The probe started out at roughly our speed and accelerated to 34,471 mph, or about 15.4 km/s. In the absence of a complex acceleration history, the simple, first-order approximation of the probe's average speed over the last 6 years is about 7.7 km/s or about 2.6e-5 c. At that speed, the relativistic effect is about 0.99999999967015470011, meaning that the probe has aged about 62 milliseconds less than you have.
Oops! Sorry, Samantha but it seems even a biologist can just be plain wrong sometimes. (Don't mind me cuz I'm a biologist,too.) If pandas are marsupials I'll eat my hat...
I don't do a lot of editing of text over images, so this might be a stupid question, but couldn't you just add and position the image after you've done typing?
I don't know how to address this in other operating systems but, in GNOME on GNU/Linux, you can get around case 1 by checking the "Disable trackpad whilst typing" option.
There is a very simple action that would invalidate the claims of atheists: that would be for a god, any god, to reveal himself in some obvious, unequivocal, unmistakable way. Like, pop up on the nightly news and heal an amputee or something.
The theists, on the other hand, are the ones making the unfalsifiable claims. They're the ones claiming that there exists a sky fairy who chooses to keep himself hidden from man and whose presence can only be intimated by reading an ancient book or books with the aid of some sort of secret decoder ring.
Please, put aside your rancour for a second and tell me, truthfully, which side is making a claim which cannot be falsified...
Oh, wait, you're an AC. I should have known better than respond because you're only here to make yourself feel like you're too good to be living in mommy's basement among piles of pizza boxes and soiled Kleenex.
Well, okay. You're right, it's all just fun and games at this point.
In any case, Einstein was not the issue. Everything that Einstein knew, the Germans knew since it had all been published in readily-available journals. Einstein really had nothing to do with the development of the bomb aside from the theoretical underpinnings, known to the Germans, and a letter he wrote to the POTUS.
Now, if you had spoken in the same terms of Oppenheimer, I might have said, "Game on!":-)
All of this is somewhat simplistic speculation. If you'd refused to sell oil to Hitler he'd have been forced to launch for the Caucusus sooner, maybe even before the Western front had been opened. For sure, Hitler burned up a lot of oil before Barbarossa in 1942; oil that he'd have had to take by force if you controlled supplies and refused to sell to him.
So, after the Anschluss and the taking of Poland, maybe he'd have just rolled on into Russia instead of turning to fight France. If Hitler had gone east first, he'd have pissed off a whole lot fewer people who mattered. The only real reason the Yanks supported the war in Europe at all was because of Britain and France. If it was just a war against Stalin, lots of people would have just figured "Hell, let 'em go at it."
As for the nuclear program, the Germans had a well developed nuclear program without Einstein. They may have been just months away from developing a full-blown nuclear weapon when the end rained down upon them. If VE Day had been delayed by even a few months, the Germans might well have beaten the US to the bomb.
Consequently, all the rest of your post about WWII never happening might also be just a fantastical contruction. There are those who have speculated that time is less like an arrow and more like a meandering river, with currents and eddies.
At the end of the day, though, your post can really be summed up as: "If things had been different, they might not have turned out the same." That's trivially true but the radical departures from the historical timeline are not at all demonstrable by the type of argument you've launched here.
So, if I'm sitting on the couch and I can just make out a dime on the windowsill across the room, the whole street must be covered in dimes? This seems an odd view of reality but, hey, that's just me saying...
I'm interested in your statement that space-time is separable. Please explain, ideally, with the appropriate references.
It would appear to me that saying that time is independent of space is like saying that the length and width of a rectangle can exist separately of each other. I also am dubious of your contention that two independent things are, of neccessity, separable. I may be able to independently set the length and width of a rectangle that I draw but that does not make them separable since it ceases to be a rectangle without one of those components.
Your wife should make sure to wear her favourite perfume regularly and buy some bottles for the girls -- put the bottles away until they get a little older. You could also take her pillow and blankets and put them in one of those plastic things that you vaccuum the air out of. Take the blankets and pillow out when one of the girls is feeling badly (after a bad breakup with a boyfriend, say) and let her curl up on the couch with them. If you reseal them in the bag every time, the smell should last quite a while...
Just some off the wall ideas but I can tell you that the thing I miss most about my wife is her smell...
You're right, of course. I'd intended to say that wheat protein is 13 to 23% gluten, although, admittedly, I was pulling those numbers from an increasingly feeble memory. Thanks for catching that and correcting the record.
Historically, grains were a much poorer source of gluten than they are now. Through selective breeding and through milling processes that refine flour, wheat flour is now 13 to 23% gluten, depending on a number of factors, with whole grain flour being nearer the lower end of that range.
In addition, wheat generally and gluten specifically have become ubiquitous in the foods we eat. For example, soy sauce, which can easily be made gluten free, is often mainly wheat nowadays, especially the Japanese varieties of soy sauce. In the past, a person's gluten exposure was probably comparatively low and, combined with shorter life expectancies, gluten allergies were not as problematic.
Today, with wheat being in all sorts of foodstuffs, gluten allergies are becoming increasingly common, especially among middle-aged and elderly people. Our systems simply become so overwhelmed with gluten that the allergic inflammatory responses become a source of serious illness in some people. When coupled with the malabsoprtion syndrome that accompanies it, since an inflamed, damaged intestinal system absorbs poorly, vitamin deficiencies (especially vitamins E, D and K) gluten allergies cause real illness in many people.
Such illnesses probably remained sub-clinical in people in previous centuries but now, aided by enhanced severity, we better understand what's happening and we are better able to diagnose the trouble.
As for peanuts, just think of how peanuts have become readily available the world over and how they are contained in all sorts of foods, now. Historically, peanuts were a local food that formed a small part of the diet for people in areas near where they were found. In ways similar to what I mentioned above, peanut allergies are much more common and much more severe than ever before.
And somehow sauerbraten isn't sausage and weizenbock isn't beer?
Actually, no... Sauerbraten is a type of roast, often beef but sometimes venison or such. Just because the 'brat' part is also in the famous sausage 'bratwurst' does not make it sausage. Actually, it's the 'wurst' part that translates as sausage. Sauerbraten is usually 'soured' by marinating and cooking the roast in a mixture of wine and vinegar. 'Braten' is the German word for 'to roast', as in the common saying: "Eine gut gebratene Gans is eine gute Gabe Gottes."
A nanodot is 1/1000 of a microdot. I suppose that will work for memory. All I know is I did a microdot a few times and had trouble remembering much of anything afterwards.
This is so incredibly simple that I can't believe I'm reading scores of responses about significant digits and rounding, etc. For a motion to be passed by a 2/3 majority, at least twice as many people have to vote in favour as those who vote against. Since 136 is less than 70*2, the vote fails. No calculator required, no consideration of significant digits. It's the kind of thing a reflective schoolchild should be able to reason out, frankly.
I think this is a symptom of a generation raised with calculators...
if all they're saying is this would be a rare event, then blah. You would expect to find one of those now and then. But it sounds like the scientists are saying they don't even understand how this event is possible. Which is what I was trying to get at with my freaky bridge hand example.
Perhaps, and I have no difficulty leaving it at that, especially for brevity's sake. But what the original poster was reacting to and what I was supporting him on was this passage from TFA:
A second possibility is that the planet hasn't been in its current position very long, Hellier said. Wasp-18b could have spiraled inward to its current position over millions of years. It may have been bumped out of its original orbit by another planet, for example.
"However, that does not solve the problem," Hellier said, because the planet's lifetime should still be very short and it would be very unlikely for his team to find it where it did.
You see, he said it would be "unlikely... to find it... [there]". That's what this discussion was about. Whether finding an unlikely thing is sufficient to say that we need to re-examine our cosmological models. Even the summary's title is mired in histrionics. The researchers found an unlikely thing in an unusual place and this becomes "Astrophysicists Find 'Impossible' Planet". The point the OP, who I was supporting, was making is that it seems strange to suggest that finding an odd thing in an unlikely place can be construed as being "impossible" or revolutionary.
What Hellier said (at least according to the article) was that this condition should be so short-lived and hard to find that finding it is "unlikely". I liken that to saying that some esoteric sub-atomic particle with an incredibly short half-life is hard to find. If we just happen to see one by chance, though, does that fact alone make it revolutionary? Does the fact that it has a short life mean that finding it, even by accident, would be "impossible"?
Anyway, thanks for your contributions. I enjoyed reading them.
That's not a very good analogy, because what they're studying (planetary systems) isn't random. It would be more like if you dealt bridge hands that were all the 8 of hearts - it shows that there is something you didn't understand about the deck.
Ummmm, no. Presumably, we are sighting essentially random plants from some larger population of planets. This is not at all like dealing a succession of highly unlikely hands in bridge because we've seen a single instance of this phenomenon, just like the hand you've been dealt in bridge is a single instance of that seemingly unlikely hand. It's the exact same circumstance.
It's like a genetic disorder with odds of 1 in 10000 live births. If I happen to be visiting the hospital this afternoon and it just so happens that the only child born at that hospital has that disorder, what does that tell me about how rare the event is? Answer: nothing at all. The probability of a single event is not revealed or influenced by whether or not I witness it.
If I see a rare thing happen, all that says is that I randomly was present when it happened. It doesn't mean I should run out and buy a lottery ticket nor does it mean that I should re-examine the models of probability that reveal the likelihood of an event's occurence.
As another poster stated elsewhere in this thread, it may be highly unlikely that any specific individual should win the lottery tonight but, nonetheless, it will happen that someone wins it. The probability of the event is 100%. The probability of it striking a specific individual is small.
And so it is with this planet. The probability of seeing such an event can be small but that does not imply, in any way, that seeing the event means that the probability calculation is wrong and that we need to re-examine our models. I would admit that , if we saw some succession of these events we might be able to say something about the model but a single observation says nothing at all about it -- other than the trivial fact that the probability of occurrence must be non-zero.
Unlikely != impossible. And I'd even question the unlikely bit. With many researchers looking for interesting objects, don't be surprised when you find...an interesting object.
You are correct. By way of illustration, consider the following. In a bridge game I, as the dealer, distribute the cards resulting in an assemblage of four distinct hands. What is the probability of any single deal producing that particular constellation of hands? The rigorous answer is 1 in 52!/(13!)^4 = 1/53,644,737,765,488,792,839,237,440,000. Clearly, it is exceedingly unlikely that I would have dealt those specific hands but, yet, here we are...
By the way, this is the precise error that you frequently see Intelligent Design people make when they say things such as: "it would be nearly impossible for a series of random mutations to produce X" which they will often back up with some ridiculous mathematical formula which shows how improbabilities multiply throughout the chain of events.
These sort of statements often signal that the speaker doesn't really understand the concept of a priori probability and statistics and when and where such concepts can be applied.
I agree that the defeat of Operation Barbarossa was a turning point. But a big reason for the failure of Barbarossa was the fact that Mussolini got into such a quagmire in Albania. In response to the Italian invasion of Greece through Albania, the Greeks managed to beat back the Italians, occupying the southeastern part of the country, handing Mussolini a substantial defeat. To protect his southern flank prior to Barbarossa, Hitler was forced to contain the Greeks, moving some resources there to bail out il Duce. As a consequence, Barbarossa didn't get off the ground until well into June. If they'd been able to roll in March/April as was the original intention, things on the Eastern Front may have gone differently. As a previous poster had indicated, Stalingrad was pretty much the turning point and it's quite likely that Stalingrad would have fallen if the Nazis had arrived there two to three months earlier. So, in some sense, it's all linked together. The Greeks kept the Axis occupied long enough to delay the invasion of the USSR which meant that winter killed the advance at the critical stage.
There are a variety of examples but I'll quote only a couple and leave others to the reader.
The northern redbelly dace, Phoxinus eos (Cope 1861), and the finescale dace, Phoxinus neogaeus Cope 1867, are two cyprinid fishes native to North America that are known to exist in stable assemblages with their hybrids. Such assemblages are composed frequently of both diploid and polyploid members and may be supported at least partly by gynogenesis. A number of genetic and other studies exist, some of which can be found through a Google search. This is a particularly fascinating example since it points out how narrow our focus is if we fail to account for asexual reproductive possibilities.
A second simple example is what some researchers have begun to call the Canis (wolf) complex, all the members of which appear to be able to interbreed and to produce fertile offspring. Nowak (1992), among others, has suggested that the red wolf, Canis lupus rufus appears to be on the verge of being subsumed into the coyote Canis latrans genome but he feels that this interbreeding has largely occured over the last century or so and that, prior, they were entirely distinct genotypes separated geographically by differing habitat dependencies.
Finally, I'd raise the example of the lake trout, Salvelinus namaycush (Walbaum in Artedi 1792) and the brook trout, Salvelinus fontinalis (Mitchill 1814), two species of salmonid fishes which are known to produce fertile hybrid offspring through artificial propagation but appear to be largely prevented from hybridising more than very infrequently by behavioural separation, even where the species exist sympatrically.
Now, it's true that these sorts of closely-related species can cause us to examine how it is we define species. Who knows, perhaps one day we'll arrive at the point where we classify all of the canids as a single species, for example. We're certainly not at that point right now, though, and most wolf researchers would suggest that it's unlikely that that will be the outcome.
In terms of the animal kingdom, the concept of 'species' may easily be understood in terms of the concept of breeding. When two organisms cannot produce fertile offspring, they are separate species. This is a well defined barrier. A population does not become a new species overnight.
This is an incredible oversimplification, especially when you realise that asexual reproduction is very common in the animal kingdom. The idea you quote is often cited but is, in itself, an insufficient criterion. For example, there are organisms which can interbreed and can produce fertile offspring that are clearly considered separate species by any objective measure. In many species, lots of individuals are incapable of interbreeding with lots of individuals of the same species. Interbreeding is a complex thing that synthesises anatomical, behavioural, geographical and genetic components. A failure in any of these can cause a failure to interbreed which does not necessarily equate to a different species. There are also complexes of closely related species that interbreed frequently and produce fertile offspring but they are still distinct species.
In any case, TFA is about bacteria and not animals. The principle of using inability to interbreed as a definition of species in animals is even more removed from reality in bacteria which often share genetic material across species, even species that are not closely related.
Finally, the postulate that two creatures that are functionally similar within a diverse community, despite genetic dissimilarity, might not be considered different species is simply ludicrous. For example, in fish community assemblages, there are normally planktivores and piscivores. From a broad community perspective, the top-level piscivores all perform precisely the same function. No one, however, would argue that that makes them the same species. By way of illustration, the lake trout in a salmonid/coregonid community fulfills the same functional role as the northern pike in an esocid/coregonid community. That doesn't make lake trout and northern pike the same species.
In my estimation, the most useful statistics text ever written is Draper and Smith's "Applied Regression Analysis" (ISBN 0-471-17082-8). I know that that book caused me to write more computer algorithms than any other book I've ever read.
Slashdot Mirror
The probe started out at roughly our speed and accelerated to 34,471 mph, or about 15.4 km/s. In the absence of a complex acceleration history, the simple, first-order approximation of the probe's average speed over the last 6 years is about 7.7 km/s or about 2.6e-5 c. At that speed, the relativistic effect is about 0.99999999967015470011, meaning that the probe has aged about 62 milliseconds less than you have.
Oops! Sorry, Samantha but it seems even a biologist can just be plain wrong sometimes. (Don't mind me cuz I'm a biologist,too.) If pandas are marsupials I'll eat my hat...
I don't do a lot of editing of text over images, so this might be a stupid question, but couldn't you just add and position the image after you've done typing?
I don't know how to address this in other operating systems but, in GNOME on GNU/Linux, you can get around case 1 by checking the "Disable trackpad whilst typing" option.
I'm afraid this is just silly.
There is a very simple action that would invalidate the claims of atheists: that would be for a god, any god, to reveal himself in some obvious, unequivocal, unmistakable way. Like, pop up on the nightly news and heal an amputee or something.
The theists, on the other hand, are the ones making the unfalsifiable claims. They're the ones claiming that there exists a sky fairy who chooses to keep himself hidden from man and whose presence can only be intimated by reading an ancient book or books with the aid of some sort of secret decoder ring.
Please, put aside your rancour for a second and tell me, truthfully, which side is making a claim which cannot be falsified...
Oh, wait, you're an AC. I should have known better than respond because you're only here to make yourself feel like you're too good to be living in mommy's basement among piles of pizza boxes and soiled Kleenex.
Well, okay. You're right, it's all just fun and games at this point.
In any case, Einstein was not the issue. Everything that Einstein knew, the Germans knew since it had all been published in readily-available journals. Einstein really had nothing to do with the development of the bomb aside from the theoretical underpinnings, known to the Germans, and a letter he wrote to the POTUS.
Now, if you had spoken in the same terms of Oppenheimer, I might have said, "Game on!" :-)
All of this is somewhat simplistic speculation. If you'd refused to sell oil to Hitler he'd have been forced to launch for the Caucusus sooner, maybe even before the Western front had been opened. For sure, Hitler burned up a lot of oil before Barbarossa in 1942; oil that he'd have had to take by force if you controlled supplies and refused to sell to him.
So, after the Anschluss and the taking of Poland, maybe he'd have just rolled on into Russia instead of turning to fight France. If Hitler had gone east first, he'd have pissed off a whole lot fewer people who mattered. The only real reason the Yanks supported the war in Europe at all was because of Britain and France. If it was just a war against Stalin, lots of people would have just figured "Hell, let 'em go at it."
As for the nuclear program, the Germans had a well developed nuclear program without Einstein. They may have been just months away from developing a full-blown nuclear weapon when the end rained down upon them. If VE Day had been delayed by even a few months, the Germans might well have beaten the US to the bomb.
Consequently, all the rest of your post about WWII never happening might also be just a fantastical contruction. There are those who have speculated that time is less like an arrow and more like a meandering river, with currents and eddies.
At the end of the day, though, your post can really be summed up as: "If things had been different, they might not have turned out the same." That's trivially true but the radical departures from the historical timeline are not at all demonstrable by the type of argument you've launched here.
It's not dead, it's just pining -- pining for the fjords.
So, if I'm sitting on the couch and I can just make out a dime on the windowsill across the room, the whole street must be covered in dimes? This seems an odd view of reality but, hey, that's just me saying...
I'm interested in your statement that space-time is separable. Please explain, ideally, with the appropriate references.
It would appear to me that saying that time is independent of space is like saying that the length and width of a rectangle can exist separately of each other. I also am dubious of your contention that two independent things are, of neccessity, separable. I may be able to independently set the length and width of a rectangle that I draw but that does not make them separable since it ceases to be a rectangle without one of those components.
Your wife should make sure to wear her favourite perfume regularly and buy some bottles for the girls -- put the bottles away until they get a little older. You could also take her pillow and blankets and put them in one of those plastic things that you vaccuum the air out of. Take the blankets and pillow out when one of the girls is feeling badly (after a bad breakup with a boyfriend, say) and let her curl up on the couch with them. If you reseal them in the bag every time, the smell should last quite a while...
Just some off the wall ideas but I can tell you that the thing I miss most about my wife is her smell...
You're right, of course. I'd intended to say that wheat protein is 13 to 23% gluten, although, admittedly, I was pulling those numbers from an increasingly feeble memory. Thanks for catching that and correcting the record.
Historically, grains were a much poorer source of gluten than they are now. Through selective breeding and through milling processes that refine flour, wheat flour is now 13 to 23% gluten, depending on a number of factors, with whole grain flour being nearer the lower end of that range.
In addition, wheat generally and gluten specifically have become ubiquitous in the foods we eat. For example, soy sauce, which can easily be made gluten free, is often mainly wheat nowadays, especially the Japanese varieties of soy sauce. In the past, a person's gluten exposure was probably comparatively low and, combined with shorter life expectancies, gluten allergies were not as problematic.
Today, with wheat being in all sorts of foodstuffs, gluten allergies are becoming increasingly common, especially among middle-aged and elderly people. Our systems simply become so overwhelmed with gluten that the allergic inflammatory responses become a source of serious illness in some people. When coupled with the malabsoprtion syndrome that accompanies it, since an inflamed, damaged intestinal system absorbs poorly, vitamin deficiencies (especially vitamins E, D and K) gluten allergies cause real illness in many people.
Such illnesses probably remained sub-clinical in people in previous centuries but now, aided by enhanced severity, we better understand what's happening and we are better able to diagnose the trouble.
As for peanuts, just think of how peanuts have become readily available the world over and how they are contained in all sorts of foods, now. Historically, peanuts were a local food that formed a small part of the diet for people in areas near where they were found. In ways similar to what I mentioned above, peanut allergies are much more common and much more severe than ever before.
HTH
Actually, no... Sauerbraten is a type of roast, often beef but sometimes venison or such. Just because the 'brat' part is also in the famous sausage 'bratwurst' does not make it sausage. Actually, it's the 'wurst' part that translates as sausage. Sauerbraten is usually 'soured' by marinating and cooking the roast in a mixture of wine and vinegar. 'Braten' is the German word for 'to roast', as in the common saying: "Eine gut gebratene Gans is eine gute Gabe Gottes."
A nanodot is 1/1000 of a microdot. I suppose that will work for memory. All I know is I did a microdot a few times and had trouble remembering much of anything afterwards.
This is so incredibly simple that I can't believe I'm reading scores of responses about significant digits and rounding, etc. For a motion to be passed by a 2/3 majority, at least twice as many people have to vote in favour as those who vote against. Since 136 is less than 70*2, the vote fails. No calculator required, no consideration of significant digits. It's the kind of thing a reflective schoolchild should be able to reason out, frankly.
I think this is a symptom of a generation raised with calculators...
Perhaps, and I have no difficulty leaving it at that, especially for brevity's sake. But what the original poster was reacting to and what I was supporting him on was this passage from TFA:
You see, he said it would be "unlikely... to find it... [there]". That's what this discussion was about. Whether finding an unlikely thing is sufficient to say that we need to re-examine our cosmological models. Even the summary's title is mired in histrionics. The researchers found an unlikely thing in an unusual place and this becomes "Astrophysicists Find 'Impossible' Planet". The point the OP, who I was supporting, was making is that it seems strange to suggest that finding an odd thing in an unlikely place can be construed as being "impossible" or revolutionary.
What Hellier said (at least according to the article) was that this condition should be so short-lived and hard to find that finding it is "unlikely". I liken that to saying that some esoteric sub-atomic particle with an incredibly short half-life is hard to find. If we just happen to see one by chance, though, does that fact alone make it revolutionary? Does the fact that it has a short life mean that finding it, even by accident, would be "impossible"?
Anyway, thanks for your contributions. I enjoyed reading them.
Ummmm, no. Presumably, we are sighting essentially random plants from some larger population of planets. This is not at all like dealing a succession of highly unlikely hands in bridge because we've seen a single instance of this phenomenon, just like the hand you've been dealt in bridge is a single instance of that seemingly unlikely hand. It's the exact same circumstance.
It's like a genetic disorder with odds of 1 in 10000 live births. If I happen to be visiting the hospital this afternoon and it just so happens that the only child born at that hospital has that disorder, what does that tell me about how rare the event is? Answer: nothing at all. The probability of a single event is not revealed or influenced by whether or not I witness it.
If I see a rare thing happen, all that says is that I randomly was present when it happened. It doesn't mean I should run out and buy a lottery ticket nor does it mean that I should re-examine the models of probability that reveal the likelihood of an event's occurence.
As another poster stated elsewhere in this thread, it may be highly unlikely that any specific individual should win the lottery tonight but, nonetheless, it will happen that someone wins it. The probability of the event is 100%. The probability of it striking a specific individual is small.
And so it is with this planet. The probability of seeing such an event can be small but that does not imply, in any way, that seeing the event means that the probability calculation is wrong and that we need to re-examine our models. I would admit that , if we saw some succession of these events we might be able to say something about the model but a single observation says nothing at all about it -- other than the trivial fact that the probability of occurrence must be non-zero.
You are correct. By way of illustration, consider the following. In a bridge game I, as the dealer, distribute the cards resulting in an assemblage of four distinct hands. What is the probability of any single deal producing that particular constellation of hands? The rigorous answer is 1 in 52!/(13!)^4 = 1/53,644,737,765,488,792,839,237,440,000. Clearly, it is exceedingly unlikely that I would have dealt those specific hands but, yet, here we are... By the way, this is the precise error that you frequently see Intelligent Design people make when they say things such as: "it would be nearly impossible for a series of random mutations to produce X" which they will often back up with some ridiculous mathematical formula which shows how improbabilities multiply throughout the chain of events. These sort of statements often signal that the speaker doesn't really understand the concept of a priori probability and statistics and when and where such concepts can be applied.
I agree that the defeat of Operation Barbarossa was a turning point. But a big reason for the failure of Barbarossa was the fact that Mussolini got into such a quagmire in Albania. In response to the Italian invasion of Greece through Albania, the Greeks managed to beat back the Italians, occupying the southeastern part of the country, handing Mussolini a substantial defeat. To protect his southern flank prior to Barbarossa, Hitler was forced to contain the Greeks, moving some resources there to bail out il Duce. As a consequence, Barbarossa didn't get off the ground until well into June. If they'd been able to roll in March/April as was the original intention, things on the Eastern Front may have gone differently. As a previous poster had indicated, Stalingrad was pretty much the turning point and it's quite likely that Stalingrad would have fallen if the Nazis had arrived there two to three months earlier. So, in some sense, it's all linked together. The Greeks kept the Axis occupied long enough to delay the invasion of the USSR which meant that winter killed the advance at the critical stage.
All we are saying is give peas a chance -- power to the vegetables!
(with thanks to the Arrogant Worms)
There are a variety of examples but I'll quote only a couple and leave others to the reader.
The northern redbelly dace, Phoxinus eos (Cope 1861), and the finescale dace, Phoxinus neogaeus Cope 1867, are two cyprinid fishes native to North America that are known to exist in stable assemblages with their hybrids. Such assemblages are composed frequently of both diploid and polyploid members and may be supported at least partly by gynogenesis. A number of genetic and other studies exist, some of which can be found through a Google search. This is a particularly fascinating example since it points out how narrow our focus is if we fail to account for asexual reproductive possibilities.
A second simple example is what some researchers have begun to call the Canis (wolf) complex, all the members of which appear to be able to interbreed and to produce fertile offspring. Nowak (1992), among others, has suggested that the red wolf, Canis lupus rufus appears to be on the verge of being subsumed into the coyote Canis latrans genome but he feels that this interbreeding has largely occured over the last century or so and that, prior, they were entirely distinct genotypes separated geographically by differing habitat dependencies.
Finally, I'd raise the example of the lake trout, Salvelinus namaycush (Walbaum in Artedi 1792) and the brook trout, Salvelinus fontinalis (Mitchill 1814), two species of salmonid fishes which are known to produce fertile hybrid offspring through artificial propagation but appear to be largely prevented from hybridising more than very infrequently by behavioural separation, even where the species exist sympatrically.
Now, it's true that these sorts of closely-related species can cause us to examine how it is we define species. Who knows, perhaps one day we'll arrive at the point where we classify all of the canids as a single species, for example. We're certainly not at that point right now, though, and most wolf researchers would suggest that it's unlikely that that will be the outcome.
This is an incredible oversimplification, especially when you realise that asexual reproduction is very common in the animal kingdom. The idea you quote is often cited but is, in itself, an insufficient criterion. For example, there are organisms which can interbreed and can produce fertile offspring that are clearly considered separate species by any objective measure. In many species, lots of individuals are incapable of interbreeding with lots of individuals of the same species. Interbreeding is a complex thing that synthesises anatomical, behavioural, geographical and genetic components. A failure in any of these can cause a failure to interbreed which does not necessarily equate to a different species. There are also complexes of closely related species that interbreed frequently and produce fertile offspring but they are still distinct species.
In any case, TFA is about bacteria and not animals. The principle of using inability to interbreed as a definition of species in animals is even more removed from reality in bacteria which often share genetic material across species, even species that are not closely related.
Finally, the postulate that two creatures that are functionally similar within a diverse community, despite genetic dissimilarity, might not be considered different species is simply ludicrous. For example, in fish community assemblages, there are normally planktivores and piscivores. From a broad community perspective, the top-level piscivores all perform precisely the same function. No one, however, would argue that that makes them the same species. By way of illustration, the lake trout in a salmonid/coregonid community fulfills the same functional role as the northern pike in an esocid/coregonid community. That doesn't make lake trout and northern pike the same species.
Whenever I hear 'Portland' I immediately think of 'cement'.
In my estimation, the most useful statistics text ever written is Draper and Smith's "Applied Regression Analysis" (ISBN 0-471-17082-8). I know that that book caused me to write more computer algorithms than any other book I've ever read.