My problem with infinity
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Woken up plagued by the concept of infinity again. Precursor to a difficult day ahead methinks. Infinity in my mind is that place you never get to. Try counting to infinity and you won't get there. Purists might argue that you would if you spent an infinite amount of time counting. But, seemingly we do get there. The abstraction I have in my head is this: A clock face with a straight line through it, going straight through the 6 and 12 and extending where else, but to infinity. Draw another parallel line to the left of the clock. Then, when the hour hand is on the 9 it points to the nearest point on the second line. As time progresses, the point on the second line moves up, heading straight for infinity. Now by rights, it should never get there, but it does, 3 hours later. It got there I believe at 3 hours - (1/infinity). It's a theoretical place, but it's also real because we just went through it to get to midday. So, where is it? I've expressed my concerns to my wife but she just gives me that slightly desperate lonely look. Oh dear, deep questions about the Universe always leave me feeling edgy.
Regards, Rob Philpott.
How do you mean the point on the second line 'got there'? I think I'm starting to see your idea, but I need some elucidation. Just started reading Gödel, Escher, Bach for the second time in a row, and it deals extensively with, many of the more paradoxical aspects of infinity, starting with Zeno's Paradox, which is probably some kind of cousin to Rob's Paradox. I avoided getting too involved in the math during my first pass, already committing myself to an immediate second pass to better appreciate the finer points.
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Edge of space? What a load of nonsense. It's amazing the stuff Universities will come up with in order to secure more funding for them to spend in the Student Union bar. Having said that, you could argue there's an edge of space around the earth. Space stops and a huge lump of iron begins, but you always come out the other side.
Regards, Rob Philpott.
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Woken up plagued by the concept of infinity again. Precursor to a difficult day ahead methinks. Infinity in my mind is that place you never get to. Try counting to infinity and you won't get there. Purists might argue that you would if you spent an infinite amount of time counting. But, seemingly we do get there. The abstraction I have in my head is this: A clock face with a straight line through it, going straight through the 6 and 12 and extending where else, but to infinity. Draw another parallel line to the left of the clock. Then, when the hour hand is on the 9 it points to the nearest point on the second line. As time progresses, the point on the second line moves up, heading straight for infinity. Now by rights, it should never get there, but it does, 3 hours later. It got there I believe at 3 hours - (1/infinity). It's a theoretical place, but it's also real because we just went through it to get to midday. So, where is it? I've expressed my concerns to my wife but she just gives me that slightly desperate lonely look. Oh dear, deep questions about the Universe always leave me feeling edgy.
Regards, Rob Philpott.
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How do you mean the point on the second line 'got there'? I think I'm starting to see your idea, but I need some elucidation. Just started reading Gödel, Escher, Bach for the second time in a row, and it deals extensively with, many of the more paradoxical aspects of infinity, starting with Zeno's Paradox, which is probably some kind of cousin to Rob's Paradox. I avoided getting too involved in the math during my first pass, already committing myself to an immediate second pass to better appreciate the finer points.
The second point is just the point on the left hand line which the hour hand points to. It's hyperthetical. And my problem is that it reaches infinity in a finite amount of time. Zeno's Paradox. Not sure I like the sound of that. Anything with Paradox in the title suggests headaches.
Regards, Rob Philpott.
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Rob Philpott wrote:
Infinity in my mind is that place you never get to
Man is equally incapable of seeing the nothingness from which he emerges and the infinity in which he is engulfed. ~ Blaise Pascal
Useful pub quote that. In fact, I might even use in tomorrow's agile stand up.
Regards, Rob Philpott.
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The second point is just the point on the left hand line which the hour hand points to. It's hyperthetical. And my problem is that it reaches infinity in a finite amount of time. Zeno's Paradox. Not sure I like the sound of that. Anything with Paradox in the title suggests headaches.
Regards, Rob Philpott.
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Rob Philpott wrote:
Anything with Paradox in the title suggests headaches.
Especially if that arrow ever catches up to you...
Sorry Josh, but you sometimes end up quite elusive. Can I take a CPhog issue to Web Development, or can I email you?
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daveauld wrote:
how can there be an edge? there is more space beyond......
<geek mode> The latest thinking is that space is finite in three dimensions. Four dimensional space-time is collapsed into a finite three-dimensional volume by the effect of gravity. As an example, concrete over the whole world (ignore the environmental impact for now), and then smooth out all the mountains with a really big bit of sandpaper. The surface of the earth (a two dimensional object) is finite (in three dimensions) but has no edges. Now exapnd that concept from a two-dimensional object in the three dimensions into a three-dimensional object in a four dimensions. </geek mode>
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Woken up plagued by the concept of infinity again. Precursor to a difficult day ahead methinks. Infinity in my mind is that place you never get to. Try counting to infinity and you won't get there. Purists might argue that you would if you spent an infinite amount of time counting. But, seemingly we do get there. The abstraction I have in my head is this: A clock face with a straight line through it, going straight through the 6 and 12 and extending where else, but to infinity. Draw another parallel line to the left of the clock. Then, when the hour hand is on the 9 it points to the nearest point on the second line. As time progresses, the point on the second line moves up, heading straight for infinity. Now by rights, it should never get there, but it does, 3 hours later. It got there I believe at 3 hours - (1/infinity). It's a theoretical place, but it's also real because we just went through it to get to midday. So, where is it? I've expressed my concerns to my wife but she just gives me that slightly desperate lonely look. Oh dear, deep questions about the Universe always leave me feeling edgy.
Regards, Rob Philpott.
You *can* reach infinity by counting - you just have to e.g. permanently double your speed. :cool: Is "Horizon" an equally complicated concept for you?
Personally, I love the idea that Raymond spends his nights posting bad regexs to mailing lists under the pseudonym of Jane Smith. He'd be like a super hero, only more nerdy and less useful. [Trevel]
| FoldWithUs! | sighist | µLaunch - program launcher for server core and hyper-v server -
daveauld wrote:
how can there be an edge? there is more space beyond......
<geek mode> The latest thinking is that space is finite in three dimensions. Four dimensional space-time is collapsed into a finite three-dimensional volume by the effect of gravity. As an example, concrete over the whole world (ignore the environmental impact for now), and then smooth out all the mountains with a really big bit of sandpaper. The surface of the earth (a two dimensional object) is finite (in three dimensions) but has no edges. Now exapnd that concept from a two-dimensional object in the three dimensions into a three-dimensional object in a four dimensions. </geek mode>
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Woken up plagued by the concept of infinity again. Precursor to a difficult day ahead methinks. Infinity in my mind is that place you never get to. Try counting to infinity and you won't get there. Purists might argue that you would if you spent an infinite amount of time counting. But, seemingly we do get there. The abstraction I have in my head is this: A clock face with a straight line through it, going straight through the 6 and 12 and extending where else, but to infinity. Draw another parallel line to the left of the clock. Then, when the hour hand is on the 9 it points to the nearest point on the second line. As time progresses, the point on the second line moves up, heading straight for infinity. Now by rights, it should never get there, but it does, 3 hours later. It got there I believe at 3 hours - (1/infinity). It's a theoretical place, but it's also real because we just went through it to get to midday. So, where is it? I've expressed my concerns to my wife but she just gives me that slightly desperate lonely look. Oh dear, deep questions about the Universe always leave me feeling edgy.
Regards, Rob Philpott.
It doesn't 'reach' infinity, rather it jumps (because matter is not infinitely divisible) to a place in the domain where the intersection of the hand and the second line isn't defined.
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It doesn't 'reach' infinity, rather it jumps (because matter is not infinitely divisible) to a place in the domain where the intersection of the hand and the second line isn't defined.
eh? Jumping? That doesn't exist in the linear fluid world of mathmatics!
Regards, Rob Philpott.
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You *can* reach infinity by counting - you just have to e.g. permanently double your speed. :cool: Is "Horizon" an equally complicated concept for you?
Personally, I love the idea that Raymond spends his nights posting bad regexs to mailing lists under the pseudonym of Jane Smith. He'd be like a super hero, only more nerdy and less useful. [Trevel]
| FoldWithUs! | sighist | µLaunch - program launcher for server core and hyper-v serverNo you can't. Horizon is one of my favourite TV programmes actually.
Regards, Rob Philpott.
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eh? Jumping? That doesn't exist in the linear fluid world of mathmatics!
Regards, Rob Philpott.
It doesn't make sense. The point of intersection is not 'at infinity', it's just not defined. Compare it to this.
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Woken up plagued by the concept of infinity again. Precursor to a difficult day ahead methinks. Infinity in my mind is that place you never get to. Try counting to infinity and you won't get there. Purists might argue that you would if you spent an infinite amount of time counting. But, seemingly we do get there. The abstraction I have in my head is this: A clock face with a straight line through it, going straight through the 6 and 12 and extending where else, but to infinity. Draw another parallel line to the left of the clock. Then, when the hour hand is on the 9 it points to the nearest point on the second line. As time progresses, the point on the second line moves up, heading straight for infinity. Now by rights, it should never get there, but it does, 3 hours later. It got there I believe at 3 hours - (1/infinity). It's a theoretical place, but it's also real because we just went through it to get to midday. So, where is it? I've expressed my concerns to my wife but she just gives me that slightly desperate lonely look. Oh dear, deep questions about the Universe always leave me feeling edgy.
Regards, Rob Philpott.
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You *can* reach infinity by counting - you just have to e.g. permanently double your speed. :cool: Is "Horizon" an equally complicated concept for you?
Personally, I love the idea that Raymond spends his nights posting bad regexs to mailing lists under the pseudonym of Jane Smith. He'd be like a super hero, only more nerdy and less useful. [Trevel]
| FoldWithUs! | sighist | µLaunch - program launcher for server core and hyper-v serverpeterchen wrote:
*can* reach infinity
That is a contradiction in terms. Infinity is by definition unreachable...
-- Kein Mitleid Für Die Mehrheit
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Woken up plagued by the concept of infinity again. Precursor to a difficult day ahead methinks. Infinity in my mind is that place you never get to. Try counting to infinity and you won't get there. Purists might argue that you would if you spent an infinite amount of time counting. But, seemingly we do get there. The abstraction I have in my head is this: A clock face with a straight line through it, going straight through the 6 and 12 and extending where else, but to infinity. Draw another parallel line to the left of the clock. Then, when the hour hand is on the 9 it points to the nearest point on the second line. As time progresses, the point on the second line moves up, heading straight for infinity. Now by rights, it should never get there, but it does, 3 hours later. It got there I believe at 3 hours - (1/infinity). It's a theoretical place, but it's also real because we just went through it to get to midday. So, where is it? I've expressed my concerns to my wife but she just gives me that slightly desperate lonely look. Oh dear, deep questions about the Universe always leave me feeling edgy.
Regards, Rob Philpott.
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Woken up plagued by the concept of infinity again. Precursor to a difficult day ahead methinks. Infinity in my mind is that place you never get to. Try counting to infinity and you won't get there. Purists might argue that you would if you spent an infinite amount of time counting. But, seemingly we do get there. The abstraction I have in my head is this: A clock face with a straight line through it, going straight through the 6 and 12 and extending where else, but to infinity. Draw another parallel line to the left of the clock. Then, when the hour hand is on the 9 it points to the nearest point on the second line. As time progresses, the point on the second line moves up, heading straight for infinity. Now by rights, it should never get there, but it does, 3 hours later. It got there I believe at 3 hours - (1/infinity). It's a theoretical place, but it's also real because we just went through it to get to midday. So, where is it? I've expressed my concerns to my wife but she just gives me that slightly desperate lonely look. Oh dear, deep questions about the Universe always leave me feeling edgy.
Regards, Rob Philpott.
That's not a problem with infinity, that's a problem with geometry. If you setup two straight line equations for the lines, and solve them for where they intersect, you will see that there is no solution for when the lines are parallel. That's not cheating infinity - it is you who are assuming that the lines will always cross, but the assumption is wrong.
-- Kein Mitleid Für Die Mehrheit
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Woken up plagued by the concept of infinity again. Precursor to a difficult day ahead methinks. Infinity in my mind is that place you never get to. Try counting to infinity and you won't get there. Purists might argue that you would if you spent an infinite amount of time counting. But, seemingly we do get there. The abstraction I have in my head is this: A clock face with a straight line through it, going straight through the 6 and 12 and extending where else, but to infinity. Draw another parallel line to the left of the clock. Then, when the hour hand is on the 9 it points to the nearest point on the second line. As time progresses, the point on the second line moves up, heading straight for infinity. Now by rights, it should never get there, but it does, 3 hours later. It got there I believe at 3 hours - (1/infinity). It's a theoretical place, but it's also real because we just went through it to get to midday. So, where is it? I've expressed my concerns to my wife but she just gives me that slightly desperate lonely look. Oh dear, deep questions about the Universe always leave me feeling edgy.
Regards, Rob Philpott.
According to some physics theories, information cannot be transferred faster than the speed of light, and that includes torquing and gravity. Turning a clock hand by torquing it from the center will lead to a wave that travels no faster than the speed of light from the center of the clock outward to the end of the hand. Since the hand will have to be infinitely long at noon (or right before it), that wave will never reach the end of the hand, and so infinity will never be reached. It would probably also take infinite energy to move an object of infinite size. But in pure math world, I wouldn't really say it reaches it anyway. Any slight angle will be amplified massively as the hand approaches noon. Only once it reaches noon could it be said that it reached infinity. But then the lines are parallel and they do not intersect at infinity. Every length shorter than infinity is intersected, but never infinity. Just gets skipped over. Now, what happens when an unstoppable force meets an immovable object? :-\
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According to some physics theories, information cannot be transferred faster than the speed of light, and that includes torquing and gravity. Turning a clock hand by torquing it from the center will lead to a wave that travels no faster than the speed of light from the center of the clock outward to the end of the hand. Since the hand will have to be infinitely long at noon (or right before it), that wave will never reach the end of the hand, and so infinity will never be reached. It would probably also take infinite energy to move an object of infinite size. But in pure math world, I wouldn't really say it reaches it anyway. Any slight angle will be amplified massively as the hand approaches noon. Only once it reaches noon could it be said that it reached infinity. But then the lines are parallel and they do not intersect at infinity. Every length shorter than infinity is intersected, but never infinity. Just gets skipped over. Now, what happens when an unstoppable force meets an immovable object? :-\
Hmm. What speed does gravity to work at? Say for instance the sun just disappeared suddenly (which would be bad). Does the earth still rotate around where it was for the 8 minutes it takes light to get here?
Regards, Rob Philpott.
