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Infinite Or Closed Universe
Can any of the scientific minds here please tell me what the current scientific understanding of the universe is at the present? (or at least the general consensus). Is it closed or infinite?
I have trouble wrapping my head around either model. Is there another one that I havnt heard about.
Thanks.
I have trouble wrapping my head around either model. Is there another one that I havnt heard about.
Thanks.
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Morning Nailit -- not sure if you've had a chance to browse this thread or not. Anyway I hope that the answers are useful and it is important to make the point that, strictly speaking, we don't know either way at the moment. Current observations, though, are consistent with a universe that is "almost flat", where "flat" here means something close to "like an infinite cube" (there is a good reason for calling this shape "flat" even if it seems like a contradiction).
However it's worth stressing that the "infinite" part may not actually be true, because as I said before you'd need to wait infinitely long to see light from infinitely far away. Also, there are apparently other, more exotic shapes, that are at this point also consistent with observation. This means that, for example, NJ's assertion that space is definitely infinite is, at the very least, a tad premature.
Equally, Naomi's "current knowledge is irrelevant" is somewhat of a contradiction in terms. If the Universe were observed to be finite then "current scientific knowledge" would certainly be very relevant indeed. As it's not been observed to be so -- at least, not yet -- then this fact is still relevant because it makes the question open. Simply saying that we don't know is often technically true but doesn't really advance the discussion much, if at all.
So, in short then, the best answer is "we don't know but current data suggest that it's very probably infinite (or, at least, the universe is larger than what we can see)".
However it's worth stressing that the "infinite" part may not actually be true, because as I said before you'd need to wait infinitely long to see light from infinitely far away. Also, there are apparently other, more exotic shapes, that are at this point also consistent with observation. This means that, for example, NJ's assertion that space is definitely infinite is, at the very least, a tad premature.
Equally, Naomi's "current knowledge is irrelevant" is somewhat of a contradiction in terms. If the Universe were observed to be finite then "current scientific knowledge" would certainly be very relevant indeed. As it's not been observed to be so -- at least, not yet -- then this fact is still relevant because it makes the question open. Simply saying that we don't know is often technically true but doesn't really advance the discussion much, if at all.
So, in short then, the best answer is "we don't know but current data suggest that it's very probably infinite (or, at least, the universe is larger than what we can see)".
//Morning Nailit -- not sure if you've had a chance to browse this thread or not//
Yes I have Jim and as usual, when I post anything in science, its left me with a headache :-(
All still very interesting stuff though. I suppose that if I'd posted this in R&S I'd have got the various brands of religious fruitcake telling me that ''God did it'' and that would have been it...
Yes I have Jim and as usual, when I post anything in science, its left me with a headache :-(
All still very interesting stuff though. I suppose that if I'd posted this in R&S I'd have got the various brands of religious fruitcake telling me that ''God did it'' and that would have been it...
Jim, something that bothers me is that if the universe is infinite, then presumably time would be so as well. And if time was infinite then why are we (humans, animals etc) still evolving. Given that we have had an infinity to evolve, we should have already reached the point where theres nothing left to evolve into. (if that makes sense? My head starts melting at this point...)
-- answer removed --
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"Jim, something that bothers me is that if the universe is infinite, then presumably time would be so as well."
To be fair, before I finish the rest of this post, I'm pretty sure this was probably the default assumption until around about 70-80 years ago. Even Einstein in his original formulation of the shape of the Universe famously included a "cosmological constant" term in his equations for the express purpose of allowing the Universe to be infinite in time.
But, as it happens, it's not necessary that the universe be infinitely old for it to be infinitely large. I think people tend to have this idea that the Big Bang is when the Universe was of zero size, so that a finite time later it would still be finite -- and therefore it can't possibly be infinite now -- but, again, what was increasing wasn't the size of the Universe but the distance between given points within it.
The balloon analogy can be helpful here. Take an uninflated balloon and mark two points on its outside. Then blow it up. The points get further and further apart, but there's never actually a time when you are adding more balloon material in between the points. In the same way, when the Universe was expanding you never need to add more Universe, you just need points within the Universe to get further apart as it "inflates". I hope that makes sense (although, as always with analogies, don't take everything here too literally).
Finally it's worth noting that even in an infinitely old Universe, the Solar System itself wasn't around forever. For our own evolution, that's the timescale that matters most. On Earth, we've only had around 4 billion years or so to evolve. Although it's no longer the prevailing understanding, this is the sort of picture that you'd have for the "Steady State" model of the Universe. Solar systems and galaxies continue in a cycle of being created and destroyed, each one lasting for only a finite amount of time even though the Universe itself would be infinitely old and long-lasting.
I really hope that all makes (some) sense, and goes some way to answering your questions :)
To be fair, before I finish the rest of this post, I'm pretty sure this was probably the default assumption until around about 70-80 years ago. Even Einstein in his original formulation of the shape of the Universe famously included a "cosmological constant" term in his equations for the express purpose of allowing the Universe to be infinite in time.
But, as it happens, it's not necessary that the universe be infinitely old for it to be infinitely large. I think people tend to have this idea that the Big Bang is when the Universe was of zero size, so that a finite time later it would still be finite -- and therefore it can't possibly be infinite now -- but, again, what was increasing wasn't the size of the Universe but the distance between given points within it.
The balloon analogy can be helpful here. Take an uninflated balloon and mark two points on its outside. Then blow it up. The points get further and further apart, but there's never actually a time when you are adding more balloon material in between the points. In the same way, when the Universe was expanding you never need to add more Universe, you just need points within the Universe to get further apart as it "inflates". I hope that makes sense (although, as always with analogies, don't take everything here too literally).
Finally it's worth noting that even in an infinitely old Universe, the Solar System itself wasn't around forever. For our own evolution, that's the timescale that matters most. On Earth, we've only had around 4 billion years or so to evolve. Although it's no longer the prevailing understanding, this is the sort of picture that you'd have for the "Steady State" model of the Universe. Solar systems and galaxies continue in a cycle of being created and destroyed, each one lasting for only a finite amount of time even though the Universe itself would be infinitely old and long-lasting.
I really hope that all makes (some) sense, and goes some way to answering your questions :)
Part 1:
OK, so I’ll bite.
But be warned, it’s way too long. Jim360 said it much more concisely
It’s a few years since I looked at this stuff, so my knowledge is not as cutting edge as it was – which is why I held off for a while. But seeing the answers from others, I think there may be some confusion about the terms, finite, bounded, closed and so on.
Much of this can only be fully described using multi-dimensional maths (second- or third year university level maths courses), but since I can no longer do that proficiently, and there are one or two people here who (I suspect) may not have the necessary mathematical background, I’ll do what I can without maths.
That’s unfortunate, because to understand it properly, you do need the maths, and anyone who claims they understand it without the mathematical background is probably exaggerating a little (that includes me, of course).
There are two aspects to this – the classical descriptions which rely on more or less conventional descriptions of the universe in multi-dimensional space. In classical descriptions, space is separate from time. And the relativistic descriptions that mix up space and time as different aspects of the same thing.
Let’s start with the classical descriptions.
We are all used to 3-dimensional space. Things have height, width and length. If you want to describe a point on the earth, such as the peak of a mountain, you can give the latitude, longitude and height above sea level, and that describes the point well enough for someone else to find it.
Mathematicians can use various equations and analytics to describe this 3-dimensional space (I’ll abbreviate that to a ‘3-space’) in all kinds of different ways.
The curious thing is that if you add a fourth, fifth or sixth spatial dimension to the equations, they still hold up. Things get a bit more difficult, but a mathematical description of a 5- space is not significantly different from our more familiar 3-space, except that you need five co-ordinates to describe each point in that space.
This kind of analysis is named Riemannian geometry after Bernhard Riemann, who invented it about 150 years ago.
Having sorted that out, let’s talk about Flatland.
Flat land is a thought-experiment in which a universe exists on a sheet of paper (or a larger flat surface). A 2-space.
It is inhabited by the Flatlanders. They can move left and right; forward and backward across the surface of the paper, but not upwards, out of the surface of the paper.
In fact, they have no concept of what ‘upwards’ might mean. (Rather like we have very little concept of what a fourth spatial dimension might look like). They know all about their 2-dimensional world, but the concept of what their world exists ’in’ is completely alien to them. It just exists – there is nothing outside of their own little universe.
If their world is a square sheet of elastic, then it is both finite and bounded. That is to say, the sheet has a specific (finite) area. It also has edges (boundaries).
If we (from our 3-dimensional position) now stretch that sheet of elastic around a large sphere and form perfect joins around the edges, the flatlanders now live on a large spherical surface.
So now the Flatland universe is finite (it has a limited area) but unbounded (no edges). If a Flatlander wishes to move in one direction, they can keep on going for ever, without meeting any kind of boundary. They will, eventually return to their starting point, and that will surely cause some confusion.
But if we make the sphere large enough – say bigger than the surface of the earth, or the diameter of the solar system, or the size of our galaxy, those Flatlanders can just keep on going without ever repeating the scenery. From our 3-space positions, we can see that the flatland universe is finite, but they cannot.
-Continued-
OK, so I’ll bite.
But be warned, it’s way too long. Jim360 said it much more concisely
It’s a few years since I looked at this stuff, so my knowledge is not as cutting edge as it was – which is why I held off for a while. But seeing the answers from others, I think there may be some confusion about the terms, finite, bounded, closed and so on.
Much of this can only be fully described using multi-dimensional maths (second- or third year university level maths courses), but since I can no longer do that proficiently, and there are one or two people here who (I suspect) may not have the necessary mathematical background, I’ll do what I can without maths.
That’s unfortunate, because to understand it properly, you do need the maths, and anyone who claims they understand it without the mathematical background is probably exaggerating a little (that includes me, of course).
There are two aspects to this – the classical descriptions which rely on more or less conventional descriptions of the universe in multi-dimensional space. In classical descriptions, space is separate from time. And the relativistic descriptions that mix up space and time as different aspects of the same thing.
Let’s start with the classical descriptions.
We are all used to 3-dimensional space. Things have height, width and length. If you want to describe a point on the earth, such as the peak of a mountain, you can give the latitude, longitude and height above sea level, and that describes the point well enough for someone else to find it.
Mathematicians can use various equations and analytics to describe this 3-dimensional space (I’ll abbreviate that to a ‘3-space’) in all kinds of different ways.
The curious thing is that if you add a fourth, fifth or sixth spatial dimension to the equations, they still hold up. Things get a bit more difficult, but a mathematical description of a 5- space is not significantly different from our more familiar 3-space, except that you need five co-ordinates to describe each point in that space.
This kind of analysis is named Riemannian geometry after Bernhard Riemann, who invented it about 150 years ago.
Having sorted that out, let’s talk about Flatland.
Flat land is a thought-experiment in which a universe exists on a sheet of paper (or a larger flat surface). A 2-space.
It is inhabited by the Flatlanders. They can move left and right; forward and backward across the surface of the paper, but not upwards, out of the surface of the paper.
In fact, they have no concept of what ‘upwards’ might mean. (Rather like we have very little concept of what a fourth spatial dimension might look like). They know all about their 2-dimensional world, but the concept of what their world exists ’in’ is completely alien to them. It just exists – there is nothing outside of their own little universe.
If their world is a square sheet of elastic, then it is both finite and bounded. That is to say, the sheet has a specific (finite) area. It also has edges (boundaries).
If we (from our 3-dimensional position) now stretch that sheet of elastic around a large sphere and form perfect joins around the edges, the flatlanders now live on a large spherical surface.
So now the Flatland universe is finite (it has a limited area) but unbounded (no edges). If a Flatlander wishes to move in one direction, they can keep on going for ever, without meeting any kind of boundary. They will, eventually return to their starting point, and that will surely cause some confusion.
But if we make the sphere large enough – say bigger than the surface of the earth, or the diameter of the solar system, or the size of our galaxy, those Flatlanders can just keep on going without ever repeating the scenery. From our 3-space positions, we can see that the flatland universe is finite, but they cannot.
-Continued-
Part 2
How could the flatlanders work out that they do not live on a flat, infinite plane?
Like our 3-D mathematicians, the Flatland geometers know that the internal angles of a triangle on a plane flat surface add up to 180°.
Now think of our earth. If you draw a line from the North Pole down the Greenwich Meridian to the Equator, turn 90° and continue the line along the equator for about 10,000 km (90° of longitude) and then turn through another 90° heading north along a line of longitude back to the North Pole, the triangle described by those three lines has three angles, each of which is 90°. That, of course, adds up to 270° which confuses most teachers of maths…
Likewise, if the Flatlanders draw a triangle sufficiently large, then they will find that the angles do not add up as they expect. This gives them a clue that something strange is going on.
It may be that they eventually work out that their geometry fits a higher-dimensional universe (a 3-space), but they still have no concept of what their universe lies ‘in’ because they have no concept (beyond mathematical descriptions) of what that a third spatial dimension might look like.
Now, think of the original Flatland universe as a large, flat sheet of paper. Roll that up into a long, thin tube. Now curve that tube into a circle, so that the paper now looks like a tire inner tube – a torus.
That is a perfectly acceptable shape for a 2-D universe. As is a sphere. Both are finite in size, but unbounded (but geometry on the surface of a torus is strangely weird).
Now think of that spherical Flatland universe as sitting on a balloon. What happens when you inflate the balloon? The Flatlanders see that a line between two fixed points on the surface gets longer. They see that every point on the surface of the balloon is getting further away from every other point (as measured along the surface of the balloon). Furthermore, the rate of increase depends on the original distance between the two points.
You get the connection with our own universe. We can see three spatial dimensions, but most of the clues that astronomers and cosmologists get from large-scale observations suggest that we exist in a multi-dimensional space. Not least is the fact that (almost) every astronomical object we see outside our own galactic local group is receding from us, and the speed of recession depends on the remoteness of the object.
Very few cosmologists think that there is anything special about the location of the earth that might make us the centre of expansion, so we have to think we exist within a geometry that allows everything to recede from everything else.
That is the expansion of the universe. Our perceived 3-space is expanding in a multi-dimensional environment and most of us have no concept of what the other spatial dimensions might be.
Actually, we do –but then we get into string theory and so on, and these are developments of the last 20-30 years and, to be honest I don’t fully understand.
-continued-
How could the flatlanders work out that they do not live on a flat, infinite plane?
Like our 3-D mathematicians, the Flatland geometers know that the internal angles of a triangle on a plane flat surface add up to 180°.
Now think of our earth. If you draw a line from the North Pole down the Greenwich Meridian to the Equator, turn 90° and continue the line along the equator for about 10,000 km (90° of longitude) and then turn through another 90° heading north along a line of longitude back to the North Pole, the triangle described by those three lines has three angles, each of which is 90°. That, of course, adds up to 270° which confuses most teachers of maths…
Likewise, if the Flatlanders draw a triangle sufficiently large, then they will find that the angles do not add up as they expect. This gives them a clue that something strange is going on.
It may be that they eventually work out that their geometry fits a higher-dimensional universe (a 3-space), but they still have no concept of what their universe lies ‘in’ because they have no concept (beyond mathematical descriptions) of what that a third spatial dimension might look like.
Now, think of the original Flatland universe as a large, flat sheet of paper. Roll that up into a long, thin tube. Now curve that tube into a circle, so that the paper now looks like a tire inner tube – a torus.
That is a perfectly acceptable shape for a 2-D universe. As is a sphere. Both are finite in size, but unbounded (but geometry on the surface of a torus is strangely weird).
Now think of that spherical Flatland universe as sitting on a balloon. What happens when you inflate the balloon? The Flatlanders see that a line between two fixed points on the surface gets longer. They see that every point on the surface of the balloon is getting further away from every other point (as measured along the surface of the balloon). Furthermore, the rate of increase depends on the original distance between the two points.
You get the connection with our own universe. We can see three spatial dimensions, but most of the clues that astronomers and cosmologists get from large-scale observations suggest that we exist in a multi-dimensional space. Not least is the fact that (almost) every astronomical object we see outside our own galactic local group is receding from us, and the speed of recession depends on the remoteness of the object.
Very few cosmologists think that there is anything special about the location of the earth that might make us the centre of expansion, so we have to think we exist within a geometry that allows everything to recede from everything else.
That is the expansion of the universe. Our perceived 3-space is expanding in a multi-dimensional environment and most of us have no concept of what the other spatial dimensions might be.
Actually, we do –but then we get into string theory and so on, and these are developments of the last 20-30 years and, to be honest I don’t fully understand.
-continued-
Part 3 - in which I reveal that it's all a waste of time...
Relativity merges space and time
Those of you who have read that dreadful turgid tome called A Brief History of Time will have gathered that there is some relationship between Space and Time and that a bloke called Albert Einstein back in 1915 developed the concept of Spacetime that effectively brings those two concepts together.
(Before any one suggests I’m arguing with prof Hawking about cosmology, banish that thought from your minds – I am merely calling out his editors on their utter failure to make the book intelligible. It is, without doubt, the least-accessible book on the subject that I have read)
At the risk of over-simplifying, Relativity does not really make much difference to the multi-dimensional model of the universe described above.
Classical (Newtonian) mechanics is good enough to describe pretty much every event here on earth. You only need Relativistic corrections for the most extreme events.
If you are a cosmologist studying Black Holes, or neutron stars for the quirky clues to the nature of the universe (much like the Flatlanders measuring triangles), then you need to correct for Relativistic effects, but to understand the basics of multi-dimensional worlds, it’s not really necessary (thank googness)
Anyway, the answer to Nailit’s question has been given – we don’t really know.
Probably the Universe is finite but unbounded (like the Flatlanders’ sphere). We know it is expanding today, but whether it will collapse back into itself in the future depends on the amount of dark matter/dark energy out there, and no-one even knows what that stuff is, let alone how to measure it.
And in any case, all this stuff is billions of years away, so it’s not worth worrying about.
I spent way too much time as a young adult trying to understand it all, to see if it was relevant to life and if it would make my life any more fulfilling. The answer was No, it doesn’t. –shrug-
Relativity merges space and time
Those of you who have read that dreadful turgid tome called A Brief History of Time will have gathered that there is some relationship between Space and Time and that a bloke called Albert Einstein back in 1915 developed the concept of Spacetime that effectively brings those two concepts together.
(Before any one suggests I’m arguing with prof Hawking about cosmology, banish that thought from your minds – I am merely calling out his editors on their utter failure to make the book intelligible. It is, without doubt, the least-accessible book on the subject that I have read)
At the risk of over-simplifying, Relativity does not really make much difference to the multi-dimensional model of the universe described above.
Classical (Newtonian) mechanics is good enough to describe pretty much every event here on earth. You only need Relativistic corrections for the most extreme events.
If you are a cosmologist studying Black Holes, or neutron stars for the quirky clues to the nature of the universe (much like the Flatlanders measuring triangles), then you need to correct for Relativistic effects, but to understand the basics of multi-dimensional worlds, it’s not really necessary (thank googness)
Anyway, the answer to Nailit’s question has been given – we don’t really know.
Probably the Universe is finite but unbounded (like the Flatlanders’ sphere). We know it is expanding today, but whether it will collapse back into itself in the future depends on the amount of dark matter/dark energy out there, and no-one even knows what that stuff is, let alone how to measure it.
And in any case, all this stuff is billions of years away, so it’s not worth worrying about.
I spent way too much time as a young adult trying to understand it all, to see if it was relevant to life and if it would make my life any more fulfilling. The answer was No, it doesn’t. –shrug-
“I really hope that all makes (some) sense, and goes some way to answering your questions :)”
It makes some sense, jim, but does not satisfy my craving for infinity.
The balloon theory is fine. But what’s the balloon in? Is that all there is? I cannot escape from the idea that there can be no ultimate bounds to the universe. All the theories I have read about (and I have not studied them in great depth because it’s not really my thing) fail to provide an explanation to my fundamental question. If you set off from the Earth in any direction and provided you did not collide with any other body, where would you eventually come to a halt? If you subscribe to the idea that space is somehow “curved” and you would go round in a gigantic circle, what’s on the outside of that curve? So it is with time. There cannot be a point when “time began”. If so, what was there before then? If there was nothing (as there is in most of the universe) that nothing still existed.
There seems to be a consensus among all these theories that space, the matter within it, gravity and time are all interconnected in some way. All the theories seem to me to have a common purpose – to dismiss infinity (either in space or time) as a concept because it is uncomfortable.
It makes some sense, jim, but does not satisfy my craving for infinity.
The balloon theory is fine. But what’s the balloon in? Is that all there is? I cannot escape from the idea that there can be no ultimate bounds to the universe. All the theories I have read about (and I have not studied them in great depth because it’s not really my thing) fail to provide an explanation to my fundamental question. If you set off from the Earth in any direction and provided you did not collide with any other body, where would you eventually come to a halt? If you subscribe to the idea that space is somehow “curved” and you would go round in a gigantic circle, what’s on the outside of that curve? So it is with time. There cannot be a point when “time began”. If so, what was there before then? If there was nothing (as there is in most of the universe) that nothing still existed.
There seems to be a consensus among all these theories that space, the matter within it, gravity and time are all interconnected in some way. All the theories seem to me to have a common purpose – to dismiss infinity (either in space or time) as a concept because it is uncomfortable.
//
If you set off from the Earth in any direction and provided you did not collide with any other body, where would you eventually come to a halt?
//
If the Universe were "flat" but finite in size then I have literally no idea how to answer this question. Boundary effects are weird, and I don't really want to say anything as it is likely to be either wrong or certainly very misleading. But it's (probably) not worth worrying about in practice.
//
If you subscribe to the idea that space is somehow “curved” and you would go round in a gigantic circle, what’s on the outside of that curve?
//
The unhelpful answer is, as always, that I don't know, but it's a remarkable truism that there needn't be anything at all. Returning to Kidas's "Flatland" analogy where the inhabitants of Flatland lived on the surface of a sphere, the remarkable mathematical point is that they would only need two reference points to define their position on the sphere, and this would be enough to describe any point in their "Universe". You can think of these points as latitude and longitude, for example. Put another way, the surface of a sphere is actually two-dimensional, even though it looks three-dimensional to us! The only way to describe what is "outside" the surface of the sphere is to invoke a third dimension, one that doesn't exist and isn't even necessary to completely describe the surface of the sphere.
It would be the same with our Universe. If it were closed -- or, indeed, if it were infinite -- then anything "outside" it would exist in a higher dimension of space than the three we currently need to describe it. But from the Universe's point of view that dimension may be redundant -- entirely unnecessary to describe the Universe, and therefore you can do without it.
I know it's compelling to assume that a "closed" (finite) universe requires something "outside" that closed Universe, the reason being because you are always tempted to look at something from "outside" it, for how else can you see its full shape? But it really isn't necessary after all, tempting as it may be, and you can have a consistent description of a four-dimensional, "closed", shape, without needing a fifth dimension in which it lives.
I know it's confusing but the basic idea is that objects can exist without needing to be referenced to, or looked at by, something "outside" them.
If you set off from the Earth in any direction and provided you did not collide with any other body, where would you eventually come to a halt?
//
If the Universe were "flat" but finite in size then I have literally no idea how to answer this question. Boundary effects are weird, and I don't really want to say anything as it is likely to be either wrong or certainly very misleading. But it's (probably) not worth worrying about in practice.
//
If you subscribe to the idea that space is somehow “curved” and you would go round in a gigantic circle, what’s on the outside of that curve?
//
The unhelpful answer is, as always, that I don't know, but it's a remarkable truism that there needn't be anything at all. Returning to Kidas's "Flatland" analogy where the inhabitants of Flatland lived on the surface of a sphere, the remarkable mathematical point is that they would only need two reference points to define their position on the sphere, and this would be enough to describe any point in their "Universe". You can think of these points as latitude and longitude, for example. Put another way, the surface of a sphere is actually two-dimensional, even though it looks three-dimensional to us! The only way to describe what is "outside" the surface of the sphere is to invoke a third dimension, one that doesn't exist and isn't even necessary to completely describe the surface of the sphere.
It would be the same with our Universe. If it were closed -- or, indeed, if it were infinite -- then anything "outside" it would exist in a higher dimension of space than the three we currently need to describe it. But from the Universe's point of view that dimension may be redundant -- entirely unnecessary to describe the Universe, and therefore you can do without it.
I know it's compelling to assume that a "closed" (finite) universe requires something "outside" that closed Universe, the reason being because you are always tempted to look at something from "outside" it, for how else can you see its full shape? But it really isn't necessary after all, tempting as it may be, and you can have a consistent description of a four-dimensional, "closed", shape, without needing a fifth dimension in which it lives.
I know it's confusing but the basic idea is that objects can exist without needing to be referenced to, or looked at by, something "outside" them.
blimey well done Kidas and Jim !
[yeah as soon as s/o mentioned balloon, s/o else would say - what is it blowing up into ?] - did we have on the balloon, as fly would know if it were expanding because more fly-steps would be needed to get from A to B later than earlier - {fly would have to be able to count}
[yeah as soon as s/o mentioned balloon, s/o else would say - what is it blowing up into ?] - did we have on the balloon, as fly would know if it were expanding because more fly-steps would be needed to get from A to B later than earlier - {fly would have to be able to count}
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