# Assuming an Infinite amount of time, are all things inevitable? **URL:** \ **Category:** Factual Questions\ **Created:** [January 8, 2012, 9:33pm UTC](https://boards.straightdope.com/t/assuming-an-infinite-amount-of-time-are-all-things-inevitable/608850 "2012-01-08T21:33:00Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [January 9, 2012, 4:40am UTC](https://boards.straightdope.com/t/assuming-an-infinite-amount-of-time-are-all-things-inevitable/608850/21 "2012-01-09T04:40:53Z")
> [@Exapno\_Mapcase](#): > > And the number of possible arrangements of states I mentioned is 10[sup]236[/sup]!. > > There’s no way to express that number I’ve snipped off the context that clarifies what you mean, but the wording above is terribly amusing to me. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [January 9, 2012, 4:46am UTC](https://boards.straightdope.com/t/assuming-an-infinite-amount-of-time-are-all-things-inevitable/608850/22 "2012-01-09T04:46:41Z")
Re: the OP: One might well take “possible” to mean “Happens somewhere at some point”. On that account, everything possible happens somewhere at some point, tautologically… If you do not want to use that definition of “possible”, well, I daresay, the burden is on you to first clarify what you mean by “possible” before we can tackle the question “Must everything possible happen somewhere at some point”? (While you are it, you may as well clarify what “Must” means, if you are interested in asking the question with a notion of “Must” less stringent than tautological necessity) (Similar considerations apply to the use of probabilistic language rather than possibilistic language, if that’s what floats your boat.) ---
**Author:** ![MikeS](https://avatars.discourse-cdn.com/v4/letter/m/919ad9/32.png) [@MikeS](https://boards.straightdope.com/u/MikeS)\ **Post date:** [January 9, 2012, 5:02am UTC](https://boards.straightdope.com/t/assuming-an-infinite-amount-of-time-are-all-things-inevitable/608850/23 "2012-01-09T05:02:32Z")
In statistical mechanics, a system that (eventually) takes on all of its possible states (to within some precision) is known as an [ergodic](http://en.wikipedia.org/wiki/Ergodic_theory) system. Whether or not a given system is ergodic is not always easy to ascertain, though. ---
**Author:** ![Peter\_Morris](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/peter_morris/32/359_2.png) [@Peter\_Morris](https://boards.straightdope.com/u/Peter_Morris)\ **Post date:** [January 9, 2012, 5:19am UTC](https://boards.straightdope.com/t/assuming-an-infinite-amount-of-time-are-all-things-inevitable/608850/24 "2012-01-09T05:19:13Z")
Okay, let’s take a specific example. Pi has an infinite number of digits in a non-repeating sequence. Will every possible sequence of numbers occur there sooner or later? Suppose you take the digits as text encoding. Will every conceivable message appear in the text somewhere? [This one](http://xkcd.com/10/)? The entire text of Hamlet? The near complete text of Hamlet, but with one word omitted? ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [January 9, 2012, 5:27am UTC](https://boards.straightdope.com/t/assuming-an-infinite-amount-of-time-are-all-things-inevitable/608850/25 "2012-01-09T05:27:40Z")
> [@Peter\_Morris](#): > > Okay, let’s take a specific example. > > Pi has an infinite number of digits in a non-repeating sequence. Will every possible sequence of numbers occur there sooner or later? > > Suppose you take the digits as text encoding. Will every conceivable message appear in the text somewhere? > > [This one](http://xkcd.com/10/)? The entire text of Hamlet? The near complete text of Hamlet, but with one word omitted? The answer to all these questions is “Almost everyone thinks ‘Yes’, but no one has ever proven it one way or another”. ---
**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\ **Post date:** [January 9, 2012, 5:47am UTC](https://boards.straightdope.com/t/assuming-an-infinite-amount-of-time-are-all-things-inevitable/608850/26 "2012-01-09T05:47:05Z")
I think this little back and forth is extremely interesting. Just a shout out. > [@Exapno\_Mapcase](#): > > … > > We can do a quick calculation of how many states our universe has been through since the big bang. Using the Planck time, we get 10[sup]60[/sup] units of time and using the Planck length, we get 10[sup]176[/sup] units of volume. That gives 10[sup]236[/sup] states. (I may be off a few powers of ten in rounding and assumptions, but that doesn’t matter for this discussion.) > > That’s a number too ridiculously large to put in any human terms. But obviously it is approximately 0% of an infinity of possible larger numbers. If we make the assumption - and it’s currently only an assumption - of a truly infinite number of universes, then there will be an infinite number of universes that have exactly the same 10[sup]236[/sup] states and an infinite number of universes that differ by one state and an infinite number of universes that differ by two states and so on. In fact, any set of states that is physically possible will occur an infinite number of times. So yes, anything possible must occur if infinity is posited. > > Which is why so many scientists dislike that assumption. Kinds takes the fun of the game. > [@Exapno\_Mapcase](#): > > And the number of possible arrangements of states I mentioned is 10[sup]236[/sup]!. > > There’s no way to express that number since even the base number couldn’t be written out in our universe no matter how small (above the Planck length) you made the zeroes. The permutations are so far beyond that number that some special notation that mathematicians use for huge numbers may not even fit in our universe. > > And so what? Compared to other really large numbers, that’s still essentially 0. > > That’s the amazing thing about infinity. If you can think of even a theoretical way to express a number, then the number is finite, it’s trivially small, and an infinite number of those number strings can be found. > [@Indistinguishable](#): > > I’ve snipped off the context that clarifies what you mean, but the wording above is terribly amusing to me. ---
**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:** [January 9, 2012, 6:03am UTC](https://boards.straightdope.com/t/assuming-an-infinite-amount-of-time-are-all-things-inevitable/608850/27 "2012-01-09T06:03:15Z")
> [@Peter\_Morris](#): > > Okay, let’s take a specific example. > > Pi has an infinite number of digits in a non-repeating sequence. Will every possible sequence of numbers occur there sooner or later? > [@Indistinguishable](#): > > The answer to all these questions is “Almost everyone thinks ‘Yes’, but no one has ever proven it one way or another”. But notice what this means, that it hasn’t been proven: it means that it’s not _necessarily_ true _just_ because the digits of pi go on forever (without repeating). We don’t (yet) know a reason why it couldn’t be false. And that, to me, settles the OP’s question with a No. Since you can have an infinite string of digits without all substrings being inevitable, you can have an infinite stretch of time without all events being inevitable. ---
**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\ **Post date:** [January 9, 2012, 6:12am UTC](https://boards.straightdope.com/t/assuming-an-infinite-amount-of-time-are-all-things-inevitable/608850/28 "2012-01-09T06:12:13Z")
> [@Thudlow\_Boink](#): > > But notice what this means, that it hasn’t been proven: it means that it’s not _necessarily_ true _just_ because the digits of pi go on forever (without repeating). We don’t (yet) know a reason why it couldn’t be false. > > And that, to me, settles the OP’s question with a No. Since you can have an infinite string of digits without all substrings being inevitable, you can have an infinite stretch of time without all events being inevitable. Just checking: we don’t know a reason why the digits of pi keep spooling on, or if there is a repetition “gotcha” moment? ---
**Author:** ![brittekland](https://avatars.discourse-cdn.com/v4/letter/b/aeb1de/32.png) [@brittekland](https://boards.straightdope.com/u/brittekland)\ **Post date:** [January 9, 2012, 6:14am UTC](https://boards.straightdope.com/t/assuming-an-infinite-amount-of-time-are-all-things-inevitable/608850/29 "2012-01-09T06:14:43Z")
Things, perhaps: should all things _mutate_ by themselves or by some external influence such as unpredictable future events. Concepts, probably not: Ideas such as mathematical concepts cannot because they are not things. ---
**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:** [January 9, 2012, 6:19am UTC](https://boards.straightdope.com/t/assuming-an-infinite-amount-of-time-are-all-things-inevitable/608850/30 "2012-01-09T06:19:07Z")
> [@Leo\_Bloom](#): > > Just checking: we don’t know a reason why the digits of pi keep spooling on, or if there is a repetition “gotcha” moment? We know the digits of pi “keep spooling on” without ever just repeating the same sequence over and over; what we don’t know is whether the digits of pi contain every possible finite subsequence. That is, we know for sure that pi is **irrational** , but we only suspect (can’t prove) that it’s **[normal](http://en.wikipedia.org/wiki/Normal_number)**. (Although it’s not all that obvious why pi is even irrational. It was relatively late in the history of mathematics, compared to when pi was known of, before anyone managed to prove its irrationality.) ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [January 9, 2012, 6:20am UTC](https://boards.straightdope.com/t/assuming-an-infinite-amount-of-time-are-all-things-inevitable/608850/31 "2012-01-09T06:20:24Z")
> [@Thudlow\_Boink](#): > > But notice what this means, that it hasn’t been proven: it means that it’s not _necessarily_ true _just_ because the digits of pi go on forever (without repeating). We don’t (yet) know a reason why it couldn’t be false. > > And that, to me, settles the OP’s question with a No. Since you can have an infinite string of digits without all substrings being inevitable, you can have an infinite stretch of time without all events being inevitable. Sure; for very simple example, the infinite string “00000…” never contains a 1. But who knows whether that’s the sort of thing which will satisfy the OP. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [January 9, 2012, 6:24am UTC](https://boards.straightdope.com/t/assuming-an-infinite-amount-of-time-are-all-things-inevitable/608850/32 "2012-01-09T06:24:46Z")
> [@](#): > > Quoth **MattProle** : > Do we actually have enough information to perform the integration that you alluded to? Would we have to assume the expansion of the Universe will continue to accelerate at it’s current rate? The exact calculation would depend on the exact functional form of the evolution of the Universe, as well as on just which particular unlikely event you’re trying to find the probability of. Under any reasonable set of assumptions, though, the integral would converge very quickly. **Leo Bloom** , it’s known with proven certainty that pi is irrational, which means we’re sure the digits won’t repeat. What we _don’t_ know, but very strongly suspect, is that it’s normal, which means that all possible digit strings of any given length are equally abundant. And even if it’s not actually normal, it might still have the property that all digit strings show up in it. Then again, it’s also quite conceivable (for all we know) that there might be some digit strings which never show up in it. For comparison, consider the number 1.101001000100001000001000000100000001… (with an ever-increasing number of 0 digits between the 1 digits). This number is certainly irrational, since it never repeats, but it’s also certainly not normal, since you’ll never find the digit string “2” in it. ---
**Author:** ![Mangetout](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mangetout/32/19_2.png) [@Mangetout](https://boards.straightdope.com/u/Mangetout)\ **Post date:** [January 9, 2012, 7:28am UTC](https://boards.straightdope.com/t/assuming-an-infinite-amount-of-time-are-all-things-inevitable/608850/33 "2012-01-09T07:28:48Z")
> [@Little\_Nemo](#): > > An infinite amount of time will be filled mostly with repetitious events. Some common events will occur billions of times. Less common events will happen millions of times. Some rare events might only occur a few thousand times. And some events will never happen at all. In infinite time, how can any possible thing happen, but only a finite number of times? After the rare event has happened a few thousand times, there is still an infinite duration remaining. Did you perhaps mean to express this in terms of relative frequencies, rather than absolute totals? ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [January 9, 2012, 8:07am UTC](https://boards.straightdope.com/t/assuming-an-infinite-amount-of-time-are-all-things-inevitable/608850/34 "2012-01-09T08:07:20Z")
> [@Mangetout](#): > > In infinite time, how can any possible thing happen, but only a finite number of times? After the rare event has happened a few thousand times, there is still an infinite duration remaining. It’s easy… think of a string like 101101001011010000000000000… [all 0s from thereon out]. 1 only shows up finitely many times. Is there some reason a string like this _doesn’t_ describe a possible way for eternity to go? (This is why I wanted the word “Must” clarified before…) ---
**Author:** ![Mangetout](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mangetout/32/19_2.png) [@Mangetout](https://boards.straightdope.com/u/Mangetout)\ **Post date:** [January 9, 2012, 8:14am UTC](https://boards.straightdope.com/t/assuming-an-infinite-amount-of-time-are-all-things-inevitable/608850/35 "2012-01-09T08:14:54Z")
Well, OK, but that’s a non-normal scenario constructed specifically to achieve the outcome in question. Is there any evidence that the universe is like the string you describe? ---
**Author:** ![Lust4Life](https://avatars.discourse-cdn.com/v4/letter/l/ecc23a/32.png) [@Lust4Life](https://boards.straightdope.com/u/Lust4Life)\ **Post date:** [January 9, 2012, 10:15am UTC](https://boards.straightdope.com/t/assuming-an-infinite-amount-of-time-are-all-things-inevitable/608850/36 "2012-01-09T10:15:39Z")
> [@Si\_Amigo](#): > > She is never going to have sex with you. Never. Although possible it ain’t going to happen. Never, no matter if you throw infinite in there. Never. Move on. 😃 Well you’ve ruined MY daY ! ---
**Author:** ![Gagundathar](https://avatars.discourse-cdn.com/v4/letter/g/a183cd/32.png) [@Gagundathar](https://boards.straightdope.com/u/Gagundathar)\ **Post date:** [January 9, 2012, 10:30am UTC](https://boards.straightdope.com/t/assuming-an-infinite-amount-of-time-are-all-things-inevitable/608850/37 "2012-01-09T10:30:28Z")
I think when you throw in the concept of multiple universes, this question is unanswerable. ---
**Author:** ![Dr.Colossus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.colossus/32/9423_2.png) [@Dr.Colossus](https://boards.straightdope.com/u/Dr.Colossus)\ **Post date:** [January 9, 2012, 11:03am UTC](https://boards.straightdope.com/t/assuming-an-infinite-amount-of-time-are-all-things-inevitable/608850/38 "2012-01-09T11:03:10Z")
> [@Indistinguishable](#): > > It’s easy… think of a string like 101101001011010000000000000… [all 0s from thereon out]. 1 only shows up finitely many times. > > Is there some reason a string like this _doesn’t_ describe a possible way for eternity to go? (This is why I wanted the word “Must” clarified before…) Typically I’m not welcome into discussions like this, I’m venturing outside my intelligencia here. You dudes are \*smart \*(this thread makes me need a freakin’ nap.) This number sequence helps guys like me make sense of the universe–Finite occurrences in an infinite string. Just in practical terms, I imagine putting all the required fundamental base elements (minerals, metals, organic matter, etc) in a big bag. Given an infinite chances to shake the bag up, I guess there’s a theoretical number model for the odds that all these base elements will congeal together in precisely the required formation for a working 1981 Pontiac Trans Am being shaken together. A black one. With leather trim, wood grain steering wheel and galaxy black paint with a gold flamin’ chicken on the hood. There’s, I guess, a calculation for the odds shaking the bag up will yield that extremely specific result–but in practical terms, it simply wouldn’t ever happen. _ **EVER** _. Would it…? A theoretical number model’s potential result of, hypothetically, _1million gazillion:1_ odds doesn’t at all mean that if you actually built a perpetual shaking-the-bag-up machine, it will ever, EVER happen…? ---
**Author:** ![Mangetout](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mangetout/32/19_2.png) [@Mangetout](https://boards.straightdope.com/u/Mangetout)\ **Post date:** [January 9, 2012, 11:13am UTC](https://boards.straightdope.com/t/assuming-an-infinite-amount-of-time-are-all-things-inevitable/608850/39 "2012-01-09T11:13:30Z")
The question is more like: if you put a thousand raisins in a cake mix of infinite size, would they all sink to the bottom? If an event is of sufficient rarity that it can only occur a finite number of times in an infinite period, that means the infinite period can be divided into two separate infinite periods, in one of which, the event doesn’t occur at all. ---
**Author:** ![Gagundathar](https://avatars.discourse-cdn.com/v4/letter/g/a183cd/32.png) [@Gagundathar](https://boards.straightdope.com/u/Gagundathar)\ **Post date:** [January 9, 2012, 11:16am UTC](https://boards.straightdope.com/t/assuming-an-infinite-amount-of-time-are-all-things-inevitable/608850/40 "2012-01-09T11:16:23Z")
If we posit that all units have a certain set of characteristics, then all combinations are resolvable. If all units are random, then maybe not. [Previous page](https://boards.straightdope.com/t/assuming-an-infinite-amount-of-time-are-all-things-inevitable/608850.md?page=1) [Next page](https://boards.straightdope.com/t/assuming-an-infinite-amount-of-time-are-all-things-inevitable/608850.md?page=3)