Neither of these has a uniform distribution. In the former example, lower numbers are more likely. In the latter example, higher numbers are more likely.
No, then zero will occur more often than other numbers.
I suppose xor ought to work if the two sources are totally unrelated. But then you have to be sure that they really are completely unrelated. For example, feed it the same source twice and all you get is zero.
So I imagine they must have done something a lot more clever than that.
You do have a point there. There are many ways of raising children, and the standards change all the time. Children should be punished regularly. No, they should not be punished at all, let them find their own way in life. No, wait, turns out that turns them into criminals and drug addicts, better punish them after all. But certainly not physically, we'll even outlaw that! Oh, wait, turns out that...
Same with breast feeding, which used to be bad (bottles were better, less bacteria, scientifically controlled nutrition, etc.) until they decided that breast feeding was actually better, and ads for baby formula were outlawed. I wouldn't be surprised if in a couple of decades women will be discouraged from breast feeding again.
I wonder what kind of "advice" my kids will get when they grow up.
So by all means, give some freedom to parents so they are not forced to follow the current "best practice" which will turn out to be wrong afterwards.
In this case, however, it's pretty clear that these children should be protected from their parents' ignorance.
BMW has a similar, simpler parking system where you can let the car move forward and backward while you're outside of it. Audi has shown prototypes navigating a parking garage by themselves. It's going to be a standard feature on high end cars very soon.
That's not the impression I get when I google car crash images. Some compact cars, like the old model Mercedes A-class, were indeed designed that way. But most larger cars apparently aren't. Or maybe the manufacturers claim that the engine goes underneath the car while in reality only a small part of it does.
The actual article is behind a pay wall, but the Daily Mail summary unambiguously says:
- That was finding of a study looking at particles from tyre and brake wear - Made heavier by batteries and parts meaning tyres and brakes wear faster
The Daily Mail article itself continues with multiple references to brake wear. Not once does it mention regenerative braking.
Now I do admit that I should know better than to assume that a Daily Mail article about a paper would be in any way related to the actual contents of the paper, and it's entirely possible that the actual paper, behind the paywall, says exactly the opposite. Maybe it will even say that EVs are cleaner after all.
That's not the impression I get after googling something like "Mercedes crash images" (just to pick a random luxury car brand). In head on collisions the mangled engine always seems to remain in front of the cabin. I can't find a single picture with an engine underneath the cabin.
I do remember Mercedes being very proud of that feature in their old A-class models. Those were indeed engineered that way. But for most other cars, the engine just stays in front.
The Tesla has a much better crumple zone in front because it doesn't have a huge heavy engine block in there. Just look at the pictures, the front end is essentially gone yet the passenger compartment is intact. I would say that's a pretty important advantage, and it may have been just the difference required to save their lives. If it had been a Mercedes, where would the engine have gone? Even if it didn't go into the cabin, it sure would have left much less room for crumpling to absorb the impact.
The passenger compartment is also extremely strong, they actually broke the testing equipment when they tried to crush the roof, for example. They overengineered the hell out of that car. Tesla is pretty new in the car business: when they designed the Model S they hadn't figured out yet that you have to compromise on safety if you want to compete in the market. They just made it as strong as they could. Fortunately the car is compelling enough that rich people don't mind spending the extra money. The Model 3 will probably be pretty safe, but I doubt it's going to break any testing equipment. For $35000 something will have to give.
Also, the car didn't catch fire. I know real cars don't automatically burst into flames while airborne like they do in the movies, but in this kind of crash some kind of fire would have been pretty likely. Here's one from not long ago, a crash between a Tesla and an ICE vehicle, the ICE caught fire while the Tesla didn't. Yes, I know, some Teslas have caught fire as well in other accidents but it was always after at least 10 minutes or so, giving people plenty of time to get out first. With an ICE, as soon as a fuel like breaks, you have to run away fast.
Pascal has pointers too. And recent versions are object oriented just like C++. There are a few minor differences in the way parameters are passed to subroutines, the way arrays are treated, and the existence of functions within functions, but other than that, is there really that much difference between them when it comes to safety?
I admit it's been almost 20 years since I last wrote something in Pascal, but I don't remember it being that different from C/C++. I had plenty of crashes due to null pointers when programming in Pascal, just like I did in C.
With "valid", I mean you can do all your calculations in that reference frame using all the same physical laws as any other observer, and make valid predictions that can later be verified to be correct.
That's just basic special relativity, and has been verified extensively.
I'm not saying time is going backwards. Just that, if you could send a message faster than light, you could also send a message back in time to yourself via a third person. That makes it rather unlikely for faster than light transmission to be possible.
In the example I gave, Alice sent a message to Bob, who passed it to Carol, who then sent it back to Alice. Alice received the message before she sent it. She sent the message, and her perception says that she did indeed receive it before she sent it.
Her perception is that the message traveled instantaneously to Bob, and was subsequently sent back in time by Carol.
Carol's perception is that the message traveled back in time from Alice to Bob, then traveled instantaneously back to Alice.
As usual with relativistic paradoxes, different observers describe the same events in a different way but confirm the same actually observable result: Alice receives the message before she sent it.
The question about why instantaneous transmission enables messages to travel back in time is described here as well.
Asteroids tend to burn up in the atmosphere because they are coming straight towards us at very high speed. If you just put an asteroid into a low orbit inside the upper atmosphere where friction will let the orbit degrade until it comes down, it won't heat up nearly as much. Sure, it will still be a big ball of fire and make a pretty noisy impact, but nothing like the Arizona Meteor Crater. You'll be able to recover more than half of the material it contains. All you need to be able to do, is aim well and avoid airplanes.
If you can enclose the whole asteroid in some kind of hull with heat shields, retrograde rockets and parachutes, you may even be able to bring the whole thing down in one piece intact.
But maybe I've just been playing too much Kerbal Space Program...
You talk about "apparent" simultaneity as apposed to real simultaneity, but actually "apparent" simultaneity is the only kind of simultaneity that exists. I think that's the crucial bit of understanding you're still missing. Einsteins's big discovery was not the Lorentz transform (which was, obviously, named after Lorentz for a reason as he discovered it much earlier) but the realisation that appearances (things appear to shrink, clocks appear to tick more slowly, clocks appear to be out of sync) are actually real.
"Simultaneous" means: having the same time coordinate in the system of coordinates that you happen to be using. If one observer puts a label "12:00:00" onto two events in two different locations, that means he considers these to be simultaneous. Somebody else will put different time labels onto those events and say one occurred before the other.
The most important thing about relativity is: that really is all there is! People put labels onto things and use them to do calculations. Reality doesn't care, it only cares about actual interactions and, presumably, causality, but not where and when they occured precisely. They don't have "true coordinates", not in space and not in time. There's no such thing as absolute simultaneity, there can only be perceived simultaneity because no other kind exists. It's like absolute speed, there's no such thing, speed can only be measured relative to an observer.
If two observers with a different speed measure the speed of a particular ray of light, they will both measure it to be c relative to themselves, and therefore something other than c relative to the other observer. This means they disagree on the speed of that ray of light, and will therefore also disagree on when that ray of light left its source. One will say it left there yesterday, the other will say it left there two days ago. Both are correct, and it makes no sense to ask "but when did it really leave". When you ask "when", you're asking for a time coordinate, and you can only give that time coordinate if you pick a reference frame first. Otherwise the word "when" has no meaning. The answer to "when did the ray of light leave" can only be "it left yesterday if you use the first observer's coordinate system, or the day before yesterday if you use the second observer's coordinate system". When did it really leave? I just told you. There is no other answer.
If you look at the Lorentz transform ( t' = (t - v*x/c^2)/sqrt(1-(v/c)^2) ), it clearly contains an "x" in the transformation formula for time. Think about that for a moment. You know that moving clocks tick more slowly, hence the sqrt(1-(v/c)^2), but what's the x doing in the numerator there? It means that two events that are simultaneous for one observer (same t, different x) will have two different time coordinates t' for another observer and will therefore not be simultaneous from his point of view. Motion tilts the axis of simultaneity but since no observer is in any way better than any other, they are all "correct".
My point with the MET examples is that, although a message may be instantaneous for one observer, it travels back in time from a different observer's point of view and these observers are both correct.
When describing his special theory of relativity, Einstein didn't just say that the speed of light was the same for any observer. He actually said all the laws of physics are the same. In my example with Alice, Bob and Carol, Carol's view of the universe is just as correct as all the others. If Alice can send an instantaneous message to Bob in her reference frame, there's no reason why Carol wouldn't be able to send a message that arrives instantaneously in her reference frame. Both reference frames are just as valid, Carol is allowed to say that she is standing still while Alice and Bob are moving. Yet she can witness the transmission of the message from Alice to Bob and the only conclusion she can come to is that that message did, in fact, travel back in time. And from th
If probiotics really contained bacteria that could survive in our gut and make us healthier, we would just need to take one single dose and the company would not make any money on them.
So instead, I suspect they contain bacteria that may provide some short term benificial effects, but are not really suited for our gut and disappear shortly afterwards. That way, you need to take them repeatedly and keep spending money on them.
So if you want a healthy gut, probiotics are not the answer.
It's not even a test of reaction times. They asked people to predict whether the circle was going to be red (without them communicating it in any way, it's just them thinking "I think it's going to be red"), then the circle was shown (red or not), and then the people were asked to say whether or not their prediction had been correct. So they may have thought "it's not going to be red", then saw a red circle, then said "I knew it was going to be red".
All the study shows (if that), is that people might remember having made a choice while in reality they really hadn't made that choice (no choice at all, or a different one).
How this is related to free will is anyone's guess. It may just be a demonstration of poor memory.
Anyway, we already knew that people were quite capable of overestimating their free will. In trials with split brain patients, they gave different pictures to the different halves of a person's brain and asked one half to perform the task (write with the hand connected to that half of the brain) while the other half had to explain why he gave that seemingly wrong answer. The halves were still convinced they were one person, with one half doing its best to explain why it made that choice even though it was the other half that did it.
Now that's what I call an interesting experiment about free will. But this one... nah, it's just stupid.
Relativistic effects are not "apparent", they are real. If one of two twin brothers flies away at high speed and then comes back, he really will have aged less. This has been proven with atomic clocks on board of Concorde airplanes and has to be taken into account by GPS navigation systems (along with gravitational effects on top of that). Lorentz contraction, too, is very real. Let me give you one example of the latter, which is also a great example of the relativity of simultaneity (real simultaneity, not just apparent).
Two trains are approaching each other head on on a single track. Both are 100 meters long when they are at rest. Between them, there's a small train station with a switch on every side and a section of double track in between, allowing trains to pass each other. Problem is, this section of double track is only 80 meters long. The trains can't possibly pass each other there, right? Wrong. All they have to do is accelerate to 0.6 c. The Lorentz contraction shrinks the trains to 80% of their normal length, and they can pass each other just fine. The front of the first train passes the back of the second train on one side, while the front of the second train passes the back of the first train on the other side, at exactly the same time. It gets more interesting, though, if you look at this from a point of view on board one of the trains. From that point of view (and that's not just a perception, but your reality which you can check using any measurement method you like), your train really is 100 meters long since it is not moving relative to you. The section of double track that is coming towards you, however, is traveling at a speed of 0.6 c towards you and has therefore shrunk from 80 meters to just 64 meters! How can you possibly pass the other train then? Fortunately, if you measure the speed of the other train, it is traveling at a speed of just over 0.88 c (the "relativistic addition" of 0.6 c + 0.6 c). That means it has contracted to a mere 47 meters in length. This is where it gets really interesting: from your point of view, the front of your 100 meter long train reaches the end of the 64 meter double track exactly when the end of the 47 meter long train has passed that switch. That train still has 17 meters of track to go, which it will cover in 17 m / (0.88 c - 0.6 c) = about 0.2 microseconds. That gives the back of your 100 meter long train just enough time to clear the other switch before the front of the other train gets there. (100 m - 64 m) / (0.6 c) = the same 0.2 microseconds See what happened there? Two observers do not agree on the length of the trains, nor on the simultaneity of the passages on the two sides, yet both agree that the trains pass each other just fine. From one point of view, the two trains are 80 meters long and pass each other simultaneously on the 80 meter track. From the other point of view, the 100 meter train just misses the back of the 47 meter train on one end of the 64 meter track, and a very short time later the back of the 100 meter long train misses the front of the 47 meter long train at the other end.
And most importantly, neither of these points of view is better than the other! In each reference frame, some things are shrunk, and the passage would not work without this. Which parts are shrunk, and which parts are "normal", depends on the observer. But no matter what point of view you take, the effects are real because without relativity, those trains could never pass each other. Also, relativity of "real" simultaneity is vital to the solution of the paradox.
Now, if you can send a message "instantaneously" from one switch to the other in the station's reference frame precisely when the trains are passing each other, and then send it back "instantaneously" from the point of view of the train that's just reaching that second switch, it will have traveled back in time because at that moment, from the point of view of the train, its back end has not reached the first switch yet.
Slashdot Mirror
Neither of these has a uniform distribution. In the former example, lower numbers are more likely. In the latter example, higher numbers are more likely.
And the secret algorithm is... multiplication!
No, then zero will occur more often than other numbers.
I suppose xor ought to work if the two sources are totally unrelated. But then you have to be sure that they really are completely unrelated. For example, feed it the same source twice and all you get is zero.
So I imagine they must have done something a lot more clever than that.
Hell, even their CEO is a foreign worker!
You do have a point there. There are many ways of raising children, and the standards change all the time. Children should be punished regularly. No, they should not be punished at all, let them find their own way in life. No, wait, turns out that turns them into criminals and drug addicts, better punish them after all. But certainly not physically, we'll even outlaw that! Oh, wait, turns out that...
Same with breast feeding, which used to be bad (bottles were better, less bacteria, scientifically controlled nutrition, etc.) until they decided that breast feeding was actually better, and ads for baby formula were outlawed. I wouldn't be surprised if in a couple of decades women will be discouraged from breast feeding again.
I wonder what kind of "advice" my kids will get when they grow up.
So by all means, give some freedom to parents so they are not forced to follow the current "best practice" which will turn out to be wrong afterwards.
In this case, however, it's pretty clear that these children should be protected from their parents' ignorance.
Oh, I had no idea magnification could be expressed in Watts. You learn something new every day.
Hey, you don't get to see a "high-powered" camera every day! Regular cameras, sure. But high-powered ones?
Anonymous Coward didn't date Jennifer Anniston.
BMW has a similar, simpler parking system where you can let the car move forward and backward while you're outside of it. Audi has shown prototypes navigating a parking garage by themselves. It's going to be a standard feature on high end cars very soon.
So now my question is - why did this goofball park his car on the wrong side of the road?
Or: why did the Tesla cross the road?
And it live-streamed it on Periscope, too!
That's not the impression I get when I google car crash images. Some compact cars, like the old model Mercedes A-class, were indeed designed that way. But most larger cars apparently aren't. Or maybe the manufacturers claim that the engine goes underneath the car while in reality only a small part of it does.
Great, now all you need to do is run your algorithm in reverse!
The actual article is behind a pay wall, but the Daily Mail summary unambiguously says:
- That was finding of a study looking at particles from tyre and brake wear
- Made heavier by batteries and parts meaning tyres and brakes wear faster
The Daily Mail article itself continues with multiple references to brake wear. Not once does it mention regenerative braking.
Now I do admit that I should know better than to assume that a Daily Mail article about a paper would be in any way related to the actual contents of the paper, and it's entirely possible that the actual paper, behind the paywall, says exactly the opposite. Maybe it will even say that EVs are cleaner after all.
That's not the impression I get after googling something like "Mercedes crash images" (just to pick a random luxury car brand). In head on collisions the mangled engine always seems to remain in front of the cabin. I can't find a single picture with an engine underneath the cabin.
I do remember Mercedes being very proud of that feature in their old A-class models. Those were indeed engineered that way. But for most other cars, the engine just stays in front.
Yep, the one where they claim that electric vehicles' brake pads wear more quickly. That should give you a hint about the quality of their research.
The Tesla has a much better crumple zone in front because it doesn't have a huge heavy engine block in there. Just look at the pictures, the front end is essentially gone yet the passenger compartment is intact. I would say that's a pretty important advantage, and it may have been just the difference required to save their lives. If it had been a Mercedes, where would the engine have gone? Even if it didn't go into the cabin, it sure would have left much less room for crumpling to absorb the impact.
The passenger compartment is also extremely strong, they actually broke the testing equipment when they tried to crush the roof, for example. They overengineered the hell out of that car. Tesla is pretty new in the car business: when they designed the Model S they hadn't figured out yet that you have to compromise on safety if you want to compete in the market. They just made it as strong as they could. Fortunately the car is compelling enough that rich people don't mind spending the extra money. The Model 3 will probably be pretty safe, but I doubt it's going to break any testing equipment. For $35000 something will have to give.
Also, the car didn't catch fire. I know real cars don't automatically burst into flames while airborne like they do in the movies, but in this kind of crash some kind of fire would have been pretty likely. Here's one from not long ago, a crash between a Tesla and an ICE vehicle, the ICE caught fire while the Tesla didn't. Yes, I know, some Teslas have caught fire as well in other accidents but it was always after at least 10 minutes or so, giving people plenty of time to get out first. With an ICE, as soon as a fuel like breaks, you have to run away fast.
Pascal has pointers too. And recent versions are object oriented just like C++. There are a few minor differences in the way parameters are passed to subroutines, the way arrays are treated, and the existence of functions within functions, but other than that, is there really that much difference between them when it comes to safety?
I admit it's been almost 20 years since I last wrote something in Pascal, but I don't remember it being that different from C/C++. I had plenty of crashes due to null pointers when programming in Pascal, just like I did in C.
With "valid", I mean you can do all your calculations in that reference frame using all the same physical laws as any other observer, and make valid predictions that can later be verified to be correct.
That's just basic special relativity, and has been verified extensively.
I'm not saying time is going backwards. Just that, if you could send a message faster than light, you could also send a message back in time to yourself via a third person. That makes it rather unlikely for faster than light transmission to be possible.
In the example I gave, Alice sent a message to Bob, who passed it to Carol, who then sent it back to Alice. Alice received the message before she sent it. She sent the message, and her perception says that she did indeed receive it before she sent it.
Her perception is that the message traveled instantaneously to Bob, and was subsequently sent back in time by Carol.
Carol's perception is that the message traveled back in time from Alice to Bob, then traveled instantaneously back to Alice.
As usual with relativistic paradoxes, different observers describe the same events in a different way but confirm the same actually observable result: Alice receives the message before she sent it.
The question about why instantaneous transmission enables messages to travel back in time is described here as well.
Asteroids tend to burn up in the atmosphere because they are coming straight towards us at very high speed. If you just put an asteroid into a low orbit inside the upper atmosphere where friction will let the orbit degrade until it comes down, it won't heat up nearly as much. Sure, it will still be a big ball of fire and make a pretty noisy impact, but nothing like the Arizona Meteor Crater. You'll be able to recover more than half of the material it contains. All you need to be able to do, is aim well and avoid airplanes.
If you can enclose the whole asteroid in some kind of hull with heat shields, retrograde rockets and parachutes, you may even be able to bring the whole thing down in one piece intact.
But maybe I've just been playing too much Kerbal Space Program...
You talk about "apparent" simultaneity as apposed to real simultaneity, but actually "apparent" simultaneity is the only kind of simultaneity that exists. I think that's the crucial bit of understanding you're still missing. Einsteins's big discovery was not the Lorentz transform (which was, obviously, named after Lorentz for a reason as he discovered it much earlier) but the realisation that appearances (things appear to shrink, clocks appear to tick more slowly, clocks appear to be out of sync) are actually real.
"Simultaneous" means: having the same time coordinate in the system of coordinates that you happen to be using. If one observer puts a label "12:00:00" onto two events in two different locations, that means he considers these to be simultaneous. Somebody else will put different time labels onto those events and say one occurred before the other.
The most important thing about relativity is: that really is all there is! People put labels onto things and use them to do calculations. Reality doesn't care, it only cares about actual interactions and, presumably, causality, but not where and when they occured precisely. They don't have "true coordinates", not in space and not in time. There's no such thing as absolute simultaneity, there can only be perceived simultaneity because no other kind exists. It's like absolute speed, there's no such thing, speed can only be measured relative to an observer.
If two observers with a different speed measure the speed of a particular ray of light, they will both measure it to be c relative to themselves, and therefore something other than c relative to the other observer. This means they disagree on the speed of that ray of light, and will therefore also disagree on when that ray of light left its source. One will say it left there yesterday, the other will say it left there two days ago. Both are correct, and it makes no sense to ask "but when did it really leave". When you ask "when", you're asking for a time coordinate, and you can only give that time coordinate if you pick a reference frame first. Otherwise the word "when" has no meaning. The answer to "when did the ray of light leave" can only be "it left yesterday if you use the first observer's coordinate system, or the day before yesterday if you use the second observer's coordinate system". When did it really leave? I just told you. There is no other answer.
If you look at the Lorentz transform ( t' = (t - v*x/c^2)/sqrt(1-(v/c)^2) ), it clearly contains an "x" in the transformation formula for time. Think about that for a moment. You know that moving clocks tick more slowly, hence the sqrt(1-(v/c)^2), but what's the x doing in the numerator there? It means that two events that are simultaneous for one observer (same t, different x) will have two different time coordinates t' for another observer and will therefore not be simultaneous from his point of view. Motion tilts the axis of simultaneity but since no observer is in any way better than any other, they are all "correct".
My point with the MET examples is that, although a message may be instantaneous for one observer, it travels back in time from a different observer's point of view and these observers are both correct.
When describing his special theory of relativity, Einstein didn't just say that the speed of light was the same for any observer. He actually said all the laws of physics are the same. In my example with Alice, Bob and Carol, Carol's view of the universe is just as correct as all the others. If Alice can send an instantaneous message to Bob in her reference frame, there's no reason why Carol wouldn't be able to send a message that arrives instantaneously in her reference frame. Both reference frames are just as valid, Carol is allowed to say that she is standing still while Alice and Bob are moving. Yet she can witness the transmission of the message from Alice to Bob and the only conclusion she can come to is that that message did, in fact, travel back in time. And from th
If probiotics really contained bacteria that could survive in our gut and make us healthier, we would just need to take one single dose and the company would not make any money on them.
So instead, I suspect they contain bacteria that may provide some short term benificial effects, but are not really suited for our gut and disappear shortly afterwards. That way, you need to take them repeatedly and keep spending money on them.
So if you want a healthy gut, probiotics are not the answer.
I wonder how far these record attempts are going to go. Before long, people will be spending a year in VR to beat the record.
It's not even a test of reaction times. They asked people to predict whether the circle was going to be red (without them communicating it in any way, it's just them thinking "I think it's going to be red"), then the circle was shown (red or not), and then the people were asked to say whether or not their prediction had been correct. So they may have thought "it's not going to be red", then saw a red circle, then said "I knew it was going to be red".
All the study shows (if that), is that people might remember having made a choice while in reality they really hadn't made that choice (no choice at all, or a different one).
How this is related to free will is anyone's guess. It may just be a demonstration of poor memory.
Anyway, we already knew that people were quite capable of overestimating their free will. In trials with split brain patients, they gave different pictures to the different halves of a person's brain and asked one half to perform the task (write with the hand connected to that half of the brain) while the other half had to explain why he gave that seemingly wrong answer. The halves were still convinced they were one person, with one half doing its best to explain why it made that choice even though it was the other half that did it.
Now that's what I call an interesting experiment about free will. But this one... nah, it's just stupid.
Relativistic effects are not "apparent", they are real. If one of two twin brothers flies away at high speed and then comes back, he really will have aged less. This has been proven with atomic clocks on board of Concorde airplanes and has to be taken into account by GPS navigation systems (along with gravitational effects on top of that). Lorentz contraction, too, is very real. Let me give you one example of the latter, which is also a great example of the relativity of simultaneity (real simultaneity, not just apparent).
Two trains are approaching each other head on on a single track. Both are 100 meters long when they are at rest. Between them, there's a small train station with a switch on every side and a section of double track in between, allowing trains to pass each other. Problem is, this section of double track is only 80 meters long. The trains can't possibly pass each other there, right? Wrong. All they have to do is accelerate to 0.6 c. The Lorentz contraction shrinks the trains to 80% of their normal length, and they can pass each other just fine. The front of the first train passes the back of the second train on one side, while the front of the second train passes the back of the first train on the other side, at exactly the same time.
It gets more interesting, though, if you look at this from a point of view on board one of the trains. From that point of view (and that's not just a perception, but your reality which you can check using any measurement method you like), your train really is 100 meters long since it is not moving relative to you. The section of double track that is coming towards you, however, is traveling at a speed of 0.6 c towards you and has therefore shrunk from 80 meters to just 64 meters! How can you possibly pass the other train then? Fortunately, if you measure the speed of the other train, it is traveling at a speed of just over 0.88 c (the "relativistic addition" of 0.6 c + 0.6 c). That means it has contracted to a mere 47 meters in length. This is where it gets really interesting: from your point of view, the front of your 100 meter long train reaches the end of the 64 meter double track exactly when the end of the 47 meter long train has passed that switch. That train still has 17 meters of track to go, which it will cover in 17 m / (0.88 c - 0.6 c) = about 0.2 microseconds. That gives the back of your 100 meter long train just enough time to clear the other switch before the front of the other train gets there. (100 m - 64 m) / (0.6 c) = the same 0.2 microseconds
See what happened there? Two observers do not agree on the length of the trains, nor on the simultaneity of the passages on the two sides, yet both agree that the trains pass each other just fine. From one point of view, the two trains are 80 meters long and pass each other simultaneously on the 80 meter track. From the other point of view, the 100 meter train just misses the back of the 47 meter train on one end of the 64 meter track, and a very short time later the back of the 100 meter long train misses the front of the 47 meter long train at the other end.
And most importantly, neither of these points of view is better than the other! In each reference frame, some things are shrunk, and the passage would not work without this. Which parts are shrunk, and which parts are "normal", depends on the observer. But no matter what point of view you take, the effects are real because without relativity, those trains could never pass each other. Also, relativity of "real" simultaneity is vital to the solution of the paradox.
Now, if you can send a message "instantaneously" from one switch to the other in the station's reference frame precisely when the trains are passing each other, and then send it back "instantaneously" from the point of view of the train that's just reaching that second switch, it will have traveled back in time because at that moment, from the point of view of the train, its back end has not reached the first switch yet.
By the way, this is a variation of the l