Epistemology in a Multiverse

No, it's zero amount. Anything divided by infinity is zero.

Your math is just as borked as mine. And there are an infinite number of universes where you know this.

"So why can't you use quantum tunneling to walk through a wall? Quantum mechanical calculations show that for something as big as a person, the probability is so small that you could wait until the end of the universe and most likely still not find yourself on the other side."
http://www.sciencemag.org/news/2011...-possible-humanmade-object-physicists-predict

Do you see your error? The probability is not zero. Given an infinite amount of different worlds, whatever is possible, so long as it doesn't violate known laws of nature (e.g., stars moving around to spell out "Eat at Joes"), will happen.

I shouldn't have to explain this. This is an elementary concept.
 
Last edited:
In the lifetime of a universe like ours, I think it pretty much is impossible. In a universe with different laws, maybe.

Why would you need different laws? Enough monkeys typing away will eventually recreate the works of Shakespeare. Aside from the obvious objection that nobody will flip a coin a billion times in a row, the odds of a billion heads-in-a-row coin tosses is not zero. You could postulate a world where every coin toss ever done comes up heads. The total number of coin tosses in a world of billions of people might not be a billion, but it would be a hell of a lot. Given an infinite number of worlds, such a world exists. An infinite number of them, in fact.

This is not a new concept. See Library of Babel.
 
Last edited:
You could postulate a world where every coin toss ever done comes up heads. The total number of coin tosses in a world of billions of people might not be a billion, but it would be a hell of a lot. Given an infinite number of worlds, such a world exists. An infinite number of them, in fact.


No. Let's use your example. Say we only want to count world where all coin tosses come up heads. After the first toss, we've already eliminated half the universes. After the second toss, we're down to a quarter. Three tosses eliminates 7/8th of all universes. By twenty tosses, we're at less than one universe in a million. And the number keeps getting smaller. In fact, given an infinite number of tosses, it tends towards zero. The total number of universes like the one you postulate is zero.

Of course, the chance of our own universe existing is also zero. But we do exist. How is that possible? Because you can't do math with infinity and expect a logical result.

Your math is wrong.
 
No. Let's use your example. Say we only want to count world where all coin tosses come up heads. After the first toss, we've already eliminated half the universes. After the second toss, we're down to a quarter. Three tosses eliminates 7/8th of all universes. By twenty tosses, we're at less than one universe in a million. And the number keeps getting smaller. In fact, given an infinite number of tosses, it tends towards zero. The total number of universes like the one you postulate is zero.

Of course, the chance of our own universe existing is also zero. But we do exist. How is that possible? Because you can't do math with infinity and expect a logical result.

Your math is wrong.

What?
 
Long odds aren't impossible, you realize. You're not claiming it's impossible to flip a fair coin heads a billion times in a row, are you?


Is that a bet?! :)

Don't forget that in your imaginary universe, when you toss the coin again after having tossed it a billion times, there is still a 50-50 chance that it will come out tails. And so on.
And let's assume that there are a lot of coin tossers.

You should also consider that the chance of passing an ESP test is considerably less than 50-50.

And even in a multiverse, a universe rarely has coins ... or tossers ... or fantasies about ESP.
I think your idea would require a bit more than one infinity!

And, yes, the idea of several infinities is probably not mathematically sound. :)

 
Fascinating. The question wasn't "why should you" debate such a person, but "how could you convince them".

Please keep the discussion along those lines.

Employ fallacies. Hoodwink them into accepting them.

Anything more valid than that would require significantly more data about the possibilities, and even then, the qualification that that's just the data that's been obtained by your people. If it's an infinite multi-verse, there can also be an infinite number of oddities and, without more information, one can't rule out possibilities like that universes with similar oddities are far easier to access from one another.




No, it's zero amount. Anything divided by infinity is zero.

Your math is just as borked as mine. And there are an infinite number of universes where you know this.

Errr... an infinitely small number is inherently not zero. It may be rounded to zero in some situations, but it is not actually zero.
 
Also, in an infinite multiverse, there couldn't be a bell curve, since all countable infinite sets are equal. That is to say, there will be the same number of worlds where a fair coin is flipped heads a thousand times in a row as there are where an even distribution of heads and tails occurs: an infinite number.
There's countably infinite integers divisible by 2 and there's countably infinite integers divisible by a Googolplex. That doesn't mean that they're equally distributed amongst the set of all integers.

If you were to randomly pick numbers from the set of all integers, you'd find that the numbers divisible by 2 are far more commonly found than the numbers divisible by a Googleplex, despite both sets being countably infinite.

So even if it's taken for granted that what you say is true and there's an infinite number of universes with all sorts of crazy things going on in those universes, that those crazy universes are equally likely as each other or as likely as the non-crazy (from our perspective) universes, is not necessarily a given.

Your conclusion here simply doesn't follow from the premise.
 
Last edited:
... Suppose you were in a debate with someone from such a world. How could you convince them they're the outlier and not you? ...

Why would you want to "convince" them of this?

Since we're talking about infinity (a subset of which -- any subset at all -- would also be infinite), is the word "outlier" even meaningful?

(Haven't read the entire thread. Just reacting to the OP. Perhaps others have said this already, and probably said it better!)
 
They would also claim there's more than one way to do science (e.g., look for truths in more erosion patterns), and that their way is easier. I would imagine they would posit some higher intelligence that is giving them these truths, since extreme random chance might not be their preferred hypothesis.


This is what I was waiting for.

In our world it translates to "there is a god who revealed to us everything we need to know".
This scenario you built had to be imagined in other hypothetical worlds since "revealed religions" didn't get most of what we need to know right, right in this world..
We weren't able to live in a world that religious revelation became indisputably the "norm".
The religious is not legitimately able to tell us that maybe our scientific way is not the only way.

There should be a way to defeat the person in a debate. I can't see how to do it though.


I wouldn't worry about it until I meet such a person, in such a world.
At that time I may become a believer in that "higher intelligence".
 
Last edited:
This is what I was waiting for.

In our world it translates to "there is a god who revealed to us everything we need to know".
This scenario you built had to be imagined in other hypothetical worlds since "revealed religions" didn't get most of what we need to know right, right in this world..
We weren't able to live in a world that religious revelation became indisputably the "norm".
The religious is not legitimately able to tell us that maybe our scientific way is not the only way.




I wouldn't worry about it until I meet such a person, in such a world.
At that time I may become a believer in that "higher intelligence".

Read the whole thread, specifically post 31.
 
Given a large enough/infinite multiverse, there are going to be worlds like this one, but where scientific/mathematical truths are spelled out in detail in erosion patterns. Where the writers of holy books make accurate predictions of future events, like earthquakes, supernova, etc., where people routinely score 100% on things like Zener card tests, where people's predictions about Pi digits are always right, etc. Call these worlds "extreme coincidence worlds" (ECW). In an infinite multiverse, the number of ECW's would be infinite.

Suppose you were in a debate with someone from such a world. How could you convince them they're the outlier and not you? You could try to explain that their incredibly fluky world will eventually revert back to a statistical norm, but of course your opponent will call you out for assuming you're the norm, and there will be an infinite set of ECW's where there is no reversion to the mean: fantastical coincidence will continue to be the norm and not the exception.

You could try to point to the distribution of worlds like ours (which presumably would vastly outnumber the fluky ones), but A) that would require being able to survey universes in the multiverse, which might not be possible in the debate, and B) in an infinite multiverse, the number of ECW's would be infinite, and countable infinite sets are always equal.

Infinite variations in infinite worlds means that all and none are outliers at the same time.
 
Say we only want to count world where all coin tosses come up heads. After the first toss, we've already eliminated half the universes. After the second toss, we're down to a quarter. Three tosses eliminates 7/8th of all universes. By twenty tosses, we're at less than one universe in a million. And the number keeps getting smaller. In fact, given an infinite number of tosses, it tends towards zero. The total number of universes like the one you postulate is zero.
I don't think this is correct.

If there were an infinite number of universes, and they each get different rolls of the dice that decide random events, then any outcome which is possible will exist, and exist an infinite number of times.

e.g. the universe where every coin that has ever been flipped has always landed heads requires a coincidence of the order of 2^(-numberOfFlips) - a very small number - but not zero - therefore in an infinite multiverse it will happen (infinitely many times!).

The key point is that you selected that universe by that coincidence - but that says nothing about future coin tosses which would be random. Therefore if I was debating someone from that universe that believed coins always land heads because of a law of nature - I would just ask them to toss the coin a few more times...

There's countably infinite integers divisible by 2 and there's countably infinite integers divisible by a Googolplex. That doesn't mean that they're equally distributed amongst the set of all integers.

If you were to randomly pick numbers from the set of all integers, you'd find that the numbers divisible by 2 are far more commonly found than the numbers divisible by a Googleplex, despite both sets being countably infinite.
You can't randomly select an element from an infinite set. What you have to do is define a measure (ordering) of the set, then you can look at the frequency in the first n elements - and take the limit as n tends to infinity.

However - depending on which ordering you choose you will get different results. For integers there is a natural ordering - but lets say I chose to use this ordering instead :
1, Googleplex, 2, 2*Googleplex, 3, 3*Googleplex...

Under that ordering you would conclude that numbers divisible by a Googleplex are just as frequent as even numbers.

We don't have a natural ordering to use when considering infinite sets of universes (if you can justify one I reckon there's a Nobel prize in it for you). This is the measure problem in cosmology. Without any measure we are left with the dilemma of the OP - we can't make any predictions at all. By introducing a measure we can avoid that (i.e. conclude the bizarre universes are very unlikely) but the choice of measure seems arbitrary and the current ones on the table give very different predictions.

- Drelda
 
Last edited:
Read the whole thread, specifically post 31.

I don't know if i can convince them that they're not living in a simulation in their world.
You're saying that they're gonna be aware of the statistical improbability they live in.
How can they be if that world is their normal?
I like the brain exercise you propose though. It'll keep me thinking..
 
Last edited:
Faulty premise.

Infinity doesn't imply unlimited options.

I can have an infinite number of fruits*, and there's still no potatoes.

*-much like this board, it seems

Correct! You can have an infinite number of numerals but not potato.
 
"Somewhere, the Nazis won World War II; somewhere, Hillary Clinton is president; somewhere, humans have driven themselves to extinction; somewhere, we've achieved world peace. We still have just the one Universe, though, and still have no prospects for gathering information outside of what's observable to us. But if the Universe was born infinite, if the state that gave rise to it existed for an infinite amount of time, or we simply created enough pocket Universes for these parallel Universes to exist today, then they're real."
https://www.forbes.com/sites/starts...to-make-parallel-universes-real/#1f442dd53eff

Oh Lord! You have just about offered up a new argument for the existence of God.
Somewhere James Randi is a Christian. Somewhere there is a God.
But God can't be just somewhere. God has to be everywhere!
So God exists in all the multiverse! (Max, what have you done?) :wackybiglaugh:
 
Oh Lord! You have just about offered up a new argument for the existence of God.
Somewhere James Randi is a Christian. Somewhere there is a God.
But God can't be just somewhere. God has to be everywhere!
So God exists in all the multiverse! (Max, what have you done?) :wackybiglaugh:

Where are you getting that from Siegel's quote?
 
How would you argue with a person from one of those worlds about which world is normal?

I wouldn't. There isn't a "normal." the normality for each empirical matrix would simply be its own self consistencies. None are the "real" world.
 
I don't think this is correct.

If there were an infinite number of universes, and they each get different rolls of the dice that decide random events, then any outcome which is possible will exist, and exist an infinite number of times.

e.g. the universe where every coin that has ever been flipped has always landed heads requires a coincidence of the order of 2^(-numberOfFlips) - a very small number - but not zero - therefore in an infinite multiverse it will happen (infinitely many times!).

The key point is that you selected that universe by that coincidence - but that says nothing about future coin tosses which would be random. Therefore if I was debating someone from that universe that believed coins always land heads because of a law of nature - I would just ask them to toss the coin a few more times...

You can't randomly select an element from an infinite set. What you have to do is define a measure (ordering) of the set, then you can look at the frequency in the first n elements - and take the limit as n tends to infinity.

However - depending on which ordering you choose you will get different results. For integers there is a natural ordering - but lets say I chose to use this ordering instead :
1, Googleplex, 2, 2*Googleplex, 3, 3*Googleplex...

Under that ordering you would conclude that numbers divisible by a Googleplex are just as frequent as even numbers.

We don't have a natural ordering to use when considering infinite sets of universes (if you can justify one I reckon there's a Nobel prize in it for you). This is the measure problem in cosmology. Without any measure we are left with the dilemma of the OP - we can't make any predictions at all. By introducing a measure we can avoid that (i.e. conclude the bizarre universes are very unlikely) but the choice of measure seems arbitrary and the current ones on the table give very different predictions.

- Drelda

Wouldn't there be another infinite set of worlds the person you're debating could belong to: the set of fluky worlds that don't regress to the mean? You would be taking a gamble: what if you tell the person, Go ahead, flip it ten more times, see what you get and he gets ten more heads? But it seems like a gamble worth taking, because the odds are on your side.

It doesn't seem fair to stipulate, for the purposes of the debate, that the person exists in a world where future fantastical coincidences are also the norm, although an infinite amount of such worlds would exist, so maybe I could say you're debating someone from some such world. It seems fishy, though.

Also, even if he gets a normal mix of heads and tails, he could point to the fact of his world's crazy history of coincidences as evidence that he's still not an outlier, things have just suddenly changed. Although that would seem very ad hoc reasoning.
 
Last edited:
Wouldn't there be another infinite set of worlds the person you're debating could belong to: the set of fluky worlds that don't regress to the mean? You would be taking a gamble: what if you tell the person, Go ahead, flip it ten more times, see what you get and he gets ten more heads? But it seems like a gamble worth taking, because the odds are on your side.

It doesn't seem fair to stipulate, for the purposes of the debate, that the person exists in a world where future fantastical coincidences are also the norm, although an infinite amount of such worlds would exist, so maybe I could say you're debating someone from some such world. It seems fishy, though.

Also, even if he gets a normal mix of heads and tails, he could point to the fact of his world's crazy history of coincidences as evidence that he's still not an outlier, things have just suddenly changed. Although that would seem very ad hoc reasoning.
There was a Derren Brown show where he constructed a scenario a bit like this. He sent predictions of horse races to thousands of people by email in advance of the race, then for the ones where he was right he made a prediction for the next week. He carried on until he had one person who he had made a long series of correct predictions for - and that person was completely convinced he had some magic way of predicting the future. Of course - in fact he had just selected one of thousands of initial candidates that happened to receive good predictions - like you selecting the one universe where coins had always landed heads. Obviously he didn't really have any predictive powers - just like the future coins tossed in that universe would be random.

If there is an infinite multiverse where all possibilities are explored then we need a 'measure' to be able to say which ones are more likely than others. It seems reasonable to assume that the correct 'measure' is one that makes the universe we observe a typical one - ie that discounts the bizarre scenarios into improbability since we don't observe them. Personally I like the idea of a measure that orders the universes by something like Kolmogorov complexity because that would predict that we find ourselves in a universe that is beautifully elegant with simple rules that lead to layers of complexity - which seems to fit our observations.

- Drelda
 
There was a Derren Brown show where he constructed a scenario a bit like this. He sent predictions of horse races to thousands of people by email in advance of the race, then for the ones where he was right he made a prediction for the next week. He carried on until he had one person who he had made a long series of correct predictions for - and that person was completely convinced he had some magic way of predicting the future. Of course - in fact he had just selected one of thousands of initial candidates that happened to receive good predictions - like you selecting the one universe where coins had always landed heads. Obviously he didn't really have any predictive powers - just like the future coins tossed in that universe would be random.

Yeah, I've heard of that scam before. I forget the name.

If there is an infinite multiverse where all possibilities are explored then we need a 'measure' to be able to say which ones are more likely than others. It seems reasonable to assume that the correct 'measure' is one that makes the universe we observe a typical one - ie that discounts the bizarre scenarios into improbability since we don't observe them. Personally I like the idea of a measure that orders the universes by something like Kolmogorov complexity because that would predict that we find ourselves in a universe that is beautifully elegant with simple rules that lead to layers of complexity - which seems to fit our observations.

- Drelda

How do you deal with an infinite multiverse and the fact that countable infinite sets are always equal? There would be no way to measure which worlds are more likely, since the sets of worlds (e.g., set of worlds like ours, set of worlds with fantastical coincidences) would all be equal to each other.
 
Last edited:
How do you deal with an infinite multiverse and the fact that countable infinite sets are always equal?

*raises an eyebrow* "Countable infinite sets" are not always equal, though. They're simply infinite, which cannot actually be turned into a number. Infinity is a concept related to numbers, but is not a discrete number, after all. One can create a superficial false equivalence using countable infinite sets, certainly, but that's a slightly different matter.

There would be no way to measure which worlds are more likely, since the sets of worlds (e.g., set of worlds like ours, set of worlds with fantastical coincidences) would all be equal to each other.

The main way to determine likelihood would be to have a working Theory of Everything that applied to all of the universes, individually and fully. Determining that it does so would be effectively impossible, though, by the look of it.
 
Last edited:
Infinite variations in infinite worlds means that all and none are outliers at the same time.


The premise reminds me of solipsism as applied to "do we live in a simulation?". It can be used to explain anything and everything, and it's just as much a philisophical dead end.
 
*raises an eyebrow* "Countable infinite sets" are not always equal, though. They're simply infinite, which cannot actually be turned into a number. Infinity is a concept related to numbers, but is not a discrete number, after all. One can create a superficial false equivalence using countable infinite sets, certainly, but that's a slightly different matter.

I wonder what you mean here.

Any two countably infinite sets are, of course, in bijective correspondence with one another. That is, after all, what countably infinite more or less means.

Now, you've uttered some nonsense about numbers, but what counts as a number is a matter of convention, and most trained mathematicians have no qualms about calling either ordinals or cardinals numbers. If you have such qualms, I sure don't know why.
 
The premise reminds me of solipsism as applied to "do we live in a simulation?". It can be used to explain anything and everything, and it's just as much a philisophical dead end.

The problem (if there is one for epistemology), is that, unlike simulation theory, it's looking more and more likely we're one universe in a very large multiverse, perhaps infinitely large. I think there might be implications.
 
*raises an eyebrow* "Countable infinite sets" are not always equal, though. They're simply infinite, which cannot actually be turned into a number. Infinity is a concept related to numbers, but is not a discrete number, after all. One can create a superficial false equivalence using countable infinite sets, certainly, but that's a slightly different matter.



The main way to determine likelihood would be to have a working Theory of Everything that applied to all of the universes, individually and fully. Determining that it does so would be effectively impossible, though, by the look of it.

Phiwum probably put it better than me. From what I understand, if you could pair up each fantastical coincidence world with a mundane world like ours, and if there's an infinite amount of both kinds of worlds, then the two infinite sets are equal.
 
The thing you have to realise about infinity is that it is a really, really really BIG number.

If you have an infinite number of multiverses, and just 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001% of them are universes in which ESP is commonplace, you actually have an infinite number of universes in which ESP is commonplace.
 
Last edited:
I wonder what you mean here.

Any two countably infinite sets are, of course, in bijective correspondence with one another. That is, after all, what countably infinite more or less means.

Not quite. [1,2,3,4,5,etc] and [100,200,300,400,500,etc] are sometimes treated as being in bijective correspondence, as someone tried to argue earlier in the thread, solely because infinity causes an interesting error in the logic, given that infinity is inherently uncountable. In this case, it really would be more proper to acknowledge that every member of the second set can be directly found in the first, but not every member of the first set can be found in the second set, even though there are an infinite number of members in each set.

Now, you've uttered some nonsense about numbers, but what counts as a number is a matter of convention, and most trained mathematicians have no qualms about calling either ordinals or cardinals numbers. If you have such qualms, I sure don't know why.

Are you claiming that ordinals are discrete numbers?

Phiwum probably put it better than me. From what I understand, if you could pair up each fantastical coincidence world with a mundane world like ours, and if there's an infinite amount of both kinds of worlds, then the two infinite sets are equal.

What you said here, in short, is "If X is equal to Y, than X is equal to Y." That's entirely true, but begs the question of what basis one has to regard X to be equal to Y in the first place. An infinity does not necessarily equal another instance of an infinity even though they share some similar properties, rather like an integer is not necessarily the same as a different instance of an integer. 1=1, yes, but 1 does not equal 5, even though both are integers and thus share some similar properties.
 
Last edited:
How do you deal with an infinite multiverse and the fact that countable infinite sets are always equal? There would be no way to measure which worlds are more likely, since the sets of worlds (e.g., set of worlds like ours, set of worlds with fantastical coincidences) would all be equal to each other.
A: The set of even numbers is countably infinite. B: The set of numbers divisible by 65,537 is countably infinite. In a sense, those sets are 'equal'.

Yet if you wander through the set of all integers, you'll find that every second one belongs to A, and only 1 in 65,537 belongs to B, so you'll come across A a lot more often than B.

How do you know that an infinite set of universes wouldn't be the same, with some things being much more common, despite being countably infinite?
 
Not quite. [1,2,3,4,5,etc] and [100,200,300,400,500,etc] are sometimes treated as being in bijective correspondence, as someone tried to argue earlier in the thread, solely because infinity causes an interesting error in the logic, given that infinity is inherently uncountable. In this case, it really would be more proper to acknowledge that every member of the second set can be directly found in the first, but not every member of the first set can be found in the second set, even though there are an infinite number of members in each set.

We are getting a bit off track, but you are mighty confused. There is an obvious bijection between those two sets, namely the map sending n to 100 n. This map is clearly one-to-one and onto and hence is a bijective correspondence.

Of course, it's also true that the second set is a subset of the first, but that is irrelevant to the question: is there a bijection between the two sets?

Are you claiming that ordinals are discrete numbers?

I'm not sure what the word "discrete" means here, without a given topology. And I'm not sure that the standard topology on the ordinals is.

In any case, the simple definitions of cardinality and ordinality are a long-established part of set theory. To deny that there is a bijective correspondence between {0,1,2,...} and {0,100,200,...} is simple silliness, a crankish tantrum due to counterintuitive mathematical results of no controversy whatsoever.
 
We are getting a bit off track, but you are mighty confused. There is an obvious bijection between those two sets, namely the map sending n to 100 n. This map is clearly one-to-one and onto and hence is a bijective correspondence.

Of course, it's also true that the second set is a subset of the first, but that is irrelevant to the question: is there a bijection between the two sets?



I'm not sure what the word "discrete" means here, without a given topology. And I'm not sure that the standard topology on the ordinals is.

In any case, the simple definitions of cardinality and ordinality are a long-established part of set theory. To deny that there is a bijective correspondence between {0,1,2,...} and {0,100,200,...} is simple silliness, a crankish tantrum due to counterintuitive mathematical results of no controversy whatsoever.
The standard topology on the ordinals is the order topology. The ordinals are not discrete under that topology.

I don't really know why you think discreteness matters, honestly.
 
This thread is very occupied with issues about infinities, but if Multiverse theory is right, who says there are infinite universes?

AIUI the people who propose specific ideas, like Everett (EMW interpretation is probably the most popular) propose finite boundaries.

Here's an interesting paper I found quickly on google: https://arxiv.org/pdf/0910.1589.pdf

They propose a limit of 10^10^10^7 or 10^10^16, whittling down from the maximum quantum fluctuations of e^e^3N [where N = 'e-folds of slow-roll post-eternal inflation'...]

These are all enormous numbers, but they are finite. And I cannot find anything to support the idea of an infinite multiverse from modern cosmology, although the idea of an infinite multiverse is common enough in sci-fi etc.



Of course even if there is an infinite multiverse then the posters in this thread who point out that does not mean all things must happen are right imo. But why even go down that rabbit hole? There appears to be no good reason to think there might be infinite universes anyway.
 
Last edited:

Back
Top Bottom