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.
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
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Infinity is not a number therefore by trying to represent it with numbers you are doomed.
Join the cool kids - Come fold with us[^]
:~
Luc Pattyn [Forum Guidelines] [Why QA sucks] [My Articles]
Merry Christmas and a Happy New Year to all.
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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:
Now exapnd that concept from a two-dimensional object in the three dimensions into a three-dimensional object in a four dimensions.
There's the rub! That's where our spatial, or solids, models of perception break down.
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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:
You *can* reach infinity by counting - you just have to e.g. permanently double your speed.
Oooh! +5
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Which infinity? There are many.[^]
All those who believe in psycho kinesis, raise my hand.
how many exactly? :)
Luc Pattyn [Forum Guidelines] [Why QA sucks] [My Articles]
Merry Christmas and a Happy New Year to all.
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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.
Hi Rob, Both Cantor and Godel went insane working on the problem of the "Aleph," or the ordinality of infinities : careful, there. I like Blaise Pascal's words : "A fearful sphere whose center is everywhere, and circumference is nowhere." Jorge Borges, one of my favorite writers, traces the origins of that metaphor from ancient Greek times, up through the middle ages, in one of his best known essays (citation on request : note the word 'fearful' was first used in a 1941 scholarly translation that, for the first time, accurately included and translated the French word "effroyable" (fearful) : whereas earlier translations/editions rendered the quote starting with "Nature is a sphere ..."). 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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:~
Luc Pattyn [Forum Guidelines] [Why QA sucks] [My Articles]
Merry Christmas and a Happy New Year to all.
But that's just convention - arguably a sensible one. But Troll is right (something you read only on CP...) - infinity is not on that line, and it sems to me you are still looking for it there.
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 -
But that's just convention - arguably a sensible one. But Troll is right (something you read only on CP...) - infinity is not on that line, and it sems to me you are still looking for it there.
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:
still looking for it
Not at all. There are at least two infinities on every straight line, so we'll never run out of infinities. Unless you start claiming there is no such thing as a straight line... :)
Luc Pattyn [Forum Guidelines] [Why QA sucks] [My Articles]
Merry Christmas and a Happy New Year to all.
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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!
