Clown

Agreed. How did we get so far off track from the topic of hypershapes? Actually, I know how. There must have been some misunderstanding with what it means for a brain only being able to percieve the world from a 2D screen, because that's how the topic changed into a physics lesson. I've already explained why this is not the case. You are only seeing one image (per area) at a time, be in the reflected light or the object directly behind a transparent object. Same applies to the question of colored surfaces. I think I have also already established that human perception is dependent on the actual physics. Also, I have also shown that the perception that goes on in the brain is retinotopic, so even then you are still looking at a 2D geometric pattern. Umm, that was my point. The mouse will block out any part of the elephant behind it. If we could see fully 3D images, we could see through it. But that also has to do with physics and geometry. Excuse me? You are the one who is arguing semantics here. There is nothing inprecise about the proposal that our vision only allows us to view the world from one 2D perspective at a time. That is a scientific fact not only from physics, but from our understanding of the brain. I have explained exactly what this means, and only brought it up to show why we can't visualize what a 4D object looks like (hence the need for clumsy balloon analogies), but you are the one who brought this way off topic with questions of glass surfaces, transparencies and the like. Those are basic physics questions and any amount of thought put into them should allow you to solve them. There is no need to go off topic like that.

Yes, that is a good definition for transparent objects. Not quite, because you don't actually *see* the transparent object you are looking through! So again, you're only seeing one object along the axis at a single time. The key point is that we can't see invisible objects, by definition. Once again, if you can see through an object, you are not actually *seeing* the object at all. I don't know why you're making this out to be complicated when it's quite simple. No, I think you need to read more carefully, because you're attacking a strawman here. Not quite. If the window is invisible, then by definition you cannot see it. No problem there. In such a case, you're looking at the reflected image from the glass as opposed to the actual object behind it.

Are you saying the universe was created out of nothing then?

Yeah, I see what you're saying. Basically, space cannot be seperated by any distance, because that distance would necessarily be space as well. So any multiverse (such as those born from inflation theories) that postulates many universes running around in some meta spacetime, are not true multiverse theories. The universe then would actually be the mother spacetime in which the different inflation epochs (or big bangs if you will) occur. MrL_JaKiri mentioned a multiverse with universes contained in the same medium. That would be a true multiverse in a sense, with the universes being contained in the same wave function. That one is not so easily to imagine though.

I wasn't aware there was a big explosion when BH's die, and if they did, it would still not compare to the energy released in the big bang.

What about it? I didn't see anything that refutes my claim in it, so here's another look: As far as the eye is concerned, a perfectly transparent object is invisible. It's as simple as that. Air typically cannot be seen at all, and that's why we can see through it. It has nothing to do with whether or not the atoms in the air could cause the transparency to be lost. If you learned something about how light works, you wouldn't find it so ludicrous. Come again? Nope, sorry. You can only see the actual glass when certain regions relfect light. Dirty windows are a good example, and in actual locations where you can actually see the glass itself (actually smudges or reflections), you cannot see what lies behind. Try it out for yourself. Fortunately for us, windows do reflect a lot of light, and are clearly visible. Otherwise, they would just appear to be holes in the walls of houses.

I'm only talking about definitions here. Classically, a vacuum is just a region devoid of matter/energy. The gravitational field doesn't change that, and it's just QM that prevents this perfect vacuum from being attainable.

It's a little complicated, but in any case, being able to *see* such curvature would require 4 dimensions. Some non technical info on curvature: http://www.friesian.com/curved-1.htm

Nonsense. As someone already pointed out, a wine bottle is not completely transparent. You're going to get reflected light that gives the object visibility. The same applies to water and other almost transparent objects. A perfect example of something that actually is transparent, is air. As far as our eyes are concered, the air isn't there.

Welcome to modern physics.

That definition would work for extrinsic curvature, though not the instrinsic curvature the universe is thought to posses.

If an object is transparent, you can't see it. As far as the eye is concerned, the object doesn't even exist. So you are still only seeing things along a 2D axis.

Deleted.

Yes, the balloon sits in an extra 3rd dimension, making it quite clumsy. But as I said, it's only a crude analogy to show a geometric concept. One result of a closed universe is that traveling in one direction far enough will get you right back to where you started! How on earth can a cosmologist explain this weird concept to someone with no experience in Non-Euclidean geometry? So they use this analogy that shows how a 2D stick person would not find an edge or center in his expanding universe. It's not a perfect analogy, but it does at the very least get across a difficult geometric idea. The area of the brain processing images seems to maintain the spatial structure of the image striking the retina. That is to say, the retina takes a 2D geometric pattern and converts it into a signal that gets sent to the brain. But the 2D geometric pattern is maintained as the data reaches the visual cortex. In the V1 area, the membranes that process the images also maintain this 2D pattern, all the way to perception. So as far as geometry perception goes, our brain deals in 2 dimensions. Hmmm, come to think of it, curved is sometimes misleading. I think (I'm not sure though) it's just a bad translation for the German word meaning Non-Euclidean. Someone will have to clarify on that one. Why such geometry is difficult, we can still use lower dimension analogies to get basic ideas across. So long as you don't take them so literally.

Then why can you still only see one object at any given x,y position at one time?

It wasn't in reply to your post. Don't worry, I'm reading your post. See my post above. This would only be possible if you want to claim the mind is not dependent on the brain, namely the visual cortex for perception of geometric objects. Really? Can you draw a picture of what you imagine? Actually, I have shown that the human brain can only view volume through one area at a time. It follows then that if memory and imagination are based on our visual experience, we cannot possibly imagine what a curved volume looks like.

Don't be silly. The balloon is just an analogy cosmologists use to compare to the idea of a closed, expanding universe. In other words, it's just to show that moving along the x,y axis you will never find an edge or center. Nope, it's required. As you probably already know, the idea of spacetime curvature comes from Einstein's GR. This curvature will give spacetime an overall shape, and if the average density is high enough, space will be warped so much that it folds over itself as in the balloon model. No center, no edge. That is why cosmologists began using the balloon analogy in the first place. Well, the expanding part of it also helps. See general relativity. Keep in mind, it's only a geometric analogy used by cosmologists to show the concept of a closed universe. They use it because we cannot visualize 3D curvatures. Good, then you should know very well how the eye works. Given that, you can see why such clumsy balloon analogies are used. I said we only perceive the 3D world one 2D slice at a time. That is, we see images that have as much light packed into a 2D pattern. It is absolutely relevant when the discussion is that we cannot imagine 3D curvature. The main issue is non Euclidean geometry. So basically, the argument is about the balloon analogy. Let me summarize: Curved spacetime is a result of GR. And since we cannot see curved volumes, cosmologists use the 2D balloon analogy as a way of visualizing a geometric idea.

Yes, read about fields.

Since the visual cortex displays a 2D image based on the retina image, we cannot ever see anything outside this 2D perspective. The only way it would be possible if both things below were true: 1. The data for visual perception is not processed in the visual cortex. 2. Light could travel freely in 4 spatial dimensions, thereby being able to reach not a 2D retina, but a 3D one. 3. Your body would need to be 4D in order to have a 3D retina. Actually, there is an easy way to see this. Take any image of the cube (or anything with depth) any plot an X,Y axis. You'll notice that if there is something behind an object at any specific location, you won't be able to see it. In other words, only one object per X,Y coordinate can be seen. An object at (12,2,3) for expample, would be blocked out by an object at (12, 2, 2). So while we can view the depth of a cube or anything else, we are doing so one 2D slice at a time.

No one would seriously debate that people perceive objects through a 2D screen. At least not scientifically.

Yes, QM forbids any such concept. But the point is that even if it were possible (as that is the classic definition) it wouldn't make the vacuum any less of a thing.

You can only see anything one 2D slice at a time. That's just how the brain works. Unless of course, your mind can somehow transcend the limitations of the eye and the visual cortex.

Spacetime is just the gravitational field. A vacuum in that case, would be devoid of energy but is not the nothingness people usually think space is.

Yes it does. The bit where you tie it up doesn't count - with the analogy you are supposed to imagine it as a completely smooth. Ok, here is a better one. Picture a basketball, and note that the surface is boundless. Since humans can only see a 2D projection of our 3D universe at any given time, it is not possible to imagnie what a curved volume actually looks like. It's just a 2D analogy. That is, the equivalant in lower dimensions. If you treat the surface as something with only an x y axis, you can see how there is no center. This only applies to a closed universe. Though I suppose the same would apply to a 2D edgeless torus. (5) To claim the universe requires a 4D brain to imagine it is a bit vague. Define '4D brain'. And explain why my puny brain can visualise and manipulate a model of a hypercube if what you say is true. A model we can imagine is not an actual hypercube. Consider that our ability to imagine objects is based on our visual memory. That is, any dimensional object we are able to see, we should be able to imagine. But when you consider that the retina only displays a 2D image pattern that is sent to the brain, you can clearly see that viewing a full 3D image at one time is not possible. Hence, neither is a curved volume. Depth perception is based on the experience of motion through our 2D viewing area, but we still can't see more than one object at any given x,y coordinate at any given time.

The surface is not. And the universe, though having 3 spatial dimensions, has non Euclidean geometry and it would require a 4 dimensional brain to be able to imagine "what it looks like".