Article in New Scientist

[flaninacupboard]

Made me chuckle

edited for pointless content:

Is space rolled up like a funnel?

A new model of the universe, called a Picard topology, curves in a strange way. one end is infinitely long, but so narrow that it has a finite volume. At the other the huge horn flares out, but not forever - if you left one side of the funnel you would come back in on the other. The curve of the horn could be just righ to explain some anomalies seen in WMAP data. If you look at any little piece of the horn it is saddle shaped like a Pringle - curving down in one direction and up in another. This "negatively curved" space would act like a warped lens, distorting images into line with WMAP finidings.

So there you have it, our universe is curved like a pringle, shaped like a horn and named after a Star Trek character!

[Tommyknocker]

Where is the part that made you chuckle?

[Cobra]

one end is infinitely long, but so narrow that it has a finite volume.

If it is infinitely long, how can it have a finite volume? Is this not a contradiction?

Cobra

[flaninacupboard]

presumably if it is too thin for anything to exist in, it still has length, but not volume. essentially becomes, one dimensional? non-dimensional? not sure how you would explain that.

Edit: the pringle and the Picard thing made me laugh - i know, it's not that funny but NS always makes me laugh.

[Cobra]

One dimensional = a point in space, no volume
Two dimensional = a plane in space, no volume
Three dimensional = space, has volume

I think?

Cobra

[teegee420]

Great. Gone cross-eyed again.

[flaninacupboard]

i suppose it still has the normal four perceptible dimensions but if they are smaller than the planck length then our measurement system would say it has zero volume.

[Capmaster]

Who's to say that the universe isn't shaped like a pencil or a tree?

Space has areas that require we abandon Newtonian physics and use quantum physics or some other system. Black holes come to mind. They used to be viewed as the result of an overactive imagination, but now that we have identified many black holes and, in fact, it may be that every elliptical galaxy has one at the center, we're realizing just how little we know.

Dark matter is another that has always fascinated me because it makes up between 90 and 99% of the mass in the universe, yet we know next to nothing about it. We can only observe the effects it has on other cosmic bodies.

[flaninacupboard]

If you can get hold of the article online it goes into a bit more detail to explain how the picard shape and the WMAP data tie together.

Be interesting to see if that gravity probe deal goes ok......

[Cobra]

if they are smaller than the planck length then our measurement system would say it has zero volume

I suppose this could hold true, especially in a situation like this where the net result of going infinitely accurate would be negligable. However, it does raise the interesting point of the atomic fractal. No matter how small you go, there must be something with mass making that sub-particle up, and so on... I think?

Cobra

[flaninacupboard]

well yes, obviously something smaller than a planck length exists, at the moment we think it's string! yes, the universe is all stringy...

It's just that the unpredictability of the quantum world makes it impossible for us to -measure- anything smaller.

[vitualis]

one end is infinitely long, but so narrow that it has a finite volume.

If it is infinitely long, how can it have a finite volume? Is this not a contradiction?

Cobra

No, it isn't a contradiction.

Consider the following summation:

x = 1 + 1/2 + 1/4 + 1/8 + 1/16 + ......

It has an infinite number of terms.

However, it has a finite value (x = 2).

Lots of things can be like this.

Regards.

[vitualis]

http://www.newscientist.com/news/news.jsp?id=ns99994879

When we say space is "curved like a pringle" (i.e., "saddle" type curvature), this isn't anything new. It has been suggested before. Interestingly, this model for the shape of the universe supports that.

-----------------------------------------

Big Bang glow hints at funnel-shaped Universe
11:58 15 April 04

Could the Universe be shaped like a medieval horn? It may sound like a surrealist's dream, but according to Frank Steiner at the University of Ulm in Germany, recent observations hint that the cosmos is stretched out into a long funnel, with a narrow tube at one end flaring out into a bell. It would also mean that space is finite.

Adopting such an apparently outlandish model could explain two puzzling observations. The first is the pattern of hot and cold spots in the cosmic microwave background radiation, which shows what the Universe looked like just 380,000 years after the Big Bang.

It was charted in detail in 2003 by NASA's Wilkinson Microwave Anisotropy Probe. WMAP found that the pattern fades on the largest scales: there are no clear hot or cold blobs more than about 60 degrees across.


The shape of the cosmos
Steiner and his group claim that a finite, horn-shaped Universe fits this observation. It simply does not have room to hold very big blobs.

The present-day volume of their model universe is nearly 10^32 cubic light years. Back when the Universe was only 380,000 years old it would have been a fraction of that size, too small to allow big fluctuations.




Infinitely long

In the model, technically called a Picard topology, the Universe curves in a strange way. One end is infinitely long, but so narrow that it has a finite volume. At the other end, the horn flares out, but not for ever - if you could fly towards the flared end in a spaceship, at some point you would find yourself flying back in on the other side of the horn (see diagram).

Horn-shaped models were suggested in the 1990s to fit a similar anomaly seen by the COBE satellite, but Steiner's group is the first to show that this idea fits the WMAP data. In 2003, another group claimed that the Universe might be finite (New Scientist, 8 October 2003.)

In this group's model, space had a soccer ball-like shape. But the model has run into trouble. It should have left a clear signature on the microwave sky - a set of circles that mirror each other's spot patterns - but these circles do not seem to be there.

The horn universe is harder to pin down. It would also make matching circles, but the pattern depends on what part of the horn we are in. "Our published search for matching circles probably does not rule out the Picard topology," says Neil Cornish of Montana State University in Bozeman.


Little ellipses

And the idea has another advantage. In the flat space of conventional cosmology, the smallest blobs on microwave sky maps ought to be round. But they are not. "If you look at the small structures, they look like little ellipses," says Steiner. The curve of the horn-shaped universe could be just right to explain this. If you look at any little piece of the horn, it is saddle-shaped like a Pringles potato chip - curving down in one direction and up in the perpendicular one. This "negatively curved" space would act like a warped lens, distorting the image of round primordial blobs in a way that makes them look elliptical to us. Mathematicians can construct an infinite number of different kinds of negatively curved space, most of them with one or more horns, and many of which might fit the data, but the Picard topology is one of the simplest.

This model would force scientists to abandon the "cosmological principle", the idea that all parts of the cosmos are roughly the same. "If one happens to find oneself a long way up the narrow end of the horn, things indeed look very strange, with two very small dimensions," says Holger Then, a member of the team.


Statistical flukes

At an extreme enough point, you would be able to see the back of your own head. It would be an interesting place to explore - but we are probably too far from the narrow end of the horn to examine it with telescopes.

Both of the crucial observations are still ambiguous, however, and may be statistical flukes. Over the next year or so, WMAP and other experiments will test whether large blobs really are lacking and whether small ones really are elliptical.

If they are, then our Universe is curved like a Pringle, shaped like a horn, and named after a Star Trek character. You could not make it up.


Stephen Battersby

-----------------------------------------

[Cobra]

No, it isn't a contradiction.

Consider the following summation:

x = 1 + 1/2 + 1/4 + 1/8 + 1/16 + ......

It has an infinite number of terms.

However, it has a finite value (x = 2).

I understand now. It's still damn weird, but it makes sense. Thanks.

It is a bit like the atomic thing I mentioned - an atom has a known mass, and the atom must be made up of smaller units of a certain mass and so on, forever. I just saw it from the "other end" as it were, and didn't think about it as logically as you have.

What would happen if you were to be able to somehow fly into that part of the universe? Would you end up with a humerously-shaped spacecraft? What's outside of this universe - nothing? In which case, how do we define where the universe ends, and where nothingness starts?

will have to do. There isn't a cross-eyed smiley.

Cobra

[vitualis]

What would happen if you were to be able to somehow fly into that part of the universe? Would you end up with a humerously-shaped spacecraft?

By "that part" do you mean the narrow part of the horn? The above article explained what would happen. The physical dimensions would get smaller and in extreme case you will be able to see your own head.

Presumably, physical laws will be disorted as well so you may not be able to survive in that part of the universe (and you may never be able to reach it anyway).

What's outside of this universe - nothing? In which case, how do we define where the universe ends, and where nothingness starts?

You have to remember that the above is only a two dimensional representation of the curvature of space-time which has at least 4 dimensions...

As to what is "outside" the universe? As beings WITHIN the universe it would be extremely difficult for us to know unless things outside it interact some way with the universe.

It would be like a deep ocean fish trying imagine what is "outside" of the ocean. It could be anything or nothing. Or the question may not even make sense if there is no "outside".

What is "outside" the universe? That's why we have religion.

Regards.

[Cobra]

This just about sums it up!

Cobra

[Capmaster]

It would also mean that space is finite.

But ....the question that will always nag us is ...if space is finite, what's beyond it. Is there a wall there ....just how does space end?

That problem has been bugging me since I was old enough to know what space is: If space is infinite ...how could anything be infinite? If space is not infinite, what's on the other side? It
s enough to turn a reasonably intelligent person into a DVDRHELP lurker

[pacmania_2001]

It would also mean that space is finite.

But ....the question that will always nag us is ...if space is finite, what's beyond it. Is there a wall there ....just how does space end?

That problem has been bugging me since I was old enough to know what space is: If space is infinite ...how could anything be infinite? If space is not infinite, what's on the other side? It
s enough to turn a reasonably intelligent person into a DVDRHELP lurker

My cats breath smells like cat food.

It used to be a quandry me as well but then I realised the only good it was doing was hurting my head from all the thinking.

[Cobra]

The way I have been trying to see it is that the universe is finite, and beyond it is pure nothingness. However, if you were to go there, there wouldn't be nothingness there any more, but you wouldn't be out of our universe - you'd just be expanding it! I think, anyway...

Cobra

[flaninacupboard]

well if you understand the concept of a black hole, that's a good way to imagine our universe, we can never escape it. plus the fact it's continually expanding doesn't help....

[vitualis]

It would also mean that space is finite.

But ....the question that will always nag us is ...if space is finite, what's beyond it. Is there a wall there ....just how does space end?

That problem has been bugging me since I was old enough to know what space is: If space is infinite ...how could anything be infinite? If space is not infinite, what's on the other side? It
s enough to turn a reasonably intelligent person into a DVDRHELP lurker

Remember the CURVATURE of space.

Consider the surface of the Earth. It "looks" flat to a small being living on the surface and it would seem like it should be endless (i.e., you can walk endlessly in one direction). However, because of the curvature of the surface, if you walk far enough in a certain direction, you end up where you start. Thus, the surface of the Earth is finite.

Extend that concept into 3/4 dimensional space. So space can be FINITE but that doesn't mean that there is "nothingness" beyond unless you can view it from a even higher dimension (but that preassumes that a high physical dimension actually exists). Just like you can walk along the Earth and not "fall off the edge" even though the surface of the Earth is finite.

Best regards.

[Capmaster]

It would also mean that space is finite.

But ....the question that will always nag us is ...if space is finite, what's beyond it. Is there a wall there ....just how does space end?

That problem has been bugging me since I was old enough to know what space is: If space is infinite ...how could anything be infinite? If space is not infinite, what's on the other side? It
s enough to turn a reasonably intelligent person into a DVDRHELP lurker

Remember the CURVATURE of space.

Consider the surface of the Earth. It "looks" flat to a small being living on the surface and it would seem like it should be endless (i.e., you can walk endlessly in one direction). However, because of the curvature of the surface, if you walk far enough in a certain direction, you end up where you start. Thus, the surface of the Earth is finite.

Extend that concept into 3/4 dimensional space. So space can be FINITE but that doesn't mean that there is "nothingness" beyond unless you can view it from a even higher dimension (but that preassumes that a high physical dimension actually exists). Just like you can walk along the Earth and not "fall off the edge" even though the surface of the Earth is finite.

Best regards.

It would have to be on an enormous scale. If you look at pics from the Hubble, they did a special study and gazed out to a distant point. What they ended up with was a picture of hundreds of galaxies at a distance of well over 10 billion light years. Like looking back in time to just after the big bang. Look at the pic and figure that each of the objects is a galaxy. Even at warp 9 Picard's Enterprise couldn't cross ONE of those in a lifetime. The universe is one bitchingly big place

http://hubblesite.org/newscenter/newsdesk/archive/releases/2004/07/

The curvature would have had to fool the camera into seeing that when in reality it was not looking in a straight line. The possibilities are mind-boggling 8)

[northcat_8]

one end is infinitely long, but so narrow that it has a finite volume.

If it is infinitely long, how can it have a finite volume? Is this not a contradiction?

Cobra

No, it isn't a contradiction.

Consider the following summation:

x = 1 + 1/2 + 1/4 + 1/8 + 1/16 + ......

It has an infinite number of terms.

However, it has a finite value (x = 2).

Lots of things can be like this.

Regards.

I disagree.

It does not have a finite value of x = 2.

It has a limit of 2. The value will never actually be 2.

It could be argued that since the value would continue to get infinitely closer to 2 but never equal 2 the value of the function will continue to increase and would then be considered infinite since no exact value of the increasing function can be determined.

[Capmaster]

It's the old paradox of the frog in the well. If the frog jumps halfway up the well, then half of that distance, then half again, the frog can jump an infinite amount of time and never reach the top, theoretically. x can never reach 2.

[vitualis]

It would have to be on an enormous scale. If you look at pics from the Hubble, they did a special study and gazed out to a distant point. What they ended up with was a picture of hundreds of galaxies at a distance of well over 10 billion light years. Like looking back in time to just after the big bang. Look at the pic and figure that each of the objects is a galaxy. Even at warp 9 Picard's Enterprise couldn't cross ONE of those in a lifetime. The universe is one bitchingly big place

http://hubblesite.org/newscenter/newsdesk/archive/releases/2004/07/

The curvature would have had to fool the camera into seeing that when in reality it was not looking in a straight line. The possibilities are mind-boggling 8)

My analogy isn't quite correct because we are a THREE dimensional being on the 2D SURFACE of Earth. As we have a higher physical dimension (height) than the surface of Earth, we can perceive the curvature. However, since the Earth is so much bigger than our "height", we "approximate" a 2D being.

If there was a 2D being living on the surface of a sphere, it CAN'T perceive the curvature of it surface (i.e., its "space" directly) either. To these beings, if the sphere was big enough, it would be very difficult for them to determine whether they lived in a FLAT plane (i.e., infinite universe) or in a SPHERE (i.e., finite universe).

Similarly for us 3D beings living in what is at least a 3 physical dimensional universe. We can't directly SEE the curvature of space as light follows the curvature. Where there is a small LOCALISED effect, we may be able to detect something odd (for example, gravity lensing) but the general curvature is something we at present are only theorising on cosmological models to try to explain radiation patterns in the sky.

If, for example, space was heavily curved (say down the narrow end of the "horn shaped universe"), what would you see? It means that that area of space has only a very small finite range in one or two dimensions. Say for example, "width" dimension of the universe at that part is only 10 metres across. What you would experience then if you could go there and survive is a hall of mirrors sort of effect where you could see the back of your own head ten metres in front and then your own head again ten metres in front that and so on...

I disagree.

It does not have a finite value of x = 2.

It has a limit of 2. The value will never actually be 2.

That argument is incorrect. It can be argued that it approaches 2 as the number of terms approaches infinity. Saying that you can never reach infinity is somewhat false. We are not talking about physicality here. We are talking about pure maths. There is a whole branch of mathematics looking at different forms of infinity.

In that summation, as the number of terms approaches infinite, the value of x approaches 2. If the number of terms = infinite, x = 2.

Denying the above is denying that calculus works.

It could be argued that since the value would continue to get infinitely closer to 2 but never equal 2 the value of the function will continue to increase and would then be considered infinite since no exact value of the increasing function can be determined.

UM, NO. If you don't every want to reach infinity (and you can in maths) then the value will infinitesimally (different from infinite) less than two. That is still a finite number. It is a real value between 1 and 2.

It's the old paradox of the frog in the well. If the frog jumps halfway up the well, then half of that distance, then half again, the frog can jump an infinite amount of time and never reach the top, theoretically. x can never reach 2.

If it made a jump every second then that is right.

Actually the paradox is Zeno's paradox. If a hare was racing a tortoise and the tortoise got a head start, by the time the hare reached the tortoises starting position, the tortoise would have moved ahead. By the time the hare reached the new position, the tortoise would have moved ahead again. Since this can happen an infinite number of times, the hare can't ever overtake the tortoise.

Another version is when you shoot an arrow towards a target. It first has to reach half way, and then half way again and again and again... inifinite number of steps. Thus, the argument from Zeno is that the arrow can't every reach the target.

Zeno thus concluded that motion is in fact an illusion and can't exist.

Empirically, we know that both examples above are absurd. In fact, the paradox isn't a paradox at all. Both examples, simply show that the hare can't overtake the tortoise in a certain period of time and the arrow can't reach the target again in a certain period of time. If you do the maths and do the summation of the infinite sequence, you can actually work out what the time is.

Regards.

[Capmaster]

My analogy isn't quite correct because we are a THREE dimensional being on the 2D SURFACE of Earth. As we have a higher physical dimension (height) than the surface of Earth, we can perceive the curvature. However, since the Earth is so much bigger than our "height", we "approximate" a 2D being.

I'm not sure your analogy between the curvature of space and that of the earth is really valid. The curvature of earth is not an anomaly, but rather the normal shape of the globe resulting from gravity acting upon it for so long. It isn't even a true sphere. But there's nothing mysterious about the earth looking flat from our perspective. Viewed from the moon the earth is obviously spherical. Viewed from an ant hill it's obviously flat.

Curvature of space isn't simply a matter of perspective ....it's an unproved theory among many theories about the nature of our universe.

[indolikaa]

well if you understand the concept of a black hole, that's a good way to imagine our universe, we can never escape it. plus the fact it's continually expanding doesn't help....

Much like Capmaster's waistline, I suspect...

[Capmaster]

well if you understand the concept of a black hole, that's a good way to imagine our universe, we can never escape it. plus the fact it's continually expanding doesn't help....

Much like Capmaster's waistline, I suspect...

How'd you know? That 30-inch waist I had most of my life is only a fond memory now. It's 34 inches now No curvature of space there There's more curvature on my ass, though

[indolikaa]

She-it. Considering my 38" waistline abhors exercise in all forms, who am I to talk?

[Capmaster]

She-it. Considering my 38" waistline abhors exercise in all forms, who am I to talk?

It all depends on how tall you are. I have a 34" waist and I'm only 12" tall