A layman's questions about universes

The reason it's an analogy is because you have to go from the ballon example, which is a 2d surface expanding in 3 dimensions, to our universe, proposed as a 3d hypersurface expanding in 4 dimensions.Since human beings can't really visualize that, we communicate it by analogy. So, we are on the hypersurface of an expanding hypersphere, like the 2d surface of the 3d balloon.

buzsaw responds to me:

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Thanks for response rather than insult.

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Considering that I have never insulted you, one wonders where you get this impression that I would.

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The problem is that you haven't defined what you mean by "infinite." And in the process, you have equivocated among many possible definitions.

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Which specific statement of mine do you refer to here?

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All of them. That's why I said what I said, pointing out for each of your questions where you talk about "infinite," that you seem to be asking about thus-and-so, noting that it is different from the definition that was seemingly implied before.

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The interval is "unbounded" and even though we know there is a line it cannot cross, it never manages to reach that line. No matter what number you give me, I can always find another number that is bigger.

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Imo, herein lies your first problem. "...we know there is a line it cannot cross,..." You're contradicting yourself.

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Incorrect.You're saying that the mathematics of set theory contradicts itself in the concept of "unbounded"?We have notation for it, buzsaw. When you're dealing with a continuous numeric interval, if you wish to indicate that the boundary is included, you write a bracket. If you wish to indicate that the boundary is excluded, you write a parenthesis.Thus, the bounded interval from 0 to 1 where we include 0 and 1 is written as:[0, 1]The unbounded interval from 0 to 1 where we do not include 0 nor 1 is written as:(0, 1)You can even mix and match. If you want to write the interval from 0 to 1 where 0 is included but 1 is not, you write:[0, 1)

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If it is infinitely boundless, why not just say so and leave it at that.

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Because that isn't what it is. Things can be finite and yet unbounded.This is what I was talking about when I said that the subject is extremely complex and requires a fair amount of mathematical prep work. I don't expect you to believe me just because I say so, but I would hope that you would recognize that you are contradicting a great deal of well-understood mathematics.One of the mathematical definitions of "unbounded" (actually "open") is that for every element of the set, you can draw a neighborhood around it such that all elements in the neighborhood are included in the set. A bounded set (actually "closed") is such that there exists at least one element for which no neighborhood can be drawn that doesn't include elements from both inside and outside the set. The set of points that meet that criterion is the boundary.In our example of using the interval from 0 to 1, exclusive (meaning neither 0 nor 1 are included), there is no boundary point. For every element you give me inside the interval, I can draw you a neighborhood that includes only other points inside the set. Here's the formula:If x <= 1/2, draw a neighborhood of x +/- x/2
If x > 1/2, draw a neighborhood of x +/- (1 - x)/2That is, if x is less than or equal to 1/2, draw a neighborhood of radius one-half the distance between x and 0. If x is greater than 1/2, draw a neighborhood of radius one-half the distance between x and 1.But notice, neither 0 nor 1 is in the set. Those two points define te boundary. You cannot draw a neighborhood around those two points without including elements both inside the set and outside the set.The interval is finite in that it does not extend to infinity, but it is unbounded in that you can never reach the boundary.

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What gives you the idea there's a line/boundary it cannot cross?

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Because we have mathematically defined it as such. The interval of 0 to 1 has a set of points that meet the mathematical definition of a boundary. Specifically, 0 and 1.

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That like saying, for example eternity is not eternal.

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But that's just it: Without a definition of those terms, there's no reason to think it isn't. In fact, even with a definition, there's no reason that it can't be.Take the empty set. Is it open or closed? Given the above definition of a boundary, we say that a set is open if and only if it does not contain its boundary. Similarly, a set is closed if and only if its complement is open. That is, a set is closed if and only if the set of all points not in the set does not contain the boundary.Well, the empty set fits both of those definitions. The empty set has no elements, thus does not contain its boundary and thus is open. But the complement of the empty set is the universal set, which also doesn't contain its boundary. Thus, the universal set is open and the complement of an open set is closed. Thus, the empty set is closed.And thus, because the empty set is both open and closed, that means the universal set is both open and closed, too.The point I am trying to make is that you are treading into waters where "common sense" simply does not apply. It is perfectly logical for a set to be both open and closed at the same time.

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"There has to be a beginning." But there doesn't.

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Precisely.But the thing is, if time goes away, it becomes nonsensical to talk about "before."

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Nevertheless, just as time is a segment of eternity, so matter is part of the universe which, being everthing includes all matter, rays and infinite space/area.

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Not necessarily. There might be something beyond that. Our "common sense" definitions of what matter is don't seem to work when we're looking at the very small. That's one of the things that Einstein discovered when he showed that matter and energy are equivalent. Not just "convertible" but are actually the same thing.F'rinstance, if you shine light through a diffraction grating, you get an interference pattern which is what we expect from light as a wave, a type of energy. But if you do the same thing with electrons, you get an interference pattern. But electrons are made of matter, right? Surely they shouldn't be behaving like a wave. But they do.And similarly, if you shine light on metal of an appropriate frequency, you can knock electrons off...just as if light were not waves but particles. That's what Einstein won his Nobel Prize for: The explanation of the photoelectric effect.Light, which we consider to be energy, is both a wave and a particle. Electrons, which we consider to be matter, are both particles and waves. The two are exactly the same.

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Given the fact that universe is expanding (and for the moment, we will not worry about what it is expanding "into"), there is another reasonable claim that it is "infinite" in the sense that were you to start on a journey toward the "edge" of the universe, you would never reach it.

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Herein, imo, lies problem two with you people. Imo, since by definition the universe includes everything, it is impossible for it to expand. Why? Because the area/space where expansion occurs is already inclusive by definition as part of IT, THE UNVERSE.

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That's why I said that for the moment, we will not worry about what it is expanding "into."You are trying to use a "common sense" definition of "expansion" that does not apply. In essence, the universe is not expanding "into" anything. Here's where the balloon analogy comes in handy. Suppose the universe is the surface of a balloon. Now, blow up the balloon. When you do this, all the points in the rubber of the balloon expand away from each other. No matter where you are on the balloon, you see every other point moving away from you...and the points further away are receding more quickly than the ones closer.But the rubber of the balloon isn't expanding "into" anything that the balloon contains. From the surface of the balloon, you cannot see where the balloon is managing to come up with this extra space.Now, we are not a balloon. For one thing, the balloon is a two-dimensional surface and we live in a three-dimensional space. To mathematically expand this into our universe requires a great deal of mathematics.

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Rrhain
WWJD? JWRTFM!

buzsaw responds to NosyNed:

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Ned, but numbers can have bounds. How can infinite space/area possibly have a bound?

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The same way. Fractal geometry provides a wonderful example of this:Take a cube. In each of the three directions, drill out the center square. In each of the remaining sections, drill out the center square. Continue this infinitely. What do you get?You get an object that has a finite volume but infinite surface area.

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By definition, infinite space/area can have no bounds.

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Why not? Why can't it have both? You're trying to use a "common sense" definition where it doesn't apply.

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Rrhain
WWJD? JWRTFM!

mike the wiz responds to me:

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So please DON"T give no mathematics.

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And yet...

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surely a Big Bang can only create an finite universe?

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No. It can easily create an infinite universe. But to explain it requires extremely hefty mathematics which not even I really want to go into. Barbie was right...math is hard. To get into this requires a deep understanding of multidimensional topography and to be honest, I never studied that far. There's a reason that it's the Ph.D. physicists who are doing this work and not the undergraduates. It literally takes a good 10 years simply to become competent enough to even begin asking the appropriate questions, let alone trying to answer them.

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Yet how can a larger structure exist outside a boundless infinite universe?

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Because there are things bigger than infinity.Let's go back to the comparison of the rationals and the reals.I hope you can just trust me that we can put the rationals into a one-to-one correspondance with the natural numbers. That is, if we had a list of 1, 2, 3, ... and a list of every single fraction out there, we could put this list of fractions right up alongside the list of natural numbers and every single one would pair up without there being anything left over. Mathematically, it is called "denumerable."But what about the irrationals? As I described in another post (Message 35 of "International High IQ Society" thread), the irrationals cannot be put into this one-to-one correspondance. There is always an irrational number left over. The set of irrationals is bigger than the set of rationals, even though the rationals are infinitely large.The mathematician Georg Cantor came up with a hierarchy of infinities. He used the Hebrew letter aleph to distinguish them. The size of the rationals he called "aleph-null." The next infinity in the series, "aleph-one," is equal to 2^aleph-null. The next one, "aleph-two," is 2^aleph-one.One of the biggest questions in mathematics is just how big the real numbers are. We know that they're bigger than the rationals, but are they equal to aleph-one? Aleph-two? Any of the alephs? Turns out we don't know. In fact, this question is one of the famous undecideable questions that are predicted by the Incompleteness Theorems.But let's pull back from that and try to come up with another example.What does it mean to be a "boundary"? Mathematically, it means that if you draw a neighborhood around the point, you will necessarily grab elements both inside and outside the set, no matter what the radius size of the neighborhood.With a bit more mathematical coaxing, we come up with a definition of an "open" set meaning that it is a set that does not contain its boundary. Every point in the set is an "interior" point of the set. A "closed" set is one where its complement is "open."What we end up discovering is that by this definition, the universal set is both open and closed. Similarly, the empty set (being the complement of the universal set) is both open and closed.My point is that when you're talking about infinity and nothingness, things do not behave in "common sense" ways. How can something be both open and closed? Well, by the definitions that we have come up with that work so well for so much lead us to conclude that there are at least two things that are both.And in the end, why not? Why can't something be both? So much of what we have found out about our universe is that our distinctions of "or" really don't apply when carefully scrutinized.

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I suppose I meant the universe with no boundary. Infinite without one.

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Just because something has no boundary doesn't mean it is "infinite" in the sense that it contains "everything." The interval (0,1) is unbounded, but it is also considered "finite" in the sense that it doesn't go all the way out to infinity (see what I mean about the word "infinity" having so many definitions?)The universe can be infinite and unbounded and still not contain everything. The set of rational numbers from negative infinity to positive infinite is infinite, unbounded, and still doesn't contain everything.You need to be very careful about trying to use "common sense" definitions of what "infinity" means. We have to be extremely formal and pedantic. It's tedious, but necessary.

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Rrhain
WWJD? JWRTFM!

Fair enough. I doubt I'd understand the mathematics anyway. Didn't Eta say that Big Bangs can't create infinite universes? Maybe I am wrong, but there seems to be some conflicting opinions. Am I then right in assuming that scientists could also disagree with one another concerning this issue?Being a layman on this whole thing, I'm unlikely to get this stuff. I suppose this debate is speculation really. As surely there is only evidence of this universe. The "bigger structure" and multiple Big Bang's, I'm guessing there's no evidence for.So basically I'm going to now just read this topic and see what happens with Buz and the others.Thanks for the replies. I now understand that this is a complex thing.

I agree, it is nonsensical and meaningless to say "you idiot" rather than supplying a refutation.As for your post to me, I am sorry I've been "over-posting" in numerous topics, but I do like your idea that the universe is "everything" in that, there is only evidence for one fine tuned universe which contains well, everything.Regards, Mike.This message has been edited by mike the wiz, 06-22-2004 09:47 AM

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But how, pray tell, can you analyze a 3d balloon with a 2d analogy and come up with the right answer?? If you do this with a sperical universe, you must begin from the surface of the sphere and we're not on the surface. We're in it which requires a 3d analogy to come up with any sense atol!

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Since we cannot visualize what curved space looks like (it's physically impossible to see anything but surfaces) we must drop down to lower dimensions for any meaningful analogy. There are 2 main ideas that this analogy successfully conveys. One, that the universe can be curved with no edges or center, as the 2D surface has none of either. Second, it relates how an object moving about in a finite, unbounded universe will eventually end up at it's starting point if traveling far enough. On a surface, any object only able to move about along the X,Y axis will meet this condition, so the analogy works.

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And how so are laymen, made of the same stuff upstairs as physicists incapable of understanding a 3d analogy/model? It does not take a doctorate degree for that, imo.

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But it takes an understanding of the math. That is something the vast majority of people lack. Fortunately, most people have the intelligence to understand the concept of an analogy and the application here does not go over their heads.

Mike's immediatly previous post Have you been over posting ( a very serious crime you know )? Not that I've noticed. It's not Buz's idea. It was (and really still is ) the consensus scientific view, I think. It would be a bad idea to hang any theological positions on it however. It is subject to change.

It means words are the things that get in the way of what I want to say. Lol. That's all I mean really, that basically we only have evidence for this universe. I know Buz is getting a lot of flack but really, all he's saying is that there is only one universe - this one, which is also scientifically sound.So these multiple Big Bang's seem to be a bit speculative. Even if I am the one causing this induced speculation infiltration relation particle process of excess. Now let me lurk.

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A better illustration is if you're inside a 3d ball or and go in a straight line toward the outer edge in any direction, you will come to the surface, disect/cross it and walk straight out into space and go infinitely, assuming you can go through objects which come in your straight path. The same would be true with a sperical (ball) universe.

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Your illustration uses a 3d ball that is within the confines of the universe, so it obeys the "common sense" rules that humans are used to. With the 3d ball of the universe, these common sense rules break down at the 3d hypersurface of the universe. As an analogy, common sense rules = Newtonian physics and 3d hypersurface rules = Relativity. Sometimes what we think should happen doesn't happen because the human brain is meant to distinguish patterns in a zero velocity system within the confines of an already defined space/time area. In other words, the rules at the edge of the universe are not going to make sense to our puny little protein bags we call brains.

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They do as you. As if they were on the surface of the outer edge of what they consider a closed system finite spherical universe they would have an endless straight line like yours eventually going full circle and coming around back to it's starting point (2 dimension).

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According to current theories, that's exactly what would happen. The velocity that would have taken past the "barrier" is instead bent to take you along the expanding surface of the universe. As far as I know, the universe is expanding at the speed of light. We would have to break the universal speed limit before we could observe such an effect. The math is well beyond my comprehension, but my experience in talking to physicists is that they are above and beyond my intelligence (and I happen to think I'm a pretty smart guy).Perhaps the best way to explain how the human mind expects certain things is the use of a Mobius Strip. The first time I tried to cut one in half it was a "what the hell" moment. I don't know if you have ever tried this, but I'll list the instructions anyway (mike the wiz would like this one too).1. Cut a strip of paper about 9 inches in length and 2 inches wide.2. On one side, draw a straight line lengthwise on one side.3. Twist the strip lengthwise one half turn.4. Bring the ends together and tape them in place. What you should have is a 2 dimensional loop that has no inside or outside. That is, the line that you drew is half inside and half outside.5. With a pair of scissors, cut down the length of the line.6. Report your predictions on what you think will happen and the actual outcome. I predicted that I would have two separate loops.This is a pretty elementary experiment which you may be very familiar with. I just thought I might mention it for you and possibly some of our younger lurkers who are interested in physics.

That's what you may consider a subpoint to my point. Space/area is nothing but that, space/area into which things can be created or expand into. It's infinite. There's no way you can visualize it, no matter how many dimensions you use. Imo, the problem science is spinning up from wholecloth is that there is nothing about space/area itself to visualize because there can be no boundary to area, no wall of somekind, because if there were to be a boundary, that boundary would need to contain substance, i.e. something besides more space and there is nothing that would fit the ticket. If you have some kind of fantasy of a curved boundary in your mind, it's just that, a fantasy in your mind, because space/area just can't be bound to a point where on the other/outer side of that bounds there's no more apace. There's gotta be more space/area beyond any imaginary bounds humans like to conjure up in the mind. We are temporal creatures who tend to think in terms of what we see on earth -- boundaries, and up in the sky, -- things/stars, etc. Modern science, imo, is trying to have it both ways. It wants all space/area to be inclusive in the term, "universe," but wants to call it a closed system which has bounds. By the nature of space/area, you can't have both. On a surface, any object only able to move about along the X,Y axis will meet this condition, so the analogy works.[/qs]How do you know it works? What proof does science have that curves somehow need to be involved an any theory about the universe?? They are so bulligerent in their contention that it MUST BE A CLOSED SYSTEM that they just have to have this alleged surface/bounds out there some place and can't come up with a model to justify their claim, so they resort to a model/analogy that's really bogus and unreal. Just because they figure what is seen seems to be following some kind of a curve proves nothing. What we can observe likely is a speck in the overall universe. The more powerful our instruments, the more that keeps coming into view. We haven't a clue as to what all the universe has in it.You use the phrase, "finite, unbounded universe." Say what?? How can an unbounded universe be finite??How can there be a surface to space? I know, "do the math and you come up with the answer." Doing the "math" is like the kid caught with his the cookie and there's this great long desortation as to how the cookie rightfully belonging in the jar ends up in sonny's hands. Science and physics are cool for some things, but when it comes to explaining the universe, origins, etc academia seems to be more interested in the hunt more than the kill, or like the medical establishment, it is found more profitible to look for cures than to find them, so the money making knife, needle and pill becomes their focus, treating the symptoms rather than wholeistic natural herbal and dietary correction of the causes for healing the whole body.I know modern physicists have this disdain for logic and common sense. They remind me of the dark ages when the bishops and popes of Vatican City insisted that the laymen couldn't be trusted with the Bible or to interpret it via their own common sense and the words in it. They MUST be explained by the educated and established heirarchy clergy. Thus the dark ages. Imo, we're there again when it comes to modern scienced in areas of origins and the universe, in spite of all the sophisticated equipment. As the Bible puts it for our time, "ever learning and unable to come to the knowledge of the truth." I don't see how this pleudo analogy explains anything sensible or logical. Yah, it's something to throw out there to gullible folks who don't stop to analyze space itself. Yah, it's easy to say there's an end to space, a boundary if you will to it, but no model or analogy is going to make any sense when you hunker down and think about it's implications.

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Space/area is nothing but that, space/area into which things can be created or expand into. It's infinite.

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How can something without energy, mass, or dimension be infinite? Beyond the edge of the universe is nothing. No dimension. Something without dimensions can not be called an area or a space. Therefore the edge of the universe is bounded and the universe is finite with regards to space/time.

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There's gotta be more space/area beyond any imaginary bounds humans like to conjure up in the mind. We are temporal creatures who tend to think in terms of what we see on earth -- boundaries, and up in the sky, -- things/stars, etc. Modern science, imo, is trying to have it both ways. It wants all space/area to be inclusive in the term, "universe," but wants to call it a closed system which has bounds. By the nature of space/area, you can't have both.

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What? There's "gotta" be more space beyond the edges of the universe? If I said there's "gotta" be a Santa Claus, will presents appear on the mantle? It is the fact that humans are bound to a temporal 3d world that doesn't allow us to directly visualize what is beyond space/time. The universe is inclusive of all areas that obey the laws of space/time. Outside of this area is a dimensionless void that is not accessible to those bound within a space/time system. It is only through the use of analogies that we can properly relate the MATHEMATICAL relationships that occur at the edges of the bound universe.

But in your cube model you already begin with/assuming bounds exist. My question is how can infinite space/area have bounds. With your cube model you have visible surfaces, but with space/area you have none. If you could somehow travel all the way out to the end of space, what would you expect to see? Nothing, i.e. more space. Keep traveling forever in the same direction. Still nothing but MORE SPACE! Your model doesn't match the problem/question! Mmmm, but common sense makes a whole lot more sense! Imo, you hadn't oughta have let the ejukaters talked you outa all that money you spent to replace yours with sofistikated theerees. This message has been edited by buzsaw, 06-22-2004 04:31 PM

By "curving back on itself". It's analogous to the surface of a ball, which is also unbounded but finite in extent.Your claims about what can or cannot be, and what must or must not be, are based solely on your extremely limited knowledge and incredulity. Not a good basis for practicing, learning, or questioning science.This message has been edited by JonF, 06-22-2004 03:26 PM

This is a perfect example of what you loose when you jetison common sense and logic and go cold turkey with these bazzare ideas PHDs dream up. It's pseudoscientific doublespeak, imo. Here you admit to a universe analogous to a ball and we all know that the third dimension of a ball is finite, but "oh well, no problem --just explain that problem away using a 2 dimension explanation of your 3d ball universe. Your universe has outer boundaries/bound, yet you devise up a textbook full of formulas, matmatical equasions and such and come out of the classroom having somehow devised a way to be convinced that what is essentially a ball has a surface but no boundary. But, oh yes your, phantam ball universe contains ALL SPACE, so there can't even be any space/area outside your ball, for indeedy space can only exist within your universe. Yah, your ball can expand, but into what if all space/area is in your universe ball? ......and alas, I'm afraid your inability to think for yourself, using good ole logic and common sense has been hampered by the stuff you've had programmed into your young impressionable minds in the classroom when you were in school.Let me be specific. True or false? Your ball universe, curling around into itself has a surface if somehow a picture of the ball were taken from a great distance from it. I'm not buying your notion that your model of the universe has no bounds. Even though those bounds may expand, bounds would presently exist.