# Is Everything Inevitable if Time is Infinite? **URL:** \ **Category:** Great Debates\ **Created:** [May 4, 2013, 8:05pm UTC](https://boards.straightdope.com/t/is-everything-inevitable-if-time-is-infinite/657492 "2013-05-04T20:05:59Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [May 5, 2013, 12:08am UTC](https://boards.straightdope.com/t/is-everything-inevitable-if-time-is-infinite/657492/21 "2013-05-05T00:08:39Z")
If time is infinite, will this particular question keep coming up infinitely often, and will we see all possible answers to it? [Given infinity, is everything imaginable inevitable?](http://boards.straightdope.com/sdmb/showthread.php?t=648579) [“Anything that can happen, will happen, given enough time.” – Really?](http://boards.straightdope.com/sdmb/showthread.php?t=637765) [Assuming an Infinite amount of time, are all things inevitable?](http://boards.straightdope.com/sdmb/showthread.php?t=520614) ---
**Author:** ![Czarcasm](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/czarcasm/32/4050_2.png) [@Czarcasm](https://boards.straightdope.com/u/Czarcasm)\ **Post date:** [May 5, 2013, 12:34am UTC](https://boards.straightdope.com/t/is-everything-inevitable-if-time-is-infinite/657492/22 "2013-05-05T00:34:16Z")
> [@Thudlow\_Boink](#): > > If time is infinite, will this particular question keep coming up infinitely often, and will we see all possible answers to it? > > [Given infinity, is everything imaginable inevitable?](http://boards.straightdope.com/sdmb/showthread.php?t=648579) > [“Anything that can happen, will happen, given enough time.” – Really?](http://boards.straightdope.com/sdmb/showthread.php?t=637765) > [Assuming an Infinite amount of time, are all things inevitable?](http://boards.straightdope.com/sdmb/showthread.php?t=520614) Actually we have already seen all the possible answers..which just keep repeating themselves. ---
**Author:** ![Lobot](https://avatars.discourse-cdn.com/v4/letter/l/ce7236/32.png) [@Lobot](https://boards.straightdope.com/u/Lobot)\ **Post date:** [May 5, 2013, 1:16am UTC](https://boards.straightdope.com/t/is-everything-inevitable-if-time-is-infinite/657492/23 "2013-05-05T01:16:06Z")
Something to look into is the [Hartle-Hawking state](http://en.wikipedia.org/wiki/Hartle-Hawking_state). > [@](#): > > Hartle and Hawking suggest that if we could travel backward in time toward the beginning of the universe, we would note that quite near what might have otherwise been the beginning, time gives way to space such that at first there is only space and no time. Beginnings are entities that have to do with time; because time did not exist before the Big Bang, the concept of a beginning of the universe is meaningless. According to the Hartle–Hawking proposal, the universe has no origin as we would understand it: the universe was a singularity in both space and time, pre-Big Bang. Thus, the Hartle–Hawking state universe has no beginning, but it is not the steady state universe of Hoyle; it simply has no initial boundaries in time nor space. Or, as [David St. Hubbins](http://www.imdb.com/title/tt0088258/) put it… > [@](#): > > Well, I don’t really think that the end can be assessed as of itself as being the end because what does the end feel like? It’s like saying when you try to extrapolate the end of the universe, you say, if the universe is indeed infinite, then how - what does that mean? How far is all the way, and then if it stops, what’s stopping it, and what’s behind what’s stopping it? So, what’s the end, you know, is my question to you. ---
**Author:** ![John\_Mace](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/john_mace/32/185_2.png) [@John\_Mace](https://boards.straightdope.com/u/John_Mace)\ **Post date:** [May 5, 2013, 2:20am UTC](https://boards.straightdope.com/t/is-everything-inevitable-if-time-is-infinite/657492/24 "2013-05-05T02:20:01Z")
> [@Der\_Trihs](#): > > The Big Bang wasn’t a fiery explosion _expanding into_ space, it filled all of space. And as I recall, if the universe is flat or [hyperbolic](http://en.wikipedia.org/wiki/Shape_of_the_universe#Hyperbolic_universe), it was always infinite. Not really. There was no space. There was no time. The BB created space and time. As for infinity, the numbers between 1 and 2 have a biginning and end yet there are an infinite number of them. Also you can’t really speak of “before” the BB since time begins there. ---
**Author:** ![Trinopus](https://avatars.discourse-cdn.com/v4/letter/t/2bfe46/32.png) [@Trinopus](https://boards.straightdope.com/u/Trinopus)\ **Post date:** [May 5, 2013, 2:49am UTC](https://boards.straightdope.com/t/is-everything-inevitable-if-time-is-infinite/657492/25 "2013-05-05T02:49:23Z")
Kind of a “Gaudere’s Law” here: **Der Trihs** corrected my sloppy phrasing, and then **John Mace** corrects his somewhat informal phrasing. One problem on the observation that there are an infinite number of numbers between one and two is that this doesn’t have any physical representation. The same for the number pi: beyond the 700th digit or so, the ratio has no meaning, as there are no circles large enough, and no measurement scale fine enough. There certainly aren’t an infinite number of “measured spaces” between the one-inch and two-inch marks on my ruler. Dividing it up into more than, say, 10^2000 points is an exercise in absurdity. And, again, mathematicians can sling off numbers so unutterably much larger than that without batting an eye! The “granular” nature of space itself precludes any measure of infinity in the direction of smallness. Largeness? Well… ---
**Author:** ![David\_H\_Singanas](https://avatars.discourse-cdn.com/v4/letter/d/ac8455/32.png) [@David\_H\_Singanas](https://boards.straightdope.com/u/David_H_Singanas)\ **Post date:** [May 5, 2013, 9:18am UTC](https://boards.straightdope.com/t/is-everything-inevitable-if-time-is-infinite/657492/26 "2013-05-05T09:18:57Z")
> [@John\_Mace](#): > > Not really. There was no space. There was no time. The BB created space and time. > > As for infinity, the numbers between 1 and 2 have a biginning and end yet there are an infinite number of them. > > Also you can’t really speak of “before” the BB since time begins there. I think you mean “our space and time.” Our space and time begins with the BB, not all space and all time. All space and all time is unknowable. ---
**Author:** ![Yumblie](https://avatars.discourse-cdn.com/v4/letter/y/76d3ee/32.png) [@Yumblie](https://boards.straightdope.com/u/Yumblie)\ **Post date:** [May 5, 2013, 4:54pm UTC](https://boards.straightdope.com/t/is-everything-inevitable-if-time-is-infinite/657492/27 "2013-05-05T16:54:52Z")
> [@David\_H\_Singanas](#): > > I think you mean “our space and time.” Our space and time begins with the BB, > not all space and all time. All space and all time is unknowable. Our very notion of space and time come from what we can measure. Anything outside our universe is not measurable. So it doesn’t really make sense to talk about space and time outside our universe, because we have no way of knowing if such concepts can even exist there. ---
**Author:** ![Great\_Antibob](https://avatars.discourse-cdn.com/v4/letter/g/e47c2d/32.png) [@Great\_Antibob](https://boards.straightdope.com/u/Great_Antibob)\ **Post date:** [May 5, 2013, 8:26pm UTC](https://boards.straightdope.com/t/is-everything-inevitable-if-time-is-infinite/657492/28 "2013-05-05T20:26:51Z")
Consider the positive integers. This set can be formed by starting at 1 and incrementing by 1: 1, 2, 3, 4, 5, 6, etc This set of numbers clearly has a ‘beginning’ and is also clearly infinite. ---
**Author:** ![ralph124c](https://avatars.discourse-cdn.com/v4/letter/r/8797f3/32.png) [@ralph124c](https://boards.straightdope.com/u/ralph124c)\ **Post date:** [May 5, 2013, 8:30pm UTC](https://boards.straightdope.com/t/is-everything-inevitable-if-time-is-infinite/657492/29 "2013-05-05T20:30:31Z")
What if DeSitter (Einstein’s Dutch contemporary) was right? Infinite space, infinite time, and no discernible expansion (because of the increasing curvature of spacetime? ---
**Author:** ![Chimera](https://avatars.discourse-cdn.com/v4/letter/c/8e8cbc/32.png) [@Chimera](https://boards.straightdope.com/u/Chimera)\ **Post date:** [May 5, 2013, 9:34pm UTC](https://boards.straightdope.com/t/is-everything-inevitable-if-time-is-infinite/657492/30 "2013-05-05T21:34:40Z")
Ok, ok, smoke a great big bowl of weed before you read this… Nothing is a compound word. No Thing. 😉 ---
**Author:** ![Trinopus](https://avatars.discourse-cdn.com/v4/letter/t/2bfe46/32.png) [@Trinopus](https://boards.straightdope.com/u/Trinopus)\ **Post date:** [May 5, 2013, 11:36pm UTC](https://boards.straightdope.com/t/is-everything-inevitable-if-time-is-infinite/657492/31 "2013-05-05T23:36:33Z")
Weed comes in bowls? ---
**Author:** ![\_3Bill](https://avatars.discourse-cdn.com/v4/letter/_/b9e5f3/32.png) [@\_3Bill](https://boards.straightdope.com/u/_3Bill)\ **Post date:** [May 7, 2013, 9:44am UTC](https://boards.straightdope.com/t/is-everything-inevitable-if-time-is-infinite/657492/32 "2013-05-07T09:44:59Z")
I doubt that “possible event” is a well-defined notion. If it is, and by “the universe never ending” we mean an endless succession of temporal units, then I am pretty sure that the cardinality of of possible events is greater than that of an infinite number of temporal units. ---
**Author:** ![Buck\_Godot](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/buck_godot/32/6573_2.png) [@Buck\_Godot](https://boards.straightdope.com/u/Buck_Godot)\ **Post date:** [May 7, 2013, 3:56pm UTC](https://boards.straightdope.com/t/is-everything-inevitable-if-time-is-infinite/657492/33 "2013-05-07T15:56:26Z")
Suppose we started flipping coins and each time we got a head we took one step to the left and each time we got a tail we took two steps to the right. As we run this process we will always tend to move further to the right. The likelihood that we will ever reach a point 100 steps to the left of our starting position is near zero no matter how long we run this series. This is basically the idea behind increasing entropy. As time goes on we get more and more disorder and no amount of waiting is going to get us back. ---
**Author:** ![Lemur866](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lemur866/32/434_2.png) [@Lemur866](https://boards.straightdope.com/u/Lemur866)\ **Post date:** [May 7, 2013, 4:47pm UTC](https://boards.straightdope.com/t/is-everything-inevitable-if-time-is-infinite/657492/34 "2013-05-07T16:47:16Z")
One possible outcome of flipping a coin an infinite number of times is an infinite series of heads. While this seems unlikely, it’s just as likely as any other series of outcomes. HHHHHHHHHHHHHHHHHHHH is just as likely as HTHTHTHTHTTTHTTTHTHH. But you could also flip the coin and get an infinite number of tails. But you can’t have a universe where you get infinite heads and also get infinite tails. You could have one or the other, but not both. And so we see not everything is inevitable in an infinite amount of time. Some outcomes make alternative future outcomes impossible. ---
**Author:** ![Blaster\_Master](https://avatars.discourse-cdn.com/v4/letter/b/cab0a1/32.png) [@Blaster\_Master](https://boards.straightdope.com/u/Blaster_Master)\ **Post date:** [May 7, 2013, 7:21pm UTC](https://boards.straightdope.com/t/is-everything-inevitable-if-time-is-infinite/657492/35 "2013-05-07T19:21:27Z")
> [@Lemur866](#): > > One possible outcome of flipping a coin an infinite number of times is an infinite series of heads. While this seems unlikely, it’s just as likely as any other series of outcomes. HHHHHHHHHHHHHHHHHHHH is just as likely as HTHTHTHTHTTTHTTTHTHH. > > But you could also flip the coin and get an infinite number of tails. But you can’t have a universe where you get infinite heads and also get infinite tails. You could have one or the other, but not both. And so we see not everything is inevitable in an infinite amount of time. Some outcomes make alternative future outcomes impossible. I’m not sure I can agree with this. You’re saying that the infinite series of HHHHHHHHHH… is just as likely as some other HTHTHTHHTTTHHTH… series, but that’s misleading. There is exactly one possibility to have no tales, but with an infinite number of flips, there’s an infinite number of other possibilities. It’s sort of like the does 0.999… = 1 problem. Does 1/inf have a non-zero value? The other problem is, assuming the stated probability. Sure, if I flip a fair coin a hundred times, it might come up all heads with 0.5^100 chance and that is just as possible as any other one, though it is outside of any reasonable margin of error. But once we’re talking an infinite number of trials, I don’t think we can reasonably say that it’s a fair coin if we can now effectively say that exhaustively it will never land on tails. It’s an utterly paradoxical result. For that matter, on top of zero is there a meaning to some series with an infinite number of Heads but a finite number of Tail results? ---
**Author:** ![Mijin](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mijin/32/9369_2.png) [@Mijin](https://boards.straightdope.com/u/Mijin)\ **Post date:** [May 8, 2013, 12:25am UTC](https://boards.straightdope.com/t/is-everything-inevitable-if-time-is-infinite/657492/36 "2013-05-08T00:25:58Z")
> [@Blaster\_Master](#): > > I’m not sure I can agree with this. You’re saying that the infinite series of HHHHHHHHHH… is just as likely as some other HTHTHTHHTTTHHTH… series, but that’s misleading. There is exactly one possibility to have no tales, but with an infinite number of flips, there’s an infinite number of other possibilities. It’s sort of like the does 0.999… = 1 problem. Does 1/inf have a non-zero value? > > The other problem is, assuming the stated probability. Sure, if I flip a fair coin a hundred times, it might come up all heads with 0.5^100 chance and that is just as possible as any other one, though it is outside of any reasonable margin of error. But once we’re talking an infinite number of trials, I don’t think we can reasonably say that it’s a fair coin if we can now effectively say that exhaustively it will never land on tails. It’s an utterly paradoxical result. For that matter, on top of zero is there a meaning to some series with an infinite number of Heads but a finite number of Tail results? The point is this: for this experiment the universe must have only one, countably infinite set. Whatever this result set is, prior to doing the experiment, the chance of it occurring was zero. Such is the paradox of considering infinitesimally likely events in an infinite experiment. I linked the [Almost surely](https://en.wikipedia.org/wiki/Almost_surely) page earlier, but I recommend you specifically read the section [Throwing a dart](https://en.wikipedia.org/wiki/Almost_surely#Throwing_a_dart). ---
**Author:** ![Measure\_for\_Measure](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/measure_for_measure/32/557_2.png) [@Measure\_for\_Measure](https://boards.straightdope.com/u/Measure_for_Measure)\ **Post date:** [May 8, 2013, 1:52am UTC](https://boards.straightdope.com/t/is-everything-inevitable-if-time-is-infinite/657492/37 "2013-05-08T01:52:37Z")
It seems to me that if the number of possibilities increases exponentially with time, then not all things will happen given infinite time, even ignoring heat death. But then again, perhaps all things that are possible _now_ will happen. Though I’m not sure what that means. And we are talking about a lot of possibilities. Consider the Dinner Party problem. Say you have 60 guests. How many possible seating arrangements are there? Something like 60! = 8.320987113 x 10^81, which exceeds the number of atoms in the universe. Any problem where you put 60 objects in 60 locations will involve this, including structures composed of 60 bricks, planks or whatever. And usually, placement is a continuous problem, not a discrete one: we don’t just consider matching person A to Seat A, but rather where in the entire room they are situated at any given time. 70! = 1.197857167e100 80! = 7.156945705e118 90! = 1.485715964e138 100! = 9.332621544e157 ---
**Author:** ![Lemur866](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lemur866/32/434_2.png) [@Lemur866](https://boards.straightdope.com/u/Lemur866)\ **Post date:** [May 8, 2013, 5:25pm UTC](https://boards.straightdope.com/t/is-everything-inevitable-if-time-is-infinite/657492/38 "2013-05-08T17:25:11Z")
> [@Blaster\_Master](#): > > I’m not sure I can agree with this. Another way to think of it is, if everything possible must happen in an infinite universe, a possible thing can also be considered in the negative. If getting a million heads is possible, what about NEVER getting a million heads? It’s logically possible to consider an infinite universe in which no one ever flips a coin and gets a million heads. But if it’s guaranteed that eventually someone will get a million heads, it’s guaranteed that never getting a million heads will never happen. If everything possible is inevitable, then there are a bunch of things that can’t NOT happen. Do those count as things that could happen? Then they don’t happen, and thus not everything possible is inevitable. ---
**Author:** ![Icarus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/icarus/32/72_2.png) [@Icarus](https://boards.straightdope.com/u/Icarus)\ **Post date:** [May 8, 2013, 9:12pm UTC](https://boards.straightdope.com/t/is-everything-inevitable-if-time-is-infinite/657492/39 "2013-05-08T21:12:23Z")
> [@George329](#): > > Assuming the universe has no end can we assume everything will eventually happen, subject to its inviolable laws? Clearly the only possible answer is yes,…AND no. ---
**Author:** ![CJJ](https://avatars.discourse-cdn.com/v4/letter/c/ecc23a/32.png) [@CJJ](https://boards.straightdope.com/u/CJJ)\ **Post date:** [May 8, 2013, 9:24pm UTC](https://boards.straightdope.com/t/is-everything-inevitable-if-time-is-infinite/657492/40 "2013-05-08T21:24:19Z")
The word “happen” implies a finite event; an infinite string of coin tosses can be initiated, and we can verify that the first X happen, but since it’s infinite the string can never be completed, hence it never “happens” (or at least we can never verify it happened). So, limiting ourselves to finite events, we have to rule out cases such as “The earth will never fall into the Sun” or “The earth will always be plagued by Justin Bieber fans.” I also think we need to rule out logical contradictions like “2+2=5”, which by definition can never be true. I’m also quietly exempting cases where the language or original intent of the predicted event can be so twisted to mean anything; the event has to be something clearly defined. Finally, we have to rule out events that by their nature are restricted to occur in a specific period of time or place; this seems to go against the spirit of the question of presuming “infinite” time (and, I’m assuming, space). So given these four conditions–that the event is finite in extent, not self-contradictory, unambiguous and one whose occurrence is not restricted by time or place–are there still event that cannot happen given infinite time? [Previous page](https://boards.straightdope.com/t/is-everything-inevitable-if-time-is-infinite/657492.md?page=1) [Next page](https://boards.straightdope.com/t/is-everything-inevitable-if-time-is-infinite/657492.md?page=3)