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Thread: Infinite

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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 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 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 profloater View Post
    Ok I am just saying I find infinity easier than 10^27 .
    In many ways it's easier to "understand", or convince ourselves we understand, an abstract concept than a concrete amount.
    "I'm planning to live forever. So far, that's working perfectly." Steven Wright

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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 “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.
    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 profloater View Post
    Ok I am just saying I find infinity easier than 10^27 .
    Best I can come up with is, number of molecules in 30 litres of water.

    The number of ways to shuffle a deck of 52 cards is way too large.
    You have meddled with the primal forces of nature, and I won't have it!

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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 Noclevername View Post
    In many ways it's easier to "understand", or convince ourselves we understand, an abstract concept than a concrete amount.
    Yes exactly, it is a problem with the big bang theory for example, that having the universe there for ever back into infinity seems a lot easier to understand than a beginning. Many now “believe” that the big bang was some kind of transformation, rather than a 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

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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

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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

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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

    Crossed in the wire!
    You have meddled with the primal forces of nature, and I won't have it!

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    Quote Originally Posted by profloater View Post
    Many now “believe” that the big bang was some kind of transformation, rather than a creation myth.
    Belief is what makes a myth. What can be tested is what makes science. So far there's no way to test any pre-BB hypotheses. T=0 is the end of our evidence.

    As far as we can prove, the Universe was not around forever. How it "got there" is not within our power to know. But it means time is not infinite in the past direction, anyway. Is the future infinite? Wait and see.
    "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
    Belief is what makes a myth. What can be tested is what makes science. So far there's no way to test any pre-BB hypotheses. T=0 is the end of our evidence.

    As far as we can prove, the Universe was not around forever. How it "got there" is not within our power to know. But it means time is not infinite in the past direction, anyway. Is the future infinite? Wait and see.
    Well I think imagination makes a myth, and then some people believe it. Of course the mainstream view is that we cannot know before the extrapolated big bang and that matter and antimatter arrived and separated. In terms of creation myth that is as good as it gets. We have to be agnostic about time, our perception of time, and whether our current perception has any meaning in the bang, just before or just after it. You have to acknowledge that just starting up is a pretty weak story. There are ideas like Penrose’s that the pattern of the cosmic background suggests a pattern pre-existing the bang.

    In terms of infinities, the big bang has to be a singularity, which is a very polite way to say the model breaks down at that point, and something happens infinitely fast, or something. Unfortunately singularities are untestable. Actually all creation myths are untestable.

    As are infinities, they are not necessarily singularities in experience, only in a mathematical model that is useful most of the time.
    We must be a bit humble in science when our models are untestable.
    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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    Since our understanding stops sometime after T=0, we don't actually know that there was any such time.

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    Quote Originally Posted by profloater View Post
    You have to acknowledge that just starting up is a pretty weak story.
    There is no story. We don't actually know how or why it "started up". Anyone who claims otherwise is indulging in a Creation Myth.

    There's simply no evidence to base any theories on.
    "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
    There is no story. We don't actually know how or why it "started up". Anyone who claims otherwise is indulging in a Creation Myth.

    There's simply no evidence to base any theories on.
    And lacking evidence, an infinite existence with no beginning is no better a creation myth...or at least an origin myth. In fact, it would be harder to explain the lack of evidence...an infinite history that left no marks on the latest 13 billion years or so.

    As far as the evidence goes, extrapolating from current data and understanding indicates that there was an event a finite time in the past that fundamentally changed the universe, and even the notion of "before that event" may not make physical sense. That may be due to flaws in our understanding, but at the moment we don't have anything better.

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    Yes, t=0 is a definite bridge-wizard that says "You Shall Not Pass!"
    "I'm planning to live forever. So far, that's working perfectly." Steven Wright

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    Quote Originally Posted by cjameshuff View Post
    And lacking evidence, an infinite existence with no beginning is no better a creation myth...or at least an origin myth. In fact, it would be harder to explain the lack of evidence...an infinite history that left no marks on the latest 13 billion years or so.
    Not necessarily. I read an article sometime back that was discussing the limitations an alien long in the future (I think it was projecting trillions of years from now, maybe longer) would have projecting back. The CMB temperature would be far down, galaxies would be much dimmer and with the expansion of the universe most would be impossible in principle to see or reach. The argument was that they would have extreme limitations attempting to extrapolate back to the current era, let alone 14 billion years ago. They might not be able to come to the same conclusions that we have because the evidence simply would no longer exist.

    My only interests in this issue are the limits on knowledge and certain creationist arguments I’ve run into. We can reasonably say the universe was very hot and dense 13.8 billion years ago, but beyond that? The universe may be eternal, it may be cyclic, time may be a local phenomenon and not applicable outside certain conditions, etc. We can’t say.

    But I’ve run into creationists that insist that science shows the universe started a finite time back and claim that means it must have a cause which they always attribute to their beliefs. However, science does not show that. In reality, science can only point to a hot and dense point we can’t currently, and may not ever, be able to extrapolate beyond that means less than some people think.

    "The problem with quotes on the Internet is that it is hard to verify their authenticity." — Abraham Lincoln

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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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