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raekuul
Lives under a bridge & tells stories.
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 Posted: Mon Aug 22, 2011 3:48 am Post subject: 41 |
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extro: Thank you for taking the time to explain that to me. I'm not sure I understood all of that, but you've at least helped me to un-know things that weren't true. I think. I'm still not sure.
Here's what I'm having a problem wrapping my head around. How, exactly, do they know that their hypotheses are proven correct by their observations? If the universe is "flat", why can we move along three axes? Wouldn't a source of matter sufficient for a universe to spontaneously explode out of be such a supermassive gravity sink as to be equivalent to a black hole? Do scientists even bother with questioning established truths anymore?
Also, the very end of that article actually agrees with my first point, which is that we can't make an accurate model of the entire universe. |
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extropalopakettle
No offense, but....
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| Posted: Mon Aug 22, 2011 4:41 am Post subject: 42 |
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| raekuul wrote: |
| Here's what I'm having a problem wrapping my head around. How, exactly, do they know that their hypotheses are proven correct by their observations? |
First, I'm not well versed in this myself, but it's not so much that they had a single hypotheses, but several, and there were predictions about what would be observed under each. Then they looked, and saw what was consistent with a flat universe, which leads to:
| raekuul wrote: |
| If the universe is "flat", why can we move along three axes? |
"flat" doesn't refer to the number of dimensions. The 2-dimensional surface of a sphere is 2-dimensional, but not flat. If the sphere is big enough, it seems flat locally. But on a large scale, things are different. If I'm at the equator, and start walking directly north, while a mile to my east, someone else starts walking directly north, in parallel, our paths will eventually meet (at the north pole). This doesn't happen on a flat surface.
"flat" means not curved. A 3-dimensional space can be flat (the way we usually picture it), or curved, and if curved, there a multiple ways in which it can be so.
Yes, it's hard or impossible to visualize - because we evolved in a world that three dimensional and "locally flat" (any curvature is negligible). We get some grasp of a curved 3-D space through analogy to a curved 2-D plane.
| raekuul wrote: |
| Also, the very end of that article actually agrees with my first point, which is that we can't make an accurate model of the entire universe. |
Well, we can only see so far. We can't confirm by observation beyond a certain (huge) radius. But if I'm out in a desert and can see sand for miles around, and I walk many miles more and still see sand for miles around, then turn left and walk for miles and see sand for many miles around, I think it's a safe bet that there's a lot more sand than what I've seen. And that's without any theory, that matches observation, about how all that sand came to be (the analogy fails in that the sand ends ... but there's an explanation for that). The Big Bang has confirming observations, and it would be hard to explain why things should be radically different beyond where we can observe. |
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raekuul
Lives under a bridge & tells stories.
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| Posted: Mon Aug 22, 2011 5:19 am Post subject: 43 |
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I'd argue that they made the observations fit the hypotheses (which is a plural word, by the way - the singular is hypothesis), but that's neither here nor there at this point. Benefit of the doubt and all that.
Okay, so all of the axes upon which we can travel do not curve, no matter how close we arbitrarily bring ourselves to infinity. All of the dimensions that we can observe point to a non-curved universe. What if the universe is curved in such a way that we can't observe the curve? I get the "locally flat" thing, but the WMAP measurements operate on a lot of assumptions that I don't know what they are. We are told - and we are asked to accept as true - the following:
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| "If the universe were flat, the brightest microwave background fluctuations (or "spots") would be about one degree across. If the universe were open, the spots would be less than one degree across. If the universe were closed, the brightest spots would be greater than one degree across." |
I don't know enough about how the universe works to know if that's a reasonable assumption to make or not, but what if it's wrong? Is there any way to know for certain whether or not those three basic assumptions are correct or not? (NOTE: I am not asking whether or not it is wrong, I'm asking you to tell me what would happen if they were wrong.)
And as for the analogy of a desert: Even if we limit ourselves to just what's in the desert, if all we see is sand, we won't know about mesas or dunes or cacti. The universe is the same way - even with limiting it to what we've been able to observe, we can't make an accurate model of all of it. |
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extropalopakettle
No offense, but....
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| Posted: Mon Aug 22, 2011 2:46 pm Post subject: 44 |
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| raekuul wrote: |
... the WMAP measurements operate on a lot of assumptions that I don't know what they are. We are told - and we are asked to accept as true - the following:
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| "If the universe were flat, the brightest microwave background fluctuations (or "spots") would be about one degree across. If the universe were open, the spots would be less than one degree across. If the universe were closed, the brightest spots would be greater than one degree across." |
I don't know enough about how the universe works to know if that's a reasonable assumption to make or not, but what if it's wrong? Is there any way to know for certain whether or not those three basic assumptions are correct or not? (NOTE: I am not asking whether or not it is wrong, I'm asking you to tell me what would happen if they were wrong.) |
I don't know all the science behind it, but I'd bet those aren't merely assumptions. |
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raekuul
Lives under a bridge & tells stories.
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| Posted: Mon Aug 22, 2011 2:58 pm Post subject: 45 |
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| I still have no way of knowing if they're reasonable starting points or not. They're asking me to take their word for it, and they're not showing me how they even got to their starting point. |
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Thok*
Guest
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| Posted: Mon Aug 22, 2011 9:09 pm Post subject: 46 |
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| raekuul wrote: |
| I still have no way of knowing if they're reasonable starting points or not. They're asking me to take their word for it, and they're not showing me how they even got to their starting point. |
Open/Flat/Closed correspond to measurements of the average curvature of the universe, which is a real number. Flat = 0 curvature on average, and I believe open = negative curvature, closed = positive curvature. (I may have switched open and closed around, but the point is that the three cases correspond to positive, zero, negative in some way.) |
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L'lanmal
Daedalian Member
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| Posted: Mon Aug 22, 2011 10:43 pm Post subject: 47 |
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| Thok* wrote: |
Complex numbers can also be realized as a subset of 2x2 matrices, where
a+bi is represented by the matrix
[a b]
[-b a]
One can check that addition and multiplication works out correctly.
If you don't believe 2x2 matrices are real, I'd like to see you try to rotate. |
And while one does not normally observe a complex amount of apples, that doesn't mean we are just imagining Electrical Impedance. (Wait, or does that mean we are imagining it?) |
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raekuul
Lives under a bridge & tells stories.
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| Posted: Tue Aug 23, 2011 2:16 am Post subject: 48 |
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Thok, the average curvature thing requires that we be able to take the average of an infinite, which defeats the purpose of using subsequent observations to prove the finiteness (or lack thereof) of the universe.
...wait, what? Let me try that again. I confused myself.
| Quote: |
| Open/Flat/Closed correspond to measurements of the average curvature of the universe, which is a real number. |
That's nice. What real number would that be? How can we measure the average curvature of the universe, anyway? Am I missing something here? The last time I checked we can only legally take the average of a finite amount of data. |
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BraveHat
Last of the Daedalians
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| Posted: Tue Aug 23, 2011 2:51 am Post subject: 49 |
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| extro wrote: |
| No idea what you're talking about. Our 3-dimensional universe being embedded in a higher dimensional one? And that implying that if our universe is finite, only finite universes are possible? |
I'm not saying that would definitely imply such a thing, I'm saying it's possible that could imply such a thing.
Let A=some observable physical occurrence.
Suppose there is some A such that the following argument is sound:
| Code: |
If the Universe is infinite in size, then
~A (given, from some property of that type of infinity)
A (given, from observation of A)
Therefore the Universe is not infinite in size
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If that's the case, then it's possible we could also have the following argument on our hands:
| Code: |
If the object containing the multiverse is infinite in size, then
~A (given, from some property of that type of infinity)
A (given, from observation of A)
Therefore the object containing the multiverse is not infinite in size
Therefore, every Universe within the multiverse is not infinite in size |
The reason that 2nd argument could be very possible is because we see in Euclidean geometry that there is a kind of inter-dimensional transitive property at work. If 3-dimensional cube Z contains 2-dimensional line segment Y and 2-dimensional line segment Y contains a smaller 2-dimensional line segment X, then 3-dimensional cube Z contains the 2-dimensional line segment X. It seems perfectly probable that this transitive property would hold for any higher dimensions as well, with respect to the lower dimensions. So if a 4-dimensional object D contains our 3-dimensional Universe and our 3-dimensional Universe contains our 3-dimensional observable occurrence, then it stands to reason that the 4-dimensinal object D contains our 3-dimensional observable occurrence.
_________________
"I am declaring it a terrible tragedy for me to die. You may disagree..." --Antrax |
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BraveHat
Last of the Daedalians
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| Posted: Tue Aug 23, 2011 2:56 am Post subject: 50 |
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By contrast it's not possible to prove that the Universe is infinite in space. Even if the Universe must have flat space for a vast, vast distance, it could still be curved at some place that would be impossible for us to detect, possibly analogous to a really long conveyor belt.
_________________
"I am declaring it a terrible tragedy for me to die. You may disagree..." --Antrax |
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Thok*
Guest
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| Posted: Tue Aug 23, 2011 9:07 am Post subject: 51 |
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| raekuul wrote: |
| That's nice. What real number would that be? How can we measure the average curvature of the universe, anyway? Am I missing something here? |
The experiment in question is an attempt to measure the average curvature of the universe by observing background radiation. We don't know what it is yet.
And yes, you can take an average of a function f over an infinite manifold M if you have a probability distribution p(x) on it. It's just the (properly normalized) integral of f*p(x) over the space of the manifold. The question is making sure you have the right probability distribution.
Your criticism seems to be "what if space is different near Earth"; that fails Occam's Razor (it's much simpler mathematically and physically to assume that space has a similar curvature everywhere, since a different nearby curvature would force us to explain why the curvature suddenly changes.) |
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extropalopakettle
No offense, but....
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| Posted: Tue Aug 23, 2011 12:46 pm Post subject: 52 |
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First:
| BraveHat wrote: |
| Code: |
If the Universe is infinite in size, then
~A (given, from some property of that type of infinity)
A (given, from observation of A)
Therefore the Universe is not infinite in size
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For sake of economy, you can just say here "We observe the universe to be finite" ... it's the same thing.
| BraveHat wrote: |
If that's the case, then it's possible we could also have the following argument on our hands:
| Code: |
If the object containing the multiverse is infinite in size, then
~A (given, from some property of that type of infinity)
A (given, from observation of A)
Therefore the object containing the multiverse is not infinite in size
Therefore, every Universe within the multiverse is not infinite in size |
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What multiverse? What object containing it?
Im questioning if, when we observe the universe to be one way, does that mean it was, is, will be, would have been, etc. impossible for a universe to be otherwise.
And you can replace 'universe' in the prior sentence with 'multiverse' or 'object containing the 'multiverse'.
I'm not talking about a multiverse. I'm asking how a universe might possibly be. Not how this universe is, but how a universe could possibly be.
| BraveHat wrote: |
| The reason that 2nd argument could be very possible is because we see in Euclidean geometry that there is a kind of inter-dimensional transitive property at work. If 3-dimensional cube Z contains 2-dimensional line segment Y and 2-dimensional line segment Y contains a smaller 2-dimensional line segment X, then 3-dimensional cube Z contains the 2-dimensional line segment X. |
No. Some dimensions can be flat and infinite, others curved and finite (or infinite).
| BraveHat wrote: |
| It seems perfectly probable that this transitive property would hold for any higher dimensions as well, with respect to the lower dimensions. |
Define 'perfectly probable' in this context, and the senses via which it seems so.
| BraveHat wrote: |
| So if a 4-dimensional object D contains our 3-dimensional Universe and our 3-dimensional Universe contains our 3-dimensional observable occurrence, then it stands to reason that the 4-dimensinal object D contains our 3-dimensional observable occurrence. |
No, it doesn't. But I don't see the relevance anyway. |
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raekuul
Lives under a bridge & tells stories.
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| Posted: Tue Aug 23, 2011 1:01 pm Post subject: 53 |
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So, extro, you're saying that objects can't contain logically simpler (if not actually simpler) objects, or am I misunderstanding the principles involved?
Thok, you're raising a very good point there. I was under the impression that we can't make any measurements that aren't influenced at least in part by the proximity of the Earth. Background Radiation I can give you, though... as soon as I figure out exactly what that is. I'm told that it's effectively the "edge of the map" in the sense that we haven't seen past the point where we get BR as a result of the observations. |
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extropalopakettle
No offense, but....
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| Posted: Tue Aug 23, 2011 1:01 pm Post subject: 54 |
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| BraveHat wrote: |
| By contrast it's not possible to prove that the Universe is infinite in space. Even if the Universe must have flat space for a vast, vast distance, it could still be curved at some place that would be impossible for us to detect, possibly analogous to a really long conveyor belt. |
First, what he says:
| Thok* wrote: |
| Your criticism seems to be "what if space is different near Earth"; that fails Occam's Razor (it's much simpler mathematically and physically to assume that space has a similar curvature everywhere, since a different nearby curvature would force us to explain why the curvature suddenly changes.) |
It could be possible for a finite sphere to be so large that what small part of it we see appears flat to within our ability to measure it.
But I really thought the whole discussion stemmed from attempts to "prove my intuition that the Universe can't be infinite (in space or time)". Not simply that maybe it isn't infinite, that we observe it not to be infinite, but that it being infinite is a logical impossibility for a "physical reality". Are we abandoning that question, or confusing the two? Do we disagree that they are completely different questions? |
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extropalopakettle
No offense, but....
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| Posted: Tue Aug 23, 2011 1:27 pm Post subject: 55 |
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| raekuul wrote: |
| So, extro, you're saying that objects can't contain logically simpler (if not actually simpler) objects, or am I misunderstanding the principles involved? |
Not saying that at all. Certainly things can contain simpler things, and often do.
| raekuul wrote: |
| Thok, you're raising a very good point there. I was under the impression that we can't make any measurements that aren't influenced at least in part by the proximity of the Earth. Background Radiation I can give you, though... as soon as I figure out exactly what that is. I'm told that it's effectively the "edge of the map" in the sense that we haven't seen past the point where we get BR as a result of the observations. |
That's a different sort of background radiation. The cosmic microwave background radiation was predicted to exist from the Big Bang theory, and is leftover microwave radiation from the very early stages of the Big Bang. It was eventually observed by accident by a couple of guys working for Bell Labs in NJ who noticed that no matter which way they pointed this antenna they had, it picked up a signal. They puzzled over what it was, thinking their antenna was buggy, they even got inside it to clean out pigeon poop to try to fix, and they ended up stepping right in it when they got a Nobel prize. Seriously, I don't think anyone ever got a Nobel prize in physics so unaware of what they were doing. |
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Shy*
Guest
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| Posted: Tue Aug 23, 2011 2:07 pm Post subject: 56 |
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| Death Mage wrote: |
| The amount of space taken up by a finite object in an infinite space can be best described as the difference of 1-0.999...(repeating). Therefore, if you believe that 0.999...(repeating) = 1, you do not exist. |
The amount of space taken up by a finite object in an infinite space can better be described as the span of 1-2 in an infinite set of numbers. |
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raekuul
Lives under a bridge & tells stories.
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| Posted: Tue Aug 23, 2011 4:08 pm Post subject: 57 |
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So, wait, we've got the background radiation that exists as a logical conclusion of the Big Bang theory, and then we've got the background radiation that exists as part of the explanation as to the universe being an infinite expanse that, according to the numbers, has an average curve of zero.
Ah, I think I'm seeing where I'm confused - I'm reading "average curve" as though that's an absolutely fixed value, when you can still get an average curve of 0 if you get inverse measurements (for example, if I were to get measurements of 90 and -90, the average would still be 0) |
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extropalopakettle
No offense, but....
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| Posted: Tue Aug 23, 2011 6:02 pm Post subject: 58 |
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| raekuul wrote: |
| So, wait, we've got the background radiation that exists as a logical conclusion of the Big Bang theory, and then we've got the background radiation that exists as part of the explanation as to the universe being an infinite expanse that, according to the numbers, has an average curve of zero. |
Same background radiation.
That it exists, all over, corroborates the Big Bang Theory (as does increased doppler red shift of galaxies further away, indicating the further they are, the faster they're moving away).
The nature of the fluctuations in the radiation across the sky tell whether space has positive, negative or zero curvature (and how exactly I don't know, but I expect google will help). Zero curvature would mean either an infinite universe, or a boundary ... edges ... the implications of which would be a lot less simple than an infinite universe. If I'm at the edge of space, what stops me from poking my finger beyond it? |
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Zag
Tired of his old title
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| Posted: Tue Aug 23, 2011 8:22 pm Post subject: 59 |
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| extropalopakettle wrote: |
Same background radiation.
That it exists, all over, ... |
What gives you the impression that it exists all over? We only know about it existing in one tiny part of one smallish galaxy. |
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Thok*
Guest
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| Posted: Tue Aug 23, 2011 8:51 pm Post subject: 60 |
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| Zag wrote: |
| What gives you the impression that it exists all over? We only know about it existing in one tiny part of one smallish galaxy. |
The background radiation that we measure is essentially light/energy from X light years away that has travelled towards us for X years, where by varying what wavelengths we measure we can change X. If there was an irregularity in the universe at some point, we would notice that for some X the background radiation has an interesting distribution.
And the cool point is that because of the Big Bang, at some point everything was close enough to us to throw background radiation at us in time to reach us. |
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extropalopakettle
No offense, but....
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| Posted: Tue Aug 23, 2011 8:54 pm Post subject: 61 |
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| Zag wrote: |
| extropalopakettle wrote: |
Same background radiation.
That it exists, all over, ... |
What gives you the impression that it exists all over? We only know about it existing in one tiny part of one smallish galaxy. |
I meant all over our sky. It comes equally from parts of the sky that point into the heart of our galaxy and from parts that point outward. Yes, we only know from direct observation that it's coming from all directions toward the Earth - uniformly from all directions regardless of whether there are nearby galaxies or stars in that direction. The only reasonable assumption is that it's coming from far away and long ago - not emanating recently from nearby empty space (Occam's razor). And it was predicted before it was observed (by two guys who weren't looking for it). |
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BraveHat
Last of the Daedalians
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| Posted: Tue Aug 23, 2011 9:16 pm Post subject: 62 |
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| extro wrote: |
| But I really thought the whole discussion stemmed from attempts to "prove my intuition that the Universe can't be infinite (in space or time)". Not simply that maybe it isn't infinite, that we observe it not to be infinite, but that it being infinite is a logical impossibility for a "physical reality". Are we abandoning that question, or confusing the two? Do we disagree that they are completely different questions? |
No, I'm understanding what you are getting at, I just might have veered off course a little. Let's go back to what you said before:
| extro wrote: |
| I'm trying to ask, but not doing it well, what is the difference between "impossible in physical reality" (as we're talking about it), versus "impossible as a coherent abstraction"? We can have a continuous real number line extending infinitely in both directions, positive and negative. No contradictions arise from assuming such a thing exists. It's possible. So what is it about "possible in physical reality" that it should be any different? |
Physical space is 3-dimensional space. For an object to possibly exist in physical reality it must have at least 3 dimensions: width, length, and depth (I'll accept, for the time-being, that an object may have infinite width, infinite length, and infinite depth). If we agree on that, we can say that it's impossible for a geometric point to exist as an object in physical reality, because it has no dimensions. It is equivalent, in physical space, to nothing. It doesn't exist. It's impossible for a Euclidean geometric line to exist as an object in physical space because it only has 1 dimension, and it's impossible for a Euclidean geometric plane to exist as an object in physical space because it only has 2 dimensions. Yet all these objects exist coherently in abstract space. So that is one difference between "impossible in physical reality" and "impossible as a coherent abstraction". It gets trickier when attempting to actually define this difference.
Now there are at least two ways to verify a fact. One way is to observe it occurring in physical reality. A ball bouncing. An odor emitting from a truck. A headache occurring in your head. When we observe these things, we've already verified their truth value from the observation itself. We say "the ball bounced" or "the truck smelled bad" or "I have a headache". We don't need to infer them from some system of thought. The other way to verify a fact is by inferring it from previously established axioms. Now it's possible that something we observe in physical reality contradicts something we logically infer from an abstract concept. My original question in the post was essentially asking "has anyone ever come up with such a thing?" If someone has, then it stands to reason that the abstract concept cannot apply to physical reality. If no one has, than it remains possible that it can.
_________________
"I am declaring it a terrible tragedy for me to die. You may disagree..." --Antrax |
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BraveHat
Last of the Daedalians
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| Posted: Tue Aug 23, 2011 10:07 pm Post subject: 63 |
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| Antrax wrote: |
| Percentage doesn't imply that at all. Ten percent of the real numbers from 0 to 1 lies within the region 0 to 0.1, despite there being an infinite amount of real numbers between 0 and 1. |
Yes, but we're talking about two different categories of infinities. I'm not sure how they are distinguished in name officially. 0 and 1 are end points. The type of infinity we talk about when we assume the Universe is infinite in space is a type that has no endpoints. Percentage would not apply to that type of infinity.
| Antrax wrote: |
| Your other argument is just as flawed. Mathematically, it's quite possible that earth takes up no percentage of the universe's space, and still exists. Let's say you pick a random integer with uniform probability. Mathematically, the odds for you to pick any specific number (1, 2, 1000000) or even any finite group of numbers (1 to 10) are exactly 0. Yet, these numbers exist, and in an intuitive sense you might pick any one of them. |
So let's say I pick 572098475029347520. You're saying that mathematically, before I picked that number, I had no chance of picking it? And yet I picked it. So obviously math is wrong or you aren't understanding it correctly.
Incidentally, I agreed that the Earth takes up no percentage of an Infinite Universe's space, but for other reasons.
_________________
"I am declaring it a terrible tragedy for me to die. You may disagree..." --Antrax |
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Thok*
Guest
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| Posted: Tue Aug 23, 2011 10:12 pm Post subject: 64 |
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| BraveHat wrote: |
Yes, but we're talking about two different categories of infinities. I'm not sure how they are distinguished in name officially. 0 and 1 are end points. The type of infinity we talk about when we assume the Universe is infinite in space is a type that has no endpoints. Percentage would not apply to that type of infinity.
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The normal distribution is by far the most commonly used probability distribution in statistics, and it's defined on the entire real line, aka a region with no endpoints.
Also, as sets the real line and (0,1) are isomorphic, and one can even preserve the topology. |
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raekuul
Lives under a bridge & tells stories.
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| Posted: Tue Aug 23, 2011 10:13 pm Post subject: 65 |
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| Extro, if they're the same background radiation, how is it that the Background Radiation from the Big Bang is a different sort of BR than what was measured by WMAP? |
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Thok*
Guest
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| Posted: Tue Aug 23, 2011 10:17 pm Post subject: 66 |
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| BraveHat wrote: |
| So let's say I pick 572098475029347520. You're saying that mathematically, before I picked that number, I had no chance of picking it? And yet I picked it. So obviously math is wrong or you aren't understanding it correctly. |
You aren't picking integers with a uniform distribution. The odds of you picking an integer tends to go to 0 as a number gets large, simply because you can't write it down because of the increasing complexity needed to write it down.
(This takes care to say precisely, since there are local maxima: you are more likely to say Ackerman(6) then many numbers significantly smaller than Ackerman(6).) |
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BraveHat
Last of the Daedalians
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| Posted: Tue Aug 23, 2011 10:27 pm Post subject: 67 |
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| Thok* wrote: |
| I wrote: |
| So let's say I pick 572098475029347520. You're saying that mathematically, before I picked that number, I had no chance of picking it? And yet I picked it. So obviously math is wrong or you aren't understanding it correctly. |
You aren't picking integers with a uniform distribution. The odds of you picking an integer tends to go to 0 as a number gets large, simply because you can't write it down because of the increasing complexity needed to write it down.
(This takes care to say precisely, since there are local maxima: you are more likely to say Ackerman(6) then many numbers significantly smaller than Ackerman(6).) |
Are you saying it's impossible for me to pick a random integer with equal distribution?
If so, then when Antrax says
| Antrax wrote: |
| Let's say you pick a random integer with uniform probability |
He's really already supposing an impossibility. In which case, every inference that follows is unfounded.
_________________
"I am declaring it a terrible tragedy for me to die. You may disagree..." --Antrax |
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extropalopakettle
No offense, but....
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| Posted: Tue Aug 23, 2011 10:49 pm Post subject: 68 |
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| BraveHat wrote: |
| Physical space is 3-dimensional space. For an object to possibly exist in physical reality it must have at least 3 dimensions: width, length, and depth (I'll accept, for the time-being, that an object may have infinite width, infinite length, and infinite depth). If we agree on that, ... |
No. Why must an object have width, length, depth, or any size at all? Do quarks have a size? I'm not sure ... they're usually described as occupying a certain minuscule volume, but I think this has something to do with Heisenberg Uncertainty principle, wherein they can't really be said to be at a particular location. The real physical universe is certainly not like what our intuition says is possible. An object can be dimensionless ( and it's location can be distributed over a certain volume).
String theory has 1-dimensional strings.
| Quote: |
| ... we can say that it's impossible for a geometric point to exist as an object in physical reality, because it has no dimensions. |
Even if this universe has no such objects (but I think it may), why is it impossible???
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| It is equivalent, in physical space, to nothing. It doesn't exist. |
It has a location, it interacts with other objects in certain ways, perhaps it has mass. It just has no size. It exists.
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| Now it's possible that something we observe in physical reality ... |
in the physical reality of this universe
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| ... contradicts something we infer from an abstract concept. My original question in the post was essentially asking "has anyone ever come up with such a thing?" If someone has, then it stands to reason that the abstract concept cannot apply to physical reality. |
Our physical reality, as it happens to be. Doesn't mean a physical reality can't have such a thing as physically real. |
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extropalopakettle
No offense, but....
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| Posted: Tue Aug 23, 2011 10:54 pm Post subject: 69 |
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| raekuul wrote: |
| Extro, if they're the same background radiation, how is it that the Background Radiation from the Big Bang is a different sort of BR than what was measured by WMAP? |
They're not different. I was saying it's different than what you described (below), but maybe I just didn't understand your description.
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| I'm told that it's effectively the "edge of the map" in the sense that we haven't seen past the point where we get BR as a result of the observations. |
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extropalopakettle
No offense, but....
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| Posted: Tue Aug 23, 2011 11:04 pm Post subject: 70 |
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| A photon's length in the direction it is moving is zero, if I understand correctly. |
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Thok*
Guest
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| Posted: Tue Aug 23, 2011 11:21 pm Post subject: 71 |
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| BraveHat wrote: |
| Are you saying it's impossible for me to pick a random integer with equal distribution? |
Yes. The word uniform makes it impossible. One can define a probability distribution that assigns a probability to each integer, but not one that assigns an equal probability to each integer.
My complexity argument just shows why the "I'll just say an integer" distribution isn't a uniform distribution.
There are ways to sort of make Antrax's argument work, but that requires going into how to define a probability distribution on an infinite space so that you can get useful results, and that requires throwing away some of the intuition you get from finite probability distributions. (The short of it is the probability of picking any individual number would be zero, but you really care about the probability of picking a number in an interval. Plus some calculus.) |
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Zag
Tired of his old title
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| Posted: Wed Aug 24, 2011 1:47 am Post subject: 72 |
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| BraveHat wrote: |
| So let's say I pick 572098475029347520. You're saying that mathematically, before I picked that number, I had no chance of picking it? And yet I picked it. So obviously math is wrong or you aren't understanding it correctly. |
The vast majority of integers have more than a billion digits in them. I'm pretty sure that when you picked a "random" integer, there was never any chance that you were going to pick one of them. In fact, I'm pretty comfortable saying that the range of the integers from which you were going to choose one at random (and put it into a post) includes only those between plus and minus a googol, and is pretty heavily weighted for those few (!) integers with 10-30 digits in them. I think you can acknowledge that your selection wasn't random over the range of "all integers." |
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extropalopakettle
No offense, but....
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| Posted: Wed Aug 24, 2011 2:01 am Post subject: 73 |
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| Antrax wrote: |
| Ten percent of the real numbers from 0 to 1 lies within the region 0 to 0.1, .... |
Is that true? |
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extropalopakettle
No offense, but....
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| Posted: Wed Aug 24, 2011 2:07 am Post subject: 74 |
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| extro...* wrote: |
| Antrax wrote: |
| Let's say you pick a random integer with uniform probability. |
Not possible. The probabilities have to add up to 1. |
Again - not possible. An infinite number of equal non-zero probabilities can't add to 1 (nor can an infinite number of zero probabilities). |
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Thok*
Guest
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| Posted: Wed Aug 24, 2011 2:58 am Post subject: 75 |
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| extropalopakettle wrote: |
| Antrax wrote: |
| Ten percent of the real numbers from 0 to 1 lies within the region 0 to 0.1, .... |
Is that true? |
It is for a reasonable definition of a uniform probability on [0,1] (which is that the probability of being in a subinterval (a,b) is b-a.) you can make this more precise with calculus (the probability of being in a subset of [0,1] is the integral of 1*dx over that subset.)
This is a generalization of probabilities on a finite set (in the same sense that an integral is a generalization of a finite sum) but the probability you get out isn't as intuitive. For example, the probability of pick exactly .2 = probability of picking the interval [.2,.2] = .2-.2 =0. But for the appropriate application we don't care about picking exactly .2.
(For example, when measuring heights, you could use this continuous probability and then notice that we only care about somebody's height to the precision of the ruler, and not precisely.) |
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BraveHat
Last of the Daedalians
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| Posted: Wed Aug 24, 2011 3:27 am Post subject: 76 |
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| extro wrote: |
| No. Why must an object have width, length, depth, or any size at all? Do quarks have a size? I'm not sure ... they're usually described as occupying a certain minuscule volume, but I think this has something to do with Heisenberg Uncertainty principle, wherein they can't really be said to be at a particular location. The real physical universe is certainly not like what our intuition says is possible. An object can be dimensionless ( and it's location can be distributed over a certain volume). |
I'm really not understanding that concept, mainly because I don't know a lot about quarks. But. How can they possibly take up no volume??? If they take up absolutely no volume, what would it even mean for them to exist?
Since we disagree on the impossibility of non 3-dimensional objects existing in physical space, we can go no further with that branch of the discussion.
| extro wrote: |
| extro wrote: |
| Antrax wrote: |
Let's say you pick a random integer with uniform probability. |
Not possible. The probabilities have to add up to 1. |
Again - not possible. An infinite number of equal non-zero probabilities can't add to 1 (nor can an infinite number of zero probabilities). |
Here's where I think we agree, which is that it isn't possible to pick a random integer with uniform probability, but more along the lines of why Zag thinks so, namely, that I'm more likely to pick an integer with less than a billion digits. Although if we treat the integer like the berry number, I don't necessarily have to name the integer in order to pick it. I could simply describe the integer such as "the highest integer ever named to the power of the highest integer ever named" or something. But that's a digression.
I think this is also another candidate for the argument proving the Universe is not infinite in space.
(btw, even though I don't personally believe that any Universe could be infinite in space, I never actually claimed that in these discussions, so I'm not sure why you think I'm arguing that. I'm only claiming that my intuition is that the Universe (meaning the one we're in) is not infinite)
If the Universe is infinite in space, then the chances that the Earth could have formed within in any particular block of space is 0. Therefore, before it was formed, the Earth had no chance of forming within in any particular block of space. Yet, the Earth formed within a particular block of space. Therefore, the Universe is not infinite in space.
At this point, I know you will find some sort of hole in that argument, so I'm not expecting you to agree. I'm just saying it's another candidate.
_________________
"I am declaring it a terrible tragedy for me to die. You may disagree..." --Antrax |
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Thok
Oh, foe, the cursed teeth!
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| Posted: Wed Aug 24, 2011 3:42 am Post subject: 77 |
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| BraveHat wrote: |
| If the Universe is infinite in space, then the chances that the Earth could have formed within in any particular block of space is 0. Therefore, before it was formed, the Earth had no chance of forming within in any particular block of space. Yet, the Earth formed within a particular block of space. Therefore, the Universe is not infinite in space. |
This argument is too strong to be valid; if it works it applies even in finite space. If the Earth is contained with a finite sized cube, there are infinitely many places to put it (you can slide it over a tiny amount for any sufficiently tiny amount.) So the probability is appeared at one position and not even a fraction of an inch over is 0; if not then I can add up the infinitely many epsilons and get a probability of over 1.
Basically, you have a problem with how probability is defined on infinite sets. You can either accept that probability is defined differently on a set with infinitely many points to get something that works, or claim there are only a finite number of positions in space. The latter seems weird to me. |
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extropalopakettle
No offense, but....
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| Posted: Wed Aug 24, 2011 3:43 am Post subject: 78 |
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| Thok* wrote: |
| extropalopakettle wrote: |
| Antrax wrote: |
| Ten percent of the real numbers from 0 to 1 lies within the region 0 to 0.1, .... |
Is that true? |
It is for a reasonable definition of a uniform probability on [0,1] ... |
I didn't think the fragment of what I quoted from Antrax called for any definition of probability.
If he had said "ten percent of the integers from 1 through 100 is divisible by 10 (or is in the range 1 to 10)" ... I'd have no problem with that, obviously - 10 out of 100 elements is 10 percent.
Let's say I create an infinite set of triplets consisting of (r1, r2, r3), for all real r1 in the range 0 to 0.1, and r2 = r1 * 0.5, and r3 = 0.5+ r2.
Clearly, the r1 values constitute at least a third of the combined r1, r2, r3 values (more actually - some of the r2 values are also r1 values).
But the r1 values are the reals from 0 to 0.1, and the combined r1, r2, r3 values are the reals from 0 to 1. |
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Zag
Tired of his old title
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| Posted: Wed Aug 24, 2011 4:05 am Post subject: 79 |
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| BraveHat wrote: |
| extro wrote: |
| extro wrote: |
| Antrax wrote: |
Let's say you pick a random integer with uniform probability. |
Not possible. The probabilities have to add up to 1. |
Again - not possible. An infinite number of equal non-zero probabilities can't add to 1 (nor can an infinite number of zero probabilities). |
Here's where I think we agree, which is that it isn't possible to pick a random integer with uniform probability, but more along the lines of why Zag thinks so, namely, that I'm more likely to pick an integer with less than a billion digits. |
But my argument and his were exactly the same. He stated it mathematically and I stated it by example, but we said essentially the same thing.
| BraveHat wrote: |
| If the Universe is infinite in space, then the chances that the Earth could have formed within in any particular block of space is 0. Therefore, before it was formed, the Earth had no chance of forming within in any particular block of space. Yet, the Earth formed within a particular block of space. Therefore, the Universe is not infinite in space. |
No one tried to claim that the chances of Earth forming in any particular place is evenly distributed across all of space -- there were regions that were more likely than others.
Here's an algorithm for picking a "random" positive integer. Note that it is weighted, some integers are more likely than others, but for any integer you can name, there is a non-zero chance of it being picked. (The chance gets pretty slim as you get into the billion-digit integers, but it is still non-zero.)
1. Generate a random integer from 1 to 9, with a uniform probability of each value being selected. Write it down.
2. Generate a random integer from 0 to 10, with a uniform probability of each value being selected, and we'll call it x
3. If x < 10, write it down after the last digit you wrote and go to 2.
4. (here only if x == 10) you're done. Interpret all the digits you've written as an integer.
Also, the fact that the a priori chances of any particular position being selected is zero does not mean that it can't be selected. I CAN request a random real number between zero and one, with uniform probability. Any one you might pick has, a priori, zero chance of being selected, but that doesn't prevent one from being selected. I probably can't describe precisely that number (because most of them have more than a billion digits after the decimal, and don't repeat) but I could still pick a spot on the number line. Realistically, I am limited by my measuring tools, but doesn't mean that I haven't actually picked precisely one number. |
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raekuul
Lives under a bridge & tells stories.
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| Posted: Wed Aug 24, 2011 4:56 am Post subject: 80 |
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| Quote: |
| If the Universe is infinite in space, then the chances that the Earth could have formed within in any particular block of space is 0. Therefore, before it was formed, the Earth had no chance of forming within in any particular block of space. Yet, the Earth formed within a particular block of space. Therefore, the Universe is not infinite in space. |
Wow... I think you've just injured my brain with logic. For any given point within an infinite universe, there is a probability that the circumstances required for Earth to have reached the state it is in now will happen. The probability is so low as to be practically nil... yet looking around, you'll notice that you're not floating around in a void. This is because of the fact that, in an infinite universe, as long as the probability of something happening is not actually zero, there are an infinite number of chances for something to occur - and the law of averages guarantees that it will have happened somewhere.
The main reason you're not right is that you're assuming that it's impossible for the Earth to form and working from there. Besides which, it's infinitely less likely for the Earth to form in a finite universe than an infinite universe simply because, in a finite universe, you can only make so many attempts at forming the Earth before you run out of spots to try it.
Last edited by raekuul on Wed Aug 24, 2011 5:03 am; edited 1 time in total |
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