Is the universe finite or infinite? That is, does it go on forever in at least one direction, or is there unlimited detail in at least one place? This question has been asked as long as we’ve understood the concept of infinity, and many feel we are making substantial progress lately. In particular, many cosmology papers consider the differing physical implications of infinite vs.

Here I give a simple proof from the Vedic theories that the universe is finite in size, and periodic in time. (a) It is clear that the life is periodic on earth. We take birth, die, remain dead for some time, and then reincarnate [1] with a new life. Thus the life of every human has a living period and a dead period.

We next use another Vedic theory: (b) every object in the universe is created by its own individual soul [1]. Therefore all objects in the universe will have the same life cycle as described in item (a) above. That means every object will be periodic with a living time and a dead time.

Now we use a common sense that (c) summation of all periodic waves will be a periodic wave. Therefore the entire universe must be periodic with a living time and a dead time. Thus the universe is eternally existent in time.

Finally we conclude that: (d) since the dead time of the universe is finite, all objects in the universe must die in that time. Therefore the universe must be finite in size. For more details take a look at [1] https://www.academia.edu/38...

How big is the observable universe in light years? How big is the suggested universe in light years? What is the tenable size (and also the observable size) of the universe in terms of lights years? quantized units of space-time? mass? particles? galaxies? stars? Planets? From our best knowledge. Inquiring minds want to know.

each one is numbered with a possible size of the universe. So A and B certainly see distinct evidence.

Of course. But the numbering doesn't really help; lets assume the boxes are numbered in powers of two, in meters, starting at 2^0 = 1. After opening ten boxes, the next box is 2^10 m. Let me define a new unit, M = 2^10 m. Then the situation is the same as before.

Of course, m and M are distinct - but we have no way of preferring one of them, apart from arbitrary choices.

If the physical laws we discover require the universe to be finite or infinite, well, then we know. Even if they don't, they can still inform our choice of prior.

That used to be my argument. Turns out it's pretty circular - it depends on the physical laws being the same everywhere - including in the unobserved portion of the universe. Getting that sort of result, all the way out to infinity, is at least as hard as showing an infinite universe in the first place.

LP, I pretty much agree with your analysis. I'd say that "the universe is infinite" is half of a scientific statement - it's disprovable if it's wrong. But if it's right, then there does not exist an experiment that can distinguish between it and its inverse "the universe is finite".

James, if the universe doesn't exist, it would still be nice to know whether it's an infinite or a finite universe that doesn't exist.Are you a Catholic Jew or a Protestant Jew?

Jens, to amplify: in an infinite Big Bang cosmology, space can still expand even if the universe is and always has been infinite. (To extend the classic analogy, think of an infinitely large loaf of raisin bread being baked. The raisins will still move apart from each other as the loaf expands.) Any region in the universe would have been much smaller in the past.

This post, and its discussion, are pretty absurd in that they make no reference to, nor do they correspond with, any current cosmological science. It's pretty telling that, beyond referring to "many cosmology papers", no one here has actually mentioned any specific papers.

You folks can philosophize all you like about the scientific method, but among actual cosmologists (at least non-fringe ones) there's no debate about the finite-ness of the universe. The Big Bang theory requires a finite universe that grew from a point singularity, at a finite rate, a finite time ago; and that theory has been so incredibly strongly confirmed by observation (like COBE) that it's nearly universally (sic) considered correct.

There were, in the past few decades, questions of the age of the universe, and whether it will keep expanding forever (meaning time is potentially infinite); both of those seem to have been mostly settled by now.

Hmm. "Scientific" here means, "in accordance with the principles of the scientific method." The scientific method is fairly well known: observe some phenomena, form a hypothesis about them, do some experiments to validate or invalidate the hypothesis, repeat. But actually, experiments are generally designed to invalidate the hypothesis, because 'positive' results might just mean that we haven't checked in the one area of the universe that would invalidate the hypothesis.

So here's the problem: let's say we form the hypothesis, "The universe is finite." To verify this, we need to find a boundary somewhere, so we do experiments for a thousand years to look for one, but don't find one. Does this invalidate the hypothesis? No, because maybe we haven't looked in the right place yet. So instead, we form the hypothesis, "The universe is infinite." Again, to verify this, we need to see if there are boundaries to the universe anywhere. We search for a million years and don't find anything -- does this validate the hypothesis? No, for the same reason. And a hypothesis that can't be validated or invalidated by evidence isn't scientific, because it's not subject to the scientific method.

Nick: While there are physical laws in the universe, we don't know any. We only know models that tend to accurately describe observed phenomena. Since the models shift over time (sometimes dramatically), does this mean we ought to change our views on the size of the universe, along with these changes in model? If so, this was also my point in my original comment: pick whatever makes the math (modeling) work out better.

Stuart, you're saying that since (the boxes) and (the boxes A hasn't opened) have the same cardinality, the boxes A has opened are irrelevant, right? This may be true, but it's not like the size-of-the-universe situation, because in the size-of-the-universe situation, the boxes aren't identical to each other - each one is numbered with a possible size of the universe. So A and B certainly see distinct evidence.

More than that, you're neglecting arguments based on physical law. If the physical laws we discover require the universe to be finite or infinite, well, then we know. Even if they don't, they can still inform our choice of prior. (And, IIRC, the best arguments for the infinity of the universe are based on physical law as opposed to just observing the minimum size of the universe.)

"simply the second duplicate judges some of the evidence irrelevant (the extra boxes already opened). "

There seems to be something fundamentally flawed in your argument if one is deeming evidence irrelevant. If one person judges the universe to be infinite and the other says "no, the evidence you used to make that determination is irrelevant and I'm not going to take it into account," then why is it surprising that they have different answers?

"This is not so much a Jaynesian Mind Projection Fallacy, as an argument claiming there are no consistent priors for deciding the question "is the universe infinite?". "

There is something wrong with your claim on a deeper level. When we can't even decide what would consitute proof of an infinite universe (perhaps impossible ?), then it seems especially silly to decide the question from the bayesian point of view. In your example, any evidence that you are taking as evidence for the universe being infinite is also evidence against your assumption of the distribution of the size of the universe in the case that it is finite.

Where different individuals have different evidence, there is not anything the least bit surprising about them having different probabilities.

Here the two duplicates have the same evidence - simply the second duplicate judges some of the evidence irrelevant (the extra boxes already opened). The question is whether two situations - (situation A) and (situation B = situation A + one extra box outside situation A known to contain a black ball) - should be treated the differently. In the absence of some extra structure differentiating A and B, I don't see why this should be.

In fact, I can make the two situations precisely equivalent by adding an infinity of opened boxes containing black balls at the beginning (no longer equivalent with the size of the universe). Now the situations facing the duplicates are precisely the same, so they should come up with the same prior (at different times) and hence disagree (note: this is only true if the probability of the universe being infinite - of there being no white ball - is taken as non-zero).

This is not so much a Jaynesian Mind Projection Fallacy, as an argument claiming there are no consistent priors for deciding the question "is the universe infinite?".

Stuart, you are making many assumptions that you are not making clear to me, but the comments of this blog post are not the right place for long explanations of your analysis.

Can you give links to relevant websites? I'm not particularly enamoured with the results of my analysis, and would be quite keen to see it shown wrong.I made many assumptions about how the box model relates to the "size of the universe" model, yes. There are many ways of doing that, but I don't think that really matters.Assumptions for the box model itself: two isomorphic situations should be given identical priors, and Initial Situation is isomorphic to Initial Situation + one extra box known to contain a black ball.

Stuart, I think that you have to be careful approaching this question from a bayesian point of view. Evidence against your estimated size of the universe cannot constitute evidence that the universe is infinite...only that under your prior, you think it is more likely that the universe is infinite. In your situation, evidence against the universe being finite can also be viewed as evidence against your modeling assumptions for the distribution of the size of the universe under the hypothesis that the universe is finite. Instead, any new evidence should simply be taken into account in your posterior to portray how large you believe the universe is.

No finite amount of evidence should be able to constitute evidence that the universe is infinite... and I believe therein lies the dilemma with addressing this question with probability or statistics.

So while you have concluded, to your satisfaction, that the universe is most likely infinite, your duplicate argues it has probability p < 0.5 of being infinite. Who is correct?

Stuart, this looks to me like classic Jaynesian Mind Projection Fallacy - if we are uncertain about a phenomenon, that is a fact about our state of mind, not a fact about the phenomenon. Probabilities are states of uncertainty (the universe itself is either one way or another), and states of uncertainty have no place outside of some particular individual's mind. Where different individuals have different evidence, there is not anything the least bit surprising about them having different probabilities.

Stuart, you are making many assumptions that you are not making clear to me, but the comments of this blog post are not the right place for long explanations of your analysis.

Imagine an infinite line of boxes, each containing a ball. They represent the different sizes the universe can be. Most of them are black, and one of them (the actual "size of the universe") is white - or there may be no white ball, in which case the universe is infinite.

You arrive, and want to establish the size of the universe. However, before even arriving, you are secretly duplicated, and your duplicate placed in cold storage.

You set up a reasonable prior estimate as to the size of the universe, "P". Assume you have set P(infinity) = p, with 0 < p < 0.5. Then you start opening boxes, one by one. There will come a number "X" where after opening X boxes and seeing only black balls, you conclude the universe is more likely to be infinite than finite.

At that moment, your duplicate is released from cold storage. The situation he sees is the same as what you had at the beginning - a infinite series of boxes, with possibly a white ball in them. Since he uses the same reasoning as you, he sets the prior "P" on the size of the universe.

So while you have concluded, to your satisfaction, that the universe is most likely infinite, your duplicate argues it has probability p < 0.5 of being infinite. Who is correct?

(note: the p<0.5 statement is not needed for this argument, but makes the example more elegant)

Ways round this argument: if we have exterior evidence that fixes "P" for you but gives a different initial prior for your duplicate. For example, if you could open all the boxes in finite time (say an hour), then you can give them a cumulative probability based on the time taken to reach that box. And set the probability of infinity to the length of a second, arbitrarily. If your duplicate does the same, then you will agree.Or you could find that white ball. But in our universe, that hasn't happened.

I think this addresses the issue:But if we continue to frequently make perceptible progress on an ancient open question, that question cannot long remain open.For those who set up their priors early, the question would no longer be open. For those who only set up their priors recently, the question would remain very open. This may explain why people feel differently about the issue.

Stuart, whether or not the question is well post "scientifically" (whatever that means), it seems well-posed conceptually.

It is. But what would constitute evidence for its answer, and to what extent, is not well-posed conceptually. For normal questions this isn't so much of a problem, because extra evidence adds information. But here an extra black ball leaves the set-up exactly as before. As LP says, the question feels "metaphysical".

Here I give a simple proof from the Vedic theories that the universe is finite in size, and periodic in time. (a) It is clear that the life is periodic on earth. We take birth, die, remain dead for some time, and then reincarnate [1] with a new life. Thus the life of every human has a living period and a dead period.

We next use another Vedic theory: (b) every object in the universe is created by its own individual soul [1]. Therefore all objects in the universe will have the same life cycle as described in item (a) above. That means every object will be periodic with a living time and a dead time.

Now we use a common sense that (c) summation of all periodic waves will be a periodic wave. Therefore the entire universe must be periodic with a living time and a dead time. Thus the universe is eternally existent in time.

Finally we conclude that: (d) since the dead time of the universe is finite, all objects in the universe must die in that time. Therefore the universe must be finite in size. For more details take a look at [1] https://www.academia.edu/38...

How big is the observable universe in light years? How big is the suggested universe in light years? What is the tenable size (and also the observable size) of the universe in terms of lights years? quantized units of space-time? mass? particles? galaxies? stars? Planets? From our best knowledge. Inquiring minds want to know.

each one is numbered with a possible size of the universe. So A and B certainly see distinct evidence.

Of course. But the numbering doesn't really help; lets assume the boxes are numbered in powers of two, in meters, starting at 2^0 = 1. After opening ten boxes, the next box is 2^10 m. Let me define a new unit, M = 2^10 m. Then the situation is the same as before.

Of course, m and M are distinct - but we have no way of preferring one of them, apart from arbitrary choices.

If the physical laws we discover require the universe to be finite or infinite, well, then we know. Even if they don't, they can still inform our choice of prior.

That used to be my argument. Turns out it's pretty circular - it depends on the physical laws being the same everywhere - including in the unobserved portion of the universe. Getting that sort of result, all the way out to infinity, is at least as hard as showing an infinite universe in the first place.

LP, I pretty much agree with your analysis. I'd say that "the universe is infinite" is half of a scientific statement - it's disprovable if it's wrong. But if it's right, then there does not exist an experiment that can distinguish between it and its inverse "the universe is finite".

James, if the universe doesn't exist, it would still be nice to know whether it's an infinite or a finite universe that doesn't exist.Are you a Catholic Jew or a Protestant Jew?

Jens, to amplify: in an infinite Big Bang cosmology, space can still expand even if the universe is and always has been infinite. (To extend the classic analogy, think of an infinitely large loaf of raisin bread being baked. The raisins will still move apart from each other as the loaf expands.) Any region in the universe would have been much smaller in the past.

Jens, you are completely misinformed about modern cosmology.

This post, and its discussion, are pretty absurd in that they make no reference to, nor do they correspond with, any current cosmological science. It's pretty telling that, beyond referring to "many cosmology papers", no one here has actually mentioned any specific papers.

You folks can philosophize all you like about the scientific method, but among actual cosmologists (at least non-fringe ones) there's no debate about the finite-ness of the universe. The Big Bang theory requires a finite universe that grew from a point singularity, at a finite rate, a finite time ago; and that theory has been so incredibly strongly confirmed by observation (like COBE) that it's nearly universally (sic) considered correct.

There were, in the past few decades, questions of the age of the universe, and whether it will keep expanding forever (meaning time is potentially infinite); both of those seem to have been mostly settled by now.

Robin,

Hmm. "Scientific" here means, "in accordance with the principles of the scientific method." The scientific method is fairly well known: observe some phenomena, form a hypothesis about them, do some experiments to validate or invalidate the hypothesis, repeat. But actually, experiments are generally designed to invalidate the hypothesis, because 'positive' results might just mean that we haven't checked in the one area of the universe that would invalidate the hypothesis.

So here's the problem: let's say we form the hypothesis, "The universe is finite." To verify this, we need to find a boundary somewhere, so we do experiments for a thousand years to look for one, but don't find one. Does this invalidate the hypothesis? No, because maybe we haven't looked in the right place yet. So instead, we form the hypothesis, "The universe is infinite." Again, to verify this, we need to see if there are boundaries to the universe anywhere. We search for a million years and don't find anything -- does this validate the hypothesis? No, for the same reason. And a hypothesis that can't be validated or invalidated by evidence isn't scientific, because it's not subject to the scientific method.

Nick: While there are physical laws in the universe, we don't know any. We only know models that tend to accurately describe observed phenomena. Since the models shift over time (sometimes dramatically), does this mean we ought to change our views on the size of the universe, along with these changes in model? If so, this was also my point in my original comment: pick whatever makes the math (modeling) work out better.

Stuart, you're saying that since (the boxes) and (the boxes A hasn't opened) have the same cardinality, the boxes A has opened are irrelevant, right? This may be true, but it's not like the size-of-the-universe situation, because in the size-of-the-universe situation, the boxes aren't identical to each other - each one is numbered with a possible size of the universe. So A and B certainly see distinct evidence.

More than that, you're neglecting arguments based on physical law. If the physical laws we discover require the universe to be finite or infinite, well, then we know. Even if they don't, they can still inform our choice of prior. (And, IIRC, the best arguments for the infinity of the universe are based on physical law as opposed to just observing the minimum size of the universe.)

"simply the second duplicate judges some of the evidence irrelevant (the extra boxes already opened). "

There seems to be something fundamentally flawed in your argument if one is deeming evidence irrelevant. If one person judges the universe to be infinite and the other says "no, the evidence you used to make that determination is irrelevant and I'm not going to take it into account," then why is it surprising that they have different answers?

"This is not so much a Jaynesian Mind Projection Fallacy, as an argument claiming there are no consistent priors for deciding the question "is the universe infinite?". "

There is something wrong with your claim on a deeper level. When we can't even decide what would consitute proof of an infinite universe (perhaps impossible ?), then it seems especially silly to decide the question from the bayesian point of view. In your example, any evidence that you are taking as evidence for the universe being infinite is also evidence against your assumption of the distribution of the size of the universe in the case that it is finite.

Where different individuals have different evidence, there is not anything the least bit surprising about them having different probabilities.

Here the two duplicates have the same evidence - simply the second duplicate judges some of the evidence irrelevant (the extra boxes already opened). The question is whether two situations - (situation A) and (situation B = situation A + one extra box outside situation A known to contain a black ball) - should be treated the differently. In the absence of some extra structure differentiating A and B, I don't see why this should be.

In fact, I can make the two situations precisely equivalent by adding an infinity of opened boxes containing black balls at the beginning (no longer equivalent with the size of the universe). Now the situations facing the duplicates are precisely the same, so they should come up with the same prior (at different times) and hence disagree (note: this is only true if the probability of the universe being infinite - of there being no white ball - is taken as non-zero).

This is not so much a Jaynesian Mind Projection Fallacy, as an argument claiming there are no consistent priors for deciding the question "is the universe infinite?".

Stuart, you are making many assumptions that you are not making clear to me, but the comments of this blog post are not the right place for long explanations of your analysis.

Can you give links to relevant websites? I'm not particularly enamoured with the results of my analysis, and would be quite keen to see it shown wrong.I made many assumptions about how the box model relates to the "size of the universe" model, yes. There are many ways of doing that, but I don't think that really matters.Assumptions for the box model itself: two isomorphic situations should be given identical priors, and Initial Situation is isomorphic to Initial Situation + one extra box known to contain a black ball.

Stuart, I think that you have to be careful approaching this question from a bayesian point of view. Evidence against your estimated size of the universe cannot constitute evidence that the universe is infinite...only that under your prior, you think it is more likely that the universe is infinite. In your situation, evidence against the universe being finite can also be viewed as evidence against your modeling assumptions for the distribution of the size of the universe under the hypothesis that the universe is finite. Instead, any new evidence should simply be taken into account in your posterior to portray how large you believe the universe is.

No finite amount of evidence should be able to constitute evidence that the universe is infinite... and I believe therein lies the dilemma with addressing this question with probability or statistics.

So while you have concluded, to your satisfaction, that the universe is most likely infinite, your duplicate argues it has probability p < 0.5 of being infinite. Who is correct?

Stuart, this looks to me like classic Jaynesian Mind Projection Fallacy - if we are uncertain about a phenomenon, that is a fact about our state of mind, not a fact about the phenomenon. Probabilities are states of uncertainty (the universe itself is either one way or another), and states of uncertainty have no place outside of some particular individual's mind. Where different individuals have different evidence, there is not anything the least bit surprising about them having different probabilities.

Stuart, you are making many assumptions that you are not making clear to me, but the comments of this blog post are not the right place for long explanations of your analysis.

Rephrasing, with duplicates thrown in.

Imagine an infinite line of boxes, each containing a ball. They represent the different sizes the universe can be. Most of them are black, and one of them (the actual "size of the universe") is white - or there may be no white ball, in which case the universe is infinite.

You arrive, and want to establish the size of the universe. However, before even arriving, you are secretly duplicated, and your duplicate placed in cold storage.

You set up a reasonable prior estimate as to the size of the universe, "P". Assume you have set P(infinity) = p, with 0 < p < 0.5. Then you start opening boxes, one by one. There will come a number "X" where after opening X boxes and seeing only black balls, you conclude the universe is more likely to be infinite than finite.

At that moment, your duplicate is released from cold storage. The situation he sees is the same as what you had at the beginning - a infinite series of boxes, with possibly a white ball in them. Since he uses the same reasoning as you, he sets the prior "P" on the size of the universe.

So while you have concluded, to your satisfaction, that the universe is most likely infinite, your duplicate argues it has probability p < 0.5 of being infinite. Who is correct?

(note: the p<0.5 statement is not needed for this argument, but makes the example more elegant)

Ways round this argument: if we have exterior evidence that fixes "P" for you but gives a different initial prior for your duplicate. For example, if you could open all the boxes in finite time (say an hour), then you can give them a cumulative probability based on the time taken to reach that box. And set the probability of infinity to the length of a second, arbitrarily. If your duplicate does the same, then you will agree.Or you could find that white ball. But in our universe, that hasn't happened.

I think this addresses the issue:But if we continue to frequently make perceptible progress on an ancient open question, that question cannot long remain open.For those who set up their priors early, the question would no longer be open. For those who only set up their priors recently, the question would remain very open. This may explain why people feel differently about the issue.

Stuart, whether or not the question is well post "scientifically" (whatever that means), it seems well-posed conceptually.

It is. But what would constitute evidence for its answer, and to what extent, is not well-posed conceptually. For normal questions this isn't so much of a problem, because extra evidence adds information. But here an extra black ball leaves the set-up exactly as before. As LP says, the question feels "metaphysical".

LP, you use the word "scientific" as if you thought it had more than a vague suggestive definition. It doesn't.