My problem with infinity
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:sigh: yeah, you can't, but think of the fun we could have had with Rob ;)
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:doh:
-- Kein Mitleid Für Die Mehrheit
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:~
Luc Pattyn [Forum Guidelines] [Why QA sucks] [My Articles]
Merry Christmas and a Happy New Year to all.
That is not infinity, that is undefined. If you replace the 0 with an x, you can argue about what happens once x creeps closer to 0, but that's about it.
-- Kein Mitleid Für Die Mehrheit
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Seems to me you delved into the concept of an asymptote.
And above all things, never think that you're not good enough yourself. A man should never think that. My belief is that in life people will take you at your own reckoning. --Isaac Asimov Avoid the crowd. Do your own thinking independently. Be the chess player, not the chess piece. --Ralph Charell
What a convergent answer!
-- Kein Mitleid Für Die Mehrheit
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What a convergent answer!
-- Kein Mitleid Für Die Mehrheit
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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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Its good to see everyone's moving toward the same point ;P .
There are only 10 types of people in this world — those who understand binary, and those who don't.
Anything but a singularity would be pointless...
-- Kein Mitleid Für Die Mehrheit
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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>
Electron Shepherd wrote:
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.
This actually made sense to me. Thanks. :)
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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 are talking about infinity in projective geometry http://en.wikipedia.org/wiki/Projective_geometry[^]. It is a simpler kind of infinity than the numerical sorts that are broken into different sizes. In projective geometry every direction meets a point at infinity and every parallel line in that direction intersects in that same point. It is a completely consistent and extremely interesting geometry with a number of uses. The math gets a little hairy, but nothing more than n+1 dimensional linear algebra. Fun stuff!:thumbsup:
I can imagine the sinking feeling one would have after ordering my book, only to find a laughably ridiculous theory with demented logic once the book arrives - Mark McCutcheon
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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
Abhinav S wrote: Man is equally incapable of seeing the nothingness from which he emerges and the infinity in which he is engulfed. ~ Blaise Pascal (your choice of Namaste, Namaskaram, or Vanakkum) Sri Abhinav, Thanks for that wonderful quote ! It reminds me of something I read recently in the Dalai Lama's excellent book "The Universe in a Single Atom" : I believe it was in the context of his discussing one of Shankaracharya's non-dualistic philosophical/metaphysical statements, but I'm not totally sure of that, and I've loaned the book out to a friend. Another favorite of mine from Pascal's "Pensees" : "To make light of philosophy is to be a true philosopher." best, Bill
"Many : not conversant with mathematical studies, imagine that because it [the Analytical Engine] is to give results in numerical notation, its processes must consequently be arithmetical, numerical, rather than algebraical and analytical. This is an error. The engine can arrange and combine numerical quantities as if they were letters or any other general symbols; and it fact it might bring out its results in algebraical notation, were provisions made accordingly." Ada, Countess Lovelace, 1844
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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.
Worrisome, isn't it? Do what I do; have another drink. :-D
"A Journey of a Thousand Rest Stops Begins with a Single Movement"
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<Non geek mode> Request to translate... </Non geek mode>
There are only 10 types of people in this world — those who understand binary, and those who don't.
Abhinav S wrote:
<Non geek mode> Request to translate... </Non geek mode>
<Uber Geek Mode> It's Magic[^] </Uber Geek Mode>
“Follow your bliss.” – Joseph Campbell
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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.
I thought you were going to say that you can't get enough of it.
I wanna be a eunuchs developer! Pass me a bread knife!
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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>
For full marks you should've used the phrase "finite but unbounded". :)
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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.
I guess this would be a bad time to mention that there are an infinite number of fractions of a second in a second. ;P
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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.
It does indeed sound like a variant of Zeno's paradox: one expression of which is that a runner has to pass through an infinite amount of points to arrive at a destination (since any given distance, however small, contains an infinite number of points), so how does he manage to do that? One view to dissolve the paradox is that nothing in the universe is truly continuous: all existence, all energy transfer, and hence all movement as well, actually occurs in quanta and therefore nothing actually "passes through all the points". So the imaginary clock line was pointing to some very very high point on the line to the left of the clock at some quantified moment, and in the next, it was pointing straight upward....
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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 may be interested in this Zeno's Paradox[^] If you have studied calculus in high school or college, you may remember that Calculus and other forms of math based on calculus rely on the fact that the sum of an infinite series does have a finite value. When I first was given this as an explanation in high school, it took me a while to accept it. Part of the confusion is that the assumptions require a change of reference to a frame of reference that is not really achievable. Measurement from what frame of reference permits infinitely small measurements? It seems to me that the answer is none. So the idea of always being 1/2 the distance left is also purely imaginary. Mental exercises that stimulate ideas a fun nevertheless! :)
"Coding for fun and profit ... mostly fun"
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Agreed, parallel lines do not intersect. Although I believe you could argue they still intesect at infinity. My problem is the instant when two intersecting lines suddenly become parallel due to rotation.
Regards, Rob Philpott.
Parallel lines can intersect, depending on the geometry. Take, for example, lines of longitude. The paradox you present here is very similar, though less intuitive as we are not used to thinking of time as being 'curved' (like the earth is in the previous example).
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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.
"Anything with Paradox in the title suggests headaches." -- Aye! Just look at the Birthday Paradox... :doh: X|
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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.
Do parallel lines ever meet? No, but as you look at them from a distance as they appear to converge then the greater the distance the smaller the "care factor". Thoughts of infinity reminded me of the following mathematical problem: Let x = 0.999999... (recurring) Then 10x = 9.999999... (recurring) Then 10x - x = 9.999999... - 0.999999... So 9x = 9 So x = 1 which contradicts the first statement. :wtf:
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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 didn't get there - it just pointed there, where ever the hour hand points it is always pointing at infinity.... Regards, DoubleWord