Before I moved back to Petersburg in the fall of 2008, I had been working for five years for the Post and Courier in Charleston, S.C., as assistant business editor. In that capacity, I was asked to write a business blog, which I did for about six months before I accepted a buyout and left.
There was a sort of cognitive dissonance between me and the bosses about that blog: what I was writing turned out not to be what they had expected me to write (and I wasn't even doing any of the cosmic stuff then). So all of my posts there were taken offline pretty quickly after I left.
That's a shame, because personally I think some of them were pretty good, although that might just be my memory playing tricks on me. But one of them in particular I want to try to reconstruct, because the point it made was one that needs to be remembered.
I'm sure at some point or other, all of us have seen a sign at a business that says, "Our people are our most important asset." It's a nice sentiment, but if there's any truth at all in what it says, it's purely symbolic. Under "generally accepted accounting principles," people are not an asset.
If you look at actual corporate financial statements, you won't find "people" listed anywhere. But if you know where to look, you can find where they're hidden. It's not on the statement of assets. On the contrary, people show up on the income statement as a cost of doing business. And if the company owes money to its employee pension fund, that shows up on the statement of liabilities.
As a result, when business slows down (or goes down the toilet), it's a no-brainer for the MBAs and CPAs and other bean-counters to look at the financial statements and think, "Hey, here's a quick and easy way to make the numbers look better: Fire some workers and dump the pension plan."
If people really were treated as an asset in some way - if companies were required to account for the potential cost of training replacements, for example - then it wouldn't be such an easy decision to fire them en masse. That's because anytime a company has to write down the value of an asset, the writedown has to be reflected on the income statement as an expense. So laying people off wouldn't automatically make "the bottom line" look better.
It's ironic, or something, that businesses do account for their "property, plant and equipment" as assets, but not the employees who actually make those things work to put out products or provide services, and in general to create profits. In the real world - the world beyond the spreadsheets and trial balance ledgers and forecasting models - people do actually have value.
Saturday, June 12, 2010
Friday, June 11, 2010
On Edge
The twisted-universe model I wrote about last time clearly must involve curved space. The idea that space can be curved is pretty familiar by now, mostly because of Einstein’s idea that gravity results from a bending or curving of space by a mass of matter. That seems to be the consensus these days about how gravity works; the most popular alternative, that gravity is somehow transmitted from one mass to another, suffers somewhat from the failure so far to detect any of the “gravity waves” this theory would require.
I always had a hard time figuring out how gravity could have an effect on space, which essentially has no properties of its own to be affected. (Under relativity and quantum mechanics, empty space seems to be occupied by a “quantum vacuum” that does have some properties, but that’s not the same thing as space.) However, when I started thinking about the properties of my twisted space, I realized that any space does have one property: dimension. Which means that the only kind of change you can make to a space is a change of dimension.
As I explained last time, giving a spherical universe a half-twist through the fourth dimension raises the dimension of the universe as a whole to 4. The dimension at any point within the universe would appear to a normal physical observer to be 3, but in fact it would be slightly more than 3; we’ll say it’s D=3+(n<1). And if you add up that n<1 for all the points (at some arbitrarily selected but uniform scale, such as a light year or a parsec) in an orbit of the universe, the sum will be 1.
Now, even though this cosmos is finite, it’s still very large. So the n<1 – which I’m going to declare a fundamental universal constant, and call Ü, mostly because I like umlauts – is going to be very small, almost ininitesmal. The 3+Ü that exists at any point would then be the natural dimension of space in this bent universe of mine.
This whole idea of a non-integer dimension is exactly what Benoit Mandelbrot means by the term “fractal” that he coined to describe objects with a “fractional dimension.” And he has demonstrated that a very wide variety of objects are fractals, which means that many (perhaps most) of the objects we think of as, say, three-dimensional are in fact three-plus dimensional. The more complex the object, the higher the fractional excess; so a big, many-branched tree would be “more fractal,” if you will, than, say, a bowling ball.
But it seems likely that the fractional dimension of even a fairly smooth 3D+ object, like a planet, would have to be greater than the near-infinitesmal value of Ü. And as a result, the planet would “stretch” the dimension of the space around it, causing the kind of contour that Einstein’s conjecture associates with gravity. This would be true even with very small objects, which would account for the kind of “clumping” that scientists believe took place in the early universe, leading eventually to the formation of galaxies and so on.
There’s something else that the structure of the twisted-universe model might help account for that has puzzled me for a long time. I think some visual aids may help here.
We often hear airplane pilots talking about flying “straight and level.” But they’re actually doing anything but. What they’re really doing is flying at a constant altitude above the Earth’s surface. Because the Earth’s surface is curved, however, the plane’s actual path is also curved, as shown above. What would happen if an airplane really flew “straight and level” looks like this:
Now, the thing I’ve wondered about for years is this: We all know that the speed of light is a sort of universal speed limit, that nothing can go faster without violating all sorts of natural laws. But I’ve always wondered why it’s precisely the speed it is, 299,792.5 kilometers per second, or about 186,000 miles per second.
We’re used to the idea, again thanks to Einstein, of light traveling a curved path around massive, high-gravity objects. But since I’m supposing here that all light must travel a curved path in a curved, twisted universe, the “normal” path of light would look something like this:
Obviously, the curvature of this “universe” is highly exaggerated, but it illustrates how the rays of light in a sense “flow” along the contour of the space. What I’m going to suggest is that the speed at which light (and of course other forms of radiation) travels is actually determined by that contour or curvature, because if it travelled at a higher speed, this would happen:
What this would actually mean is hard to say. It might mean that the energy disappears into the fourth dimension, or it could even mean that it exits the universe, whatever that might entail.
Mention of the fourth dimension brings up one final point I want to make before closing this largely pointless expostulation. You’ll remember the Möbius strip from last time:
In looking at this illustration, I want you to imagine that the strip is actually transparent, because what we’re talking about here is empty space, not paper. So there’s really nothing separating point A from point B, or C from D, except space; or rather, except the twisted structure of this space. But the separation is nevertheless complete and inviolable: The only way to get from point A to point B is to go around the strip; you can’t go through it.
Why not? Well, if you travel around the strip from A to B, you’re in effect adding up Ü units, or in a sense travelling uphill dimensionally. By the time you reach point C, you’re in a dimension that’s 0.5 higher in relation to A, and when you reach B, the space you’re in is a full 1 dimension away from A. It’s still 2+ÜD from a local point of view (in the illustration; in the twisted universe, it would be 3+ÜD), but A is 3D from the perspective of B (4D in the real universe), and vice versa. So naturally, there’s no way to perceive one space from the other, much less to go there directly.
This is precisely what constitutes the boundary or “edge” of the universe, this dimensional barrier. And what that means is that every point in the universe is on the edge of the universe.
Somehow, that reminds me of the famous Hermetic saying quoted by Giordano Bruno and Pascal, among others: “God is an intelligible sphere whose center is everywhere and whose circumference is nowhere.” In the twisted universe, the circumference is everywhere, but I’m not sure whether there’s a center anywhere.
I always had a hard time figuring out how gravity could have an effect on space, which essentially has no properties of its own to be affected. (Under relativity and quantum mechanics, empty space seems to be occupied by a “quantum vacuum” that does have some properties, but that’s not the same thing as space.) However, when I started thinking about the properties of my twisted space, I realized that any space does have one property: dimension. Which means that the only kind of change you can make to a space is a change of dimension.
As I explained last time, giving a spherical universe a half-twist through the fourth dimension raises the dimension of the universe as a whole to 4. The dimension at any point within the universe would appear to a normal physical observer to be 3, but in fact it would be slightly more than 3; we’ll say it’s D=3+(n<1). And if you add up that n<1 for all the points (at some arbitrarily selected but uniform scale, such as a light year or a parsec) in an orbit of the universe, the sum will be 1.
Now, even though this cosmos is finite, it’s still very large. So the n<1 – which I’m going to declare a fundamental universal constant, and call Ü, mostly because I like umlauts – is going to be very small, almost ininitesmal. The 3+Ü that exists at any point would then be the natural dimension of space in this bent universe of mine.
This whole idea of a non-integer dimension is exactly what Benoit Mandelbrot means by the term “fractal” that he coined to describe objects with a “fractional dimension.” And he has demonstrated that a very wide variety of objects are fractals, which means that many (perhaps most) of the objects we think of as, say, three-dimensional are in fact three-plus dimensional. The more complex the object, the higher the fractional excess; so a big, many-branched tree would be “more fractal,” if you will, than, say, a bowling ball.
But it seems likely that the fractional dimension of even a fairly smooth 3D+ object, like a planet, would have to be greater than the near-infinitesmal value of Ü. And as a result, the planet would “stretch” the dimension of the space around it, causing the kind of contour that Einstein’s conjecture associates with gravity. This would be true even with very small objects, which would account for the kind of “clumping” that scientists believe took place in the early universe, leading eventually to the formation of galaxies and so on.
There’s something else that the structure of the twisted-universe model might help account for that has puzzled me for a long time. I think some visual aids may help here.
We often hear airplane pilots talking about flying “straight and level.” But they’re actually doing anything but. What they’re really doing is flying at a constant altitude above the Earth’s surface. Because the Earth’s surface is curved, however, the plane’s actual path is also curved, as shown above. What would happen if an airplane really flew “straight and level” looks like this:
Now, the thing I’ve wondered about for years is this: We all know that the speed of light is a sort of universal speed limit, that nothing can go faster without violating all sorts of natural laws. But I’ve always wondered why it’s precisely the speed it is, 299,792.5 kilometers per second, or about 186,000 miles per second.
We’re used to the idea, again thanks to Einstein, of light traveling a curved path around massive, high-gravity objects. But since I’m supposing here that all light must travel a curved path in a curved, twisted universe, the “normal” path of light would look something like this:
Obviously, the curvature of this “universe” is highly exaggerated, but it illustrates how the rays of light in a sense “flow” along the contour of the space. What I’m going to suggest is that the speed at which light (and of course other forms of radiation) travels is actually determined by that contour or curvature, because if it travelled at a higher speed, this would happen:
What this would actually mean is hard to say. It might mean that the energy disappears into the fourth dimension, or it could even mean that it exits the universe, whatever that might entail.
Mention of the fourth dimension brings up one final point I want to make before closing this largely pointless expostulation. You’ll remember the Möbius strip from last time:
In looking at this illustration, I want you to imagine that the strip is actually transparent, because what we’re talking about here is empty space, not paper. So there’s really nothing separating point A from point B, or C from D, except space; or rather, except the twisted structure of this space. But the separation is nevertheless complete and inviolable: The only way to get from point A to point B is to go around the strip; you can’t go through it.
Why not? Well, if you travel around the strip from A to B, you’re in effect adding up Ü units, or in a sense travelling uphill dimensionally. By the time you reach point C, you’re in a dimension that’s 0.5 higher in relation to A, and when you reach B, the space you’re in is a full 1 dimension away from A. It’s still 2+ÜD from a local point of view (in the illustration; in the twisted universe, it would be 3+ÜD), but A is 3D from the perspective of B (4D in the real universe), and vice versa. So naturally, there’s no way to perceive one space from the other, much less to go there directly.
This is precisely what constitutes the boundary or “edge” of the universe, this dimensional barrier. And what that means is that every point in the universe is on the edge of the universe.
Somehow, that reminds me of the famous Hermetic saying quoted by Giordano Bruno and Pascal, among others: “God is an intelligible sphere whose center is everywhere and whose circumference is nowhere.” In the twisted universe, the circumference is everywhere, but I’m not sure whether there’s a center anywhere.
Wednesday, June 9, 2010
A Twisted Universe
Last time, I argued that the overall shape or structure of the universe is unknowable, an argument that might (in light of Goedel’s incompleteness theorems) be unprovable. But despite perfectly good reasons to abandon the goal, I’m now going to present an argument in favor of what I believe may be a novel model of the cosmos.
First, what do we mean by the words “universe” or “cosmos?” The start of the Wikipedia entry for “universe” seems to me to sum it up nicely, especially because it says pretty much what I hoped it would say: “The Universe comprises everything perceived to exist physically, the entirety of space and time, and all forms of matter and energy.”
That second clause, “the entirety of space and time,” raises a point that I think a lot of people overlook: The universe is not in space, rather, all space is in the universe. This means the universe cannot have a spatial boundary: You can’t travel to the edge of the universe and find that the universe ends while space continues. As a result, the shape or structure of the universe must be such that if you travel through it in a straight line, you never reach a point where the universe is on one side and something else is on the other.
It seems to me that there are only two ways this can be possible. The first is if the universe is infinitely large. This would certainly allow for a never-ending trajectory, but it also creates serious difficulties.
First, given the equivalence between space and time, it seems necessary that an infinitely large universe also be infinitely old. Even if there were no inherent reasons for rejecting an infinite universe (and I think there are), this requirement that it be infinitely old would directly contradict the prevailing scientific cosmological model, the Big Bang theory, which holds that the universe is “only” about 13 billion years old.
Also contradicting the Big Bang theory would be any requirement that matter/energy be consistently distributed throughout an infinite space. Such consistency is required if we aren’t to allow different regions of space to have drastically different properties; in other words, if we do want to guarantee that universal laws really are universal. But if we distribute matter/energy similarly throughout an infinite universe, it’s clear that we must have an infinite amount of matter/energy to distribute.
Since matter/energy can be neither created nor destroyed, an infinite universe must have contained the same amount – i.e., an infinite amount – of matter/energy from its beginning. In other words, a less-than-infinite volume of space must have held an infinite quantity of matter/energy. This strikes me as very unlikely. In short, I don’t see any possibility that an infinite universe could have had a beginning in time (without divine agency), because it must already have been infinite at its beginning, something that contradicts the entire basis of the Big Bang theory.
But if an infinitely large universe must also be infinitely old, then one would expect certain physical phenomena to have advanced long ago to their extremes. Most obviously, the second law of thermodynamics requires that the total entropy of the universe increase over time. If it has already been increasing for an infinite time, then one might reasonably expect that entropy would long ago have reached its maximum, known as “heat death,” in which no free energy is available to cause motion or sustain order. Clearly, that is not the case.
So I’m convinced that infinity is just not on, which means we need to find another structure “such that if you travel through it in a straight line, you never reach a point where the universe is on one side and something else is on the other,” as I said earlier.
To explain what I think is the best alternative to infinity, I’ll start with an object that may be familiar to many readers:
This is the famous Möbius strip, discovered by German mathematician August Ferdinand Möbius. It’s just a strip of paper with the ends glued or taped together, with the important requirement that the paper be given a half-twist before gluing or taping, but it has a number of interesting properties, which many of you are undoubtedly familiar with.
For one, if you take a pen and draw a line along the length of the strip, the line will return to its starting point, having covered both “sides” of the paper, without lifting the pen off the paper at any time.
The standard explanation for this is that mathematically (topologically), despite all appearances to the contrary, the strip has only one surface. But there’s another way of explaining it:
If you took a strip of paper and stuck the ends together without the half-twist, the only way to draw a line on both sides of the paper would be to lift the pen from the paper and move it around to the other side. In other words, the pen would have to leave the two-dimensional surface of the paper and travel through three-dimensional space to the other side.
But the half-twist turns the Möbius strip as a whole into a three-dimensional object, and so the tip of your pen does in fact make that trip through 3D space as it makes its “orbit” of the entire strip, without ever leaving the (apparently) 2D plane.
If you consider the twist as spread evenly over the whole of the strip, then in effect the dimension of the surface at any one point is slightly more than 2D; it has a dimension of 2.00…n, with the magnitude of the fractional part at any point depending on how long the strip is. When you add the fractional parts over the whole length, the sum will be 1.0, which, when added to the nominal 2.0 dimension of the surface, makes the dimension of the object as a whole 3.0.
Now, suppose we take a three-dimensional object – a sphere, for example – and give it a half-twist and join its ends together. Obviously, this isn’t something we can actually do in three-dimensional space – a sphere has no “ends” in 3D space. (By the same token, a 2D being couldn’t make a Möbius strip.) But I hope that by bootstrapping up from the example of the Möbius strip, we can conceptualize the result of this procedure.
As was the case with the Möbius strip, the half-twist raises the dimension of the object as a whole by 1.0, in this case to 4.0. And as with the Möbius strip, the dimension at any point within the sphere will appear to be unchanged. But in fact, it will be 3.00…n, with the fractional part again adding up over a full orbit of the space to 1.0, making the total dimension 4.0.
And again as in the case of the Möbius strip, a straight-line trajectory in any direction will eventually return to its starting point, having traversed both “sides” of the sphere. But mathematically, just as the Möbius strip has only one surface, this “Möbius sphere” has only one volume, though it would appear to a four-dimensional observer to have separate “inside” and “outside” volumes, just as a three-dimensional observer (you or me) sees an “inside” and an “outside” surface on the Möbius strip.
A space of this kind would satisfy the requirement that “if you travel through it in a straight line, you never reach a point where the universe is on one side and something else is on the other.” In fact, in this twisted universe, no matter which direction you travel, there will always be as much of the universe in front of you as behind, and as much above as below. In other words, for an ordinary (physically constituted) traveler, such a universe is likely inescapable.
There are a number of other implications of this form as a cosmological model, some of which I find rather odd. But this is already a rather lengthy post, so I’ll have to take up the ramifications next time.
First, what do we mean by the words “universe” or “cosmos?” The start of the Wikipedia entry for “universe” seems to me to sum it up nicely, especially because it says pretty much what I hoped it would say: “The Universe comprises everything perceived to exist physically, the entirety of space and time, and all forms of matter and energy.”
That second clause, “the entirety of space and time,” raises a point that I think a lot of people overlook: The universe is not in space, rather, all space is in the universe. This means the universe cannot have a spatial boundary: You can’t travel to the edge of the universe and find that the universe ends while space continues. As a result, the shape or structure of the universe must be such that if you travel through it in a straight line, you never reach a point where the universe is on one side and something else is on the other.
It seems to me that there are only two ways this can be possible. The first is if the universe is infinitely large. This would certainly allow for a never-ending trajectory, but it also creates serious difficulties.
First, given the equivalence between space and time, it seems necessary that an infinitely large universe also be infinitely old. Even if there were no inherent reasons for rejecting an infinite universe (and I think there are), this requirement that it be infinitely old would directly contradict the prevailing scientific cosmological model, the Big Bang theory, which holds that the universe is “only” about 13 billion years old.
Also contradicting the Big Bang theory would be any requirement that matter/energy be consistently distributed throughout an infinite space. Such consistency is required if we aren’t to allow different regions of space to have drastically different properties; in other words, if we do want to guarantee that universal laws really are universal. But if we distribute matter/energy similarly throughout an infinite universe, it’s clear that we must have an infinite amount of matter/energy to distribute.
Since matter/energy can be neither created nor destroyed, an infinite universe must have contained the same amount – i.e., an infinite amount – of matter/energy from its beginning. In other words, a less-than-infinite volume of space must have held an infinite quantity of matter/energy. This strikes me as very unlikely. In short, I don’t see any possibility that an infinite universe could have had a beginning in time (without divine agency), because it must already have been infinite at its beginning, something that contradicts the entire basis of the Big Bang theory.
But if an infinitely large universe must also be infinitely old, then one would expect certain physical phenomena to have advanced long ago to their extremes. Most obviously, the second law of thermodynamics requires that the total entropy of the universe increase over time. If it has already been increasing for an infinite time, then one might reasonably expect that entropy would long ago have reached its maximum, known as “heat death,” in which no free energy is available to cause motion or sustain order. Clearly, that is not the case.
So I’m convinced that infinity is just not on, which means we need to find another structure “such that if you travel through it in a straight line, you never reach a point where the universe is on one side and something else is on the other,” as I said earlier.
To explain what I think is the best alternative to infinity, I’ll start with an object that may be familiar to many readers:
Möbius strip (Adapted from Wikipedia)
This is the famous Möbius strip, discovered by German mathematician August Ferdinand Möbius. It’s just a strip of paper with the ends glued or taped together, with the important requirement that the paper be given a half-twist before gluing or taping, but it has a number of interesting properties, which many of you are undoubtedly familiar with.
For one, if you take a pen and draw a line along the length of the strip, the line will return to its starting point, having covered both “sides” of the paper, without lifting the pen off the paper at any time.
The standard explanation for this is that mathematically (topologically), despite all appearances to the contrary, the strip has only one surface. But there’s another way of explaining it:
If you took a strip of paper and stuck the ends together without the half-twist, the only way to draw a line on both sides of the paper would be to lift the pen from the paper and move it around to the other side. In other words, the pen would have to leave the two-dimensional surface of the paper and travel through three-dimensional space to the other side.
But the half-twist turns the Möbius strip as a whole into a three-dimensional object, and so the tip of your pen does in fact make that trip through 3D space as it makes its “orbit” of the entire strip, without ever leaving the (apparently) 2D plane.
If you consider the twist as spread evenly over the whole of the strip, then in effect the dimension of the surface at any one point is slightly more than 2D; it has a dimension of 2.00…n, with the magnitude of the fractional part at any point depending on how long the strip is. When you add the fractional parts over the whole length, the sum will be 1.0, which, when added to the nominal 2.0 dimension of the surface, makes the dimension of the object as a whole 3.0.
Now, suppose we take a three-dimensional object – a sphere, for example – and give it a half-twist and join its ends together. Obviously, this isn’t something we can actually do in three-dimensional space – a sphere has no “ends” in 3D space. (By the same token, a 2D being couldn’t make a Möbius strip.) But I hope that by bootstrapping up from the example of the Möbius strip, we can conceptualize the result of this procedure.
As was the case with the Möbius strip, the half-twist raises the dimension of the object as a whole by 1.0, in this case to 4.0. And as with the Möbius strip, the dimension at any point within the sphere will appear to be unchanged. But in fact, it will be 3.00…n, with the fractional part again adding up over a full orbit of the space to 1.0, making the total dimension 4.0.
And again as in the case of the Möbius strip, a straight-line trajectory in any direction will eventually return to its starting point, having traversed both “sides” of the sphere. But mathematically, just as the Möbius strip has only one surface, this “Möbius sphere” has only one volume, though it would appear to a four-dimensional observer to have separate “inside” and “outside” volumes, just as a three-dimensional observer (you or me) sees an “inside” and an “outside” surface on the Möbius strip.
A space of this kind would satisfy the requirement that “if you travel through it in a straight line, you never reach a point where the universe is on one side and something else is on the other.” In fact, in this twisted universe, no matter which direction you travel, there will always be as much of the universe in front of you as behind, and as much above as below. In other words, for an ordinary (physically constituted) traveler, such a universe is likely inescapable.
There are a number of other implications of this form as a cosmological model, some of which I find rather odd. But this is already a rather lengthy post, so I’ll have to take up the ramifications next time.
Tuesday, June 8, 2010
The Vast Unknown
As we know, there are known knowns: There are things we know we know. We also know there are known unknowns; that is to say, we know there are some things we do not know. But there are also unknown unknowns, the ones we don't know we don't know.Some people in the media ridiculed the above statement when "Rummy" said it back in 2002. And as a response to questions about the Iraq War, it certainly had some inadequacies. But from a purely epistemological point of view, it's not entirely lacking in merit. Certainly, "we know there are some things we do not know," and I would add that there are some things we cannot know.
- Former Secretary of Defense Donald Rumsfeld, news briefing, Feb. 12, 2002
I mean this in a strictly rational, scientific sense (at least for now): There are some things that are inherently unknowable. Heisenberg's principle of uncertainty (or indeterminacy) provides a famous example: In quantum physics, it's impossible to know simultaneously the position of a particle and its velocity; the more precisely you measure one property, the less you know about the other. And Werner Heisenberg, the physicist who first formulated this principle, called attention to the fact that this uncertainty isn't just a result of insufficiently precise measuring tools or processes, it's a fundamental property of quantum systems; that is, of matter as such.
Equally fundamental, and possibly even more so, are Kurt Gödel's incompleteness theorems. Without going into great detail (partly because trying to do so would probably give me a severe headache), these theorems prove that many formal logical systems cannot prove all of their own possible axioms and/or cannot prove their own consistency. One reading of the implications is that if the result of a formal logical proof is something we can label as "knowledge," Gödel's theorems show that there must remain some things that are "unknowable" in this sense.
These examples may seem somewhat nitpicky or irrelevant: Surely it doesn't matter much in the larger scheme of things if we can't precisely locate every particle of matter/energy in the universe or if we can't absolutely prove or disprove every possible statement.
But what if one of the inherently unknowable things is the largest scheme of things itself - the universe? In other words, what if there's an inherent unknowability at the smallest scale, the microcosmic, and also at the largest, the cosmic, and an unprovability about any guesses we might make as a substitute for direct knowing?
Within my limited and decidedly math-impaired understanding, this does appear to be precisely the case.
When we look up at the sky on a clear night, we can see millions of glowing objects in the sky - and not one of them is actually located where it appears to be. The reason, of course, is that it takes time for light to travel through space, and during the time the light is traveling from its source (a star, galaxy or planet, for instance) to our eyes, we and that source are moving. Even our nearest neighbors in space are far away enough for there to be a time lag, and thus a displacement, between their emission of light and our reception of it: It takes light about 9 minutes to travel from the sun to the Earth. And obviously, the farther away the emitter is, the longer the time lag and the larger the spatial displacement become.
What this means is that the picture our perceptions (even as we extend them through technology such as telescopes) give us of the universe is inevitably geocentric. We can adjust the picture to some extent, in effect creating a mental or conceptual map of the real current locations of celestial bodies, and this procedure obviously works well enough for us to send space probes to the Moon, Mars and so on. But as the distance involved increases, so must the uncertainty of our conceptual map.
In other words, any model we propose for the structure of the universe in its entirety will always have a major theoretical component. It's likely that we are safe in supposing that the natural physical laws that operate within our zone of certainty will also operate outside that zone, so it's fairly safe to hypothesize that the most distant regions of the universe will be like ours in a general, qualitative sense. But we cannot know the precise structure or appearance of those regions, or of the universe as a whole, in "real time," that is, as they are at any one moment.
One implication of this unknowability is that we (and by "we" I mean all intelligent beings who happen not to be blessed with supernatural omniscience) may ultimately have to accept multiple, and possibly mutually contradictory, models of the universe. As long as a conceptual model doesn't conflict with natural universal laws, insofar as we can understand those, and does account as much as possible for the phenomena that we can observe directly, we probably must accept that it's "true," even if there exist one or more alternative models with equal claims to be "true."
In some sense, we already do live with multiple universes - that is, with multiple explanations of the structure and origin of the cosmos - though there's considerable argument about which, if any, are true. And maybe a realistic understanding of the limits of certainty should prompt us to be a bit less fiercely argumentative about our varying understandings.
Perhaps to add fuel to the fire, or perhaps to help diffuse it, I'll be writing next time about an alternative model that as far as I know - and obviously, that can't be very far - hasn't previously been proposed and is very unlikely to be provable.
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