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  1. #1
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    Infinite

    Why is it the only concept we cannot accept, define, discuss, rationalize?

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    Quote Originally Posted by diverdude7 View Post
    Why is it the only concept we cannot accept, define, discuss, rationalize?
    It can be defined mathematically (or metaphorically), but it isn't a concept the average person can really wrap our heads around because it's --by necessity-- outside the experience of finite beings. To our perceptions and imagination, it's irrational.

    Nevertheless, there are some extremely brilliant people who seem to understand infinity, or multiple infinities. I envy such geniuses.
    "I'm planning to live forever. So far, that's working perfectly." Steven Wright

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    There are lots of books that will "define, discuss and rationalize" the concept(s) of infinity for you.
    John D. Barrow's The Infinite Book is excellent; Rudy Rucker's old Infinity And The Mind is a wacky classic, but fairly hard work and very much not for everyone.

    Grant Hutchison
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    Quote Originally Posted by diverdude7 View Post
    Why is it the only concept we cannot accept, define, discuss, rationalize?
    I'm not sure why we can't do these things.

    Infinity is not a real number, and this is for good reason. If you try to introduce an "infinity" number, it can't follow the same rules as all the other numbers. This is an analysis homework problem.

    But we deal with infinite concepts all the time. You just can't expect infinite things to behave the same way as finite things do.
    You have meddled with the primal forces of nature, and I won't have it!

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    Quote Originally Posted by 21st Century Schizoid Man View Post
    You just can't expect infinite things to behave the same way as finite things do.
    Right. Our imaginations translate Infinity as just "a really big thing", but that's not an accurate interpretation. It's a literally endless thing.
    "I'm planning to live forever. So far, that's working perfectly." Steven Wright

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    Leaving aside the mathematics, I do not see the problem with irrationals like infinity, zero and Pi. The greek philosophers were upset by the idea, they “believed” the universe should be rational in the literal sense of ratios of whole numbers. But what is the problem in concept? It was part of their atomic theory, there has to be a smallest piece, and Xeno had his “never” paradoxes . Like Pi there may be no physical equivalent of infinity, it is a limit .
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Quote Originally Posted by profloater View Post
    Like Pi there may be no physical equivalent of infinity, it is a limit .
    And if there is such a thing, we may never know it from observation, as it's literally impossible to measure it all.
    "I'm planning to live forever. So far, that's working perfectly." Steven Wright

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    Quote Originally Posted by profloater View Post
    Like Pi there may be no physical equivalent of infinity, it is a limit .
    Draw a circle with diameter one - what is the length of the circumference?

    Looks pretty physically real to me.
    You have meddled with the primal forces of nature, and I won't have it!

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    Quote Originally Posted by 21st Century Schizoid Man View Post
    Draw a circle with diameter one - what is the length of the circumference?

    Looks pretty physically real to me.
    Yeah but it’s made of atoms. Look close and its rough. Only a mathematical concept with an infinitely thin line can be Pi. Sure an accurate drawn circle is close but the thinnest line has a thickness. So you could count the atoms of the diameter and the circumference and get a ratio. But we know Pi means a divided atom somewhere. That is the joy of maths, you can define limits which can never be drawn actually, yet we understand them.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Quote Originally Posted by profloater View Post
    Yeah but it’s made of atoms. Look close and its rough. Only a mathematical concept with an infinitely thin line can be Pi. Sure an accurate drawn circle is close but the thinnest line has a thickness. So you could count the atoms of the diameter and the circumference and get a ratio. But we know Pi means a divided atom somewhere. That is the joy of maths, you can define limits which can never be drawn actually, yet we understand them.
    Yes, and that is a good example of how its impossible to physically measure infinities.

    The human mind struggles to physically conceptualise relatively small quantities let alone infinities. Lets take the number of stars in a galaxy for example 100-400 billion this is a large number relative to our everyday experiences and very difficult to conceptualise. Yet its tiny in comparison to the number of stars in the observable universe, which again is tiny to the number of atoms that make up your body, and so on... In the current observable universe there are approximately 4.65 x 10^185 Planck lengths

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    Quote Originally Posted by cosmocrazy View Post
    Yes, and that is a good example of how its impossible to physically measure infinities.

    The human mind struggles to physically conceptualise relatively small quantities let alone infinities. Lets take the number of stars in a galaxy for example 100-400 billion this is a large number relative to our everyday experiences and very difficult to conceptualise. Yet its tiny in comparison to the number of stars in the observable universe, which again is tiny to the number of atoms that make up your body, and so on... In the current observable universe there are approximately 4.65 x 10^185 Planck lengths
    Ok I am just saying I find infinity easier than 10^27 .
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Quote Originally Posted by diverdude7 View Post
    Why is it the only concept we cannot accept, define, discuss, rationalize?
    Infinity has been a subject of rational discussion and definition since the ancient Greeks, at least. Modern mathematics in fact relies on it for the definition of calculus and defines multiple infinities of multiple different kinds and sizes.

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    Quote Originally Posted by diverdude7 View Post
    Why is it the only concept we cannot accept, define, discuss, rationalize?
    Another example of infinity is the numeric value of 2/3. Which equals 0.6666666666.... a number that can never be ďexactlyĒ written. You can get near infinity but there will always be infinity+1. So to me infinity means never ending. There you have it, infinity defined.
    I know that I know nothing, so I question everything. - Socrates/Descartes

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    Quote Originally Posted by DaCaptain View Post
    Another example of infinity is the numeric value of 2/3. Which equals 0.6666666666.... a number that can never be “exactly” written. You can get near infinity but there will always be infinity+1. So to me infinity means never ending. There you have it, infinity defined.
    This is a property of the way we write numbers down, not a property of the number itself. OK, maybe it is a joint property of the number and our writing system.

    You wrote it exactly yourself, as 2/3.

    And we tend to write numbers in base 10. If humans had twelve fingers instead of ten, then maybe we'd be writing the number 2/3 as 0.8, exactly. And then the number 1/5, which we write exactly as 0.2, would have a never ending representation.
    You have meddled with the primal forces of nature, and I won't have it!

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    Quote Originally Posted by 21st Century Schizoid Man View Post
    This is a property of the way we write numbers down, not a property of the number itself. OK, maybe it is a joint property of the number and our writing system.

    You wrote it exactly yourself, as 2/3.

    And we tend to write numbers in base 10. If humans had twelve fingers instead of ten, then maybe we'd be writing the number 2/3 as 0.8, exactly.
    Similarly, 0.1 has no finite representation in binary and can't be represented exactly with a binary floating point number.

    As for "never ending", there are infinitely many real numbers in any interval of real numbers, such as from 0 to 1.

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    Quote Originally Posted by cjameshuff View Post
    Similarly, 0.1 has no finite representation in binary and can't be represented exactly with a binary floating point number.
    It looks like I was editing my post to include an example like that, while you were writing yours

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    Quote Originally Posted by DaCaptain View Post
    Another example of infinity is the numeric value of 2/3. Which equals 0.6666666666.... a number that can never be “exactly” written. You can get near infinity but there will always be infinity+1. So to me infinity means never ending. There you have it, infinity defined.
    Yes but it , 2/3 , is a ratio of whole numbers., zero, Pi and infinity are not.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Quote Originally Posted by profloater View Post
    Yes but it , 2/3 , is a ratio of whole numbers., zero, Pi and infinity are not.
    It was a bad example. The idea of having something that continues without an end was the premise.
    I know that I know nothing, so I question everything. - Socrates/Descartes

  19. #19
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    Quote Originally Posted by DaCaptain View Post
    It was a bad example. The idea of having something that continues without an end was the premise.
    Yes indeed, but in that we see how a mathematical convention produces a never ending series while we can understand dividing a cake into thirds or separating eight sheep from a flock of twelve. Time conventions are similar even without the modern understanding that there is no universal time. If there was a time before change, a nothingness stretching back in infinity, does that actually mean anything? Two objects in mutual orbit for ever, that, to me, is easy to understand.

    In history that puzzle was solved by a mystery, a creation myth usually, and those live on. I was always unconvinced by creation myths, preferring for as long as I can remember, an infinity of existence. Mutation from energy to matter is no worry, but nothing to something is disturbing, for me. Matter plus antimatter summing to zero is, for me, just another unsatisfactory creation myth.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

  20. #20
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    Since our understanding stops sometime after T=0, we don't actually know that there was any such time.

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    Look we have scientific evidence that points back to the big bang, lots of consistent evidence. Other versions of creation have no evidence at all. The evidence can be examined by anyone, in the sense of peer reviewed papers. But the infinity point is that the story ends back there at a singularity.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Quote Originally Posted by profloater View Post
    Look we have scientific evidence that points back to the big bang, lots of consistent evidence.
    The big bang evidence is about how the universe developed, not how it (or if it) began.

    Other versions of creation have no evidence at all. The evidence can be examined by anyone, in the sense of peer reviewed papers. But the infinity point is that the story ends back there at a singularity.
    We donít know that, we can only say the universe was very dense and hot about 13.8 billion years ago.

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    Maybe use the Planck Time as our limit?
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    Quote Originally Posted by Tom Mazanec View Post
    Maybe use the Planck Time as our limit?
    That is at least consistent. Even if it turns out to be not a constant, it avoids that zero. So if you divide by it as a rate, you get a big number but not infinity.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Something that presents a paradox in my mind is to consider a universe that had ( T=0 ) beginning but then extends for infinity into the future. If you flip this argument on its head and consider looking back from "infinitely" far in the future, then the timeline line would appear to extend infinitely back into the past thus no beginning.

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    Quote Originally Posted by cosmocrazy View Post
    Something that presents a paradox in my mind is to consider a universe that had ( T=0 ) beginning but then extends for infinity into the future. If you flip this argument on its head and consider looking back from "infinitely" far in the future, then the timeline line would appear to extend infinitely back into the past thus no beginning.
    How could you look back from infinite anything? If it takes time to reach that point, it's finite by definition. Any observing being has a beginning, middle, end. It's like C, mass can approach it but never reach it.
    "I'm planning to live forever. So far, that's working perfectly." Steven Wright

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    Quote Originally Posted by Noclevername View Post
    How could you look back from infinite anything? If it takes time to reach that point, it's finite by definition. Any observing being has a beginning, middle, end. It's like C, mass can approach it but never reach it.
    Absolutely, but do you agree that if the universe extends for infinity then theoretically there should be a point infinitely far away? But really there can never be such a point, since for every point along the journey there is a finite distance from the beginning and an infinite distance ahead. My point was rather to highlight paradoxes that occur when considering infinity from certain perspectives.

    The logical answer and definition is what you state

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    Quote Originally Posted by cosmocrazy View Post
    Absolutely, but do you agree that if the universe extends for infinity then theoretically there should be a point infinitely far away?
    Since a point is finite, I think there can't be "a point infinitely far away". It's like saying "If time is infinite when is the last moment"? By definition it won't have one.
    "I'm planning to live forever. So far, that's working perfectly." Steven Wright

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    Quote Originally Posted by Noclevername View Post
    Since a point is finite, I think there can't be "a point infinitely far away". It's like saying "If time is infinite when is the last moment"? By definition it won't have one.
    Actually a mathematical point is infinitely small and you could have in (x,y) , (inf,inf) but it has no practical meaning just as you can have inf ^ inf or an infinite set within a larger infinite set. All maths for manipulating equations. There can be an infinity of numbers between zero and one. But as has been said, if you put practical constraint you have a smallest step or planck length. Like those parallel lines of the infinite railway track, if you travel them they never meet. Infinity is a limit in a maths model.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Quote Originally Posted by Noclevername View Post
    Since a point is finite, I think there can't be "a point infinitely far away". It's like saying "If time is infinite when is the last moment"? By definition it won't have one.
    I may be misunderstanding. But isnít the question about the distance between two points? The distance between two points is a line, and a line can be infinitely long, so Iím not sure what the size of the point has to do with it. When you talk about the distance arenít you referring to the line between the two points?


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