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/sci/ - Science & Math

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1350647 No.1350647 [Reply] [Original]

OK, so I have a question about infinity.

Lets say you knew you were at a point in an infinite sequence, with a beginning, but no end. For example, say you knew there had been an original Big Bang, then an endless cycle of big bangs and big crunches, all with people in them. But you don't know what number universe you are in.

Now, presumably you would assume your number to be pretty big. but here is the question - would the number of your position in the sequence be infinite or finite?

For any finite number n the ratio of numbers bigger than n to those smaller is infinity to one, so your number will always be bigger than any finite number.

This suggests that our number will be infinite, but are infinite numbers even possible?

I suppose you could also say that the situation is not possible, but this would rule out a lot of theories about the universe, eg the one above

>> No.1350650

Divide by zero
\thread

>> No.1350659

Inifinite numbers don't exist.

>> No.1350937

tl;dr.

Infinity doesn't exist, it's just a concept

>> No.1350966

>>1350937
Irrational numbers

>> No.1351014

>For any finite number n the ratio of numbers bigger than n to those smaller is infinity to one
well yes, there are only finitely many natural numbers less then any given natural number N.

>so your number will always be bigger than any finite number.
what the shit, are you retarded? how do you conclude that? do you use some botched statistical/probability argument?
if so, say exactly what you thought. because your conclusion is just bullfuck.

for fucks sake.

>> No.1351054

>>1351014
Well, presumably you would not expect to be in say the first few universes, as out of an infinity of possible universes it is unlikely to say the least that you would be in the first few. But this argument applies to the first 10, the first 1,000, the first million.

As we are dealing with infinity here, you would presumably not expect to be even in the first grahams number of universes. In fact, there is no finite number you could name that you would expect to be less than.

Therefore, your number will always be bigger than any finite number.

This argument could obviously be wrong, but HOW is it wrong?

>> No.1351069

>Lets say you knew you were at a point in an infinite sequence, with a beginning, but no end
this is not an infinite sequence.
If you are at a point in a sequence which had a beginning you are at a well defined point.
The notion that this will go on infinitely long has no meaning whatsoever about the status now.

>> No.1351084

>>1351054
>Well, presumably you would not expect to be in say the first few universes
It doesn't matter what you expect. You have no idea of probability, so don't go wielding it around like your dad's gun, someone might get hurt.

If we represent the nth bigbang cycle with the nth natural number, what you're saying basically is:
A random number out of the natural numbers will always be infinite.
Now that's obviously wrong, since there are no infinite natural numbers (there's an infinite AMOUNT of finite natural numbers, but that's something entirely different).

Your probability argument uses rules which are established for finite sets: if you pick a number at random out of a finite set X = {1,2,3,4,5} for example, the possibility of getting a number smaller than 2 is less then the probability of getting a number greater than 2.

But why do you think you can just go around and expand that reasoning to infinite sets?

>> No.1351092

>>1351069
yes it is. look:
1, 2, 3, 4, 5, ....
it has a beginning and no end. just like every sequence, which is just a function from the natural numbers into some set:
f(1), f(2), f(3), ...
again, a beginning and no end.

>> No.1351100

>>1351084
Well, what reasoning should I be using?

Are you saying that if Scientist found out that out of an infinite series of Universes, all with people in them, we were in universe number 4, say, you would not be surprised?

If you are right, where would you expect to be in the sequence? finite but incredibly large? You criticize my reasoning without providing an alternative.

>> No.1351107

>>1351100
he's saying that probability with infinite sets doesn't work like probability with finite sets

>> No.1351113

>>1351100
>Are you saying that if Scientist found out that out of an infinite series of Universes
There's your problem, right there. There wouldn't EVER be an infinite amount of universes. At every point in time there would only have passed a finite amount of big bang cycles.
You don't need any maths/probability for that.

>> No.1351117

>>1351100
>If you are right, where would you expect to be in the sequence? finite but incredibly large? You criticize my reasoning without providing an alternative.
There is no expected value of our point in the sequence. There is no such thing as a uniform probability distribution over an infinite range, and therefore there isn't an expected value either. I do not know a method to properly model this mathematically.

>> No.1351124

>>1351113
i know nothing about physics, but how do you know there can only be finitely many universes? for example, suppose that <span class="math"> (x_i)_{i\in I} [/spoiler] is an ordinal indexed sequence of universes, where our universe is <span class="math"> x_{i_0} [/spoiler]. how do you know that <span class="math"> i_0 [/spoiler] is a natural number?

>> No.1351158

>>1351124
>how do you know there can only be finitely many universes
dude, I used your construction. You said "imagine there was an initial big bang and then the universe keeps on collapsing and big banging indefinitely". Obviously a hypothetical outside observer could just count the big bangs, so you get the natural numbers.

>for example, suppose that [pseudo intellectual rubbish] ...
Oh well, I never said anything about that at all. I was just referring to your explicit constructing.

>> No.1351166

>>1351158
just to clarify i wasn't op. also how do you there are countably many universes (so that an observer can count them)

>> No.1351184

>>1351166
>also how do you there are
dude, troll harder. I haven't said anything about the possible "number" of universes at all, so stfu with your lame shit.
The construction given by OP, which I referred to throughout, obviously yields a sequence of big bang cycles which is in bijection with the natural numbers.

Now stfu or I'll have to punch you in the dick.

>> No.1351199

>>1351184
>I haven't said anything about the possible "number" of universes at all
>>1351113
>There wouldn't EVER be an infinite amount of universes.

>> No.1351207

>>1351166
I think you are confused about what "countably" means. As long as each universe is discrete, then the number of universes is countable.

>> No.1351214

>>1351207
What exactly does it mean for an entity to be discrete?

>> No.1351222

OP here.

Just to clarify, my original question was: If you thought you were in an infinite sequence with a beginning but no end, but you did not know where you were in that sequence, where you would you expect to be.

possible answers: any finite number, any incredibly large finite number, infinitely far from the beginning, don't know the answer, situation is impossible (bear in mind this would rule out a lot of theories about the universe), other.

So far all I have is that infinite numbers don't exist, but no answer to the original question

>> No.1351227

>>1351207
i will clarify once and for all that i'm not familiar with physics, but mathematically i know perfectly well what i am talking about. i will now give a generalized version of op's construction.

suppose there was an ordinal indexed sequence <span class="math"> (x_i)_{i\in I} [/spoiler] of universes (precise definition of what "universe" means is up to interpretations since i'm not too familiar with physics as i've admitted), and that our current universe is at the <span class="math"> i_0 [/spoiler]th index. The question is, how do we know that <span class="math"> i_0 [/spoiler] is a finite ordinal (and hence a natural number)? How do we know <span class="math"> i_0 [/spoiler] is a countable ordinal? etc.

>> No.1351229

>>1351199
as I said earlier, troll harder.
You quoted my first sentence, but didn't quote the second sentence which showed what construction I was talking about (OP's construction).
Or wait, perhaps you're serious. Haha, let me explain:
the OP was talking about a scenario where there's actually just 1 universe, but called the universe after n big bang cycles universe n+1.
Perhaps that's your problem. Damn you're stupid.

>> No.1351232

>>1351214
Meaning that each universe is separate from every other universe. For example, the natural numbers, 1, 2, 3, etc... are discrete. But real numbers aren't, because they all flow into each other.

>> No.1351233

>>1351222
Here's your answer OP: >>1351117

>> No.1351238

>>1350647

>> No.1351241

>>1351232
So which two real numbers are not separate from each other?

>> No.1351246
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1351246

>>1351241

>> No.1351251

>>1351246

>> No.1351252

>>1351232
Is the powerset of the natural numbers discrete according to your definition? Because it certainly isn't countable.

>> No.1351253

>>1351232
that doesn't mean we can't make them discrete (see: discrete topology, well-order, etc)

>> No.1351254

>>1351252

>> No.1351258

>>1351253

>> No.1351263

>>1351238
>>1351254
>>1351258
>>1351258

>> No.1351264
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1351264

>>1351263

>> No.1351268

>>1351252
Fortunately the universes are created in sequence and would not be modeled by a power set of the natural numbers.

Also, cool, I didn't know that about power sets.

>> No.1351274

>>1351268
But that's not the point - I'm just disproving the reasoning in >>1351207.

>> No.1351286

>>1351274
I did not claim that everything that is discrete is countable. You disproved nothing.

>> No.1351290

>>1351286
>As long as each universe is discrete, then the number of universes is countable.

>> No.1351292

>>1351286
If you aren't claiming it, you certainly are >implying it. Also, if you aren't claiming it, what exactly IS your argument that
>As long as each universe is discrete, then the number of universes is countable.
?

>> No.1351313

>>1351292
It's not an argument. It was an example, to hopefully develop the concept of countability for the person I was responding to.

>> No.1351323

>>1351313
A wrong one then, as your claim isn't necessarily true (see >>1351124 for reasons).

>> No.1351326

>>1351323
No, it is correct. The universes, as described here, are countable if they are discrete. They are uncountable if they are not discrete. Nothing I said was false.

>> No.1351336 [DELETED] 

>>1351326
you need to define what "discrete" means, because obviously the real numbers with the discrete topology is uncountable and points are separated from each other (i.e. points are DISCRETE and in a continuum)

>> No.1351344

>>1351336
Clearly, with the examples I gave, points in a continuum would not be considered discrete.

>> No.1351346

>>1351326
first of all the entire point of this thread is to determine whether there are finitely many (similarly countably many) universes. the only thing described so far is that there is a least element in an ordered set of universes, but there are uncountable ordered collections that satisfy that property (for example, any uncountable ordinal)

>> No.1351352

>>1351326
Ah, you were talking about the situation as sketched by OP. In that case, I stand corrected and I apologize, good sir.

>> No.1351360

>>1351346
Yes, but we would not use ordinal numbers to describe this set. We would simply use natural numbers.

>> No.1351386

>>1351360
i would again ask that why are we able to index using the natural numbers? also don't say "because op said sequence" since the op clearly doesn't understand that sequence automatically implies countable.

>> No.1351410

>>1351386
Because OP said sequence. That is the reason. If you would like to discuss some other kind of multiverse, what I have said does not apply.

>> No.1351422

>>1351410
right ok. now please refer to my generalization in >>1351227
are there anything in physics that can say that it would be wrong?

>> No.1351424

>>1351346
Actually, OP mentioned an (infinite) sequence, a.k.a a function from natural numbers to universes.

>> No.1351430

You are all niggers falling and swirling down in a big troll circle, trolling each other even though you might not have intended to do that at the beginning.

Now back to OPs question:
>For example, say you knew there had been an original Big Bang, then an endless cycle of big bangs and big crunches
Observations today suggest that there won't be a big crunch at the end of our universe, but ok, let's assume that for now, just for the lulz.
>Now, presumably you would assume your number to be pretty big
well yes, probably...
>would the number of your position in the sequence be infinite or finite?
It would be finite, because we know:
>there had been an original Big Bang
So the sequence of big bangs and big crunches had a beginning. So every fucking number we can think of is finite. Even if that number is somewhere around <span class="math">10^{10^{10^9000}}[/spoiler], which certainly is an unimaginably big number, it is finite. In fact every definite number is finite. [/thread]

>For any finite number n the ratio of numbers bigger than n to those smaller is infinity to one
seems legit

>so your number will always be bigger than any finite number
What? No! You said we know there was an original big bang! So our universe has to have a certain number (like <span class="math">10^{10^{10^9000}}[/spoiler]). We just don't know this number for sure.

Rest of your post is utter nonsense.

>> No.1351432

anyone picking on the op's use of the term "sequence" is clearly missing the point.

>> No.1351441

>>1351432
Why? What point?

>> No.1351456

>>1351441
i put the op in better mathematical terms in >>1351227

>> No.1351466

>>1351456
The thread isn't about you man

>> No.1351469

>>1351456
You put it in different mathematical terms, but I'm not remotely convinced your version is better. It sure sounds (to me) like OP has a normal infinite sequence in mind, not an extended ordinals thing.

>> No.1351475

>>1351430
OP here. Thanks for one of the few posts in this thread directly answering my question. I think that you are right, it is just that the thing I cant get my head around is that you agree that the number would have to be pretty big, and you would presumably be surprised if your number was small. The problem is that even 1010109000 is small in relation to infinity - any finite number is.

So if you found out your position was 1010109000, or indeed any number, you would still be surprised.

>> No.1351482

>>1351469
clearly not, because otherwise he would've answered his own question in that we must have been at some <span class="math">n[/spoiler]-th term for some natural number <span class="math"> n[/spoiler]. he wanted to know if we could have been at some "infinite-th" place and for that we need to generalize to ordinals.

>> No.1351484

>>1351475
OP here again - btw I am just talking about a "normal" infinite sequence - basically the natural numbers

>> No.1351496

>>1351484
instantrimshot.com

>> No.1351506

>>1351475
Certain numbers have particular appeal to humans. We probably wouldn't be surprised to hear 1010109000, because it's a thoroughly uninteresting number and still much larger than we can conceive of without abstractions. It's a psychological thing.

>> No.1351547

>>1351484
thank you for confirming that your original post is retarded, and disregarded my attempt at trying to turn it into a legitimate question

>> No.1351575

>>1351547
What exactly is retarded about the original post? He announced at the very start that he has "a question about infinity", which kind of implies that he doesn't know what he's talking about (otherwise he wouldn't be asking).

>> No.1351593

>>1351575
his question was if our universe's index was finite or infinite. except this question means nothing if he really meant sequence as in indexed by natural numbers (which he later confirmed). i just assumed that he said sequences for a lack of a better term (and hence didn't know that this automatically implies that all terms are indexed by the natural numbers)

>> No.1351603

>>1351593
>except this question means nothing if he really meant sequence as in indexed by natural numbers
It does in fact, and the answer is "finite, by definition". That this sounds trivial to us doesn't mean the question any less valid.

>> No.1351607

>>1351484

OP, are you reasoning something like this:

Suppose we knew we were in a \finite\ sequence, say of 13 numbers, but we didn't know which term we were at. Since we have no other information, we might as well assume that the probability of being at any given point is 1/13. We can then calculate the expected value of our position as

1 * 1/13 + 2 * 1/13 + 3 * 1/13 ... + 13 * 1/13 = 7.

This makes intuitive sense since the seventh position is right in the middle. Likewise if the sequence had 101 entries, we'd expect to be at the 51st position, and 5 entries the 3rd.

But now if the sequence is infinite can we apply the same reasoning? In other words you want to say that each of the positions is equally likely and so what is the expected position?

If that's your thinking then your problem is that there's just no way to assign such a probability density to the positive integers. You can't ponder the expected value because you can't construct the probability space to begin with.

>> No.1351612

>>1351603
right, but what i personally thought was the core of his question, was the possibility that there have been infinitely many universes before ours.

i'm saging because i realize i'm also retarded for giving him enough of a credit.

>> No.1351632

>>1351607
What if it is half as likely to be in each universe as it is to be in the previous universe.

>> No.1351667

>>1351632
Your expected universe number becomes 2.

>> No.1351668

>>1351632

Well that's a perfectly good probability measure on the set of positive integers.

P(n) = 2^-n.

In that case, we could calculate an expected position

<div class="math">E = \sum_{i=1}^\infty \frac{i}{2^i} = 2</div>

That is, we'd expect that we were at the second position which makes some sense as half the mass is on the first element and so half is after it...

>> No.1351681

>>1351612

I though that for a second, too, but then I actually read what he said

>with a beginning, but no end

>> No.1351685

>>1351681
that's not really a huge problem as long as you index with a set with a least element

>> No.1351698

>>1351607
I understand that you can't put a probability distribution across the natural numbers, but you can think of a situation in which it seems that the distribution is effectively random. e.g. an infinite sequence of universes, all with people in them.

Basically, everyone who has answered my original post has said that you would expect to be a finite number of universes from the first one. Does this mean that if you found out you were in universe number 5, for example, you would not be surprised, even though this is incredibly early compared to all the universes with people in them.

My question here is about infinity, by the way - the universes are just an example to illustrate my point.

>> No.1351704

>>1351685

I guess first element in this case, but yeah. I'm not sure how the problem is well posed in that case either.

>> No.1351706

>>1351698
you can put a probability distribution on the natural numbers... just not a uniform one

>> No.1351724

>>1351632
If people think that this is correct, then everyone in all the universes will think that they are probably in the first few. Therefore the people in, say, the first 5 universes will be correct, and the people in infinity universes will be wrong.

A theory that is correct 5 times out of infinity is not, in my view, a very good theory.

>> No.1351728

>>1351698

You can put a probability distribution on the naturals, you just can't (as far as I know, although I can't think of a quick proof) put any kind of uniform probability measure.

If you look above, we considered a measure that was exponentially decreasing and everything worked out fine.

I've explained the mathematical issue, I think the conceptual issue that you need to get past is the idea that infinite lengths don't have mid-points and so geometric intuition is useless here. There's no reason to "expect" that you are one place on a ray more than any other.

>> No.1351749

>>1351724

It's not a theory. It's an expected value calculation.

If you put a uniform distribution on the points of a dartboard, you're expected to hit the bulls-eye. On the other hand, your probability of doing so is zero.

If you flip a fair coin with a zero on one side and a one on the other, the expected value of your flip is 1/2, but there's no way that will happen.

>> No.1351797

>>1351728
I get the mathematical issue, but my point is that you can think of a situation e.g. the universes where saying there is no expected place leads to weird situations.

For example, lets say in every universe two philosophers debate this argument. Philosopher A says that there is no realistic way they could be in the first, say, 100 universes. Philosopher B says that you can't put a uniform probability distribution on an infinite set, and therefore B would not be surprised if they were in the first 100.

If this happens in every universe, Philosopher A is right infinite times and wrong 100 times. B is only right 100 times

>> No.1351831

>>1351797
There's a difference though. Philosopher B isn't claiming that they're in the first 100, he's just saying he wouldn't be surprised. Philosopher B made no claim, and rightfully so.

>> No.1351871

>>1351797
you can put a uniform distribution on an infinite set. however, you can't do it for the natural numbers.

>> No.1351879

>>1351871
Which infinite set can you put a uniform distribution on?

>> No.1351880

> infinite numbers

Get the fuck out.

>> No.1351889

>>1351879

The set of real numbers between 0 and 1, say.

>> No.1351890

>>1351879
you can do it on any subset of R of finite lebesgue measure

>> No.1351893

>>1351890
...finite and nonzero i should have said

>> No.1351901

Okay, but lets say that there was an experiment to determine the number of the universe, with 1,000/1 odds in favour of it being in the first 100. Philosopher A would not take this bet. Philosopher B would, however (as he has been offered 1,000/1 odds on an event he would consider "not surprising").

If this happens in every universe, 100 B's make lots of money, but infinite Bs lose.

>> No.1351935

>>1351901

Maybe if B were a philosopher he'd take that bet, but he certainly wouldn't take it as a mathematician (probabilist).

>> No.1351940

I'd say there is a difference between something being surprising and something being very unlikely, but now we're talking semantics...

>> No.1351975

>>1351935
But then this means that A is right - you would be surprised to find your self in a low numbered universe.

Basically what I am asking is: given that ITT we have eliminated infinite numbers, would you expect the number of your universe to be any finite number (as in, you find out your universe to be number 4 and are not surprised - philosopher B), or any finite number that is very large (We can't know the number but it will be huuuuuuge - philosipher A)

Put another way, someone in a universe in this situation makes the statement "We are almost surely in a universe with a number so large that we could never even write it down" - are they correct

>> No.1351988

>>1351975
The correct answer is to not make any bet, because it is impossible to even vaguely determine the probability of the outcome. Remember, philosopher B would not be surprised if it was in the first 100, but he would not be surprised if it was NOT in the first 100 either.

>> No.1352017

>>1351988

Yes, but is it correct to say "We are almost surely in a universe with a number so large that we could never even write it down"?

As if it is not correct, betting might be justified if the odds were favorable

>> No.1352026

>>1352017
It is not correct to say that. It is not correct to make any claims regarding the likelihood of which universe you may be in.

>> No.1352114

>>1352026
But why not? If someone in every universe made that claim, a finite number would be wrong and an infinite number would be right.

Therefore, why is it not correct for someone to claim "We are almost surely in a universe with a number so large that we could never even write it down"

That is what I do not understand.

>> No.1352143

>>1352114
Yes, but you simply can't compare the two sets. What are the odds that you are a person in the finite set? What are the odds that you are a person in the infinite set? There is no way of describing the probability that you are in one set or the other.

It's because you can't think of infinity as a number. Looking at the situation as the whole, it is tempting to say "there are infinitely more B than A" but this doesn't allow you to judge probability. From the perspective of the person making the claim, they have no way of knowing whether they are A or B.

>> No.1352147

>>1352114
The problem is that despite this, no probability can be defined, and as "almost surely" is a probability claim it is therefore wrong.

>> No.1352167

>>1352143
>Looking at the situation as the whole, it is tempting to say "there are infinitely more B than A" but this doesn't allow you to judge probability. From the perspective of the person making the claim, they have no way of knowing whether they are A or B.

This is the part that I don't understand. I know that, infinity is not a number, and I know that you can't put a uniform probability distribution over it. But to go from that to a situation in which an infinite amount of people are wondering if they are in a finite set seems ridiculous.

If someone has no reason to think that they are special, would they not assume they are in the infinite set? Perhaps using words like "likely" and "probability" are incorrect, but is that not just semantics?

>> No.1352273

Well, it's like, you can choose any arbitrary point to divide A and B. So even if you make A arbitrarily large, B is larger. If you consider the likelihood that a person in universe X is in set A, all you have to do is expand set A to include X and the odds are 100%. But even in this scenario, B is infinitely larger than A. With your thinking, it is infinitely more likely to be in B than in A, even with this size of A. So we can deduce that no matter which X we use, it is infinitely unlikely (0%) to be in that X or prior. But, we have to be in SOME X. So this is a contradiction and we see that we cannot judge probability in this way.

>> No.1352422

>>1352273
So if this is a contradiction, then what would a person in one of the universes think?

If there was someone in one of the universes, who knew that all the universes had people in them, who had no reason to believe that there was anything special about themselves or their universe, who had to guess if they were in the first twenty universes, are you really saying that the correct answer would be "I dunno lol" rather than "no"?

>> No.1352434

>>1352422
They would think exactly what we think, using the same mathematical logic, because we could hypothetically be people in one of these universes.

And yeah, the correct answer would be "I dunno". You can't say "no" because there is a possibility that you are in the first 20, and you can't say "probably not" because probability has no meaning in this context.

>> No.1352492

>>1352434
Lets say that someone in one of those universes was offered a bet on if they are in the top 20. If they say they are and win, they get $10,000. If they say they are not and win, they get $100. They do not have the option to not bet. What would you think they should choose?

>> No.1352501

>>1352492
There's no correct answer. Even with different rewards, we have no probability to multiply them by. Whichever answer seems more fun to them is the best choice.

>> No.1352524

>>1352501
Well I suppose that's it then - I still think that in a situation like this, It would be correct for someone to assume their position to be almost certainly very large, even if there is no probability and words like certainly have no meaning. You disagree, and I can't think of any more examples. Unless you can think of any resources or examples of when this has been considered before (e.g. by philosophers, scientists etc) we will have to agree to disagree. Thanks anyway

>> No.1352581

>>1352524
That would be just relying on intuition. I don't recall disagreeing that you can use your intuition in such a case. My only point ever was that there is no mathematical probability for one case or the other, and therefore there is no correct decision.

If you think differently, you'll have to come up with some way to determine the probability of being in universe X or earlier.

>> No.1352620

>>1352581
here's an (stupid) example of a probability measure that might better reflect intuition. call a set <span class="math"> X \subseteq \mathbb{N} [/spoiler] cofinite if its complement is finite. then we define the measure <span class="math"> \mu [/spoiler] by <span class="math"> \mu(X) = 1 [/spoiler] if <span class="math"> X [/spoiler] is cofinite, and zero otherwise. i'm pretty sure this is a probability measure.

>> No.1352670

>>1352620
why is that stupid?

>> No.1352688

>>1352670
because it doesn't give us too much information on anything, aside from "infinite is more likely than finite". feel free to refine it.

>> No.1352725

actually nvm i realized it wasn't a probability measure (it doesn't satisfy <span class="math">\sigma[/spoiler]-additivity)