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### Complex Life May Be Possible In Only 10% of All Galaxies

....

OK, I think this part of this thread is done. If you ever fancy reading that post, and any others I've made on the topic, feel free, and you might see just how little I'm talking "religion", and what a self-important jackass you sound.

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### Complex Life May Be Possible In Only 10% of All Galaxies

OK, I think we've probably run into the same ambiguity that I mentioned in a different comment in this thread. There are basically two definitions that we might have of this "infinite" business. I'm working from the viewpoint of general relativity -- or some other metric-based theory of gravity -- since I'm wanting to be work with a theory capable of quantifying statements. Given this, I have (at least) two definitions of "infinite" here:

1) The model we are driven to employ, the Friedman-Lemaitre-Robertson-Walker model (or some mildly inhomogeneous or mildly anisotropic generalisation of this) says that the universe extends spatially to an extent that is infinite (in two of the three subcases) and is finite (in the other), and our data is only good enough to state that none of these is preferred over the other (but that given the level of non-flatness, the flat case is *theoretically* preferred, as a theoretical, non-observational, bias.)

2) The past light cone is finite-volumed, as it obviously is, pending some revolution in our understanding.

So far as I understand your point, you're stating that the past light cone is finite-volumed. If that's what you're saying, excellent, we're in agreement. The problem is you used the word "space", which I interpret to mean "space", and the spatial extent of the universe is basically untestable except by reference to the density of the universe; if it is at the critical density, then it is flat (and infinite), and if it is at less than the critical density then it is hyperboloidal (and infinite). If it is greater than the critical density, then it is spherical (and finite).

If we're not talking about spatial extent but instead talking about the 4-volume of the past light cone then we agree.

(I might also add that in GR the entire manifold is basically set -- the "future" of an event (mapped out by the future light cone), the "present" which are regions connected by spacelike geodesics, and then the "past" which is mapped out by the past light cone. From this point of view, which is one that GR forces us to (although it may very well be in contradiction of quantum mechanics), we can't tell if the universe is finite or not temporally. We do know that the past light-cone appears to be finite, but we cannot know what the future light-cone is since we do not have backwards-propagating photons to bring us information along them. The future light-cone could be finite, which would imply that the universe recollapses in the future. The likeliehood right now is that the future lightcone is infinite. That would mean that if we're going to generalise what we mean by "infinite" to four dimensions, we still end up with an infinite 4-volume. However, that's ultimately supposition and extrapolation.

(It can also be commented that actually we don't know that the past light cone itself is finite, since the theory cannot be used to propagate the light cone to, let alone beyond, the singularity. This doesn't actually mean that the universe formed at the singularity; it means that our theory cannot be used to propagate light that near to it - or anything else, for that matter. It may very well be that in a quantum theory of cosmology, there is no singularity, and that we have a bouncing universe. In that event, the past light cone is *not* finite and may very well, in fact, be infinite.

(This part of it though is academic in many ways too since as I commented in another post, we can't see back anything like to the singularity anyway. Our only probe is light, and the universe goes inconveniently opaque at the CMB, which is effectively a photo of the universe when it was a bouncing baby of 300,000 years or so. We simply cannot see beyond this, other than indirectly, unless we manage to observe the gravitational wave background or, even less plausibly, the neutrino background.)

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### Complex Life May Be Possible In Only 10% of All Galaxies

So I guess the short answer is no it isn't, but yes it is, and there's a bit more to it than that. In my time on Earth, during which I've studied history and physics and worked professionally at cosmology for quite some years, I've learned that "there's a bit more to it than that" is a valid answer to practically anything anyone has ever said. There are always more depths at which one can examine something...

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### Complex Life May Be Possible In Only 10% of All Galaxies

Thank you for this comment, by the way. I think adding it up I've probably spent quite a lot of time trying to do my best to explain and discuss cosmology on here, so it's nice to know it's appreciated.

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### Complex Life May Be Possible In Only 10% of All Galaxies

On a practical level, yes it is -- the microwave background stands in our way. As the universe expands it cools down (same as if you pump up a tyre both the pump and the tyre get hot, but in reverse) -- which means that tracking it back, in the past it was seriously fucking hot. The universe is also, even at the present day, composed of more or less 75% hydrogen and 25% helium. The ground state of the lowest energy level of helium isn't really very high, while hydrogen's is high but not *that* high. And if you start working it out, it turns out that if you look back to when the universe was very roughly 300,000 years old, you suddenly find a universe that was at the temperature where every single photon was energetic enough to ionise hydrogen (let alone helium). That then immediately implies that any photon would propagate a short distance (and a very short distance - the universe was vastly smaller then than it is now) before it was absorbed by a hydrogen atom which then spat out its electron. That electron would propagate a short distance before it fell into a proton and emitted another photon, which would almost immediately slam into another hydrogen atom, and so on.

That means that the universe was totally opaque. Using light, and we have no other probe right now (though a direct observation of a gravitational wave background would ease this somewhat, as would a brutally unfeasible detection of a cosmic neutrino background), we therefore have a hard limit back at the CMB.

Even if the CMB somehow wasn't there, yes, looking back we run eventually and inevitably into the beginning of the universe. The distinction is born entirely of the theory we're couching cosmology in -- general relativity or, at least, a geometric theory of gravity very similar to general relativity. In these theories the universe is actually described as a whacking great four-dimensional blob which we've sliced for convenience into spatial surfaces along some time direction. (Those choices aren't arbitrary; there are conditions on what you can choose as a time coordinate, and on what you can choose as a spatial coordinate.) It's those spatial surfaces that seem likely to be infinite in extent.

However, since we're working in something like GR we also have the restriction that we can't see outside of our past light cone. Nothing can propagate faster than the speed of light, and in GR that is actually described by the type of paths that things can propagate along, with light propagating along "null" paths, normal matter along "timelike" paths and either nothing or "tachyons" propagating along "spacelike" paths. These paths, intrinsically, *cannot* overlap. A timelike path will never be a null path and cannot cross one to become a spacelike path. That would be geometrically nonsensical. Spacetime is then mapped out by these "null geodesics", and if you map them back into the past you get what's known as a light cone -- formed of all the light that could possibly have reached us. What we can possibly observe has to come from within, or on the boundaries of, that light cone.

Now, that light cone *is* finite, and if we extend it all the way back to the singularity then we'll obviously run into problems. At a singularity everything genuinely dies, and our theory doesn't even begin to work. Even geometry doesn't. All this tells us is that our dynamical theory is missing something (which many - including myself - believe is a quantum theory of gravity that smooths out that singularity, quite possibly by enforcing a maximum density within a minimum volume, or some similar process). If we decide we're not going to wilfully put a load of infinities in our denominators and instead cut out light cone shortly after this singularity -- let's say when the universe was less than a femtosecond old; I'm sure that's young enough to satisfy everyone -- then we can even calculate the 4-volume of that light cone. And it is finite.

I think this might be one of the causes of the confusion on this point.

I'd also like to apologise again if I cam across as a bit curt.

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### Complex Life May Be Possible In Only 10% of All Galaxies

No, I'm talking about the spatial extent of the universe. I'm not sure how you're defining "universe" but it doesn't appear to coincide with the definitions used by cosmologists.

I'm also talking from a position that can be backed up by a large amount of both theory and data. The data cannot show that the universe is infinitely extended, but it very definitely does not say that it *isn't* infinitely extended, and the theory actually favours infinitely extended over finite. You're free to disagree but frankly if you can't disagree backed up by a theoretical model that fits both the background cosmological evolution and, more importantly, both the perturbations on the CMB, the shape of hte matter power spectrum, the *oscillations* on the matter power spectrum, *and* the dimming of distant Type 1a supernovae, then you're on a hiding to nothing. You have to fit this data.

I don't like Lambda CDM. Very few people who've examined the fundamentals of cosmology do. It's wrong. It has to be wrong. It's wrong on principle, and it can be proven to be wrong extremely quickly, to those who have been trained. It goes like this: cosmology is a theory built on averages, but those averages are implicit. No-one has a clear idea of how to take an average in general relativity (or any geometric theory of gravity) and end up with another covariant theory. The averages we do have rely on spacetime being globally hyperbolic. This means that there are no geodesic crossings, and this condition is necessary because every current way of averaging tensor fields, including Zalaletdinov's, little though he'd want to admit it, involves taking your tensor field, casting it along null geodesics to the centre of your averaging domain, taking the average, and then casting it back out again. If we have geodesic crossings, then that process is not one-to-one -- the average is ambiguous and is therefore not covariant. Since cosmology is (implicitly, and ham-fistedly) based on averaging a locally-covariant theory, phrased as a globally-covariant theory, cosmology is dead in the water.

The problem is that Lambda CDM works extraordinarily well. Anything that replaces it *has* to fit all the data that Lambda CDM does, at least as well as Lambda CDM, and with fewer of its problems. And that doesn't exist. There is nothing on the horizon that can do that, and I don't see much hope for something to come up. Cosmologists who do examine the fundamentals are aware of this and are trying to find exactly why LCDM emerges as such an astonishingly successful phenomenology - it may well be a thermodynamic theory, in many ways - while everyone else just gets on with it, knowing that it works. Because it does, amazingly well.

And Robertson-Walker cosmology, and the Lambda CDM cosmology that is based on it, do not agree with the strength of your statement. The current universe may be finite. True. Our past light cone is finite. True. Our future lightcone is finite. Probably not true. The universe has a finite spatial extent. No-one has the slightest clue.

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### Complex Life May Be Possible In Only 10% of All Galaxies

Ah, but here you're falling into one of the common misconceptions about cosmology. The universe isn't expanding *into* anything -- if it were, the universe would have a centre. While observationally we (obviously) can't prove that the universe doesn't have a centre, it's a fundamental principle that if it did we almost certainly aren't in there. This is dubbed the Copernican principle and is one of the key tenets of cosmology. You can build cosmological models that violate the Copernican principle but they all leave you feeling a bit soiled - and even then you end up with cosmologies that typically (but not always) are composed of spatial surfaces of infinite extent.

The key to this is that if we're going to build a model of cosmology we have to employ a theory of gravity. The only serious theories we have are all "metric-based", in that they treat gravity as a geometry theory. (There are very firm reasons for doing so, including the observation that gravity is almost certainly a fictional force, given that it imparts the same acceleration to all objects regardless of mass. To do so implies that either the gravitational and inertial masses must be identical (down to changes of units) or else that the force is fictional, and on the same basis as the likes of centrifugal and Coriolis forces -- very real in the reference frame they're measured in, and zero in a different frame.) In any metric-based theory, if you impose that the universe is isotropic, as it is to a high degree if one observes the microwave background, and then additionally impose that the Earth is not at the exact centre, you're lead basically to Robertson-Walker models. In these models, the universe is composed of a "foliation" of sheets; basically, a lot of three-dimensional surfaces stacked one on the other and filling the whole of the 4-d spacetime. Two of the three RW models are composed of *infinitely extended* spatial slices. Only one of them is composed of finite surfaces. Observation can't tell between them, but there is no more reason to assume we live in a finite universe than an infinite -- and indeed there's a mild hint towards the opposite, in that something so close to flat is most likely flat (and if it isn't could well be open - both are infinitely extended). It's true that this is a theoretical bias, but when observation fails we don't have much to fall back on, and observation leaves the distinct probability that the universe is spatially extended to infinity.

It's all a bit academic, of course, since we can never observe, let alone travel to, that infinite extent - we can only see back within our own light cone and that *is* of finite volume, both spatially and hyperspatially.

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### Complex Life May Be Possible In Only 10% of All Galaxies

Fancy adding a bit of weight to the random abuse? I don't know where Kjella got the idea that as far as we know there's a finite amount of energy around, for one thing. While there may be a finite amount within our horizon, that's a very different thing, since all we need to do is move a few megaparsecs and we've got a slightly different horizon. The statement that there is a finite number of galaxies within our horizon is completely uncontroversial (and indeed obvious, not least since our horizon extends back before the formation of galaxies at all...), while the statement that there is a finite number of galaxies *outside* our horizon is unsubstantiated and unlikely to be substantiated from that starting point.

On the other hand, gameboyhippo's statement that space is not infinite because it is expanding is also very much arguable. In this case we're on firmer ground, since we can look at the models actually employed in cosmology. If we restrict ourselves to the (Friedman-Lemaitre-)Robertson-Walker models, which are far and away the most widely used, then we've got three of them. One of them is formed of a three-dimensional spherical surface (so not a sphere you'd recognise, but the same in 4d), which is evolving. This is a "closed" universe, and in this model, indeed, space is not infinite but is expanding. But there are two other models. One of them, the universe is composed of a foliation of saddle-shapes (in 4d). This is an "open" universe, and here space is infinite and expanding. Or the universe can be composed of flat sheets. This is (unsurprisingly enough) the "flat" universe, and is *also* infinite and expanding.

It can certainly be argued that the data currently prefers a closed universe, but it does so at a statistically meaningless level (it covers both other cases, well within one standard deviation); the data cannot currently tell us anything. At this point theoretical bias comes in and we have to ask ourselves if there's any good reason that the universe would be almost, but not exactly, flat? The answer is sure, we can come up with reasons, but justifying the actual numbers involved is a posterior exercise. Instead, the preference is for the simpler model, flatness, until the data improves.

Do you see why I might have stated that both statements are so arguable that they're close to meaningless? I could have phrased it better, and I apologise for sounding brusque, but I stand by it.

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### Complex Life May Be Possible In Only 10% of All Galaxies

Yeah well I'm not going to go into a protracted lecture on parameter estimation here. The point is that the data is consistent with the universe being flat, and the theoretical bias is towards the universe being flat rather than a tiny bit away from it. These taken together explain why so many cosmologists - myself included - simplify the calculations by making the universe exactly flat. Sure, we might be wrong in doing so, because the theoretical bias is just that, but in most contexts the error is genuinely tiny given just how flat it seems to be.

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### Complex Life May Be Possible In Only 10% of All Galaxies

Dude, I'm a cosmologist, and a general relativist. I'm very well aware of how the universe can be spatially infinite, and have a finite age. Making pithy (and erroneous) statements such as "13.8 billion years ago is not an infinite amount of time. The universe is not infinite" does not change this.

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### Complex Life May Be Possible In Only 10% of All Galaxies

Both statements are so arguable as to be nearly meaningless.

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### Complex Life May Be Possible In Only 10% of All Galaxies

No, it's definitely false. Current data strong favours a universe that is flat (ie infinite), while it only narrowly supports a universe that is open (ie infinite and shaped like a foliation of saddles), and only slightly better favours a universe that is closed (ie finite and shaped like a foliation of spheres.) More carefully speaking, I believe the constraints at the minute are something like \Omega = 1.02 +- 0.03 (at one sigma, or aroudn 67% confidence). Meaning that while it is possible the universe is open or closed our best evidence at the minute is that it is entirely consistent with flat, and that this consistency linked with Occam's razor suggests that we may as well take it as flat.

Meaning that the universe is probably infinite.

These considerations do not take into account the universe's topology, of course. The universe can be flat but finite if it is, for instance, on a torus. It could also be on any number of absurdly-shaped topological structures. This is because cosmology is based on general relativity which is, by definition, a local theory. Topology is, by definition, a global theory, and unless the characteristic length-scale of the topology of the universe happens to be within the characteristic length scale of the universe itself (ie if the "radius" of the torus is roughly of the order of the horizon), we're not realistically going to tell the difference between an infinite, flat universe and a flat, toroidal universe.

Occam's razor can again come into play here and suggest that the universe is, as a result, flat but we should probably begin wondering whether that razor's getting a bit blunt.

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### Statistician Creates Mathematical Model To Predict the Future of Game of Thrones

Actually he did average them. The paper is at http://arxiv.org/abs/1409.5830... and he discusses this issue in section 3.2.

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### LLVM 3.5 Brings C++1y Improvements, Unified 64-bit ARM Backend

"GNU Fortran is widely used even in high-performance computing because the commercial compilers aren't really better at all (and generally more buggy)."

While I've certainly encountered (and notified Intel of) bugs in ifort, and more than I'd expect in something that cost the university a pretty parcel of money, I wouldn't even begin to pretend that gfortran is as good for high-performance computing as ifort. Unless you're triggering an ifort bug, and I haven't hit a genuinely serious one since a weird memory cap back in 2005, or using ifort on some esoteric architecture, you are *never* getting better performance out of gfortran optimised code compared to ifort optimised code. They may be equivalent for a lot of operations, but for others ifort is simply a lot better, particularly when tuned to a particular Intel chipset. I use gfortran a lot and I don't have any serious complaints about its optimisation, but ifort's is better.

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### LLVM 3.5 Brings C++1y Improvements, Unified 64-bit ARM Backend

Actually I still use gcc for gfortran - I can't personally afford to use the commercial license, and I have code I want to maintain and develop in Fortran. But on Windows I develop C++ in either MSVC, due chiefly to the fact I like its debugger better than any other I've worked with, or in Clang, and on Linux I develop C++ in Clang. I'm glad gcc is there but my default these days is certainly Clang.

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### Welcome To Laniakea, Our New Cosmic Home

Thankfully for our aching heads, unless our understanding of the laws of physics is very wrong, probably not. The structure of the universe being fractal in nature doesn't imply that *everything* in reality is fractal -- it implies that gravity will tend to construct fractal structures, when dealing with objects in a large enough number. Down at our level, there's too much competition with other forces, primarily electromagnetic although on some Solar and planetary scale objects such as neutron stars the forces are a bit more exotic in nature, to be purely governed by gravity and so a different framework takes shape. A fundamental interconnectedness of everything is a nice idea, but it would make my head hurt, and isn't justified by our current understanding of physics. (Which, of course, may change - and which also in itself doesn't rule out there being at least some level of self-similarity between systems dominated by electromagnetic forces and systems dominated by gravitational forces, given the similarity in their behaviour.)

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### Welcome To Laniakea, Our New Cosmic Home

You're not the only one to start thinking along these lines. You might be interested in this somewhat random and unrepresentative set of papers:

http://arxiv.org/abs/astro-ph/...

http://arxiv.org/abs/1101.4280

http://arxiv.org/abs/1103.0552

http://arxiv.org/abs/1201.4688

http://arxiv.org/abs/1201.5554

I know very little about this area myself but it seems relatively settled that the fractal dimension of the universe - if such can be defined and has a meaningful interpretation - is between 2.5 and 3.

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### Why the Universe Didn't Become a Black Hole

It would certainly change the stability analysis, yes, but the universe does not have a significant angular momentum. That would leave a characteristic signature on the CMB, a preferred direction, and it's been hunted, with each new and improved dataset, and we still don't have it. The hunt has turned up other interesting anomalies such as the appallingly-named "axis of evil", but those signatures are also (probably) not due to an intrinsic net angular momentum. That doesn't say there isn't one, just that it's not particularly significant and is, as yet, unobservable. (In case you're interested, a universe with a net angular momentum could be described by one of the Bianchi models rather than a (Frieman-Lemaitre-)Robertson-Walker. A simpler case that might interest people is the Goedel universe, notorious because it contains closed timelike loops, which allow for the possibility of time travel. The Goedel universe wouldn't form a realistic model of the universe but it's an interesting spacetime.)

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### Why the Universe Didn't Become a Black Hole

Well, it violates the weak energy condition, although it does satisfy (just) the strong energy condition. The weak energy condition says that density + three times pressure is greater than zero, and that's pretty easy to violate if you've got a scalar field. The strong energy condition says that density + pressure is greater than zero, which is far harder to violate; dark energy is right on the border of it, and a cosmological constant *is* the border (pressure = - density).

Of course, you're totally right - none of this means that they violate conservation of energy. That's built in to the theory...

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### Why the Universe Didn't Become a Black Hole

"What they've proved mathematically as that at the event horizon of a black hole the math fails. It falls apart and no longer makes any sense because the numbers get too large on one side of the equation."

Not so. The maths dies at the singularity at the centre of the hole, but it doesn't at the event horizon except in a badly-chosen coordinate system. Alas, the usual coordinate system we'd present the Schwarzschild solution in is indeed badly-chosen and has an apparent singularity at the horizon, but this is not an actual singularity, as can be seen quickly by calculating a scalar curvature invariant - the Ricci scalar is the immediate choice, it's basically a 4d generalisation of the more-familiar Gaussian curvature - and seeing that it's entirely well-behaved except at the centre of the hole. So we look for a coordinate system well-behaved at the horizon and quickly come across Painleve-Gullstrand coordinates, in which spacetime is locally flat and perfectly behaved at the horizon. The implication is the poor sod wouldn't be able to tell that he'd got to the horizon, except through tidal forces (which depend on the size of the hole), and then he'd struggle to navigate before slamming into a singularity.

Even more confusingly, for a *realistic* hole, the insides are rather different. A Schwarzschild hole has a singularity inevitably in the future - all future-directed paths one can travel on, or light can travel on, end at the singularity. That's a bit of a bummer if you happen to be in a Schwarzschild hole. But a Schwarzschild hole is not physical; it is a non-rotating, uncharged hole, and that's not a realistic setup. In a charged (Reisser-Noerdstrom) or a rotating (Kerr) or, come to that, a charged rotating (Kerr-Newman) hole the singularity is "spacelike" -- there exist paths on which we could, in principle, travel, that avoid the singularity. In the case of a Kerr(-Newman) hole it's even smeared out into the edge of a disc. In reality, good luck navigating in there, but the singularity is not inevitably in the future in there.

A bit closer to the point, you're right that speed doesn't really have anything to do with it. Instead it's the type of path you can travel on, and where *they* go. An event horizon can be defined as the surface on which "null" geodesics, on which light travels, remain equidistant from the hole. If you travel, as massive particles do, on a "timelike" geodesic then you're fucked; you're never going to be able to accelerate enough that you even travel on a null geodesic, let alone a "spacelike" geodesic along which you can basically access anywhere. On a spacelike geodesic you could get out of a hole no problem. You could also travel in time, and you could break causality fifteen times before breakfast. I'd like to travel on a spacelike geodesic - it would be fun. Though managing to get back to a timelike geodesic might be significantly less so.

"Another obvious but often overlooked theory is that our universe IS a black hole inside a larger universe."

That's an extraordinarily strong statement. Our universe might be indistinguishable from a black hole from the outside, yes, but there's a big "might" in there, and an "outside" that doesn't necessarily make much sense either. It all depends on the setup you're assuming. Sure, we could end up finding that the universe is "inside" a black hole for a given definition of "universe", "inside" and "black hole", or we might find that that statement does not make any extent. I wouldn't want to say anything stronger than that, frankly, not least as I'm aware of models of cosmology that are observationally indistinguishable from a standard, infinitely-extended, flat universe, which are also flat, but which have finite extent. One way to do so is to simply put the universe into a toroidal topology. Since GR is a local theory it says nothing about topology, and it would be hard to argue that a universe extended on a torus would look like a black hole from the "outside", since that would be the entire extent of spacetime.