• Lets say the universe is infinite. What possibilities are there?
    69 replies, posted
[QUOTE=JohnnyMo1;37887257]hey look here's a number with an infinitely long decimal expansion that never repeats: .010010001000010000010000001... but you're never going to find ...1234567890... in there[/QUOTE] Don't know if i'm looking at this the completely wrong way, but that figure only contains 1's and 0's that follow a set pattern, implying that in that 'universe' those are the building blocks for everything, 2 3 4 6 7 8 and 9 do not exist, and everything that exists and thus could exist has to fit into said pattern.
[QUOTE=RobbL;37888056]Don't know if i'm looking at this the completely wrong way, but that figure only contains 1's and 0's that follow a set pattern, implying that in that 'universe' those are the building blocks for everything, 2 3 4 6 7 8 and 9 do not exist, and everything that exists and thus could exist has to fit into said pattern.[/QUOTE] .201001000100001...
Space and time don't have an ordered sequential nature last time I checked, so those numbers are a bad analogy anyway. Plus my original point still applies to the second number you posted
[QUOTE=Canuhearme?;37884177]The Universe is an effectively infinite amount of space [B]with only a finite amount of matter[/B], which means there's only so many possibilities before you run out, including possibilities which aren't possible due to existing universal laws. There are some arguments to be said about a Multiverse though, which would mean there can be a near infinite amount of universes where a near infinite amount of possibilities exist, including ones that don't obey "natural" (ie, our universe's) physical/temporal laws. In other words, there is a very real possibility of there being anything you can imagine [I]somewhere[/I], only issue is it may not even exist in our reality.[/QUOTE] So it's just empty space outside that?
Maybe, might be empty cosmic "real-estate" beyond the furthest galaxy, or there might not be spacetime if you go far enough. Either there's a "wall", or empty real-estate, or there's some weird wrap-around wherein space bends and you end up curving back towards where you came from.
[QUOTE=RobbL;37888199]Space and time don't have an ordered sequential nature last time I checked, so those numbers are a bad analogy anyway.[/QUOTE] I don't see how that's a bad analogy at all. They are infinite, they never repeat, they do not contain all possible combinations. There are infinitely many irrational expansions like that that DO NOT have a rule that can obviously be pointed out to generate them, utilize all 10 digits, and still you can't just pick ...1234567890... out of them
Infinite quests.
[QUOTE=JohnnyMo1;37888612]I don't see how that's a bad analogy at all. They are infinite, they never repeat, they do not contain all possible combinations. There are infinitely many irrational expansions like that that DO NOT have a rule that can obviously be pointed out to generate them, utilize all 10 digits, and still you can't just pick ...1234567890... out of them[/QUOTE] Wait a sec, let me word my thoughts a bit better. Basically, take your sequence- .010010001000010000010000001... You claimed the the sequence never repeats, that from the start shows it's an invalid analogy, we all know that reality does repeat itself (there's more than one proton, quark, ect. in existence) And if combinations do repeat in a number sequence, that also means they would repeat infinitely in an infinite sequence Also, you won't find in "123456789" in there, but that's because [U]it can't possibly exist[/U] in the sequence in the first place- and you said not everything [U]that can possibly exist[/U] exists infinitely. Big contradiction there And lastly, the sequence does actually repeat itself- the combinations "001", "010", ect. repeat infinitely in it- yet some combinations don't repeat themselves at all- "1001", "101", ect.. However, if one thing in the universe can exist in multiple instances then obviously everything should be able to exist in multiple instances, also- "if combinations do repeat in a number sequence, that also means they would repeat infinitely in an infinite sequence". That's another contradiction regarding your number sequence/universe analogy
[QUOTE=RobbL;37888939]Wait a sec, let me word my thoughts a bit better. Basically, take your sequence- .010010001000010000010000001... You claimed the the sequence never repeats, that from the start shows it's an invalid analogy, we all know that reality does repeat itself (there's more than one proton, quark, ect. in existence) And if combinations do repeat in a number sequence, that also means they would repeat infinitely in an infinite sequence[/QUOTE] Wat More than one particle of each type =/= repetition just like the fact that the digit 1 appears more than once in my number is not repetition (in the sense that the number cannot be represented by a finite sequence of numbers repeated ad infinitum) [QUOTE=RobbL;37888939]Also, you won't find in "123456789" in there, but that's because [U]it can't possibly exist[/U] in the sequence in the first place- and you said not everything [U]that can possibly exist[/U] exists infinitely. Big contradiction there[/quote] How do you get that it can't possibly exist in there? I haven't restricted us to the set of numbers between 0 and 1 whose decimal expansions contain only the digits 0 and 1 or anything. That number is a point in the standard real line. [QUOTE=RobbL;37888939]And lastly, the sequence does actually repeat itself- the combinations "001", "010", ect. repeat infinitely in it- yet some combinations don't repeat themselves at all- "1001", "101", ect.. However, if one thing in the universe can exist in multiple instances then obviously everything should be able to exist in multiple instances, also- "if combinations do repeat in a number sequence, that also means they would repeat infinitely in an infinite sequence". That's another contradiction regarding your number sequence/universe analogy[/QUOTE] You're not using "repetition" in the correct sense. [quote]the number cannot be represented by a finite sequence of numbers repeated ad infinitum[/quote] [editline]2nd October 2012[/editline] Basically, you've completely missed the point of the analogy. People assume "infinitely large" and "doesn't just repeat itself" equates to "ANYTHING IS POSSIBLE" but the number gives a clear example of why that logic is faulty.
Well i'm still at AS level maths, so don't expect too much from me Btw, in a set system everything that can possibly be generated within the system will repeat infinitely if the system itself is infinite. There's this project where this computer software generates characters that appear random and puts them together in attempt to reproduce the whole works of Shakespeare. Afaik it's only completed a few sentences, but it's enough to prove that everything possible will be repeated infinitely in a infinite system of set laws without any true randomness, as the software would generate every possible word or combination of words if set to run infinitely (if it allowed combinations through that didn't fit the works of shakespeare ofc) [editline]3rd October 2012[/editline] [QUOTE=JohnnyMo1;37889050]Wat More than one particle of each type =/= repetition[/quote] More than one particle of each type (and molecules, ect.) is repetition of the arrangement of matter within the universe, which is what we're talking about here in case you forgot [editline]3rd October 2012[/editline] There are a finite number of possible things in the universe (possible arrangements of matter, engery, ect.) but if the universe is infinite (and filled with infinite matter + energy) the finite number of possible things will repeat infinitely
[QUOTE=RobbL;37889131]Well i'm still at AS level maths, so don't expect too much from me Btw, in a set system everything that can possibly be generated within the system will repeat infinitely if the system itself is infinite. There's this project where this computer software generates characters that appear random and puts them together in attempt to reproduce the whole works of Shakespeare. Afaik it's only completed a few sentences, but it's enough to prove that everything possible will be repeated infinitely in a infinite system of set laws without any true randomness, as the software would generate every possible word or combination of words if set to run infinitely[/QUOTE] That's not true though. A truly random system does not HAVE to produce all the works of Shakespeare eventually, it doesn't have to do anything eventually. Imagine I flip a coin with perfect 50/50 odds infinitely many times. I could end up with heads-heads-heads-heads-heads... forever. There's just as much chance of that as there is of any other single configuration. [QUOTE=RobbL;37889131]More than one particle of each type is repetition of the arrangement of matter within the universe, which is what we're talking about here in case you forgot[/QUOTE] Thanks for talking down to me that's great You are putting words in my mouth. I am talking about repetition of sets of matter. A person, for instance. People seem to think there is a mirror you living out there somewhere if the universe but that is not true. Whether or not there are two particles out there that are the same is irrelevant. We are talking about the notion that large-scales structures of any kind must eventually repeat themselves in an infinite cosmos. [editline]2nd October 2012[/editline] [QUOTE=RobbL;37889131]There are a finite number of possible things in the universe (possible arrangements of matter, engery, ect.)[/QUOTE] Ehh what gave you that idea
[QUOTE=JohnnyMo1;37889285]We are talking about the notion that large-scales structures of any kind must eventually repeat themselves in an infinite cosmos[/QUOTE] There's no difference between protons and planets apart from their complexity. If there's more than one proton, there's more than one mars (given enough space and matter)
[QUOTE=RobbL;37889333]There's no difference between protons and planets apart from their complexity. If there's more than one proton, there's more than one mars (given enough space and matter)[/QUOTE] That is an unjustified claim. [editline]2nd October 2012[/editline] Especially considering there already IS more than one proton even in a finite universe but you wouldn't claim a finite universe has to have two Marses
[QUOTE=JohnnyMo1;37889338]That is an unjustified claim. [editline]2nd October 2012[/editline] Especially considering there already IS more than one proton even in a finite universe but you wouldn't claim a finite universe has to have two Marses[/QUOTE] A finite universe could have another Mars. The larger the finite universe is, the more likely there is to be a copy of Mars. An infinite universe would have a 100% chance of there being more than one Mars, in fact a 100% chance of there being infinite Marses. Anyway, take a look at this- (I don't know what's up with the values he chose to use) [QUOTE]To Infity to Beyond is one of those superb Horizon programmes. The UK fascinates me for many reasons but the quality of British television is one of them. ( I recently found a lot of Avengers episodes, the Spi Sci series from the sixties with John Steed, Mrs. -Emma- Peel and later with Tara King and 'Mother', what a pleasure to be able to watch them all again. But that's off-topic. ) To the Horizon programme they show how to calculate the distance between our planet Earth and the nearest exact copy. Yes. IF, the Universe is indeed infinite than there must be a planet Earth somewhere which is an exact copy of ours. This is not only some mental experiment like Hilbert's Hotel but it is possible to calculate the distance to the first copy ( there are many, of course ) in meters. In meters: 210118∗1026m where 10118 is the number of particles in our universe, and 210118 is thus the number of possible universes (arrangements of particles) and 1026m is simply the diameter of our own universe. UPDATE: I thought about this, watched the programme once more. I think the actual distance is significantly larger than the number above. The example in the program is an extrapolition of a universe consisting of 4 particles of which there are two types. The argument remains valid though. If the universe is infinite then there must be a copy of our Earth somewhere.[/QUOTE] It's relating to the video I posted, I recommend you watch it
[QUOTE=JohnnyMo1;37889338]That is an unjustified claim. [editline]2nd October 2012[/editline] Especially considering there already IS more than one proton even in a finite universe but you wouldn't claim a finite universe has to have two Marses[/QUOTE] I try to think of it in terms of "everything is unique". We just group them in order to sort them better.
[QUOTE=RobbL;37889459]A finite universe could have another Mars. The larger the finite universe is, the more likely there is to be a copy of Mars. An infinite universe would have a 100% chance of there being more than one Mars, in fact a 100% chance of there being infinite Marses. Anyway, take a look at this- (I don't know what's up with the values he chose to use)[/quote] The program is making claims that are false for the purpose of blowing people's tiny minds. Or, more accurately, it's oversimplifying things. And that calculation can only find an average. We're talking about random processes here, all I've been trying to say the whole time is that no matter what, there is never a 100% guarantee that even if your universe is infinite, that there must be multiple earths. It seems like a reasonable assumption, but it is false. All you have to do is come up with a universe where that isn't the case, and I can come up with plenty. Consider a universe that is nothing but a row of particles evenly spaced going in one dimension. Proof of what I'm saying by counterexample right there. If you roll the giant cosmic dice as many times as you want, eventually you are going to end up with a universe like that. [editline]2nd October 2012[/editline] The fact that you keep rehashing old arguments and ignoring what I've been saying makes me wonder if you've even been reading my posts at all. Your "an infinite universe has 100% chance of having infinite Marses" claim is contradicted by my earlier .101001... example. Say I roll a very large die to find an irrational number between 0 and 1. You might claim that "an irrational number does not just repeat itself indefinitely, and contains infinitely many digits, thus every irrational number must contain an infinite number of instances of the sequence ...1234567890...!" But this isn't true. Suppose you roll the dice and get .1010010001... It's irrational, but you won't find that sequence in there even once. [editline]2nd October 2012[/editline] The logic of that example is perfectly analogous to the infinite universe claim. There is NOT a finite number of ways to arrange infinitely many particles, even if each particle has only 2 possible states. Thus it's always possible to have a totally unique arrangement such that you can find some section of it, i.e. something that looks like Mars, that never arises in that universe again.
-snip-
If the universe was infinite, and we were able to browse through everything instantly without needing to travel, then after a time of browsing we eventually would come across an exact copy of ourselves. However infinity in any way is impossible to achieve, since everything has a beginning and an end no matter what.
[QUOTE=wug;37889762]If the universe was infinite, and we were able to browse through everything instantly without needing to travel, then after a time of browsing we eventually would come across an exact copy of ourselves. However infinity in any way is impossible to achieve, since everything has a beginning and an end no matter what.[/QUOTE] grarr read thread before post
This thread turned to debate so fast you'd think it was about transexuals.
I like math and physics, dammit, and I can't allow misconceptions to disseminate into the public mind!
[QUOTE=JohnnyMo1;37889584]The program is making claims that are false for the purpose of blowing people's tiny minds. Or, more accurately, it's oversimplifying things. And that calculation can only find an average. We're talking about random processes here.[/QUOTE] Obviously the calculation finds an average btw. And yeah, random processes obviously would produce an infinite combination of results if run infinitely. I'm really tired so my explaining's not the best. Anyway, it is possible for there to be two identical grains of sand (even if there are negligible or unrecognisable differences). Imagine a contained beach full of sand. There's a certain probability of there being two identical grains of sand. The larger the size of the beach, the more likely there'll be two identical grains of sand. Now make the size of the beach infinite, there's a 100% probability that there'll be at least two identical grains of sand. There's a 100% probability that there'll be at least 20 identical grains of sand. In fact there's a 100% probability that there'll be an infinite amount of identical grains of sand. Now scale the grain of sand up to a planet, and the beach to the universe. The same principle still applies. [editline]3rd October 2012[/editline] [QUOTE=JohnnyMo1;37889584]There is NOT a finite number of ways to arrange infinitely many particles, even if each particle has only 2 possible states[/QUOTE] True, but planets (or any objects- things that could have copies) don't comprise of infinitely many particles There's a finite number of ways to arrange a finite number of particles
[QUOTE=RobbL;37889849]Obviously the calculation finds an average btw. And yeah, random processes obviously would produce an infinite combination of results if run infinitely. I'm really tired so my explaining's not the best. Anyway, it is possible for there to be two identical grains of sand (even if there are negligible or unrecognisable differences). Imagine a contained beach full of sand. There's a certain probability of there being two identical grains of sand. The larger the size of the beach, the more likely there'll be two identical grains of sand. Now make the size of the beach infinite, there's a 100% probability that there'll be at least two identical grains of sand. There's a 100% probability that there'll be at least 20 identical grains of sand. In fact there's a 100% probability that there'll be an infinite amount of identical grains of sand. Now scale the grain of sand up to a planet, and the beach to the universe. The same principle still applies.[/QUOTE] Ah, I see the confusion here. We're getting into difficult notions of something that is "almost always" or "almost never" true. I'll admit that I completely understand getting confused by it, it's a really weird subject that doesn't get a rigorous treatment until very late in mathematics, stuff most people will never take, like measure theory, and the concepts are really thorny until then because they seem deceptively simple. You're technically right, the probability of having 2 grains of sand be the same is 100%, but that doesn't mean it will always happen. Imagine you throw a dart at a number line with equal probability of hitting any point. What's the probability of hitting 3? 0%, since there are infinitely many points more than just that one. What's the probability of hitting an integer? 0%, since there are infinitely many more points between the integers than there are integers. What's the probability of hitting a rational number? 0%, since there are infinitely many more irrational numbers than rational numbers. But you throw a dart, and it hits something, say .952485890858454... some ridiculous irrational. If you asked a mathematician what the probability of you hitting exactly that point before you threw, he'd say "almost 0%." Really the only thing you can call it is 0%. Probability says you'll never hit it. HOWEVER, since the set is not empty, there IS some chance of you actually hitting it. You have to hit something, but the chance of you hitting any specific number is 0%. The chance of having an infinite beach like the one you're imagining where a certain grain of sand never repeats is 0%, but there IS such a beach that can exist, so to say "Every possible infinite beach must have all of its grains of sand repeat infinitely many times" is not accurate. That is the basis of my argument, here. [QUOTE=RobbL;37889849]True, but planets (or any objects- things that could have copies) don't comprise of infinitely many particles There's a finite number of ways to arrange a finite number of particles[/QUOTE] Not true. Say I want to arrange 20 grains of sand on a number line. I can put them all one unit apart. Or two units apart. Or three. Or four. Or five, etc. That's an infinity of ways right there, and then there are more.
[QUOTE=JohnnyMo1;37890097] Not true. Say I want to arrange 20 grains of sand on a number line. I can put them all one unit apart. Or two units apart. Or three. Or four. Or five, etc. That's an infinity of ways right there, and then there are more.[/QUOTE] Objects are finite in size though, unlike the number line
[QUOTE=RobbL;37890146]Objects are finite in size though, unlike the number line that's all i'm going to reply to for now because i need to go to bed, bye[/QUOTE] but it doesn't matter, since in this infinite universe we're talking about, we can space things as far apart as we like
[QUOTE=JohnnyMo1;37890097] You're technically right, the probability of having 2 grains of sand be the same is 100%, but that doesn't mean it will always happen. Imagine you throw a dart at a number line with equal probability of hitting any point. What's the probability of hitting 3? 0%, since there are infinitely many points more than just that one.[/QUOTE] Btw you'd be throwing the dart an infinite (in an infinite universe there's an infinite number of opportunities for objects to form) number of times at a finite (number of particles in object) dartboard though
Infinite Quests! Well, that or a planet of the Gaben
[QUOTE=JohnnyMo1;37890187]but it doesn't matter, since in this infinite universe we're talking about, we can space things as far apart as we like[/QUOTE] Objects can't possibly be comprised of particles spaced any distance apart though, there's laws that govern that [editline]3rd October 2012[/editline] [QUOTE=JohnnyMo1;37890097] but there IS such a beach that can exist[/QUOTE] How so?
[QUOTE=RobbL;37890237]Btw you'd be throwing the dart an infinite (in an infinite universe there's an infinite number of opportunities for objects to form) number of times at a finite (number of particles in object) dartboard though[/QUOTE] not relevant [QUOTE=RobbL;37890266]Objects can't possibly be comprised of particles spaced any distance apart though, there's laws that govern that[/QUOTE] What are you defining as an "object?" Mars probably doesn't qualify based on what you just said, it's got an atmosphere. The only way to consistently define an "object" is by a collection of particles and the relative directions and distances between them. An abstract set of particles and their locations so that you can translate and rotate the object and it's still the same object [QUOTE=RobbL;37890266]How so?[/QUOTE] Imagine a beach consisting of a grain of sand made of two particles, and one of three, and one of four, etc. It's got infinitely many particles, none can possibly repeat. It doesn't matter how likely it is that you'll randomly generate this universe, you just have to show that one exists [editline]2nd October 2012[/editline] Aren't you going to bed
[QUOTE=JohnnyMo1;37890390]What are you defining as an "object?" Mars probably doesn't qualify based on what you just said, it's got an atmosphere. [/QUOTE] The only 'object' that could have an infinite number of ways to arrange it's particles would be an object of infinite size. Either such an object would be defined as an infinite collection of finite objects (an infinite universe really), or if it was dense enough to considered a single object it wouldn't be able to exist in the first place due to the laws of physics. Within the "infinite collection of finite objects" the finite objects would repeat themselves infinitely btw. [editline]3rd October 2012[/editline] [QUOTE=JohnnyMo1;37890390] Aren't you going to bed[/QUOTE] Yep, you'll be glad to hear I guess [editline]3rd October 2012[/editline] [QUOTE=JohnnyMo1;37890390] Imagine a beach consisting of a grain of sand made of two particles, and one of three, and one of four, etc. It's got infinitely many particles, none can possibly repeat. [/QUOTE] Still don't get that, why would a grain of sand made of a certain number of particles only be able to form once?
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