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Infinite monkey theorem  question(s) 
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#1
Apr2212, 08:10 AM

P: 21

Hello everyone, glad to be here. I'm Tom, 22 from Manchester UK.
I don't consider myself intelligent, I failed miserably at GCSE Maths but I tend to think a lot about time and space, and I'm interested in the subject and keen to learn more. I'd like to hear some peoples opinions on the topic of time and the infinite monkey theorem. Here is my question(s). Recently me and my friend were talking about if we think time is infinite. In all honesty I don't have a clue, but for some reason I feel naturally inclined to say infinite. So, is there any sort of consensus in the scientific community? Or is it still widely debated? More importantly, my friend brought up the infinite monkey theorem. I had never heard of it before, and this really got me thinking. If time really is infinite, would it be possible over an inconceivable amount of time for something similar to the infinite monkey theorem to happen on a much bigger scale? For example, is it theoretically possible that everything that has ever happened so far, Earth, our existence, and all events could happen again in exactly the same sequence? If time really is infinite, of course... I can't get my head around the notion of eternity and an infinite space/time. I'm also a guy struggling to find my way between Science and Faith, and I have lately been swaying to Creationism, but that's a different matter entirely. Would appreciate any feedback, I'd like to know your thoughts on this! Cheers! 


#2
Apr2212, 08:19 AM

P: 526

Hi Thomas, welcome to PF!
The standard model of cosmology holds that dark energy (the cosmological constant) will continue to expand the universe, for seemingly forever. Now, this does not lead to an infinite monkey situation, because star formation will eventually end, and everything in the universe will eventually decay into particles. Here is an article to read. But, if the universe is spatially infinite, then everything that can happen, does happen somewhere. The issue of spatial size is one that is strongly debated, and will remain so for a while. There is no reason to go either way right now, there is no evidence for either position. 


#3
Apr2212, 06:48 PM

P: 21

Cheers Mark! Nice to meet you.
I understand! Must say, that's quite a morbid conclusion. So after the Big Freeze, what? Eternal darkness? Grim. Brilliant read though, thanks for the link. Shortly after I posted this, I found an example of what I was thinking of in The Eternal Return theory. It is racking my brain. Such a mind boggling subject, enjoying looking around the forums though. Cheers again! 


#4
Apr2212, 10:03 PM

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Infinite monkey theorem  question(s)
In a cyclical universe model, after heat death the universe would somehow manage to undergo another big bang scenario at some unimaginably remote time in the future.



#5
Apr2212, 10:06 PM

P: 19

Hi, Thomas!
Here's a talk you might like; Brian Greene is not the most scientific of scientists, but he addresses some of the concepts of an infinite universe that you're thinking of: http://www.radiolab.org/blogs/radiol...ltiuniverses/ Essentially, if space is infinite, then everything possible is going on in an infinite number of places at all times. This is only logical. But, even if time goes on forever from an initial starting point, as Mark M was getting at, the universe is moving in a definite direction, so the monkey situation will not occur. I've never even heard of the eternal return theory, but after looking it up, I will warn you to be skeptical of things like this. Ancient philosophical constructs are almost never in agreement with reality. 


#6
Apr2312, 10:30 AM

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#7
Apr2412, 02:54 AM

P: 570

Greene is incorrect. I have discussed this argument before, but it is like trying to eradicate crabgrass. The first thing you have to do is define what equality is. How do you know whether two things are the same or not? How close is good enough? There seems to be an unstated assumption that the number of states of, say, a human being is finite. This I do not believe. Perhaps the assumption is that the number of states is countably infinite. That I do not believe either. All you need is one continuous quantity in the universe and it becomes uncountably infinite. All this needs to be cleared up before you can argue anything. I never seen anyone bother to lay this groundwork, possibly because no one knows the answer. Another bogus argument I have seen is that if something exists then the probability it exists is greater than zero. In a finite Universe that is true, but in an infinite Universe it is not true. In an infinite Universe the probability is whatever it is. Observing the Earth tells you nothing about the probability of something the "same" as the Earth, because the Earth wasn't chosen at random. 


#8
Apr2412, 03:24 AM

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The observable universe is not temporally infinite, therefore it is not spatially infinite. We cannot observe inaccessible regions of the universe so your argument is scientifically irrelevant.



#9
Apr2412, 08:11 AM

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P: 11,589

It does not matter which interpretation of QM you prefer, you can always divide your phase space in a countable number of regions with a volume of the minimal phase space a system needs (\hbar^whatever). This does not mean that these are different states (and your choice how to divide the phase space is arbitrary), but it does mean that you cannot get an uncountable amount of states which you could call "different" in a meaningful way. Apart from that, I think that you could collect a lot of quantum states and still get the same "state of a human". It does not really matter if molecule Y is at position X or 1nm above that. For the state of mind, I think (nearly) identical connections between all cells in the brain and an identical activity pattern at a certain point in time would be sufficient. @Thomas1989: While monkeys might die due to the lack of stars in the far future, you can always look at Boltzmann brains. 


#10
Apr2412, 10:11 PM

P: 19




#11
Apr2712, 02:00 AM

P: 570

The statement that everything happens an infinite number of times is equivalent to the statement that the set of events in each region is infinite. It is possible so it can't be disproved, but I don't see any particular reason to believe that. My position is that we know nothing about the sets in any of these regions. Some of them might even be empty. 


#12
Apr2712, 08:37 AM

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#13
Apr2712, 11:53 AM

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#14
Apr2712, 12:57 PM

P: 642

I'm surprised no one's brought the concept of GR implying that there must be some sort of "Big Bang" event into this.



#15
Apr2712, 01:20 PM

P: 614

When you say that it is not temporally infinite, is that because it started at some point? Are rays not considered to have infinite length? And why does "it is not spatially infinite" follow from "it is not temporally infinite"? 


#16
Apr2712, 02:12 PM

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P: 11,589

The past is finite (as far as we know), as time started with the big bang 13.7 billion years ago. Now, imagine some point in space which emitted light right after the big bang. How far away from its initial position would it be by now? Due to the expansion of space, it turns out that this value is larger than 13.7 billion light years, something close to ~45 billion ly. This is the radius of the observable universe  the part of the universe we can observe today.



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