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Richard, I always appreciate your posts. Before Simon shuts this thread down too [ :) ], I wonder if you could clarify as to "seriously threatened the destruction of the US". I am not aware of any serious threat to destroy the US since the Brits returned in 1812 to smack us around a little. Was there indeed some possibility that Germany or Japan could actually have shipped enough men and material over here to mount a serious offensive? The logistics boggle the mind.
I always enjoyed this thread, so maybe it's wrong to revive it
I enjoyed it too, Ricardo, and I am glad you revived it. We covered a lot of ground (as often happens), from black holes and cosmology, to science vs. "creationism," to conflict, intervention, and war. But let's stick to science this evening.
I have a question for all of you astro-physicists and cosmologists when you take a break from playing rasqueados, arpeggios and picados. Presumably nothing exists outside space-time, according to the General Theory of Relativity. What has always intrigued me is the question: What is space-time expanding into? A corollary would be the following question: At the moment of the Big Bang and the beginning of the expansion, what was it expanding into?
I have read a lot of the literature and understand the examples of universes maintaining their positions relative to each other, and I understand the possibility of multiple dimensions (a fourth and fifth dimension, for example). And some of it depends on whether one considers space-time as finite or infinite. Nevertheless, even if it is infinite, what did it expand into at the moment of the Big Bang?
Cheers,
Bill
_____________________________
And the end of the fight is a tombstone white, With the name of the late deceased, And the epitaph drear, "A fool lies here, Who tried to hustle the East."
The universe isn't expanding "into" anything. Probably the biggest misconception people have of the Big Bang is that there was some big ball of matter that exploded, with the fragments flying outward to populate an empty space. Blame that impression on the name if you will.
In the Big Bang, space itself expands, starting small and quickly expanding. It's still expanding. In fact, the rate of expansion is increasing, and we now know that it will continue to expand ever faster. The possibility that the expansion might stop, then reverse into a "big crunch", has been ruled out.
We can observe that, on average, everything in the universe is heading away from us. The farther away it is, the faster it's receding (this is why the Doppler red shift of an object is related to its distance from us). In fact that's true from the point of view of *any* star system. We're all receding from each other. The only way that can happen is if space is expanding. If it were an explosion into an empty universe, that would not be true even if we happened to be at the center of the explosion. A useful two dimensional analogy is a balloon. Inflate a balloon part way, then draw a grid of dots over the entire surface. Now blow up the balloon. The 2D surface area of the balloon increases as it's inflated, just as the volume of our universe increases with time. The dots on the balloon each move away from all the others, and the rate they move is proportional to how far away they are from each other. And, anticipating your question, the mathematics describing the surface of the balloon does not require or imply that there's anything "inside" or "outside" the balloon surface - it's only this flawed analogy of a 2D surface existing in a 3D space that leads us to assume it needs to expand "into" something.
I appreciate your comment, Timoteo. Nevertheless, to me it still does not adequately answer the question. I would take issue with your observation, "Probably the biggest misconception people have of the Big Bang is that there was some big ball of matter that exploded, with the fragments flying outward to populate an empty space." I don't know anyone who imagines the Big Bang to be what you describe as a common misconception. Everyone I know understands the Big Bang to have been, not a "big ball of matter that exploded...to populate an empty space," but an infinite point that "exploded" (for lack of a better term), and began expanding as space-time. In other words, we all understand that "space" (space-time to be accurate) was that which was expanding. But what existed outside the immediate perimeter of space-time as it expanded?
That everything is receding from everything else, the Red Shift, the example of the two dimensional dots on the expanding balloon: all of these are in the literature. To say that space (again, more accurately, space-time) itself is expanding is completely understandable. What is much more difficult (and this may be a problem in philosophy, rather than cosmology) is to imagine that space-time is expanding into nothing. (And by "nothing" we obviously don't just mean empty space.) We could go into an entire philosophical discussion about the definition "nothingness." Nevertheless, I would repeat the question at the end of my first paragraph above: At the time of the Big Bang, and continuing today, what is outside the immediate perimeter of expanding space-time that space-time is expanding into?
Cheers,
Bill
_____________________________
And the end of the fight is a tombstone white, With the name of the late deceased, And the epitaph drear, "A fool lies here, Who tried to hustle the East."
At the time of the Big Bang, and continuing today, what is outside the immediate perimeter of expanding space-time that space-time is expanding into?
Cheers,
Bill
I suspect this will not satisfy you, but the answer is "nothing". Another way of saying this is that in General Relativity, everything is in space-time. There's isn't anything that is not in space-time, so there is nothing for space-time to "expand into".
This is counter intuitive. But it is simply a failure of natural language. Many of the advances in physics since the time of Newton have been due to overcoming the limitations of natural language through mathematical analysis. Just because a question can be framed grammatically in natural language doesn't mean there has to be an intuitively satisfying answer.
There are quite a few things that are vastly counter-intuitive in relatively elementary parts of physics as we understand them today. For example, the answer to a simple question such as, "which happened first, event A or event B?" can be "it depends." Bob can see event A happening before event B, while Carol can see event B happening before event A, depending upon the motion of the observers. Both can be correct.
Learning mathematics is in some ways akin to learning a language. In other ways it can go strongly against the grain of intuition, following the lead of logic.
I would take issue with your observation, "Probably the biggest misconception people have of the Big Bang is that there was some big ball of matter that exploded, with the fragments flying outward to populate an empty space." I don't know anyone who imagines the Big Bang to be what you describe as a common misconception.
It sounds like you hang out with a remarkably well-informed group of people! My observation is based on my personal experience of ~30 years as a physicist (trained in experimental elementary particle physics, although I haven't done that in a while). And the statement is true in my experience, even if it's not true in yours. I don't think that's a contradiction. Most of the people I know aren't physicists, however, and they know about the Big Bang only through depictions in popular media. If they're science buffs, they might have seen a documentary or read an article, but even then I find this basic point is something that often gets overlooked. Maybe for the same reason you're asking about what the Universe expands "into" - our everyday experience mandates that if the universe is expanding, it must exist inside a larger volume. But there's nothing to support that intuition.
quote:
But what existed outside the immediate perimeter of space-time as it expanded?
Let me turn that around and ask you why you think there's an "outside"? Is it simply because your everyday experience tells you that all objects must be contained in a larger space? If the mathematics describing space-time do not indicate that, why does it have to be so? Likewise, if the mathematics says time in our universe goes back to negative infinity, why does there have to be a "before"?
Not to be pedantic or anything, but outside of space there is no space, by definition. So yes, it's somewhat of a philosophical question, and one with no answer.
quote:
That everything is receding from everything else, the Red Shift, the example of the two dimensional dots on the expanding balloon: all of these are in the literature.
Sure. I just brought them up to establish a baseline - I have no idea about your level of knowledge of the subject, so I have to start somewhere. My response was meant to address the typical (in my experience) reader, but you're in the minority of people who know way more about this than average.
quote:
What is much more difficult (and this may be a problem in philosophy, rather than cosmology) is to imagine that space-time is expanding into nothing. (And by "nothing" we obviously don't just mean empty space.)
Again, back to the question of why you think there's space outside of space-time? If you're looking for the meaning of life, the universe, and everything, I don't have the answer (but I know it's not 42). I'm also not much interested in an ontological discussion and I'll always fall back to the anthropic principle if pressed. I'm perfectly willing to accept that some questions have no meaning and/or are unanswerable. Wave-particle duality, for example, doesn't bother me - I accept it as a fact and move on. That makes me enormously effective IMO in dealing with phenomena outside of my macrophysical experience.
An analogy occurs to me. Euclidean space, with its three dimensions and uniform measue of distance conforms closely to our intuition, based on our daily experience. It conforms so closely to our intuition, that the best minds of millenia believed that it was the essence of physical reality.
The Greeks were wary of actual infinities, preferring to say that a line could be extended as far as one wished. The modern approach embraces actual infinities, and says that Euclidiean space is infinite in extent. We seem to have little problem in conceiving of three-dimensional space filling up everything.
So suppose for a moment, for the sake of analogy, that space is three-dimensional, and it fills up everything. But suppose you look around you, and notice that on average, objects are getting further away as time goes on. And that the further away something is, the faster it is receding. You might reasonably say that space is expanding. But it isn't expanding into anything. It already fills up everything. Things are just getting further apart.
I think it would be perfectly valid mathematically to re-interpret the expansion of the universe as the shrinking of everything in the universe. Relatively, the end result is the same. I heard a talk long ago where it was hypothesized that the Planck constant might be a function of time. Which would affect the scale of everything we know in the universe. It's an academic question though, because we wouldn't be able to distinguish between the two possibilities.
I appreciate your explanations and accept that "nothing" exists outside of our space-time reality, as counter-intuitive as that seems (at least to me). I have a layman's interest in theoretical physics and cosmology, and your explanations confirm what I have read as well. I wasn't trying to be contentious by pressing the question. I'm of the opinion that by stating that "nothing" exists outside a certain framework (our space-time, for example), we get into a more philosophical question about what we mean by "nothing." But we will never know because we are stuck in space-time. The question becomes circular. Probably best not to dwell on the issue too intensely, as to do so could lead to madness. Better to kick back with a bottle of wine, accept it, and marvel at those wonderful photographs taken from the Hubble Telescope.
Cheers,
Bill
_____________________________
And the end of the fight is a tombstone white, With the name of the late deceased, And the epitaph drear, "A fool lies here, Who tried to hustle the East."
Consider two sentences: "Everything is inside of space-time." and "Nothing is outside of space-time." Logically they are equivalent. But in the second sentence, "nothing" functions gramatically as a noun. We are accustomed to nouns referring to things. But "nothing" doesn't refer to anything. Philosophers and philologists can make hay over this until the cows come home. But it's just another inconsistent quirk of natural language. Most nouns refer to something. Some don't.
Spanish uses the double negative. English does not. My three-year old daughter, in a fit of negativity exclaimed, "Never, never, not no!" An English grammarian might conclude that a quadruple negative equaled a positive. But my daughter's meaning was perfectly clear to all within earshot.
Consider two sentences: "Everything is inside of space-time." and "Nothing is outside of space-time." Logically they are equivalent. But in the second sentence, "nothing" functions gramatically as a noun. We are accustomed to nouns referring to things. But "nothing" doesn't refer to anything.
I dont feel it as inconsistency at all. Nothing is not some thing or something. Its the negation of everything. When you say
"Nothing is outside of space-time",
it is not possible to think of "nothing" as "the one something" that exists outside of space-time. Its more like
"for every thing that exists, it is true that it does NOT exsists outside space-time"
It is a huge achievement that we can intellectually refer to objects like that, and as such it is a strength of language.
By the time the US a entered WW II Germany had conquered western Europe and seriously threatened to do the same to the Soviet Union. Japan ruled east Asia and the Pacific, was on course to conquer China, and seriously threatened Australia. Without U.S. support, Britain would have been unable to hold out. The danger to the USA at the time it entered WW II was not, in my perception, an immediate invasion. It was that successful conquests by Germany and Japan would leave the U.S. isolated. There is little doubt that Latin America would have capitulated to and cooperated with successful Axis powers. The resources commanded by Germany and Japan in this eventuality would in time have made the U.S. vulnerable to siege or invasion.
This was the existential threat. It was perceived by some political leaders, including Franklin Roosevelt, and by the military high command long before the public saw it as such. In 1941 the USA was not seen as the superower it became as it emerged from the ruins of WW II. The public was strongly isolationist, seeing no necessity of getting involved in events in faraway Europe and Asia. The Japanese imperialists made the mistake of turning around U.S. public sentiment instantaneously by the attack on Pearl Harbor. Since I was a kid during WW II, I can only speak for the sentiments of my large extended family and our neighbors. All these people saw the Axis powers as a threat to the continued existence of American democracy.
Philosophers and philologists can make hay over this until the cows come home.
...and they have. Whole volumes have been written about the nature and meaning of "being" and "nothingness." Martin Heidegger in his work "Being and Time," and Jean Paul Sartre in his tome "Being and Nothingness" explored the concept at length. You have managed to succinctly distill the difference between the engineer/scientist's mind and the philosopher's mind, Richard. That probably explains why engineers and scientists make a good living, while philosophers generally end up in genteel poverty.
Cheers,
Bill
_____________________________
And the end of the fight is a tombstone white, With the name of the late deceased, And the epitaph drear, "A fool lies here, Who tried to hustle the East."
That probably explains why engineers and scientists make a good living, while philosophers generally end up in genteel poverty.
A friend of mine is a Professor of Philosophy in Edinburgh. When he was studying in Paris, I came across a newsletter from the University of St. Andrews Philosophy Department in his rooms.
In the table of contents:
quote:
Do Numbers Really Exist?......................................... Page 23
Cute, but I've wondered that myself. I mean, doesn't seem strange that e=mc2? And why the heck does differentiation work to determine velocities and what not? Bizzarre!
I appreciate your explanations and accept that "nothing" exists outside of our space-time reality, as counter-intuitive as that seems (at least to me). I have a layman's interest in theoretical physics and cosmology, and your explanations confirm what I have read as well. I wasn't trying to be contentious by pressing the question. I'm of the opinion that by stating that "nothing" exists outside a certain framework (our space-time, for example), we get into a more philosophical question about what we mean by "nothing." But we will never know because we are stuck in space-time. The question becomes circular. Probably best not to dwell on the issue too intensely, as to do so could lead to madness. Better to kick back with a bottle of wine, accept it, and marvel at those wonderful photographs taken from the Hubble Telescope.
Cheers,
Bill
I think concepts CAN be explained with analogy....it just takes some clever thinking. I have asked this question myself and I did get a reasonable answer from Carl Sagan. Not sure why it's harder to say by science and math minded folks than laymen, but I am a laymen so this answer works for me.
When doing the balloon analogy, and important concept is the surface. "Where is the center of the universe?" well it has none because it is "like the surface of a balloon". Huh?? Well 2D concept is hard to deal with until you allow yourself the "penalty of projection"...then it starts to make sense. The answer that there is no center is correct to the scientist already penalizing for loss of a dimension. But the answer the LAYMEN needed is that the center is clearly floating in 3D space at the center inside the balloon skin sphere itself.
So as you can see where I am going. We are trapped as 2D beings on the surface of the balloon itself, never to know about or understand fully (only abstractly) the 3d space both inside or outside the rubber surface. All physics and experience or observation or even math deals with is that 2D space...so that is why you don't get the 3D answer. The truth you looking for is that if pretend the universe IS IN FACT a sphere you just add a dimension...boom hypersphere and you realize, as any child would but physicists avoid saying it, is that the CENTER of the universe now "floats" in 4th dimensional hyperspace. Because it is utterly outside of our experienced trapped in 3D, it is outside the realm of physics and enters the realm of philosophy.
So if you can't imagine a hypershere in your mind lets go back and say the balloon was a cube and do all the thought as before. Well how did a cube get started? You take a line segment and make right angles to those. YOu get a square. A square is 2D. To make a cube you project into the 3rd dimension using more right angles. But if you were to DRAW a cube you notice you can't make right angles you make diagonal lines that connect corners of two off set squares. So you use your IMAGINATION to experience the cube. WE can use our imagination to experience a 4d hypercube called a teserect. Simple project right angles out from the corners of the cube. No we can't do it in space, but if the corner lines are diagonals NOT right angles, you have two nested cubes one inside the other, with corners connected by straight lines. As sagan said we see the "shadow" of the 4D hyper cube in 3d, just like when we draw a cube on paper. That is penalty of projection.
We don't know the actual shape of the universe yet, if it could be hypersphere or hypercube hyper torus etc....but you can see how laymen might get the picture better. Now physicists don't want to think of 4d cuz they don't need to. Imagine a tunnle connecting one part of the balloon to the other....a short cut across the surface. To travel it we STILL need to be on the surface of the balloon material even though we can clearly SEE how the 3d space is "used" by the tunnel as a short cut. So a wormhole need not involve 4d space either though we in fact would be using it that way if we ever find a way to manipulate the fabric of spacetime itself as gravity seems to be able to.
For those of you who haven't heard about it, here's an excellent little book which delves into everything that Ricardo brought up (in fact, Sagan got some of his analogies from this book):
This short little book, written for the layman, is both a classic in multi-dimensional geometry and a social commentary. Trust me, you won't regret reading it.
My observation is based on my personal experience of ~30 years as a physicist (trained in experimental elementary particle physics, although I haven't done that in a while).
Sometime in the eighties I think, it was published in news papers that somewhere above 10% ( am not certain anymore about exact number ) of the German population of that time would still deem earth as a disc.
Somehow one seems to hardly ever run into the average mind as it is being reflected to be by statistics and surveys, but if the raisings are to be sincere ( which I doubt in some aspects) then fellow men must be duller than a brick.
Just look at how they again and again happily support their own mess around and exploitation. Only thinkable under brain defunct conditions.
quote:
ORIGINAL: timoteo
I think it would be perfectly valid mathematically to re-interpret the expansion of the universe as the shrinking of everything in the universe. Relatively, the end result is the same.
Would mean time not matter? How could shrinking allow relative distancing among objects in space? ... Oh wait, hypothetically with a shrinking of the objects, thus distances only from there appearing as encreasing?
Shouldn´t objects then have long since vanished already considering the extreme changes indicated by the `apparent´ room expansion? -
Ability of folding space ( as mentioned by Ricardo above) would be imperative for practical chance of any succeeding cosmic Noah´s Ark which some fools are projecting, fancying such twiddle as intelligent, instead of turning to preventive and retentive measures here and now on earth.
Thanks for the tip on the book, Timoteo. I had not heard of it but would like to read it. I have read quite a few books over the years on everything we've been discussing here, and one I find particularly good for the layman is Brian Greene's, entitled, "The Fabric of the Cosmos," published in 2004. He delves into all the issues of space-time, general and special relativity, the Big Bang, etc., at some length, but always keeping it at a layman's level.
One of the things I have always found interesting has been the problem of what caused the Big Bang in the first place. What triggered the event (we usually use the term "explosion" don't we?) that began the inflationary framework of space-time? One of the more interesting theories was, again, discovered by Einstein: the theory of "repulsive gravity." The theory suggests that at "time zero," the infinite point experienced an inflation field whose value provided the energy and "negative pressure" that fueled the outward burst of repulsive gravity that resulted in the Big Bang. Repulsive gravity (as opposed to attraction) is another one of those theories that sound counter-intuitive, but working through the explanation, it makes sense.
Still, I have a hard time coming to terms with the idea that "nothing" can exist outside space-time, other than that general relativity makes it impossible. I understand it perfectly on an intellectual level, but I guess the amateur philosopher in me wants to theorize that the infinite point at the time of the Big Bang, had to exist in something. I am not a religious person, and the idea of the infinite point beginning the inflationary framework of space-time, with nothing ("nothing") outside the framework, sounds like one of the "proofs" for God that dates back to medieval times: the "Unmoved Mover." The idea that if you traced all activity back far enough, there had to be an event that started the first movement that has led to everything else throughout the Cosmos, up to the present day; and that "Unmoved Mover" that started it all would have been God. I cannot accept that, but for those who would like to, superficially at least, it comes pretty close to how our understanding of the beginning looks today.
Cheers,
Bill
_____________________________
And the end of the fight is a tombstone white, With the name of the late deceased, And the epitaph drear, "A fool lies here, Who tried to hustle the East."
It is not that time doesn't matter, but the directionality of time does not seem to disturb the equations, forward or backward things are the same. Entropy however tells us that nature prefers to go from more order towards less order.
quote:
Still, I have a hard time coming to terms with the idea that "nothing" can exist outside space-time, other than that general relativity makes it impossible. I understand it perfectly on an intellectual level, but I guess the amateur philosopher in me wants to theorize that the infinite point at the time of the Big Bang, had to exist in something
It's perfectly reasonable and there are in fact tons of hypotheses about it. Going back to flatland vs 4D, the laymen can imagine all kinds of things going on in the 4D world that might be influencing us invisibly...as for me once I got the whole teserect hypercube thing I was like ok, maybe that's why dark matter is invisible, it is a gravity effect outside our world and we see the shadow...same for dark energy, dark anything... spooky actions, quantum jumping, electrons darting around could be only piece of 4D objects stabbing our 3D membrane, uncertainty principle..... then on to the "voice within" the X ray vision of a 4D entity answering the questions of spirituality, etc etc etc....
But it's not like laymen are the only ones with these thoughts. Many scientist using the imagination come from similar places, and abstract math is a great tool to explore. A lot of my initial ideas I realized later, are explored in String theory, although not exactly the same, but similar ideas. String theory has the same problem as philosophy....a lot of it implies things that are simply OUTSIDE of our 3D experience and cannot be TESTED by the tools of science. True as they may be, or good as they look on paper, if we can't make TESTABLE PREDICTIONS , is the model we use really a scientific model?
I think concepts CAN be explained with analogy....it just takes some clever thinking. I have asked this question myself and I did get a reasonable answer from Carl Sagan. Not sure why it's harder to say by science and math minded folks than laymen, but I am a laymen so this answer works for me.
When doing the balloon analogy, and important concept is the surface. "Where is the center of the universe?" well it has none because it is "like the surface of a balloon". Huh?? Well 2D concept is hard to deal with until you allow yourself the "penalty of projection"...then it starts to make sense. The answer that there is no center is correct to the scientist already penalizing for loss of a dimension. But the answer the LAYMEN needed is that the center is clearly floating in 3D space at the center inside the balloon skin sphere itself.
So as you can see where I am going. We are trapped as 2D beings on the surface of the balloon itself, never to know about or understand fully (only abstractly) the 3d space both inside or outside the rubber surface. All physics and experience or observation or even math deals with is that 2D space...so that is why you don't get the 3D answer.
Analogies can also give a mistaken impression. Watching the Sagan clip, one might think you need a third dimension in order to produce the curved space of the 2-dimensional balloon surface. Not so.
For millenia, people dealt with 2- and 3-dimensional space via Euclid's axioms. Some very clever geometry resulted. But Descartes revolutionzed the study of space by introducing the coordinate system. Two lines at right angles are imposed on the plane, the location (x, y) of a point is given by going a distance x along one line, then a distance y perpendicular to it. Negative x goes to the left, negative y goes down. The modern view simply identifies points in the Euclidian plane with the ordered pairs of number (x,y). The only other ingrediant you need is a formula for distance. The distance from (x1, y1) to (x2, y2) is
square root of [(x1-x2)^2 +(y1-y2)^2]
This is just the relationship the Pythagorean Theorem gives between the sides and the hypotenuse of a right triangle. The distance function makes the space of pairs (x,y) Euclidean--all of Euclid's axioms apply.
How do we make a sphere without going into the third dimension? Simple. Think of the latitude, longitude coordinate sytem used to locate points on the Earth's surface. Limit y to numbers from -90 to +90 degrees, x to numbers from -180 to +180 degrees. Sew things together along the International Date Line by identifying points with x = +/-180 as being the same point, and recognize that the north and south poles lie on all the meridians of longitude. The only thing remaining is to supply a distance function. The shortest distance between two points on a sphere is along a great circle. The great circle distance formulas are a little more complex than the Euclidean distance formula
The navigator doesn't worry about the third dimension when locating points on the surface of the ocean. He just thinks about latitude and longitude. The mathematician goes all the way and says that the point on the sphere is the pair (latitude, longitude).
Now you have the surface of sphere without having recourse to a third dimension. It consists of the number pairs (latitude, longitude) and the great circle distance function. All the theorems of spherical trigonometry hold for this surface, but no third dimension is involved.
The "curvature" of the 4-dimensional space-time of General Relativity refers to the metric tensor--a distance function, if you will--that depends only on the mass, energy and linear momentum contained within the space. No additional dimension is required to generate the curvature.
i'm fairly sure Sagan used the third dimension to generate a spherical surface for its visual appeal on TV. But it could give the mistaken impression that an additional dimension is required to generate a curved space.
How do we make a sphere without going into the third dimension?
But it could give the mistaken impression that an additional dimension is required to generate a curved space.
RNJ
Hi Richard, my name is David. I know the following might seem glib but I think it is relevant to your argument. The 'we' in question above is 'we humans' right ? We experience the world in three dismesions already, it is very difficult for me to imagine that any adult mind does not have ready and unavoidable recourse to three dimension.
I think that geometry itself IS the analogy that we use to model three dimensional space. Certainly our nerve synapses propagate in three dimesion so I see no reason to assume that our brain has any need to use the tricks that our geometry uses to represent space in 2D. In much the same way we are not really limited by the digital nature of our arithmetic as we can store amounts both as integers and irrational estimates/impressions since our brain is analog.
I suspect that our analogies (such as our mathematics arithmetic geometry etc etc ) ARE limited by our brain architecture.
Using geometry we can cumbersomely calculate snapshot answers to problems which we have been solving in real time since before the emergence of our species. Problems like 'how large is that object in the distance' ?, 'at what speed should I move my hand to intercept that moving ball' .
We can steer out two dimensional tools to model and imitate the ways in which we solve these things intuitively. We can do this because we have visceral understanding of a readily perceived three dimensional space.
The insights which we wish to develop about other dimensions are likely to be much more difficult to envisage since we cannot steer in four or more dimensions with the confidence that we can in two and three.
The navigator doesn't worry about the third dimension when locating points on the surface of the ocean. He just thinks about latitude and longitude.
Tell that to the navigators in the movie "Core".
Well, as far as curved space, we can tell it's curved by another way other than only gravity effects. Light bending (gravitational lensing) shows space curving 3D optically, again no "need" for a 4th dimension and higher math. But the point of the Sagan analogy was not so much for general relativity purposes (curved space do to mass, though he does mention it) so much as for the LARGE scale structure of the universe and the implications of the Big Bang theory and other cosmological concepts....because as it stands the balloon analogy by itself sucks. It's like showing a flat map of the earth with longitude and latitude as you describe to a young child and say "there is the earth in 2D, GET IT KID????". The child is better off with a GLOBE to get the true picture of what navigating the earth will REALLY be like.
A new wrench got tossed in to the cosmological models. THey just discovered a super structure not really supposed to be allowed to exist. A tight group of quasars (very distant ie existed long ago galaxies with active black hole centers) that altogether stretch across 4 billion light years of space. Such large structures were thought "not allowed" to exist especially at such an early epoc in the universe's history.
A new wrench got tossed in to the cosmological models. THey just discovered a super structure not really supposed to be allowed to exist. A tight group of quasars (very distant ie existed long ago galaxies with active black hole centers) that altogether stretch across 4 billion light years of space. Such large structures were thought "not allowed" to exist especially at such an early epoc in the universe's history.
That is not the only wrench that's recently been thrown into cosmology and theoretical physics. Just last year, the CERN Large Hadron Collider in Geneva Switzerland conducted an experiment that detected neutrinos traveling faster than the speed of light. I haven't heard if they have replicated the experiment with the same results yet, but if it turns out that subatomic particles can travel faster than the speed of light, that would put a huge dent in Einstein's Special Theory of Relativity, which states that nothing can travel faster than the speed of light in a vacuum.
We have come a long way since Newtonian physics reigned. Einstein, Planck, Heisenberg, Bohr, and all the others have revealed whole new worlds in dealing with the large-scale universe of space-time and the small-scale world of quantum mechanics. I have an intuitive sense that much of it will hold up. But if something considered as elementary as the Special Theory of Relativity's law (and it is considered a physical law) that nothing can travel faster than the speed of light is overturned, what else might be overturned in the future?
I'm not predicting this, but it is possible that 100 years from now people will look back on our era and consider it as quaint in its understanding of physics and the universe as we do the era of Newton.
Cheers,
Bill
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And the end of the fight is a tombstone white, With the name of the late deceased, And the epitaph drear, "A fool lies here, Who tried to hustle the East."
Just last year, the CERN Large Hadron Collider in Geneva Switzerland conducted an experiment that detected neutrinos traveling faster than the speed of light. I haven't heard if they have replicated the experiment with the same results yet, but if it turns out that subatomic particles can travel faster than the speed of light, that would put a huge dent in Einstein's Special Theory of Relativity, which states that nothing can travel faster than the speed of light in a vacuum.
well, it was down played in the media but it was a simple technical error with the wiring that caused the glitch. Einstein still appears to be correct. In addition Newton's physics is still used locally by NASA for example as it is simple and does the job. Einstein's refined picture can be somewhat impractical unless you are a cosmologist. However, there are some important uses for general relativity. One off hand is GPS which is corrected for Einsteins GR, curved space of the earth, helps my wife pinpoint my location at all times with her iphone....gee thanks einstein!!! But in the future, I think we will still be using the physics of newton, einstein, heisenberg, even if there is new better info...because it WORKS.
Thanks for the info. I had not heard that. In a way, I'm glad Einstein still holds up. In fact, as I mentioned in my previous, I intuitively think most (and maybe even all) of the theories and laws regarding relativity and quantum mechanics will hold up in the future. Nevertheless, it would not surprise me if some startling discovery overturns (or at least alters) our understanding of some aspect of one or the other.
Cheers,
Bill
_____________________________
And the end of the fight is a tombstone white, With the name of the late deceased, And the epitaph drear, "A fool lies here, Who tried to hustle the East."
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But in the future, I think we will still be using the physics of newton, einstein, heisenberg, even if there is new better info...because it WORKS. 
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