# The beginning of linear(?) time and matter. **URL:** \ **Category:** Great Debates\ **Created:** [February 24, 2014, 2:42am UTC](https://boards.straightdope.com/t/the-beginning-of-linear-time-and-matter/682062 "2014-02-24T02:42:29Z")\ **Posts on this page:** 20\ **Page:** 5
**Author:** ![Half\_Man\_Half\_Wit](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/half_man_half_wit/32/21766_2.png) [@Half\_Man\_Half\_Wit](https://boards.straightdope.com/u/Half_Man_Half_Wit)\ **Post date:** [March 6, 2014, 6:16pm UTC](https://boards.straightdope.com/t/the-beginning-of-linear-time-and-matter/682062/81 "2014-03-06T18:16:50Z")
> [@Gateway](#): > > I think we have an impasse. An infinite line denoting moments is an infinite amount of past moments. But your argument, to work, needs an infinite amount of moments to have _elapsed_. It’s a case where the finite and the infinite part ways, and what works for the finite case no longer works in the infinite case. If there were, say, twenty moments in the past, then twenty moments would have elapsed since the beginning. The two notions are the same, for the finite case. No longer in the infinite case. There, even though there is an infinite number of moments to the past, in time, that is, since any given moment in the past, only a finite amount of moments have elapsed. It’s similar to Hilbert’s Hotel: in the finite case, if you have twenty rooms, and twenty rooms are occupied, no more guests will fit. But again, in the infinite case, the two notions are no longer the same: even though infinitely many rooms are occupied, you can always make room for more guests. Really, you can confirm this for yourself: find two numbers such that their difference is infinity. If you can, then your argument works; but if you can’t, then this means directly that there is no infinite amount of time between any two moments, and thus, no matter ‘when’ you are, there is no moment such that from then, it would have taken an infinite amount of moments to get to now. Again, consider the finite case: twenty moments to the past, so from then to now, twenty moments have elapsed. But for the infinite case, this simply ceases to be true: ‘amount of time to the past’ and ‘time elapsed until now’ cease to mean the same thing, just as ‘number of guests in hotel’ and ‘number of rooms occupied’ cease to mean the same thing in Hilbert’s Hotel. This isn’t intuitive, but the math is easy: subtract any two numbers, and your result will always be smaller than infinity. > [@](#): > > To me, it is a contradiction in terms to have a fixed number which is infinite. I think you agree as well that it is a contradiction, but the our difference is I apply that to the past and you do not. I don’t think it’s a contradiction that a quantum field has infinitely many degrees of freedom, for instance. > [@](#): > > -The past = a fixed amount of moments _because they actually happened_. There is no adjusting them at this point. Fixed amount of past = fixed amount of time = fixed amount of moments. > -To say there is an infinite past IS an infinite amount of moments, for the past is made up of moments. Yes, but from none of those moments in the past, it takes an infinite amount of moments to get to here; the distance between any of the infinite amount of moments in the past and now is always finite. Check them one by one: time between now and one moment to the past—one moment. Time between now and two moments to the past—two moments. Time between now and n moments to the past—n moments. Time between now and n+1 moments to the past—n+1 moments. So, by induction, for all moments in the past, the time to get to now is finite. Only if that were not the case would your argument work. > [@](#): > > Have you ever SEEN infinity? > Let me ask you, if there is an infinite amount of walkers on the line, are they all observable at one time? No. Why not, considering that a walker should be a phenomenon that is observable? > Do you see how this fits with what I have been saying? This is just confusing a limit of perception with a limit on what exists. If we could perceive no greater quantities than 500, would that mean that nothing could be in greater quantity than 500? ---
**Author:** ![Canadjun](https://avatars.discourse-cdn.com/v4/letter/c/76d3ee/32.png) [@Canadjun](https://boards.straightdope.com/u/Canadjun)\ **Post date:** [March 6, 2014, 7:23pm UTC](https://boards.straightdope.com/t/the-beginning-of-linear-time-and-matter/682062/82 "2014-03-06T19:23:40Z")
> [@Gateway](#): > > It’s important because of this: if you think about pi, you can say it is an infinite number. But by the same token, to observe all of the numbers at one time in a hypothetical situation is to say that we have “fully written out pi.” This cannot be. It is different to say “pi is infinite” vs saying “I have written out all of the numbers of pi.” When you say you have infinity people, you are saying: “I have written out all of the numbers of pi.” > > Observing the infinite is impossible for us, and people existing should be observable. It is contradictory. Not because we can’t look at all of them, but because of the reason why it is impossible to look at all of them (“I have written out all of the numbers of pi”) Huh?! Pi is a **finite** number. The fact that it is irrational does not make it infinite. ---
**Author:** ![Gateway](https://avatars.discourse-cdn.com/v4/letter/g/dbc845/32.png) [@Gateway](https://boards.straightdope.com/u/Gateway)\ **Post date:** [March 6, 2014, 9:44pm UTC](https://boards.straightdope.com/t/the-beginning-of-linear-time-and-matter/682062/83 "2014-03-06T21:44:14Z")
> [@Half Man Half Wit](#): > > But your argument, to work, needs an infinite amount of moments to have elapsed. How does the past not contain only that which has elapsed? …I am not following your argument in paragraphs 2-5. > [@](#): > > I don’t think it’s a contradiction that a quantum field has infinitely many degrees of freedom, for instance. I am not familiar with quantum fields. > [@gateway](#): > > -The past = a fixed amount of moments because they actually happened. There is no adjusting them at this point. Fixed amount of past = fixed amount of time = fixed amount of moments. > -To say there is an infinite past IS an infinite amount of moments, for the past is made up of moments. > > > [@Half Man Half Wit](#): > > > > Yes, but from none of those moments in the past, it takes an infinite amount of moments to get to here; Yet you claim that this is compatable with there being an infinite amount of intervals > [@](#): > > So, by induction, for all moments in the past, the time to get to now is finite. So if there was an finite amount of time intervals leading to now, then there was not an infinite amount of intervals. I see this supporting my argument that there would therefor be a beginning of time, since ALL intervals are a finite distance away, thus there is no infinite distance. > [@Gateway](#): > > Have you ever SEEN infinity? > Let me ask you, if there is an infinite amount of walkers on the line, are they all observable at one time? No. Why not, considering that a walker should be a phenomenon that is observable? > Do you see how this fits with what I have been saying? > > > [@Half Man Half Wit](#): > > > > This is just confusing a limit of perception with a limit on what exists. If we could perceive no greater quantities than 500, would that mean that nothing could be in greater quantity than 500? My response: > [@Gateway](#): > > Observing the infinite is impossible for us, and people existing should be observable. **It is contradictory. Not because we can’t look at all of them, but because of the reason why it is impossible to look at all of them (“I have written out all of the numbers of pi”)** Consider pi. ON ONE LEVEL, all the infinite numbers of pi exist here and now. On another level, it is impossible to ever CONCRETELY write out all of the numbers. To imply an infinite past on a line implies is the same thing as concretely writing out all the numbers. For the past is a succession of CONCRETE time intervals (seconds, minutes, days, etc.) which would have to be passed through to get to now. ---
**Author:** ![CurtC](https://avatars.discourse-cdn.com/v4/letter/c/ce73a5/32.png) [@CurtC](https://boards.straightdope.com/u/CurtC)\ **Post date:** [March 6, 2014, 10:11pm UTC](https://boards.straightdope.com/t/the-beginning-of-linear-time-and-matter/682062/84 "2014-03-06T22:11:21Z")
> [@Gateway](#): > > To imply an infinite past on a line implies is the same thing as concretely writing out all the numbers. For the past is a succession of CONCRETE time intervals (seconds, minutes, days, etc.) which would have to be passed through to get to now. No, that makes no sense. It’s like you’re starting from the idea that the universe had a beginning, but it was infinitely long ago. That’s not it - if the universe is infinitely old, it simply _didn’t have_ a beginning. Would you agree that there’s no philosophical problem with time extending infinitely into the future? If you’re OK with that, can you then state how that’s substantially different from its extending infinitely into the past? ---
**Author:** ![Telemark](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/telemark/32/372_2.png) [@Telemark](https://boards.straightdope.com/u/Telemark)\ **Post date:** [March 6, 2014, 10:33pm UTC](https://boards.straightdope.com/t/the-beginning-of-linear-time-and-matter/682062/85 "2014-03-06T22:33:18Z")
> [@Gateway](#): > > For the past is a succession of CONCRETE time intervals (seconds, minutes, days, etc.) which would have to be passed through to get to now. Only if the past is finite. If the past is infinite then your assumption no longer holds. Infinities are at odds with common sense; some of your basic assumptions are wrong once you start dealing with the infinite. ---
**Author:** ![Gateway](https://avatars.discourse-cdn.com/v4/letter/g/dbc845/32.png) [@Gateway](https://boards.straightdope.com/u/Gateway)\ **Post date:** [March 7, 2014, 12:24am UTC](https://boards.straightdope.com/t/the-beginning-of-linear-time-and-matter/682062/86 "2014-03-07T00:24:46Z")
> [@CurtC](#): > > No, that makes no sense. It’s like you’re starting from the idea that the universe had a beginning, but it was infinitely long ago. That’s not it - if the universe is infinitely old, it simply _didn’t have_ a beginning. > > Would you agree that there’s no philosophical problem with time extending infinitely into the future? > > If you’re OK with that, can you then state how that’s substantially different from its extending infinitely into the past? The problem with the universe being infinitely old, is that there must have passed an infinite amount of regular time intervals (seconds, minutes, years, decades, etc.). Would you say, “this moment happened after an infinity of seconds?” That is what you must say if you have an infinity of time behind you. I think that there is a philosophical problem with time extending infinitely into the future. It keeps going, and going and going, but at no point does it ACTUALLY spread infinitely. > [@Telemark](#): > > Only if the past is finite. If the past is infinite then your assumption no longer holds. Infinities are at odds with common sense; some of your basic assumptions are wrong once you start dealing with the infinite. Again, how can you have an infinite past? An infinite past = an infinite amount of seconds in the past. An infinite amount of seconds can only be in the mind, not actually exist. You can conceptualize that an infinite amount of things but never actually physically have infinity (e.g. you can imagine pi going on for infinity, but you can’t ever have all the numbers at one time on a piece of paper. Ever. Find the reason that this is so, and you find the) What is the number right before you reach infinity? There isn’t one, because there is no number sequence leading up to it, and there CANNOT be. 4 comes before 5, 35 comes before 36, what comes before infinity? It was never written in as a number like that. Infinity denotes an infinite potential, not a numerical value. To say there is an infinite amount of seconds behind us is to say that we have passed through the fixed value of infinity. That is the flaw: there is no fixed value for infinity, as it cannot exist. Say whatever argument you will, but can you tell me the number that comes right before infinity? And nothing cute like infinity-1. If I am asking for the number before 5, I am not looking for 5-1, but 4. The reason you won’t be able to find the number is because it isn’t written in to the number sequence like 1,2,3,4,5, It is an unlimited amount. Unlimited meaning, if the past was unlimited, we would never have gotten here because we would have to wait an unlimited amount of time. In fact, this may be where the hang-up is. DEFINING MY TERMS: **Infinite:** An unlimited amount. **Linear Time:** The current moment moving into the future and away from the past constantly, while always remaining in the present. Each new moment is always the farthest in the future. ---
**Author:** ![Gateway](https://avatars.discourse-cdn.com/v4/letter/g/dbc845/32.png) [@Gateway](https://boards.straightdope.com/u/Gateway)\ **Post date:** [March 7, 2014, 12:35am UTC](https://boards.straightdope.com/t/the-beginning-of-linear-time-and-matter/682062/87 "2014-03-07T00:35:01Z")
Missed editing window. Telemark, When you say that time may extent infinitely into the future, that is the same as saying that time extends an unlimited amount into the future. It’s okay as the thought of adding one unit of time (say, seconds) to the next to the next. But you won’t ever get an unlimited amount. What I see is _an unlimited amount only describes a potential, not an existing amount_. To say that an EXISTING number is unlimited is a false statement. So I see the same problem here, thus I wouldn’t feel comfortable saying this makes an infinite past plausible. ---
**Author:** ![CurtC](https://avatars.discourse-cdn.com/v4/letter/c/ce73a5/32.png) [@CurtC](https://boards.straightdope.com/u/CurtC)\ **Post date:** [March 7, 2014, 4:27am UTC](https://boards.straightdope.com/t/the-beginning-of-linear-time-and-matter/682062/88 "2014-03-07T04:27:26Z")
> [@Gateway](#): > > The problem with the universe being infinitely old, is that there must have passed an infinite amount of regular time intervals (seconds, minutes, years, decades, etc.). Would you say, “this moment happened after an infinity of seconds?” An infinity of seconds _since when_? Any event you can name, to measure relative to, is a finite interval away. ---
**Author:** ![Telemark](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/telemark/32/372_2.png) [@Telemark](https://boards.straightdope.com/u/Telemark)\ **Post date:** [March 7, 2014, 4:55am UTC](https://boards.straightdope.com/t/the-beginning-of-linear-time-and-matter/682062/89 "2014-03-07T04:55:46Z")
> [@Gateway](#): > > What I see is _an unlimited amount only describes a potential, not an existing amount_. To say that an EXISTING number is unlimited is a false statement. So I see the same problem here, thus I wouldn’t feel comfortable saying this makes an infinite past plausible. Again, the fact that you can’t wrap your head around the concept of infinite time doesn’t invalidate the idea. The human mind has a difficult time (ha!) grasping the idea. Infinity isn’t a number - stop thinking of it that way. ---
**Author:** ![Gateway](https://avatars.discourse-cdn.com/v4/letter/g/dbc845/32.png) [@Gateway](https://boards.straightdope.com/u/Gateway)\ **Post date:** [March 7, 2014, 4:59am UTC](https://boards.straightdope.com/t/the-beginning-of-linear-time-and-matter/682062/90 "2014-03-07T04:59:07Z")
> [@CurtC](#): > > An infinity of seconds _since when_? Any event you can name, to measure relative to, is a finite interval away. There is no ‘since when.’ If you have an infinite timeline it must contain an infinite amount of seconds on it. ---
**Author:** ![Gateway](https://avatars.discourse-cdn.com/v4/letter/g/dbc845/32.png) [@Gateway](https://boards.straightdope.com/u/Gateway)\ **Post date:** [March 7, 2014, 5:07am UTC](https://boards.straightdope.com/t/the-beginning-of-linear-time-and-matter/682062/91 "2014-03-07T05:07:04Z")
> [@Telemark](#): > > Infinity isn’t a number - stop thinking of it that way. Did you not read this post? [QUOTE=Gateway] What is the number right before you reach infinity? There isn’t one, because there is no number sequence leading up to it, and there CANNOT be. 4 comes before 5, 35 comes before 36, what comes before infinity?\*\*\* It was never written in as a number like that. Infinity denotes an infinite potential, not a numerical value.\*\*\* [/QUOTE] ---
**Author:** ![simster](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/simster/32/1047_2.png) [@simster](https://boards.straightdope.com/u/simster)\ **Post date:** [March 7, 2014, 5:15am UTC](https://boards.straightdope.com/t/the-beginning-of-linear-time-and-matter/682062/92 "2014-03-07T05:15:14Z")
> [@Gateway](#): > > There is no ‘since when.’ If you have an infinite timeline it must contain an infinite amount of seconds on it. Between any two points on that line - is a finite number of seconds - if you are trying to get from -infinity to infinity on the other end - ‘that’ will never happen - but from any identifiable point (600,000,000,000 years ago when cthulu sneezed) to now - you can absolutely determine the number of seconds between the two events. ---
**Author:** ![Gateway](https://avatars.discourse-cdn.com/v4/letter/g/dbc845/32.png) [@Gateway](https://boards.straightdope.com/u/Gateway)\ **Post date:** [March 7, 2014, 5:23am UTC](https://boards.straightdope.com/t/the-beginning-of-linear-time-and-matter/682062/93 "2014-03-07T05:23:53Z")
> [@simster](#): > > Between any two points on that line - is a finite number of seconds - if you are trying to get from -infinity to infinity on the other end - ‘that’ will never happen - but from any identifiable point (600,000,000,000 years ago when cthulu sneezed) to now - you can absolutely determine the number of seconds between the two events. This actually came close to convincing me. However: How is there a finite amount of intervals (lets say seconds) on an infinite line? An infinite line can be said to be an unlimited line. So, how do you have a limited amount of seconds on an unlimited line? I get that there is a finite distance between any past interval and now, but still: _ **there is an unlimited number of finite distances.** _ So, to pass through all of those intervals to get to now is still to say events passed through an unlimited amount. An unlimited amount would take forever to pass through. The intervals (lets say seconds) all have a finite distance between the particular second and now, but there is still an UNLIMITED amount of seconds. Unlimited means it would take forever to get to now. ---
**Author:** ![simster](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/simster/32/1047_2.png) [@simster](https://boards.straightdope.com/u/simster)\ **Post date:** [March 7, 2014, 5:56am UTC](https://boards.straightdope.com/t/the-beginning-of-linear-time-and-matter/682062/94 "2014-03-07T05:56:22Z")
> [@Gateway](#): > > This actually came close to convincing me. > > However: > > How is there a finite amount of intervals (lets say seconds) on an infinite line? An infinite line can be said to be an unlimited line. So, how do you have a limited amount of seconds on an unlimited line? I get that there is a finite distance between any past interval and now, but still: _ **there is an unlimited number of finite distances.** _ > > So, to pass through all of those intervals to get to now is still to say events passed through an unlimited amount. An unlimited amount would take forever to pass through. > > The intervals (lets say seconds) all have a finite distance between the particular second and now, but there is still an UNLIMITED amount of seconds. Unlimited means it would take forever to get to now. while you are correct to say that “an unlimited amount of seconds would take forever to get thru” it is incorrect to think that we cant say that since point X, a finite amount of those seconds has passed. Your mistake is conflating the two concepts (time is infinte) with determining that X amount of time has taken place since Y event. secondly - since we are clearly @ now - we have had to pass thru ‘all’ the intervals to get to this point - but that doesn’t also mean that we have to say what “all” actually is. ---
**Author:** ![Trinopus](https://avatars.discourse-cdn.com/v4/letter/t/2bfe46/32.png) [@Trinopus](https://boards.straightdope.com/u/Trinopus)\ **Post date:** [March 7, 2014, 6:07am UTC](https://boards.straightdope.com/t/the-beginning-of-linear-time-and-matter/682062/95 "2014-03-07T06:07:27Z")
My argument – or intuition – is that, in the same way that we will never “get to” a time that is infinitely away in the future, we can also not possibly have “come from” a time infinitely away in the past. If the moment of meta-creation was “infinitely long ago” then – how can we exist here, now? Wouldn’t we still be waiting for “now?” Waiting forever, in fact? (By meta-creation, I mean what a Christian might call the “beginning of God.” If God has been around “since forever,” shouldn’t we still be waiting for the First Day?) For there to be a “now,” then that “forever” has come to an end. Messy. I think that our language isn’t up to the task. Just say “Long ago, outside a universe far, far away.” ---
**Author:** ![Half\_Man\_Half\_Wit](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/half_man_half_wit/32/21766_2.png) [@Half\_Man\_Half\_Wit](https://boards.straightdope.com/u/Half_Man_Half_Wit)\ **Post date:** [March 7, 2014, 6:41am UTC](https://boards.straightdope.com/t/the-beginning-of-linear-time-and-matter/682062/96 "2014-03-07T06:41:34Z")
> [@Gateway](#): > > How does the past not contain only that which has elapsed? We’re talking about two different things, which for all finite amounts of time happen to be equivalent, but which cease to be so in the infinite case. One of which is the totality of moments to the past—this is analogous to the totality of numbers on the infinite line, if the past is infinite. This is clearly infinite. But the other, the notion your argument needs, is the amount of time elapsed since any particular point in the past. This is analogous to the difference between any two numbers on the infinite number line. In all finite cases, these two are the same things: if we have a number line that extends 20 units to the past, then the maximum time elapsed is 20 moments, because the difference between 20 and 0 is 20. But there is no difference between two numbers that is equal to the total amount of numbers: the two notions diverge. Any interval is finite. From any point in the past, it took a finite time to get here; this is true for _all_ of the infinitely many points in the past. This is just the mathematical fact that there is no difference between two numbers that is infinite, since elapsed times are differences between numbers. > [@](#): > > So if there was an finite amount of time intervals leading to now, then there was not an infinite amount of intervals. But still an infinite amount of time, since the notions ‘total amount of moments’ and ‘time elapsed since any moment’ are no longer the same in the infinite case. > [@](#): > > Observing the infinite is impossible for us, and people existing should be observable. Why? Even for a sufficiently large universe, there are existing things that are unobservable, because they recede from us faster than the speed of light, and thus, we can never make contact with them. Your assertion is simply question-begging. > [@](#): > > Consider pi. ON ONE LEVEL, all the infinite numbers of pi exist here and now. On another level, it is impossible to ever CONCRETELY write out all of the numbers. To imply an infinite past on a line implies is the same thing as concretely writing out all the numbers. For the past is a succession of CONCRETE time intervals (seconds, minutes, days, etc.) which would have to be passed through to get to now. And all of these concrete time intervals are finite. Have you tried the check of that I proposed? Are there any two numbers such that their difference is not finite? Because if not, then this directly means that there is no infinite amount of time elapsed anywhere. > [@Gateway](#): > > The problem with the universe being infinitely old, is that there must have passed an infinite amount of regular time intervals (seconds, minutes, years, decades, etc.). This is just wrong, mathematically. There’s a concrete counter example to just this argument which I’ve pointed out a number of times now: the infinite number line. Let’s see where you disagree. [ol] [li]There are infinitely many numbers on the infinite number line. [/li][li]The difference between any two numbers on the line is finite.[/li][li]There is no infinite amount of regular intervals between any two numbers. (Say your regular interval is 1, then the number of regular intervals between any two numbers is just their difference, so finite because of 2. Any different interval size will just be a multiple/fraction of that, so remain finite.)[/li][li]There is even a finite number of differently-sized intervals between any two numbers (if we have a smallest interval size, a ‘moment’ in your sense). This again follows by induction: between now and a moment ago, there is one interval—a finite amount. If there is a finite amount of intervals between now and n moments ago, there is a finite amount of intervals between now and n+1 moments ago (since only finitely many intervals, corresponding to the total amount of partitions of a set with n+1 elements, are added). [/li][/ol] But if all of these are true, then your assertion—that from there being an infinite amount of things, it follows that there are an infinite amount of intervals between any of those things—does not follow. > [@Gateway](#): > > How is there a finite amount of intervals (lets say seconds) on an infinite line? An infinite line can be said to be an unlimited line. So, how do you have a limited amount of seconds on an unlimited line? I get that there is a finite distance between any past interval and now, but still: _ **there is an unlimited number of finite distances.** _ But not between any _point in the past_ and now. So there is no point in time _since when_ an infinite amount of time has elapsed. And all times that pass, pass between two points in time. There are, in an infinite time, no two points between which an infinite amount of time passes. ---
**Author:** ![Gateway](https://avatars.discourse-cdn.com/v4/letter/g/dbc845/32.png) [@Gateway](https://boards.straightdope.com/u/Gateway)\ **Post date:** [March 8, 2014, 12:51am UTC](https://boards.straightdope.com/t/the-beginning-of-linear-time-and-matter/682062/97 "2014-03-08T00:51:32Z")
> [@Half\_Man\_Half\_Wit](#): > > all finite amounts of time happen to be equivalent, but which cease to be so in the infinite case. Why? One of which is the totality of moments to the past—this is analogous to the totality of numbers on the infinite line, if the past is infinite. This is clearly infinite. > > But the other, the notion your argument needs, is the amount of time elapsed since any particular point in the past. This is a very convincing point. I get what this line of reasoning is saying: ALL of the numbers on the line are of finite distance to the now, so we are only dealing with finite quantities. This works up to a point for me, the point is this: Lets take seconds. All distances ARE a finite distance away from he now, but you have an infinite/unlimited amount of seconds which have the quality of being a finite distance away from the now. In having an unlimited amount of seconds you still have to pass through an unlimited length of time to get to the now, which is a contradiction in terms (this moment couldn’t have come from an unlimited amount because _an unlimited amount can’t pass by to get to a moment after the initial unlimited amount of time_) > [@](#): > > There are infinitely many numbers on the infinite number line. I agree to an extent. Whenever we see a graph with a line and two arrows representing infinity, what it is is a concept. In and of itself, I am not sure if this can exist in what we perceive to be our space-time. It exists as a potential: I can divide, and subdivide, and subdivide any length by half in real life, but I will never be able to REACH infinity if I start now. It seems that it is only a conceptual possibilty to keep going, but not that you can ever get there. Infinite ≠ Finite. To say we got there is to make it finite because we can only get to something finite, or you put something beyond being reached (such as waiting FOREVER, and THEN doing something.) So it is either finite or something which cannot be consecutively reached in regular steps. As far as an infinite line representing our timeline looks like it might be an inherently flawed premise from the get-go. > [@](#): > > There is no infinite amount of regular intervals between any two numbers. No, but there is an infinite amount of regular intervals of which to pass through before we get to the now in this model. ---
**Author:** ![Half\_Man\_Half\_Wit](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/half_man_half_wit/32/21766_2.png) [@Half\_Man\_Half\_Wit](https://boards.straightdope.com/u/Half_Man_Half_Wit)\ **Post date:** [March 8, 2014, 10:23am UTC](https://boards.straightdope.com/t/the-beginning-of-linear-time-and-matter/682062/98 "2014-03-08T10:23:15Z")
> [@Gateway](#): > > Lets take seconds. All distances ARE a finite distance away from he now, but you have an infinite/unlimited amount of seconds which have the quality of being a finite distance away from the now. In having an unlimited amount of seconds you still have to pass through an unlimited length of time to get to the now, No. The only thing you have to pass through is the finite distance from any of those points in the past. > [@](#): > > I agree to an extent. If you disagree with there being infinitely many numbers, then you should be able to quote a number such that there isn’t any bigger one. If you can’t, then this means there are infinitely many numbers, whether we can represent them or not (and of course, there are ways to represent them, such as via [stereographic projection](http://en.wikipedia.org/wiki/Stereographic_projection), where the whole infinite plane is mapped to the surface of a sphere). You’re again confusing limits or our imagination/representational tools with limits of the world. > [@](#): > > No, but there is an infinite amount of regular intervals of which to pass through before we get to the now in this model. As I’ve demonstrated most explicitly in my last post, this is just not the case. If you disagree with any of the points I made, could you please state which one it is? Perhaps hearing the argument from [Quentin Smith](http://en.wikipedia.org/wiki/Quentin_Smith) helps (aleph-zero: infinitely many, as many as there are natural numbers): [ > [@](#): > > The error in question appears in the commonly stated argument that > > (1) Aleph-zero events have occurred before the present event > entails > (2) Events separated from the present event by aleph-zero events have occurred > which in turn entails > (3) From one of the events separated from the present event by aleph-zero events the present event could not have been reached. > > The fallacy lies in the belief that (1) entails (2). It does not; for aleph-zero events could have occurred before the present event such that no one of these events is separated from the present event by aleph-zero events. It is this state of affairs that I discussed in the last section in connection with the set of negative numbers with the order type ω\*. The number of these negative numbers is aleph-zero, but no one of these negative numbers is separated from zero by an aleph-zero number of numbers. ]([http://www.jstor.org/discover/10.2307/187473?uid=3737864&uid=2&uid=4&sid=21103612944427](http://www.jstor.org/discover/10.2307/187473?uid=3737864&uid=2&uid=4&sid=21103612944427)) He goes on to discuss the implication of the infinite line having order type ω\*. Basically, this means that it’s ordered like: …,-4,-3,-2,-1,0 where the dots correspond to the infinitely many numbers before. There, clearly, no infinite distances occur, so from no point on that line would it have taken infinitely many seconds/moments/events to get to now: it’s perfectly consistent. However, one could reorder the line, putting, say, all the even numbers before the odd ones, …,-4,-2,…,-3,-1,0 thus making it of order type ω\* + ω\*. There, your argument would work: there is actually an infinite distance between -4 and -3, and to get to one from the other would require an infinite amount of time to elapse. But that’s of course not how the sequence of past events is ordered, or at any rate, there is no need to assume this (this relates back to a point I madein the very beginning that this is not just a question of cardinality, but of ordinality). While the two differently-ordered number lines can be put into one-to-one correspondence, thus making them of the same cardinality (aleph-zero), the ordinality properties are not preserved in this mapping, and it’s those that determine the question of whether there are infinite time intervals or not. And it’s quite simply a mathematical fact that there are no infinite intervals in an object of order type ω\*. ---
**Author:** ![Gateway](https://avatars.discourse-cdn.com/v4/letter/g/dbc845/32.png) [@Gateway](https://boards.straightdope.com/u/Gateway)\ **Post date:** [March 8, 2014, 6:28pm UTC](https://boards.straightdope.com/t/the-beginning-of-linear-time-and-matter/682062/99 "2014-03-08T18:28:01Z")
> [@Half\_Man\_Half\_Wit](#): > > No. The only thing you have to pass through is the finite distance from any of those points in the past. In any interval before the now, there is an finite distance. I understand this point, at least the concept, but don’t agree. Consider: \*You are saying there is no infinite distance on an infinite line. \* The infinite distance (which can’t be consecutively passed through) is implied when you start with an infinite line. [QUOTE=Gateway] No, but there is an infinite amount of regular intervals of which to pass through before we get to the now in this model. [QUOTE=Half Man Half Wit] As I’ve demonstrated most explicitly in my last post, this is just not the case. If you disagree with any of the points I made, could you please state which one it is? [/QUOTE] [/QUOTE] My disagreement is in my italicized text above. I don’t see how your last post demonstrated that this is not the case. > [@Half Man Half Wit](#): > > Perhaps hearing the argument from [Quentin Smith](http://en.wikipedia.org/wiki/Quentin_Smith) helps (aleph-zero: infinitely many, as many as there are natural numbers): > [URL=“[Client Challenge](http://www.jstor.org/discover/10.2307/187473?uid=3737864&uid=2&uid=4&sid=21103612944427)”] > > He goes on to discuss the implication of the infinite line having order type ω\*. Basically, this means that it’s ordered like: > …,-4,-3,-2,-1,0 > where the dots correspond to the infinitely many numbers before. There, clearly, no infinite distances occur, so from no point on that line would it have taken infinitely many seconds/moments/events to get to now: it’s perfectly consistent. > > However, one could reorder the line, putting, say, all the even numbers before the odd ones, > …,-4,-2,…,-3,-1,0 > thus making it of order type ω\* + ω\*. There, your argument would work: there is actually an infinite distance between -4 and -3, and to get to one from the other would require an infinite amount of time to elapse. > > But that’s of course not how the sequence of past events is ordered, or at any rate, there is no need to assume this (this relates back to a point I madein the very beginning that this is not just a question of cardinality, but of ordinality). While the two differently-ordered number lines can be put into one-to-one correspondence, thus making them of the same cardinality (aleph-zero), the ordinality properties are not preserved in this mapping, and it’s those that determine the question of whether there are infinite time intervals or not. And it’s quite simply a mathematical fact that there are no infinite intervals in an object of order type ω\*. I really just don’t understand what is being said here. I am not a math major. I did look up cardinality and ordinality though… ordinality is still unclear to me though in what it is and how it relates to cardinality. I checked on the Stereographic Projection. It really doesn’t make sense to me, although I am not saying it is untrue. ---
**Author:** ![Half\_Man\_Half\_Wit](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/half_man_half_wit/32/21766_2.png) [@Half\_Man\_Half\_Wit](https://boards.straightdope.com/u/Half_Man_Half_Wit)\ **Post date:** [March 8, 2014, 6:41pm UTC](https://boards.straightdope.com/t/the-beginning-of-linear-time-and-matter/682062/100 "2014-03-08T18:41:44Z")
> [@Gateway](#): > > \*You are saying there is no infinite distance on an infinite line. \* Which is the same thing as saying ‘there are no two numbers on the infinite number line that have an infinite difference’ or ‘…between which there are infinitely many numbers’. It might not make sense to you, but it’s how it is regardless. Otherwise, I invite you again to tell me two numbers on the infinite number line such that there are infinitely many numbers in between/their difference is infinite. But I meant more concretely the four bullet points in my previous post when I asked which one you disagree with. To reiterate: > [@Half\_Man\_Half\_Wit](#): > > [ol] > [li]There are infinitely many numbers on the infinite number line. [/li][li]The difference between any two numbers on the line is finite.[/li][li]There is no infinite amount of regular intervals between any two numbers. (Say your regular interval is 1, then the number of regular intervals between any two numbers is just their difference, so finite because of 2. Any different interval size will just be a multiple/fraction of that, so remain finite.)[/li][li]There is even a finite number of differently-sized intervals between any two numbers (if we have a smallest interval size, a ‘moment’ in your sense). This again follows by induction: between now and a moment ago, there is one interval—a finite amount. If there is a finite amount of intervals between now and n moments ago, there is a finite amount of intervals between now and n+1 moments ago (since only finitely many intervals, corresponding to the total amount of partitions of a set with n+1 elements, are added). [/li][/ol] Which one of those do you disagree with? [Previous page](https://boards.straightdope.com/t/the-beginning-of-linear-time-and-matter/682062.md?page=4) [Next page](https://boards.straightdope.com/t/the-beginning-of-linear-time-and-matter/682062.md?page=6)