didn't think of it because I was focused on detecting errors during operation.
You say they use two CPUs in lockstep, which got me thinking why not three so you can correct errors rather than just detect them? But automotives are very cost sensitive, and since a bad answer probably isn't going to make the car blow up*, and flagging an error so the 'check engine' light can be turned on and the car taken in for repair is probably good enough. Is that a good guess?
* Or blow up at the wrong time, or not at all, if we're comparing to certain military applications. :)
Perhaps the largest of those myths is "man made tools and tools made man": the idea that once tool-use, including fire, became part of proto-human life we were on a slippery evolutionary slope to big brains. Upright bipedalism in this myth is necessary to free our hands to work with and carry tools.
We happened to have a body plan that resulted in us being able to do something more useful than tell dirty jokes after run-away sexual selection blew our brain out into its current magnificent proportions. Once that entirely accidental potential was realized, about 50,000 years ago, there has likely been some evolutionary pressure toward more effective tool use and whatnot, up until the last 200 years, anyway.
Early upright bipedalism challenges all the myths, and people hate that.
Feh. Rubbish.
The only necessary role of bipedalism in the "myth" that intelligence and tool use were positively selected for in human evolution is that it provided a skeletal structure that would support a larger brain and yes using tools.
It is neither surprising nor crippling to the "myth" that bipedalism could have evolved far earlier and for other reasons. That's common with many biological traits -- they serve one purpose as they evolve, but once present have other advantages that allow other features to arise. If the only reason our two-legged gait was selected for was because it let us chase prey and run away from predators on the plains when we came down from the trees (or whatever), so what? It still freed our hands and supported our heads.
What matters is that the fossil record shows skulls of human ancestors increasing in size, indicating selection for larger brains. Archaeological records show tool use millions of years ago, not fifty thousand. Yes there was an explosion of technological and societal growth in the relatively recent past. Yet humans had clearly been heading down a path of increasing their survivability through increasing tool use and intelligence for a long time.
Why that's a myth equivalent to religion, which was a concept that came long after tool use, I don't know.
I do appreciate your hypothesis that intelligence is the result of sexual selection, and I am not about to downplay the role. But... it seems likely that doing useful things with intelligence came before dirty jokes or similar means of pleasing the opposite sex. Jokes are actually pretty advanced concepts. Abstract thinking and problem solving would have certainly had to arise first. Before that, attracting mates was more about finding food, giving the same selective pressure towards tools and intellect as the need to find food for oneself. Intelligence was a survival trait.
Though on the other hand intelligence and tool use -- at least human intelligence and tool use -- has yet to prove itself as a truly long-term survival trait. Let's see if we're around for another fifty million.
Hey, do you know if IceCube has the capability to detect and identify neutralinos or other theorized neutrino-like particles?