Page 16
E S S A Y S
By The Number
"Fred, this couple back here are all fired up about something."
Fig. 1.
e62
The Strange Case of the Kaboom in the Caboose
An Astrophysical Murder Mystery. Or was it a Double Suicide?
All aboard for understanding Albert Einstein's principles of Special Relativity! And why they're important. If you're willing to play along with me, we can play a little mind game together and have some fun in the process. And solve an intriguing railroad murder mystery while we're at it. However, before the engineer blows the locomotive's whistle and we start rolling down the tracks, it's necessary to first establish some facts of the case. At least the facts as they relate to an imaginary train ride that's about to get underway.
Number one on our list of things to remember is that everything we're about to discuss (and imagine) takes place in the last car of the train -- what used to be called the caboose. I don't know if trains still have cabooses or not, but this one does. A nice, old fashioned reddish one. Next on the list is the fact that the train tracks themselves run in an exactly north and south direction. We happen to be headed north, but we could have been traveling south just as well. The whistle just sounded up ahead; did you hear it? Those billows of steam wafting past us and the sudden jolt of the caboose have left no doubt that we've begun "chugging" along -- slow at first, but we can feel our acceleration (and excitement) increasing by the moment. Okay, so I'm easily thrilled.
The interior of the caboose is pretty sparse. Little more than four bare, wooden walls, a plain wood floor and slatted ceiling of thin planks. Also inside the car are its two sole occupants, a man and a woman whose names or other descriptions are entirely irrelevant to our story. So I left all that out. Feel free, however, to envision what these people look like, their age or whatever; makes no difference to me. One of them is about to die shortly -- the woman -- so we don't want things to get too personal, far as I'm concerned.
Something that is very relevant, though, is our next piece of information, which is the fact that the guy has a gun. A .45 caliber automatic to be specific. The pistol could just as easily have been a revolver, but I prefer an automatic and since I'm telling the story, I say it's an automatic. One additional thing you'll definitely need to know about the gun is going to sound dull, but trust me; it's more critical info that you need to remember. The muzzle velocity, which is to say, the speed of the bullet as it exits the barrel -- once the gun is fired (duhhh) -- is 850 feet per second, or about 580 miles per hour.
Talk about coincidences: that muzzle velocity stuff happens to be the exact same speed that our train is fast approaching. I checked with the engineer and despite my skepticism, he assured me that this particular train could travel that fast -- and safely. Which is to say (as if I had to) that our train will soon be hurtling down the tracks -- heading north -- at exactly 580 miles per hour. Or 850 feet per second, whichever suits you. Hard to believe, I know, but this locomotive is obviously motivated.
As the train reaches its maximum velocity and holds steady, I'll finish the basic setup inside the caboose. The woman is standing at the rear of the car, her back against the wall, her mouth frowning with pressed-together lips. She is staring at the man whose own back is against the forward wall of the caboose, and who is gazing back at the woman with a smirk on his face. That's because he's the one with the gun, which is raised and pointed at his fellow passenger. So let's make sure we've got everyone and everything in their proper place before going any further. There's also four, high-definition video cameras inside the car. One in each corner of where the walls and ceiling meet. If anything happens inside the caboose, we'll have a good photographic record of it.
The woman is facing the front of the caboose -- the front of the train -- both of which are heading north. The guy is turned in the opposite direction, facing the rear wall of the last car of the train, which has him looking directly south. Just to be clear, the gun he's holding is both pointed south and aimed at the lady's body. That now puts things and people in their final positions which will remain largely unchanged throughout the remainder of the events to follow.
It must have been a pretty serious argument the couple had prior to our eavesdropping on them, because the guy just fired the gun and shot his woman partner. Struck her right in the heart which meant she went fast with minimum discomfort. As she slumps unconscious to the floor, the first part of our little tale now concludes. Any questions? Let me jump in because I know just the right questions to ask, thanks. I know the perfect questions which will deconstruct the elapsed scenario in ways both unexpected and revelatory in nature. Let's get started and see if you're surprised by some of the answers we uncover.
First of all, remember that muzzle velocity business I mentioned earlier? I know it sounds cold and heartless to start talking mathematics and physics while the poor woman is collapsed against the rear wall, but I don't have time for the sentimental stuff, sorry. Now then, as I was saying, the muzzle velocity of the pistol, if you recall, is the same as the forward speed of the train as it travels down the tracks. The only difference is that the gun is pointed south while the train is charging north. Did anything unusual result because of this? In a subsequent review of the surveillance video from all the cameras, nothing seemed out of the ordinary. The entire event appeared to transpire in a manner that was completely unaffected by, and independent of, a really fast moving train. As seen by the two passengers inside the caboose, absolutely nothing out-of-the-ordinary took place. Which is a totally authentic, eyewitness report. Well, the woman wasn't exactly available for an interview afterwards, but we're pretty sure she'd agree to what the man testified was the case. But do you agree? And if not, why not?
I forgot to tell you about the fifth camera. Not really, I just didn't want to show my hand too soon. Did I mention that one of the side walls of the caboose is all glass, from front to rear, floor to ceiling? Guess I forgot that little tidbit also. No matter, the two new additions are only important to the final detail that will help us make sense of everything -- and solve the mystery! Which is likely more to do with what all this preliminary setup was for. The last detail is, in addition to another camera and the caboose fitted with a clear glass sidewall, the location of the extra camera. Placed far ahead of the fast-approaching train, the ultra high-definition movie camera is sitting atop a tripod (or whatever) and faces the tracks. The intended purpose of the camera was to capture a photographic record of the train as it passes. More specifically to photograph the caboose as it zoomed by with its glass wall, of course, facing the camera. Not coincidentally, the camera just happened to be rolling when the train passed its location, but more importantly, at the same exact moment when the man pulled the trigger and shot the woman. What were the odds?
This fifth (and stationary) camera will give us another view of whatever took place inside the caboose as it streaked by at 580 mph. The view of the scenery from inside the caboose must have been spectacular, but I digress. For now, we're more concerned with the view from outside, looking in. As you may have already guessed, the setup thus far is pretty straightforward and, except for the speed of the train itself, I've simply described a situation with which we're all familiar. Namely, how things look differently to a person inside a moving vehicle, compared to someone standing beside the road (in this case the train tracks) watching the person go by. For example, to the passenger inside the vehicle, it's the outside world that appears to be moving past the windows, while to spectators outside, it's obviously the vehicle which pulls away. Or try this: if the passenger was smoking a cigarette at the time (heaven forbid), the exhaled smoke would appear to hang motionless inside the vehicle. But to anyone watching the conveyance move away, both the smoker -- and the smoke -- would be moving along at whatever speed they were traveling. Whether at twenty mph -- or 580 mph. The reason the smoke "hangs" inside the vehicle, by the way, is because the air inside the compartment is carried along the same as everything else. But you knew that already. And if you didn't, then now you do.
Holy smoke, it's time we got back to our murder mystery, if you're still with me. I hope you are because this is really going to get good -- and spooky. Since we know that everything inside the caboose looked normal (too normal for the poor lady), it's time to examine what was recorded on the camera positioned right beside the tracks. Which should be pretty much the same as what the other cameras captured from the interior of the car, right? Wrong! What?
Let's quickly review: The man was backed up against the forward wall of the caboose, facing the rear wall. The woman was facing the man, her back to the rear wall of the car. He fired the pistol, she got shot, and until the police arrested him, that was about the sum of things. Okay so far. But here's where things get interesting. When police and lawyers examined and evaluated the recording made by the fifth camera, which shot the sequence of events as they sped by, the attorney for the accused pleaded innocent to all charges. The lawyer stated that, except for his client having pulled the trigger of the gun, the woman had clearly committed suicide. And he could prove it. What now follows is the case made by the defendant's lawyer.
Fortunately for the accused, the externally placed, stationary camera was equipped with a very sophisticated radar-style speed detector -- similar to what the police use when tracking speeders. Sure enough, the velocity of the northbound train as it passed was 580 mph. Or 850 feet per second. The unfired bullet chambered inside the .45 caliber automatic held by the man, was also moving, of course, at the same speed. When the guy squeezed the trigger, however, a funny thing happened. Well, the woman didn't think so, but we're getting ahead of ourselves. Or myself.
Once the round was discharged, so argued the defense attorney, the bullet actually began to slow down, to decelerate as it moved towards the end of the barrel. Remember that muzzle velocity business mentioned earlier? As you'll recall, muzzle velocity refers to the speed of a bullet as it leaves the opening of a gun's barrel. It differs according to the weapon used, but in our case, the velocity of a .45 caliber round is about 580 mph, give or take. Hmmm, there's a coincidence that didn't seem to matter before. As stated earlier, the muzzle velocity of the bullet is the same as the forward movement of the train -- just in the opposite direction. So what's the big deal? That's what the police wanted to know, also.
If you haven't already figured out where this is going, the answer is as follows: by the time the fired bullet reached the exit hole of the gun's barrel, it's "real" velocity was zero mph. In this case, the term, real, refers to an "objective" viewpoint that describes the difference between being involved -- and uninvolved -- in any given process. For all intents and purposes, as they say, the speed of the bullet had indeed decelerated to no-speed-at-all and under other circumstances, might well have just fallen straight to the floor. According to the cameras inside the caboose, however, the bullet retained its intended muzzle velocity, exited the barrel at exactly 850 mph, complete with recoil, flew across the car interior and hit the woman. Or rather -- she hit it. Say again?
That's when the defense attorney really got going. He pointed out that while it's true the discharged bullet was decelerating as it moved through the barrel, the barrel itself, including the gun, the man, the caboose, indeed the whole train, was simultaneously pulling away from the (now independent) round at the same speed of 580 mph. That wasn't all that was happening. Everything in front of the bullet was also rushing towards it at 580 mph. Including, of course, the woman. Thus by the time the bullet leaves the end of the barrel, the gun (and much of everything else) is long gone from it, and the woman has slammed head-on into it. As only lawyers can do, the defense attorney insists that the lady shot herself and had she simply stepped to one side, the rear wall of the car -- instead of her body -- would have impacted the spent round.
The police figured that a jury would never convict because of the seeming complexity of the case, and all charges were dropped. If you had been a member of that jury, you would have found the man guilty, though, right? Due to my excellent explanation of the circumstances involved, you would have realized that for those inside the caboose, the world operated just as it should, or as expected. Only those who witnessed events from outside the car (in this instance the camera) would perceive that things took place in an extraordinarily different manner than might otherwise have been imagined. If you'll indulge my little exercise for one moment longer, there's yet another brief (and fun) example of the full ramifications of the scenario as described.
If instead of the woman and rear wall of the caboose, that part of the car had been left completely open to the outside, a separate but equally interesting phenomenon might have been recorded by the stationary camera. As the man fired the gun and the caboose hurried past, left sitting in the middle of the tracks would have been the spent bullet. In reviewing what the camera saw -- in slow motion -- the fired round did indeed reach the end of the barrel and with zero velocity, fell straight to the ground below. The image is even humorous (in its own way) seeing the bullet fall out of the gun and drop harmlessly among the tracks. Were the recording seen later by the man, his response might well have been one of incredulity. From his vantage point, he shot the gun out the rear of the car and was simply thankful that no one was hit. But we know better. We know that if we'd been standing next to the tracks as the caboose went by, and he had fired the gun at any one of us, we need only reach out and catch the bullet in our hand. If you try this at home, please be careful. Recently spent rounds can be very hot to the touch.
Number one on our list of things to remember is that everything we're about to discuss (and imagine) takes place in the last car of the train -- what used to be called the caboose. I don't know if trains still have cabooses or not, but this one does. A nice, old fashioned reddish one. Next on the list is the fact that the train tracks themselves run in an exactly north and south direction. We happen to be headed north, but we could have been traveling south just as well. The whistle just sounded up ahead; did you hear it? Those billows of steam wafting past us and the sudden jolt of the caboose have left no doubt that we've begun "chugging" along -- slow at first, but we can feel our acceleration (and excitement) increasing by the moment. Okay, so I'm easily thrilled.
The interior of the caboose is pretty sparse. Little more than four bare, wooden walls, a plain wood floor and slatted ceiling of thin planks. Also inside the car are its two sole occupants, a man and a woman whose names or other descriptions are entirely irrelevant to our story. So I left all that out. Feel free, however, to envision what these people look like, their age or whatever; makes no difference to me. One of them is about to die shortly -- the woman -- so we don't want things to get too personal, far as I'm concerned.
Something that is very relevant, though, is our next piece of information, which is the fact that the guy has a gun. A .45 caliber automatic to be specific. The pistol could just as easily have been a revolver, but I prefer an automatic and since I'm telling the story, I say it's an automatic. One additional thing you'll definitely need to know about the gun is going to sound dull, but trust me; it's more critical info that you need to remember. The muzzle velocity, which is to say, the speed of the bullet as it exits the barrel -- once the gun is fired (duhhh) -- is 850 feet per second, or about 580 miles per hour.
Talk about coincidences: that muzzle velocity stuff happens to be the exact same speed that our train is fast approaching. I checked with the engineer and despite my skepticism, he assured me that this particular train could travel that fast -- and safely. Which is to say (as if I had to) that our train will soon be hurtling down the tracks -- heading north -- at exactly 580 miles per hour. Or 850 feet per second, whichever suits you. Hard to believe, I know, but this locomotive is obviously motivated.
As the train reaches its maximum velocity and holds steady, I'll finish the basic setup inside the caboose. The woman is standing at the rear of the car, her back against the wall, her mouth frowning with pressed-together lips. She is staring at the man whose own back is against the forward wall of the caboose, and who is gazing back at the woman with a smirk on his face. That's because he's the one with the gun, which is raised and pointed at his fellow passenger. So let's make sure we've got everyone and everything in their proper place before going any further. There's also four, high-definition video cameras inside the car. One in each corner of where the walls and ceiling meet. If anything happens inside the caboose, we'll have a good photographic record of it.
The woman is facing the front of the caboose -- the front of the train -- both of which are heading north. The guy is turned in the opposite direction, facing the rear wall of the last car of the train, which has him looking directly south. Just to be clear, the gun he's holding is both pointed south and aimed at the lady's body. That now puts things and people in their final positions which will remain largely unchanged throughout the remainder of the events to follow.
It must have been a pretty serious argument the couple had prior to our eavesdropping on them, because the guy just fired the gun and shot his woman partner. Struck her right in the heart which meant she went fast with minimum discomfort. As she slumps unconscious to the floor, the first part of our little tale now concludes. Any questions? Let me jump in because I know just the right questions to ask, thanks. I know the perfect questions which will deconstruct the elapsed scenario in ways both unexpected and revelatory in nature. Let's get started and see if you're surprised by some of the answers we uncover.
First of all, remember that muzzle velocity business I mentioned earlier? I know it sounds cold and heartless to start talking mathematics and physics while the poor woman is collapsed against the rear wall, but I don't have time for the sentimental stuff, sorry. Now then, as I was saying, the muzzle velocity of the pistol, if you recall, is the same as the forward speed of the train as it travels down the tracks. The only difference is that the gun is pointed south while the train is charging north. Did anything unusual result because of this? In a subsequent review of the surveillance video from all the cameras, nothing seemed out of the ordinary. The entire event appeared to transpire in a manner that was completely unaffected by, and independent of, a really fast moving train. As seen by the two passengers inside the caboose, absolutely nothing out-of-the-ordinary took place. Which is a totally authentic, eyewitness report. Well, the woman wasn't exactly available for an interview afterwards, but we're pretty sure she'd agree to what the man testified was the case. But do you agree? And if not, why not?
I forgot to tell you about the fifth camera. Not really, I just didn't want to show my hand too soon. Did I mention that one of the side walls of the caboose is all glass, from front to rear, floor to ceiling? Guess I forgot that little tidbit also. No matter, the two new additions are only important to the final detail that will help us make sense of everything -- and solve the mystery! Which is likely more to do with what all this preliminary setup was for. The last detail is, in addition to another camera and the caboose fitted with a clear glass sidewall, the location of the extra camera. Placed far ahead of the fast-approaching train, the ultra high-definition movie camera is sitting atop a tripod (or whatever) and faces the tracks. The intended purpose of the camera was to capture a photographic record of the train as it passes. More specifically to photograph the caboose as it zoomed by with its glass wall, of course, facing the camera. Not coincidentally, the camera just happened to be rolling when the train passed its location, but more importantly, at the same exact moment when the man pulled the trigger and shot the woman. What were the odds?
This fifth (and stationary) camera will give us another view of whatever took place inside the caboose as it streaked by at 580 mph. The view of the scenery from inside the caboose must have been spectacular, but I digress. For now, we're more concerned with the view from outside, looking in. As you may have already guessed, the setup thus far is pretty straightforward and, except for the speed of the train itself, I've simply described a situation with which we're all familiar. Namely, how things look differently to a person inside a moving vehicle, compared to someone standing beside the road (in this case the train tracks) watching the person go by. For example, to the passenger inside the vehicle, it's the outside world that appears to be moving past the windows, while to spectators outside, it's obviously the vehicle which pulls away. Or try this: if the passenger was smoking a cigarette at the time (heaven forbid), the exhaled smoke would appear to hang motionless inside the vehicle. But to anyone watching the conveyance move away, both the smoker -- and the smoke -- would be moving along at whatever speed they were traveling. Whether at twenty mph -- or 580 mph. The reason the smoke "hangs" inside the vehicle, by the way, is because the air inside the compartment is carried along the same as everything else. But you knew that already. And if you didn't, then now you do.
Holy smoke, it's time we got back to our murder mystery, if you're still with me. I hope you are because this is really going to get good -- and spooky. Since we know that everything inside the caboose looked normal (too normal for the poor lady), it's time to examine what was recorded on the camera positioned right beside the tracks. Which should be pretty much the same as what the other cameras captured from the interior of the car, right? Wrong! What?
Let's quickly review: The man was backed up against the forward wall of the caboose, facing the rear wall. The woman was facing the man, her back to the rear wall of the car. He fired the pistol, she got shot, and until the police arrested him, that was about the sum of things. Okay so far. But here's where things get interesting. When police and lawyers examined and evaluated the recording made by the fifth camera, which shot the sequence of events as they sped by, the attorney for the accused pleaded innocent to all charges. The lawyer stated that, except for his client having pulled the trigger of the gun, the woman had clearly committed suicide. And he could prove it. What now follows is the case made by the defendant's lawyer.
Fortunately for the accused, the externally placed, stationary camera was equipped with a very sophisticated radar-style speed detector -- similar to what the police use when tracking speeders. Sure enough, the velocity of the northbound train as it passed was 580 mph. Or 850 feet per second. The unfired bullet chambered inside the .45 caliber automatic held by the man, was also moving, of course, at the same speed. When the guy squeezed the trigger, however, a funny thing happened. Well, the woman didn't think so, but we're getting ahead of ourselves. Or myself.
Once the round was discharged, so argued the defense attorney, the bullet actually began to slow down, to decelerate as it moved towards the end of the barrel. Remember that muzzle velocity business mentioned earlier? As you'll recall, muzzle velocity refers to the speed of a bullet as it leaves the opening of a gun's barrel. It differs according to the weapon used, but in our case, the velocity of a .45 caliber round is about 580 mph, give or take. Hmmm, there's a coincidence that didn't seem to matter before. As stated earlier, the muzzle velocity of the bullet is the same as the forward movement of the train -- just in the opposite direction. So what's the big deal? That's what the police wanted to know, also.
If you haven't already figured out where this is going, the answer is as follows: by the time the fired bullet reached the exit hole of the gun's barrel, it's "real" velocity was zero mph. In this case, the term, real, refers to an "objective" viewpoint that describes the difference between being involved -- and uninvolved -- in any given process. For all intents and purposes, as they say, the speed of the bullet had indeed decelerated to no-speed-at-all and under other circumstances, might well have just fallen straight to the floor. According to the cameras inside the caboose, however, the bullet retained its intended muzzle velocity, exited the barrel at exactly 850 mph, complete with recoil, flew across the car interior and hit the woman. Or rather -- she hit it. Say again?
That's when the defense attorney really got going. He pointed out that while it's true the discharged bullet was decelerating as it moved through the barrel, the barrel itself, including the gun, the man, the caboose, indeed the whole train, was simultaneously pulling away from the (now independent) round at the same speed of 580 mph. That wasn't all that was happening. Everything in front of the bullet was also rushing towards it at 580 mph. Including, of course, the woman. Thus by the time the bullet leaves the end of the barrel, the gun (and much of everything else) is long gone from it, and the woman has slammed head-on into it. As only lawyers can do, the defense attorney insists that the lady shot herself and had she simply stepped to one side, the rear wall of the car -- instead of her body -- would have impacted the spent round.
The police figured that a jury would never convict because of the seeming complexity of the case, and all charges were dropped. If you had been a member of that jury, you would have found the man guilty, though, right? Due to my excellent explanation of the circumstances involved, you would have realized that for those inside the caboose, the world operated just as it should, or as expected. Only those who witnessed events from outside the car (in this instance the camera) would perceive that things took place in an extraordinarily different manner than might otherwise have been imagined. If you'll indulge my little exercise for one moment longer, there's yet another brief (and fun) example of the full ramifications of the scenario as described.
If instead of the woman and rear wall of the caboose, that part of the car had been left completely open to the outside, a separate but equally interesting phenomenon might have been recorded by the stationary camera. As the man fired the gun and the caboose hurried past, left sitting in the middle of the tracks would have been the spent bullet. In reviewing what the camera saw -- in slow motion -- the fired round did indeed reach the end of the barrel and with zero velocity, fell straight to the ground below. The image is even humorous (in its own way) seeing the bullet fall out of the gun and drop harmlessly among the tracks. Were the recording seen later by the man, his response might well have been one of incredulity. From his vantage point, he shot the gun out the rear of the car and was simply thankful that no one was hit. But we know better. We know that if we'd been standing next to the tracks as the caboose went by, and he had fired the gun at any one of us, we need only reach out and catch the bullet in our hand. If you try this at home, please be careful. Recently spent rounds can be very hot to the touch.
Postscript
Before we disembark entirely from the preceding events, the thought occurred to me -- to you as well, maybe -- as to how the circumstances might have been analyzed had the situation been just the opposite of what was described. Suppose it had been the woman who possessed the gun instead of the guy. And she was the one who shot the man. What would have been different -- and the same? I almost omitted this part of the story, but the results were so interesting, I decided to include them.
Had the woman pulled the trigger, the bullet would have accelerated as it traveled along the inside of the barrel. Simply loaded in the gun, unfired, the round was already moving at 580 mph in a northerly direction (a fact that was, of course, true for the man and his gun as well). Since the .45's muzzle velocity was also 580 mph, the combined velocity (580+580) would have equaled 1160 mph as the bullet exited the pistol. Or 1700 feet per second (850+850). To an outside observer, this would have represented the bullet's true, objective velocity once it was discharged. For anyone inside the caboose, however, the round never moves faster than the original 850 mph. When the man is struck by the bullet, it hits him moving at 850 mph and not at 1160 mph.
The reason for this seeming discrepancy is likely obvious by now, but I felt the idea of the woman shooting the gun further reinforced the validity of my previous claims and assertions. The answer, of course, is that the man, the wall he's leaning against, and virtually everything else in front of the round, are pulling away -- at 850 mph --from the oncoming bullet. This preexisting motion effectively cancels out the bullet's increase in velocity, but only within the caboose itself. As mentioned, the bullet does indeed double its forward, northerly speed. But only with respect to an outside, stationary observer. If a person standing still, beside the tracks, were impacted by the same bullet, it would strike them moving at 1160 mph. Ouch! Sure, like it would hurt more at twice the speed.
One last way of looking at this is to imagine how any and all events within the caboose, take place as if the train car wasn't moving at all. The motion of the caboose is irrelevant to the passengers inside it. The movement of the car, whether or not it's moving at all, is only significant in terms of the observations that might be made by stationary witnesses located outside the train. Even then, consider the ramifications if these same witnesses were themselves seated in a moving vehicle that whizzed past an unmoving caboose. And it was they who were traveling at 850 mph while the same events then transpired and were photographed accordingly.
Well, as you can no doubt further imagine, the whole business gets very complicated, very quickly. But you get the idea, I think. The true nature of reality is essentially nothing more than a matter of where you are and how fast (or slowly) you're moving -- if at all. And only compared to everything (and everyone) else in the vicinity. What makes you so special? Relatively speaking, that is.
Had the woman pulled the trigger, the bullet would have accelerated as it traveled along the inside of the barrel. Simply loaded in the gun, unfired, the round was already moving at 580 mph in a northerly direction (a fact that was, of course, true for the man and his gun as well). Since the .45's muzzle velocity was also 580 mph, the combined velocity (580+580) would have equaled 1160 mph as the bullet exited the pistol. Or 1700 feet per second (850+850). To an outside observer, this would have represented the bullet's true, objective velocity once it was discharged. For anyone inside the caboose, however, the round never moves faster than the original 850 mph. When the man is struck by the bullet, it hits him moving at 850 mph and not at 1160 mph.
The reason for this seeming discrepancy is likely obvious by now, but I felt the idea of the woman shooting the gun further reinforced the validity of my previous claims and assertions. The answer, of course, is that the man, the wall he's leaning against, and virtually everything else in front of the round, are pulling away -- at 850 mph --from the oncoming bullet. This preexisting motion effectively cancels out the bullet's increase in velocity, but only within the caboose itself. As mentioned, the bullet does indeed double its forward, northerly speed. But only with respect to an outside, stationary observer. If a person standing still, beside the tracks, were impacted by the same bullet, it would strike them moving at 1160 mph. Ouch! Sure, like it would hurt more at twice the speed.
One last way of looking at this is to imagine how any and all events within the caboose, take place as if the train car wasn't moving at all. The motion of the caboose is irrelevant to the passengers inside it. The movement of the car, whether or not it's moving at all, is only significant in terms of the observations that might be made by stationary witnesses located outside the train. Even then, consider the ramifications if these same witnesses were themselves seated in a moving vehicle that whizzed past an unmoving caboose. And it was they who were traveling at 850 mph while the same events then transpired and were photographed accordingly.
Well, as you can no doubt further imagine, the whole business gets very complicated, very quickly. But you get the idea, I think. The true nature of reality is essentially nothing more than a matter of where you are and how fast (or slowly) you're moving -- if at all. And only compared to everything (and everyone) else in the vicinity. What makes you so special? Relatively speaking, that is.
Epilogue
The foregoing was my own way of explaining some of what Albert Einstein considered when he was doing the math formulas for similar kinds of seemingly paradoxical events. He realized how events can, at one and the same time, be both the same and completely different, depending solely on our points of view, our frames-of-reference. It's a little like why eyewitness testimony is both invaluable and yet the least reliable evidence in many cases. You've long heard and understood how context is everything, and yet few of us apply that same principle to our perceptions -- and misperceptions -- of what we believe to be the real world. Such are the practical, everyday applications of the lessons that might be learned from my quaint little train story.
"Seeing is believing" is an old saying that always had a lot going for it. Now you know, if you didn't already, that such a statement is also very narrow in its scope and potentially misleading. The reflected image of ourselves that we see in mirrors is a person who doesn't exist in our world. If you have a mole on your left arm, your doppelgänger self has it on their right arm. More accurate might be a variation which says, "Believing is seeing truly." In this case, the word truly referring to "angles of perspective" that afford us the best possible view (the most information) possible. Teaching ourselves to hesitate before jumping to conclusions, to evaluate a situation with the idea that the facts of the case might be completely opposite of what we think them to be, is a learned attitude which invariably leads us to greater, more authentic truths. This is especially applicable to those things we experience at the most personal and intimate of levels. That what might be entirely true and beneficial for ourselves, may in fact be extremely detrimental or -- or worse -- for someone else. What does that tell us about our religious beliefs or moral convictions, our values and philosophies? Or all our ideas of how we think the world operates -- even our vision of the universe itself?
In attempting to make sense of what we experience and in order to comprehend the total nature of things, we are trapped in a dilemma which demands that we be simultaneously both inside the caboose and outside of it. The view from inside, generally speaking, is considered a subjective viewpoint, whereby we are caught-up within the circumstances of a given event. The view from outside, the so-called objective frame-of-reference, involve observations which are not influenced or made biased via direct interaction with the object(s) of our attention.
The ideal vantage point as an observing witness is one which incorporates both subjective and objective perspectives. Not, however, as a means of discovering the precise reality of something, but rather only as a method of determining the most authentic understanding of a given situation, then responding or reacting with the best possible course of action or behavior.
Subjective viewpoints represent individual frames-of-reference which are conditional and based on a narrow set of factors. Objective angles offer their own frames-of-reference, are equally conditional, and will invariably differ significantly from their subjective counterparts. Frames-of-reference themselves are not hierarchical (one is not necessarily superior to the other); they are simply different from one another. While it is not important to the gun or the bullet as to how they are viewed, it may be vital to a bystander whose very life might be at stake.
It is precisely the differences which occur among varying frames-of-reference which afford us the ability to choose from many possible courses of action and behavior. Some profitable, others not so much. The better the quality (detail) of our disparate frames-of-reference, the greater the quality of our thinking habits. Interestingly enough, without these frames-of-reference we could make little sense of anything happening around us. The events that transpire inside the caboose are entirely sensible at the subjective level. The same events as witnessed by a camera (or observers) outside the caboose record (or view) an equally subjective view of things from their respective location. A subsequent courtroom trial, in order to arrive at a just verdict, would necessitate an examination from both inside and outside the caboose.
We thus end with a situation where an argument can be made that no such thing as objective is realistically possible. The hypothetical inclusion of the writer (me) as part of all things considered, might be the closest we could come to a complete perspective Attempting to achieve objectivity is not what's important; rather our striving to learn and understand another person's subjective perception is the point.
So are we inside the caboose of a moving train? Or do we stand beside the tracks and watch the train cars go by? The answer, for me, is that while I might be a passenger or a casual observer at any given moment, it's far more significant that we wave to the other person and acknowledge their existence, regardless of our place (or theirs) in the scheme of things.
* * * *
"Seeing is believing" is an old saying that always had a lot going for it. Now you know, if you didn't already, that such a statement is also very narrow in its scope and potentially misleading. The reflected image of ourselves that we see in mirrors is a person who doesn't exist in our world. If you have a mole on your left arm, your doppelgänger self has it on their right arm. More accurate might be a variation which says, "Believing is seeing truly." In this case, the word truly referring to "angles of perspective" that afford us the best possible view (the most information) possible. Teaching ourselves to hesitate before jumping to conclusions, to evaluate a situation with the idea that the facts of the case might be completely opposite of what we think them to be, is a learned attitude which invariably leads us to greater, more authentic truths. This is especially applicable to those things we experience at the most personal and intimate of levels. That what might be entirely true and beneficial for ourselves, may in fact be extremely detrimental or -- or worse -- for someone else. What does that tell us about our religious beliefs or moral convictions, our values and philosophies? Or all our ideas of how we think the world operates -- even our vision of the universe itself?
In attempting to make sense of what we experience and in order to comprehend the total nature of things, we are trapped in a dilemma which demands that we be simultaneously both inside the caboose and outside of it. The view from inside, generally speaking, is considered a subjective viewpoint, whereby we are caught-up within the circumstances of a given event. The view from outside, the so-called objective frame-of-reference, involve observations which are not influenced or made biased via direct interaction with the object(s) of our attention.
The ideal vantage point as an observing witness is one which incorporates both subjective and objective perspectives. Not, however, as a means of discovering the precise reality of something, but rather only as a method of determining the most authentic understanding of a given situation, then responding or reacting with the best possible course of action or behavior.
Subjective viewpoints represent individual frames-of-reference which are conditional and based on a narrow set of factors. Objective angles offer their own frames-of-reference, are equally conditional, and will invariably differ significantly from their subjective counterparts. Frames-of-reference themselves are not hierarchical (one is not necessarily superior to the other); they are simply different from one another. While it is not important to the gun or the bullet as to how they are viewed, it may be vital to a bystander whose very life might be at stake.
It is precisely the differences which occur among varying frames-of-reference which afford us the ability to choose from many possible courses of action and behavior. Some profitable, others not so much. The better the quality (detail) of our disparate frames-of-reference, the greater the quality of our thinking habits. Interestingly enough, without these frames-of-reference we could make little sense of anything happening around us. The events that transpire inside the caboose are entirely sensible at the subjective level. The same events as witnessed by a camera (or observers) outside the caboose record (or view) an equally subjective view of things from their respective location. A subsequent courtroom trial, in order to arrive at a just verdict, would necessitate an examination from both inside and outside the caboose.
We thus end with a situation where an argument can be made that no such thing as objective is realistically possible. The hypothetical inclusion of the writer (me) as part of all things considered, might be the closest we could come to a complete perspective Attempting to achieve objectivity is not what's important; rather our striving to learn and understand another person's subjective perception is the point.
So are we inside the caboose of a moving train? Or do we stand beside the tracks and watch the train cars go by? The answer, for me, is that while I might be a passenger or a casual observer at any given moment, it's far more significant that we wave to the other person and acknowledge their existence, regardless of our place (or theirs) in the scheme of things.
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