Want to read Slashdot from your mobile device? Point it at m.slashdot.org and keep reading!

 



Forgot your password?
typodupeerror
×
Science

Evidence for a Flat Universe? 334

mattorb writes "The New York Times [free reg.req.] has an interesting article about a recent cosmological experiment whose results rather strongly imply a flat (omega equals 1) universe. Basically, the authors measured the scale of small variations in the cosmic microwave background, which yields strong constraints on allowed cosmologies. The abstract from the preprint (off LANL astro-ph) is here. Caveats: this is a preprint -- meaning that it hasn't been refereed yet. Also, questions are always raised about the precision of such "angular power spectrum" measurements -- who knows if this result will hold up. But it's an interesting thing to talk about."
This discussion has been archived. No new comments can be posted.

Evidence for a Flat Universe?

Comments Filter:
  • by Zurk ( 37028 ) <zurktech AT gmail DOT com> on Saturday November 27, 1999 @08:51AM (#1500452) Journal
    but do we fall off if we sail to the edge ?
  • I have always wondered about this idea. It is an idea that keeps coming up more and more. It is just hard to imagine a FLAT universe...
  • Only if we do a sketch about deceased parrots first.
  • by Signal 11 ( 7608 )
    Gee, so if we eventually build a inter-planetary space ship, we'd better be on the lookout not to fall off the end of the universe... *snicker*

    The concept of a "flat earth" was discredited shortly after the Roman empire fell. Besides, wouldn't this completely invalidate the big bang theory? I mean, if something explodes, it does so spherically(sp?) - not like a flat disk. Perhaps I'm missing something here... that just seems to stupid to have come from any sane scientist.


    --
  • minor correction - I should have hit preview first...(sigh)... people still thought the world was flat when columbus discovered america... my appologies to the history buffs...
    --
  • There went my plans send MicroSoft to the other side of the universe quickly by going through the middle... now we'll have to wait a little longer. Ak. Awefull! Or maybe -- just maybe -- they'll fall off the edge :)

    Also takes out some good sci-fi plots, unfortunately.

    --

  • Okay, suffice it to say, my brain isn't at all suited for this type of information, so feel more than free to correct all the mistakes I'm about to make.

    Also, be patient, I'm still trying to soak up the article...

    Okay, wasn't it the Third Law of Thermodynamics that stated that eventually all motion would slow to a stop, and (at least in my interpretation) all systems would eventually just, spin down? Isn't this "cosmological constant" in complete opposition to that theory? It seems to me, and always has seemed to me, that things slow down, each orbiting object crashes into the object it's orbiting, ie: moon crashes into earth, earth crashes into sun, sun crashes into whatever it's orbiting, etc, until everything was back at one point in the universe, until we had another big bang...

    Given that (probably fscked up) derivation on a principle, how does this work if we're constantly moving further away from the object we came from? Does this mean that if everything does end back up all in one place that it will be different place? Or that we will not ever be pulled back into one place?

    Help?

  • This to me has seemed to be the most elegant and probable value of the Omega constant.

    If this is valid, then it raises the question, Which iteration of Big Bang -> Big Crunch are we in? Or are there infinite iterations? It raises many intriguing twists in the physics of time and space. This fits nicely with the previous /. article on manyfold universe theory. [slashdot.org]

    -----------------
  • by Wah ( 30840 ) on Saturday November 27, 1999 @09:07AM (#1500462) Homepage Journal
    flat in this sense just means not curved. It has nothing to do with edges. It just means that two straight lines parallel to each other with NEVER intersect, extended throughout time and space. Basically the Universe isn't in a snow-globe, it just is.
  • Um... no... the truth is, scientists and philosophers had known the earth was round since the times of the ancient greeks. Probably first discovered by Thales of Miletus, who lived around 600 BC. Eratosthenes, who lived around 200 BC, even made a rather accurate measurement of the circumference of the Earth. The only ones who preach that Columbus discovered the earth was round are those who like to think of him as a saint that could do no wrong.
  • well actually the big bang theory was descredited about 5 years ago. The doppler effect theory it was based on was proved to be uncontinuous across the stars that were "moving". Instead there is a group of physicists, including Stephen Hawkins, that are basing the origin of our universe on sound waves, and they figure they will have a complete theory in another 15 years on our true cosmology!

  • Do some research. Not that difficult..
  • Saying "the evidence doesn't support our theory, therefore the evidence is wrong" is what scientists get frustrated by non-scientists doing. We can measure (apparently) the thickness of the universe- if that doesn't jive with the big bang theory, then the big bang theory needs to be adjusted to take into account the evidence, NOT (and NEVER EVER EVER) the other way around.

    Remember also that the Big Bang theory is somewhat more speculative than many other theories we work with. It's like doing an eight-term Taylor series for a function around 0, and then evaluating it at -8,000,000,000: better than nothing, but you'd have to be crazy to expect it to be exactly right.
  • What this means is that the universe is going to expand forever, so there is no big crunch, there is no "Omega Point", and there is no God.

    Of course, you have to believe in Frank Tipler [amazon.com] first to draw that conclusion.
  • Did I say that the data was wrong?
    --
  • Not actually flat. It means that the Omega Constant is 1, and the universe will slow it's expansion but never come to a halt.
  • Not actually flat. It means that the Omega Constant is 1, and the universe will slow it's expansion but never come to a halt.
  • rubber sheet theory may be correct.

    It's more like a 3-d dimensional rubber goo theory. All this data shows is that parellel lines won't intersect, EVER.


  • Gotcha! I understand the whole point now....But doesn't there have to be an end somewhere? Or, is there no such thing as nothing...How can there be nothing..
  • Thanks. =) I really despise /. posting NYT stories - I can't access them because I'm behind a firewall and NYT never lets me in. Well, basically they're saying that the universe is defined on a 3d plane. Okay, well... I don't have the background to disagree with them, so I won't.
    --
  • Not really, the universe will continue expanding infinitely and eventually everything will cool and become a dark, endless void.

    Not too happy a scenario :)
  • Sounded that way to me.

    "... I mean, if something explodes, it does so spherically(sp?) - not like a flat disk. Perhaps I'm missing something here... that just seems to stupid to have come from any sane scientist."

    Which sounds to me like, "The Big Bang theory obviously means that we should ignore more direct evidence."

    Perhaps I'm misunderstanding what you're saying? I think I must be, considering your response...
  • But the question remains...Is there such thing as nothing? Or IS there an end? DOes it just keep going?
  • Reading the short blurb in the NYT article about inflation intrigued me greatly because it seemed to imply that we now consider the universe to have a defined state before the Big Bang. The implications of this are quite interesting - if one considers the Big Bang to be the beginning of the universe in an absolute sense, with nothing at all before it to explain, one can in a sense simply ignore what brought the Big Bang into being - the very question seems to be undefined. By describing the Big Bang as being initiated by stretching of space caused by interactions of (I assume because of the mention of grand unified theories) super strings, this article caused me to wonder about what that pre-universe world was like, and what its origin was. Can these super strings have always existed, hanging in space, unexplained and unexplainable? This is also sort of related to the notion of space as a bounded entity - in a flat universe, wouldn't that imply that you could leave space? (albeit possibly only if you're massless) Can anyone with a much better knowledge of advanced theoretical physics shed some light on these issues for me, or at least provide further food for thought?
  • The universe had a beginning, the big bang. But if Omega does = 1 then it will have no end, and there can be no nothing.(hrmm)

    There has never been nothing in the universe, before the big bang, there was the superparticle which existed in some exotic space. We can't really know what was in that space because we have no way of observing it.

    If there was anything else, it means that there must be many universes, or other dimensions. No one really knows what existed prior to the big bang. We have to know that to say conclusively if there is a nothing before the universe or outside the universe.

    Oh wait, there is a nothing...rent the Neverending Story... :)

    The answer is 42!
  • I just have a hard time swallowing the big bang
  • then why are there such large redshifts?
  • by meni ( 2409 )
    If it is flat, doesn't it mean the universe is two-dimensional?
  • by QuMa ( 19440 ) on Saturday November 27, 1999 @09:38AM (#1500485)
    I think we al would have a hard time doing that, just think about how hot it is!
  • by Wah ( 30840 )
    eventually enough black holes get together and reverse the trend (think sine wave [strath.ac.uk]) and everything starts to come back together. Eventually everything compresses back into the size of that grapefruit of yore and we bang again (notice the "eventually"s, this takes a long time). I think the "dark(anti?) matter" is part of the equation, and there are probably other parts we don't have a grasp on yet, but a continuing pattern of death and rebirth seems to fit with pretty much everything else in the universe.

    I don't see this NYT article as discrediting my theory, we merely haven't crested the hill yet and it looks like it goes up forever from our limited perspective.

    my $.02(US) (doing very well vs. the Euro BTW)

  • I could see how that would work...but we can never "see" nothing, because if we per se, walked into "nothing" it would be "something" So from our view there isn't nothing.
  • Might burn my tongue :)
  • A flat universe is by definition not a closed universe. This research indicates that the universe is flat and not going to come back together as you suggest. Of course, given that the abstract itself only states "...(W)e find that the overall fractional energy density of the universe, Omega, is constrained to be 0.85 Omega 1.25 at the 68% confidence level." It seems whether the universe is open or closed is not really determined. The research only determined that the universe is "closer" to be closed than our observations currently indicate.
  • by Wah ( 30840 ) on Saturday November 27, 1999 @09:46AM (#1500491) Homepage Journal
    they said that the constant is very close to 1, I didn't read anybody saying, "All our data show us that the answer is EXACTLY 1." Anything that is the slightest bit off 1 in either direction will eventually unbalance the whole thing (think chaos theory). I take this data to mean that the universe isn't "in" anything, it just is. There are no external forces actuing upon it.
  • So if you are walking, and you reach that point, would it be like hitting a glass window? And you just can't go any farther?
  • ...take this discussion HERE [slashdot.org]!!!.

  • Here's a link to a Caltech Research group that is working with the UMass scientist who sent in the abstract to the xxx.lanl.gov site. This is the research group run by the phys prof I had last year for freshmen physics, all the work he does is on the Cosmic Microwave Backround Radiation (CMB). He showed us some very cool pictures that a BOOMERANG satellite had taken of the CMB. Consequently, this Slashdot article refers to information gleaned from another BOOMERANG run. More information than I can understand about this is here:
    http://astro.caltech.edu/~lgg/boom/boo m.html [caltech.edu]

  • parallel lines do intersect according to the general theory of relativity. Where there's a mass, the universe curves, thus parallel lines can intersect (as in double stars that are in fact a single star with a huge mass between it and the earth). Maybe what they mean is "do not intersect" where there's no mass...
  • I see the err in my ways, the veil of stupidity (liberalism) has been lifted from me and I repent for my evil sins.

    For I am not only Liberal, but atheist and Canadian! good god!

    Chalk this AC up as (Score:2) Funny ass Nectarine.
  • Two words for you AC: The Crusades.
    Any time we dehumanize other people, something like the Crusades is bound to happen

    --
    Harvey, who probably just fell for a joke
  • by Anonymous Coward
    The best way to think about a flat universe expanding is to do a little bit of geometry. Measure all the coordinates with respect to yourself at the origin. Then have all the coordinates increase with time by being multiplied by a time-varying factor a(t). Then dr/dt (the velocity at which a galaxy moves away from you) is r times da/dt, which we call the Hubble constant. If you transform coordinates to another origin, the universe looks the same to the guy there too. Galaxies move away from him at the rate r * da/dt as well. It is true that far away from you the galaxies are receding faster than c, but those galaxies are "causally disconnected" from the observer. This means they cannot interact with the observer in any way. Such things are not of physical interest. As for the "What does the universe expand into" difficulty, keep in mind that the Universe, by definition, has no outside. Also, we should keep in mind that the laws of physics need not conform to "common sense", which is formed through a rather limited range of physical experience.
  • If you truly believe in what you have written, then why are you an anonymous coward?
  • by Wah ( 30840 )
    no, I think this says, "By the time you could see the horizon a new one will exist beyond it."

    You can't get outside the Universe. Doing so causes a core dump.

  • by BaronCarlos ( 34713 ) <slashdotNO@SPAMgeekbrigade.com> on Saturday November 27, 1999 @09:57AM (#1500505)
    This is old news to the Astronomy Community.
    Until recently, the Universe was thought as closed (or that it will slow and contract back as Energy dictates).
    Recently, with deep space observations with a larger array of data to work with, Astronomers have calculated that the Universe it Open (under constant accelleration and would not slow down). This baffled much of the scientific community for awhile and soon lots of theories about a variable speed of light arose. (I think this appeared in the December 1998 issue of Scientific American [sciam.com], a summary of the Special Report exists here [sciam.com].)
    This latest observation, though as limited as it is, makes some sense that it is a balancing compromise between two seperate observations/beliefs.
    I can't say which is true, or which is false, just that it fits with everything else that has been said.
    *Carlos: Exit Stage Right*

    "Geeks, Where would you be without them?"

  • Thats kinda neat, Then I can make my own plot on the universe, and name it for myself :)
  • I am always suspicious when scientists take elegance into account in their analysis of data. It doesn't bother me as long as they don't allow it to turn into bad science, though, which I doubt it does.
  • I'm going to try to make an analogy here without having too great an understanding of the issue myself, so forgive me if I'm astoundingly stupid here.

    Consider the case of a two dimensional universe. Imagine it as a piece of graph paper, with parallel lines on both axes. At the edges in an open universe, the paper would stretch out, and the formerly parallel lines would splay out like a fan. The angle between them would increase. In a closed universe, the paper would scrunch together at the edge, and the angle between the parallel lines would decrease - they would eventually meet. In a flat universe, the universe would remain a perfectly undistorted plane, and the lines would stay parallel forever.

    The problem is that to understand the two dimensional universe cause we had to make use of three dimensions; hence understanding the three dimensional case will make use of four. (This is where I start guessing I'm afraid; feel free to correct me) We can imagine the effects despite not being able to imagine four dimensions. Imagine the four square wooden legs of a table. (Leave the tabletop off) Now extend them infinitely up and down. In an open universe, after following them for a very long time distortion would start to be evident - after a VERY long time the legs would become huge and splayed out upwards, curved like the tops of cathedral columns. All three dimensions are stretching, not just the two as before, so the legs would seem to get bigger and bigger and more and more splayed outward. By contrast, in a closed three dimensional universe, the legs would start to bend closer and closer together and shrink imperceptably until after a very long time they shrank to a point. In a flat universe, of course, none of this silliness occurs and the legs stay normal legs forever.

    Of course I could be - and probably am - totally on crack. If nothing else, however, I've at least given you an interesting visual. =)
  • You can experience this for yourself at a good Indian restaurant; order the "Hot" curry.
  • by Wah ( 30840 ) on Saturday November 27, 1999 @10:04AM (#1500512) Homepage Journal
    My guess is that the Universe could be classified as all three, at different times. I seriously doubt, however, that we will be able to make measurements far apart enough in time (since we live so pitifully short, relatively) to gain an accurate measure (think maxum? (vs quantum) mechanics).

  • by rde ( 17364 ) on Saturday November 27, 1999 @10:12AM (#1500517)
    I've read a few posts that seemed to imply that the big bang resulted in a big explosion, and that this somehow sent matter flying out in different directions. This is not the case.
    The big bang, rather than an explosion, was an expansion of space; every second, the distance between two points increases. The red shift noted by Hubble was not due to galaxies moving apart within space, but due to the space between galaxies increasing.
    The balloon analogy much beloved of popularisers is quite accurate in many ways; you just have to imagine that the ballon is the universe, and that there is no outside the balloon. Of course, that's not to say there aren't lots of other balloons; inflation theory suggests there are. But they're nothing to do with our universe.

    One thing that amazed me about this piece was the precision that the scientists were capable of; the background ripples have a difference with the normal background of less than one part in ten thousand; it took the COBE satellite to detect them in the first place, and to have them detectable from inside the atmosphere was truly a monumental feat.
  • ..that you would say that on the same day I discovered this [slashdot.org]. Coincidence? I think not (but then again as part of the Matrix, I can't think "about" it in any rational sense.)

  • are you the same guy who keeps getting hot grits poured down his trousers? You just outed yourself as a prankster.

    Have a nice day, meept!!
  • Actually parallel lines intersect at infinity. Imagine how cluttered infinity must be then with all those lines meeting there.
  • by Wah ( 30840 )
    so does God (roughly, and in different tenses).

  • Thank goodness for that. If the universe had come out closed then the IRS would eventually have introduced a "no time limit" law on the grounds that anyone that escaped would eventually have to come back.
  • get a login so I can recognize you. Surely as a good Christian you realize the value of knowing the source of Information or Argument.
  • by Woodlark ( 3628 ) on Saturday November 27, 1999 @10:35AM (#1500535)

    People, they are not saying the universe is flat in 3D, but 4D. We know by scientific observation that the Universe is not flat in three dimensions. Witness stars being in every direction of the sky. The Milky Way just tells us our galaxy is a relatively flat, spiral one.

    When scientists talk about a flat, spherical, or saddle-shaped universe, they are talking about space-time, a four dimensional construct. Most scientists believe the universe is closed in three dimensions, (meaning no edge to sail off of, even if we could sail faster than the edge expands, a totally different matter), but whether it is closed or open in four dimensions is another matter altogether.

    I hope that cleared things up.

    Droit devant soi on ne peut pas aller bien loin...

  • ..you don't have access to guns do you? hmm, christian fundamentalist, uh-oh.

    When people start to attribute their actions to outside forces things get scary. You do make a good joke though. :-)

  • by jpgrimes ( 15330 ) on Saturday November 27, 1999 @10:54AM (#1500545) Homepage
    First lets make sure everyone understands what they mean by a flat universe. This has nothing to do with the geometry of the universe. This we know to be small (i.e. curvature has to be on a very large scale) but this is talking about the expansion of the universe. As some people have already said this means that the universe will not grow forever or collapse. It will asymptotically approach some limit. But like I said this says ntohing about the geometry of the universe. We don't know what kind of "surface" the universe is on. Maybe the universe is on some N dimensional sphere or box, we just don't know.

    As to boomarang these results are nothing special. What could be special would the results from there Antarctica flight last winter (summer there). That result should be the best result at the time they publish. Off course a satelitte I worked on (MAP) will blow it away but it has some unfair advantages and it will be later (2002 for results I think).

    Theorists want a flat universe for the simple reason that inflationary theory more or less requires it. We don;t really know how to easily understand this problem in a non flat universe. Pure and simply the math is much more elegant in a flat universe (ask Alan Guth or Andrew Linde).

    As with all these experiments getting results, understanding your systematics and backgrounds are extremely difficult. Most importantly going from data to understanding the fundamental parameters requires some assumptions and is not as clear cut as anyone would like. However, having said that, I thnk they are on the right track here. In the near future new experiments like MAP and surveys like the Sloan All Sky Survey will bring a lot fo this together. We will understand this a lot better in 4 years I promise :)

    PS I'm currently an astronomer at Harvard but was a grad student at U of Chicago 6 months ago (where a lot of this work is getting done)

    PPS Hopefully I din't make any glaring mistakes

    PPPS There are no implications for god or theology in all this mess (whatever you believed before you should still believe, well except maybe creation but even that you could argue maybe)
  • ACtually as an astronomer I somewhat want to disagree with that. In general in astronomy this is true but not in cosmology. It moves too fast, you can't wait the 9 months for an ApJ publication or you'll be too late. Hoever, its true that all preprints are not final so things can change.
  • by newfmike ( 12047 ) on Saturday November 27, 1999 @11:24AM (#1500555)
    Seeing as I'm in astrophysics and finishing my master's thesis in a closely related field (dark matter), I thought I should reply.

    The preprint is about fitting new observational cosmic microwave backround radiation data from BOOMERANG (basically a telescope mounted in an airplane) to the existing cosmological models.

    These models are derived from some basic assumptions about the universe (homogeneous and looks the same from all directions) and Einstein's euqations. The models predict a non-static universe that can be flat, open or closed. i.e. the large-scale curvature of _space itself_.

    Since the amount of space curvature is directly related to the mass in the universe _and_ thus the amount of "gravatation", the type of universe is dictated by the amount of matter present in the universe. a flat universe means that there exixts a mass density high enough to slow the expansion of the universe until it stops at infinite time. This critical mass density is normalized to one and called OMEGA.

    an open universe has "negative" curvature, and will continue to expand forever. The universe does not have enough mass/gravity to slow the expansion to a stop. A closed universe has positive curvature and will slow to a stop, and collapse in some finite time. Maybe to a big crunch. As to where the universe expands to, and if there will be endless big bangs/crunches, people can only guess. Physics tends to break down in those areas.

    The data in question (CMBR flucuations) has a direct relation to the amount of matter, and the "lumpiness" of the matter at a very early time in the universe's history. The free parameters in the accepted cosmological models are then varied (think fitting a striaght line to data points) until the data has a "maximum liklihood" of having these parameters.

    One of these parameters, OMEGA, is confined to be between 0.85 and 1.25. So, there is a high chance that the universe is flat.

    Unfortunately, other obervational evidence (galaxy dynamics) says that the amount of mass in the universe mesured so far has OMEGA = 0.35. OOPS! What about the other 0.65 for OMEGA = 1?

    But, not to fear, this is where the cosmological constant comes in. It boils down to an added cosmological "force" that causes extra curvature (mass->gravity->curvature->state of universe) and thus can make the universe flat by boosting OMEGA to 1. Where it comes from, I don't know and don't want to hazard a guess. But the equations contain it!

    As a little bit of extra correctness, the fitted models state the part of OMEGA due to mass is about 0.5, which is close to what the galaxy dynamical evidence states. Yay!

    OK. back to writing my thesis.
  • ... Balloon Observations Of Millimetric Extragalactic Radiation ANd Geophysics!!

    This can't help but catch on with the kids...
  • by Woodlark ( 3628 ) on Saturday November 27, 1999 @11:45AM (#1500563)
    All this comes from either PBS' site for the Stephen Hawking series [pbs.org] they ran in '96, I believe, or Stephen Hawking's homepage [cam.ac.uk].

    Anyway, here's a bunch of links within there:

    Friedmann Universes [pbs.org]: The three basic models of the universe that start off just after the big bang singularity.

    No-Boundary Universe [pbs.org]: Stephen Hawking's pet theory until at least '96. I don't know where he stands on it now.

    An explanation of Space-Time [pbs.org]: What this NYT article is saying is flat. Hmm... it's not that good.

    Stephen Hawking and Roger Penrose debated on the nature of Space-Time [cam.ac.uk] in '95.

    Does that help?

    Droit devant soi on ne peut pas aller bien loin...

  • by ralphclark ( 11346 ) on Saturday November 27, 1999 @11:51AM (#1500565) Journal
    That statement doesn't make sense because we are not talking about space being flat, we are talking about spacetime being flat. In fact the geometry of spacetime itself dictates how the universe evolves over time. In a nutshell:

    A "closed" universe is one which has omega>1; the average density is sufficient for gravity eventually to halt the expansion and thus the universe recollapses down to a final "big crunch".

    An "open" universe is one which has omegapredict omega=1, gained popularity. In such a universe the energy of expansion and the universe's internal gravitational attraction are exactly balanced. The expansion of the universe continues forever but slows asymptotically, almost but never quite reaching zero.

    Our ultimate fate in a flat universe is dictated by entropy. Eventually all the energy will be evenly spread out as heat, and without energy gradients no processes which require the conversion of energy can occur (such as life, or indeed any sort of process which can perform computation).

    Fortunately, it's been calculated that as the universe cools, the energy requirement for computation decreases. In theory, an infinite amount of computation can be performed. Therefore, artificial intelligences simulated in an appropriate computer can still experience a subjectively infinite life span.

    Consciousness is not what it thinks it is
    Thought exists only as an abstraction
  • by / ( 33804 )
    The universe is flat, eh? Maybe it should talk to these people [plasticsurgery.org].
  • Not really, the universe will continue expanding infinitely and eventually everything will cool and become a dark, endless void.


    Wronggg! That's Omega1. In a flat universe the expansion slows asymptotically, so it has a maximum size that it never quite reaches. Thus, cooling also slows; the universe as a whole can only cool as it expands, so if there is a maximum size then there is also a minimum temperature. However, entropy does increase so the local temperature differences get all smoothed out. When there are no more energy gradients, you can't do any work.

    Consciousness is not what it thinks it is
    Thought exists only as an abstraction
  • In general I'd agree with you, but my impression (I don't know the authors involved, so please correct me if you know I'm wrong) was that this particular paper had gone through nothing more than the informal sort of "hey, do you see anything wrong with this" sort of critique among friends. (I'm basing this largely on the fact that a) one usually posts something like "accepted to ApJ" in the "comments" field if it's actually been accepted, and b) I'd never heard of this until a few days ago.)

  • ACs to the right of me,
    ACs to the left of me..

    (puns intended)
  • First, congrats on an informative post. I had no idea how confused people would be about the "flat universe" bit -- you're quite right, that just means that the universe is precisely at the boundary between "open" and "closed," meaning it will never collapse back on itself. This is what I get for not reading here for a whole day. :-) Although I would clarify that there is a difference between simply an "open" universe (one that never collapses, with say Omega of 0.2), and a "flat" (Omega = 1) universe -- if you like, you can think of an Omega =1 Universe as being the case where, if you added one more proton, the universe would collapse eventually, and if you subtracted one more proton the universe would expand indefinitely. There are other differences, but those are more complicated.

    BUT I strongly disagree with your comment that this was "old news." Nothing is ever old news, until it has been proven and re-proven and proven again. Period. Yes, there has been ample evidence that there is not enough matter to close the universe (ie, Omega_matter is not equal to one). There have even been articles published to the effect of "cosmology is solved" -- by something to the effect of Omega_baryonic = 0.1, Omega_non-b = 0.2, Omega_lambda =0.7, where the last term is an "equivalent density" arising from the cosmological constant term. I don't buy this (and I think a lot of other people don't buy it, either) because there are an awful lot of unanswered questions -- vacuum energy, fine, but show it to me. ("Demonstrations" of the Cassimir effect have failed to convince me so far, but maybe I'm being thick-headed.) And as I understand it (caveat: I'm no inflation expert), inflation predicts topological defects in the universe that have yet to be found (so far, anyway). It may be that we have the right picture -- then again, maybe not. Inflation's a damn good theory, but every piece of supporting evidence is still, at this point, a big deal (IMHO).

    Enough ranting. My point is just that this was really a beautiful experiment, with a reasonably significant result. That's all.

  • by ralphclark ( 11346 ) on Saturday November 27, 1999 @01:40PM (#1500595) Journal
    Stephen Hawking's view is that there is no "Before the big bang". It's a meaningless concept; exactly like saying "Further North than the North Pole". That is, 4-dimensional spacetime is tightly curved near the singularity.

    Likewise, there is no "outside the universe". Imagine being an ant trapped inside a sealed jar. You could walk around the inner surface of the glass forever, perhaps often inadvertently returning to your starting point, but there is no edge or opening you can reach which leads to the outside. If the jar has a hole, that's almost analogous to a wormhole leading outside of our universe - but it's not good to push an analogy too far ;o)

    I'm not too keen on the superparticle idea. It's not really in favour any more, it was only mooted because no-one really had any better ideas.

    The inflation theories which also predicted this "flat" result are compatible with a wide range of starting conditions.

    One idea is that our universe is a so-called "baby" universe which has budded off another, older region of spacetime when some small domain in that original continuum underwent inflation. But this is ontologically unsatisfying because all it does is postpone the question. Where did the "parent" universe come from? Back to square one.

    Well, either it always existed, or it too was a baby of some other preceding parent, and so on and so on, perhaps infinitely far back into the past. Perhaps there was no beginning, there has always been a universe endlessly spawning children.

    But I did hear one speculation as part of a lecture about inflation, and this one is really cool:

    "Before" there was just this timeless, dimensionless void. Not like spacetime, which has both dimension and duration. And not really "before": in the sense that this nothing could be said to have any existence at all, it "always" exists.

    Anyway; in this void there was a quantum fluctuation. A fluctuation in what? Consider that in a void without time or space there can be no mass or energy and basically no physics at all of any kind. But there is an obscure branch of quantum theory which claims that quantum probability is the most fundamental aspect of reality, more closely related to abstract mathematics and information theory than anything crudely physical.

    So: there was an infinitesimally small but still finite probability that anything could exist. To say that something can happen in such a realm is to be certain that it does happen. In the sense that anything could be said to "happen" at all. I imagine that events which are more likely happen more frequently then less likely events.

    There was finite probability that a blob of matter/energy could exist, and so it did exist. And in springing into existence, it generated time and space before it because matter/energy needs something to exist in. Since the spacetime was created on demand from nothing, so to speak, the blob would initially have (near)zero dimension and thus (near) infinite density and temperature. It thus expands rapidly, cooling as it goes...and the universe is born.

    Some short time later a critical temperature is reached, a phase transition takes place and the new universe inflates rapidly creating much, much more matter as it goes. The initial seed that popped into existence doesn't have to be very big at all; virtually all of the present mass of the universe was supposedly created during inflation, according to the theory.

    An inevitable consequence of the theory is that what can happen once can happen an infinite number of times. There would be an infinite number of alternative universes created out of the void in a similar way, but they need have no connection of any kind to this one or to each other.

    What is most interesting of all is that when you examine the concept of the original void, you find that what you are looking at doesn't have any "real" existence at all, it is merely an abstract mathematical space of pure probability. In fact, it is the space of all possible universal wave functions and our universe is the instantiation of one of these.

    The universes that spring from it are all merely possible universes. None are real in any universally objective sense because there is no external platform from which a universally objective measurement can be made. Our universe only exists from the point of view of its inhabitants. Or, to put it another way, to talk of "instantiation" of any universal wave function is meaningless. The wave function is simply a potential for existence, and all possible wave functions are equally valid. Within the context of the void, "exists" is indistinguishable from "could exist". All universes that could exist therefore do exist, within their own frame of reference.

    To make such statements is all meaningless philosophical speculation of course. You simply can't describe the nature of existence and reality in conventional human terms. It only make sense when you look at it from a quantum theory standpoint.

    Pah. Sorry, I could go on like this all night and get nowhere. Time to press the "submit" button...

    Consciousness is not what it thinks it is
    Thought exists only as an abstraction
  • Wait a second...I saw the title of the article and thought that they were saying the universe was not /hyperbolic/ or /convex/ but /flat/.

    Aren't they using the wrong terminology if they are trying to say that it is neither expanding nor contracting? As far as I know, the /topology/ (hyperbolic, flat, convex) is an entirely separate topic than the expansion rate (expanding, contracting, neither).

    Just to verify, last time I checked, the consensus was that the universe's topology is hyperbolic.
  • "Therefore, artificial intelligences simulated in an appropriate computer can still experience a subjectively infinite life span."

    Enter Omega Point theory, by which a super-intelligence is created during the contraction of the universe, in which we can all live an infinite amount of simulated lives. Sounds a bit hokey to me though.
  • I know what you're referring to, but this isn't what I meant.

    In Tipler's theory (which mainly focuses on our fate in a closed universe) we utilise the infinite energy density of the near-big-crunch to perform an infinite number of computational steps on a massively parallel computer whose computational states are stored as energy levels in each point in spacetime. There are a lot of rather speculative assumptions which would have to be correct before this can work (and Tipler's main justification seems to be "because it has to be so").

    But computation in the flat universe scenario I was referring to only requires that the energy requirement of computation decreases faster than the ambient temperature (and it ought to; this is based on some fairly solid physics).

    Although the amount of available energy is limited and dimishing as a flat universe approaches equilibrium, the universe still has an infinite time in which to process information assuming that there is still a small supply of energy.

    The computation would proceed very very slowly after a while, but over an infinite period of time, an infinite number of steps can be performed. Emulated beings running on this computer would not notice the slowness of their consciousness with respect to the passage of absolute time, since their "clock" would run at the same rate as the computation.

    Consciousness is not what it thinks it is
    Thought exists only as an abstraction
  • That explanation was pretty close but was slightly incorrect on some important points (I'm finishing my PhD in Astronomy, so have a least _some_ room to speak).

    A flat universe (Omega_total = 1) simply describes the geometry of spacetime -- it is flat (i.e. parallel lines do not converge, triangles have 180 degrees). It says absolutely nothing about whether the universe will expand forever or eventually collapse. These bad assumptions are the result of years of astronomy classes that nay-sayed Einstein's Cosmological Constant (his " greatest blunder"). In those days, Omega_total, which equals Omega_cosmo_const + Omega_matter, was thought to equal just Omega_matter -- since Omega_cosmo_const was obviously 0. In that case, if Omega_matter = 1 then you get a universe balanced on the brink between eternal expansion and collapse.

    But in the past couple years, numerous groups (the most famous using Type IA supernovae) have shown evidence that Omega_cosmo_const seems to be about 0.65 or so. Add that to the measurements of Omega_matter of about 0.35 and you get Omega_total = 1. The BOOMERANG measurements are simply an independent measurement of this, but this time using the cosmic microwave background -- a very important measurement.

    If there is a cosmological constant, but Omega_total = 1, than the universe is flat, but the relative proportions of the two determine whether we get eternal expansion or not.

    With current measurements, it looks like we have an open (eternally expanding) and flat universe. This saves (barely) Inflation, and solves a bunch of other Astro problems. Although now we have another big question: If this is real, Where in the hell does the Cosmological Constant come from?

  • How about: It's Space-Time. You run off the end of space, there's no time there.
  • Yep. Then you see a door marked "EXIT", God talks to you for a while, and you take a bow and leave.
    The credits roll, and you are horrified to see that you were played by Jim Carrey.
    --
  • okay. I don't know if you're just REALLY good at trolling, or clueless about what a "sig line" is. A sig line has nothing to do with the rest of the post, and is often a quote from something.
    In this case, it's a quote from Jack Handey's "Deep Thoughts".
    Deep Thoughts are humor. Most of them take some completely ordinary statement and twist it to make no sense whatsoever.
    They are not political statements. You were obviously just looking for some trigger to start your religious rant.

    BTW, your logic is great. It boils down to "My sense of morals is right because any other one is wrong according to my sense of morals, and if you don't agree it's because you're stupid."
    --
  • Your post gives me an opportunity to ask a question that bothers me:

    With all the universe present (latent?) at the initial singularity, why didn't it just remain the Mother of all Black Holes ?

    I know that BHs can radiate away their mass, but I'm not aware that they do it catastropically. (Hmmm... maybe the Big Bang was actually a Big Dribble ? Could that solve some of the problems that the inflationary models have been trying to addresss? [If so, remember that you heard it on /. first!])

    Please give a rigorous answer, support your claims of fact, and prove your claims of inference. But keep it all simple enough for a 3rd grader to absorb. Thanx.

    --
    It's October 6th. Where's W2K? Over the horizon again, eh?
  • > Stephen Hawking's view is that there is no "Before the big bang". It's a meaningless concept; exactly like saying "Further North than the North Pole". That is, 4-dimensional spacetime is tightly curved near the singularity.

    I think we can safely assume that Stevie knows substantially more about it than I do, but it's still a bothersome question to those of us who are scientifically litterate and want to know: Where did it all come from?

    When you say that it's not fair to ask about "before", the answer may be mathematically corrrect, but it isn't really any more satisfying than attributing it all to some randomly selected tribal diety.

    --
    It's October 6th. Where's W2K? Over the horizon again, eh?
  • As an outsider, I observe inflationary hypotheses with a very different kind of interest:

    The big bang was a very elegant theory, but after some outstanding early successes we started seeing problems mapping it to observations, so someone influenced inflation as an epicycle to (pardon the pun) smooth out the fit between theory and data. But as far as I can tell, the original inflationary proposal wouldn't quite do the trick, and since then we've been barraged with an ever-accelerating cycle (pardon the pun!) of revised inflationary hypotheses.

    Clearly, I'm not qualified to evaluate any of this per se, but as an outsider I think to detect all the usual symptoms of a theory that's in trouble. Therefore (and for no other reason) I suspect that the next 10-50 years will see the Big Bang thrown out, or at least transformed beyond recognition, as one of Kuhn's paradigm shifts is played out. (What the new theory will be, I do not claim to know -- after all, I'm not a complete wacko.)

    Remember, you heard it first on /. (unless, of course, you've already heard it elsewhere).

    --
    It's October 6th. Where's W2K? Over the horizon again, eh?
  • You're right in that a repulsive "cosmological constant" force greater than gravitational attraction - if lambda does indeed have such a value - would force the universe open.

    IIRC the term "flat" was used to describe a universe with a time evolution that was neither open nor closed. You seem to be implying that the term "flat" actually refers to spatial geometry rather than spacetime geometry, and that the correlation of this word with such neither-open-nor-closed universes only applies if lambda=0.

    If so, then what is the recommended terminology for a universe of indeterminate lambda which is neither open nor closed?

    Where in the hell does the Cosmological Constant come from?

    I think I read somewhere that it's the pressure created by the energy of the vacuum; sounds like those virtual particles are forcing space apart in a manner not too unlike the original primordial seed.

    Consciousness is not what it thinks it is
    Thought exists only as an abstraction
  • I understand your frustration but it's only because you don't get it. You are assuming, incorrectly, that there is some measure of time which exists independently of the universe. There isn't, anymore than there is space "outside" the universe. Time and space are the universe.

    What Hawking is saying with this assertion is that, looking at the shape of the Universe near the singularity, we see that...

    In his book Hawking drew a 2D diagram of the universe (one dimension of space, one dimension of time). It is something like a "V" as expected. But there is no tip to the triangle, instead it's rounded off and doesn't actually touch the projected position of the singularity. Hence, near the singularity (in time) the shape of spacetime is curved like a hypersphere. If you follow a geodesic back through time to the earliest point, you find yourself at the 4-dimensional equivalent of the North Pole. If you continue without changing direction you will find yourself travelling forward in time again. There is no "earlier" time.

    If you want to know where it might have come from, see my other (longer) post.

    Consciousness is not what it thinks it is
    Thought exists only as an abstraction
  • I'm by no means an expert on this, but I thought quantum mechanics required the universe to be flat.

    I'm pre-coffee this morning, but I thought one of the effects of QED was a quantum explanation of radiation pressure involving sending a wave of some variety (again, pre coffee, I think it was an electromagnetic wave? maybe not... because I'm not sure that makes sense) when an electron gains energy, both forward in time, as well as backwards in time that propogate throughout the universe. At some point they impact another electron (or other particle), which inturn reemit the same sort of radiation half of which propogates back towards the original electron (half in terms of time, not direction). The vast majority of the radiation ends up cancelling each other out, but a small amount ends up "reflecting" back to the original electron and providing that resistance? If the universe was open, there wouldn't be enough advanced waves returning to balance things out (unless our understanding of the origins were incorrect, because you can't be open in one direction in time and closed in the other and still have things balance out), and if the universe was closed, there would be too many advanced waves returning and we wouldn't get the results we get.

    If I recall correctly, it was some work that Richard Feynmann did early on in his life that involved that.
  • Almost without exception, all physics developed pre-quantum dynamics are only true in certain specialized circumstances, in average, on bodies over a certain mass.

    That explanation (and in fast the physics typically taught in school) leaves out 99% of what we really know, and are basically just plain wrong.

    The only science (IMGO) taught worse in school than evolutionary theory is physics. THey still try to teach people that, for a big example, the angle that light reflects off a mirror is same as the angle it hits a mirror at (ie, if a light source is 30 degrees above the mirror, its reflected light is reflected at 30 degrees) -- which is blatently wrong, has been proven wrong countless times, and is still taught to students.
  • This one popped into my head a few minutes ago, just a thought experiment on why the universe would have to be flat.

    If you accept the multiple-worlds interpretation of quantum mechanics, then every possible state of the universe exists (flat, closed, open, following every possible occurance throughout time).

    Assuming that we need a stable version of the universe where things occur in ways that match the observations of classical physics (special relativity, general relativity, thermodynamics, etc), then we suddenly have a defined number of states the universe must exist in where random quantum occurances don't violate thise rules to a significant enough extent to keep the physical processes we need to live from occurring. (Blending the Copenhagen and multi-worlds interpretation of quantum mechanics, I'm suggesting that the requirements for our conciousness to exist and thus be able to ponder the question forces the full range of possible universes represented by the wave function of the universe in general to collapse into discrete universes in which we're able to exist, one of which involves every instant we perceive passing through).

    If it turned out that the physical results of the radiation pressure I mentioned in my other post are inherantly needed for the proper functioning of our brain in being concious as we are, than those requirements as parameters to our conciousness cause the wave function of the universe to collapse not into discrete universes (ala the multi-worlds hypothesis) where the universe could be open or closed, but in fact our existance would force the universe we're concious of to drop into a stable state where its flat.

    Reversing that, basically I'm saying that if it turned out that the universe as we know it can't exist in a form that can support our form of conciousness without the specific form of radiation pressure we measure, and that pressure requires a flat universe because of the results of quantum electrodynamics, then our existance is either proof of the universe being flat, or the cause of the universe being flat, depending on how you want to look at it.

    Ugh, that just hurt my brain. Gotta love quantum physics.

  • This isn't entirely true.

    Special reletivity says there are no absolute points of reference, but that's the one part of special reletivity that doesn't sync well with quantum mechanics, and it seems to be is blatently wrong.

    I'm not a physicist, so I don't understand the exact mechanics behind making it work, but if you're at an arbitrary point in space, you could take measurements of the cosmic background radiation (which defines the extents of the universe, and as such provides a point of reference that inherantly defines the universe) in various directions. An arbitrary time later you take the same measurements again. Figuring the universe cools at the same rate in each direction , differences between the various measurements taken can ABSOLUTELY determine one's motion and position relative to the universe, this Einstein's concept of no absolute points of reference only works in theory -- when comparing simple systems with only two objects -- and that theory doesn't match reality.

    Actually even if the universe cools at different rates in different directions, you could still calculate it as long as the rate of cooling in a given direction remains constant, or at least calulatable. Its sort of like how Microsoft's IntelliEye mice track their motion by comparing snapshots of their background reference points.
  • by tgd ( 2822 ) on Sunday November 28, 1999 @06:09AM (#1500705)
    No one has ever said the speed of light is constant. You've read a few articles apartently and drawn the wrong conclusions.

    It was stated that the speed of light in a vacuum is an absolute barrier for mass less than light to be accellerated to with the addition of energy.

    Reletivity doesn't say anywhere that things can't go faster than light or that light has a constant speed.

    Lenses work because light moves slower in glass than in air. You get twinkles in the stars because light travels at different speeds in different densities of air. And its trivial to accellerate something faster than the speed of light in some mediums. I think its called Chernekov radiation, when an energetic particle travels faster than light in the medium its passing through. Its the blue glow you get from a nuclear reactor -- neutrons moving faster than the photons. You can picture it like a sonic boom, although physically thats not really whats happening. But the neutrons moving faster than the photons is the cause of it.
  • How do you know that the laws of God are in fact moral?


    ...phil
  • Ah but as every mathematician knows, there are different sizes of infinity. An asymptotically approached infinity isn't as big as an exponentially approached infinity.

    I'm really just arguing for the sake of it.

    You may well be right about this, but it seems to me that if the density and expansion energy of the Universe are exactly balanced then KE+PE=0 and a finite separation is approached.

    Consciousness is not what it thinks it is
    Thought exists only as an abstraction
  • You have to remember that the quantum effects I was talking about owe nothing to GUTs or quantum gravity. These big-bang epoch events all took place within a very small volume; quantum effects dominated. And nobody doubts the correctness ofquantum mechanics on small scales - in fact the transistors which make your computer work depend upon them.

    I'm well aware that this "something out of nothing" theory is spiritually unsatisfying for those who need to feel that the universe has a "purpose" which can make sense to humans.

    Ontological arguments can be logically contructed within both theological and cosmological frameworks, and both require some assumptions to be made. The difference is that the assumptions acceptable to physicists are generally rather more economical than those acceptable to priests.

    The whole point of the quantum cosmogony I wrote about is that it achieves consistency with our poor but experimentally verified understanding of quantum physics without actually requiring the intervention of any external agency. Without requiring the pre-existence of anything in fact. It doesn't require our universe to be unique or even objectively real. You can't get much more economical than that.

    What plain everyday quantum physics tells us is that it is quite plausible for the Universe to have been formed out of nothing. Given that, by Ockham's razor it seems most likely that this is precisely the case. Why look for any additional cause if there is no evidence for one, and self-consistency can be achieved without it?

    On the anthropic principle, Polkinghorne missed
    the point entirely. If all possible universes exist (as quantum theory demands), then our finding ourselves in a universe like this is hardly a free lunch. Every kind of universe is available but only a universe like this one could have produced us. So naturally this is the kind of universe we perceive as we could exist in this form in no other kind of universe. There is nothing surprising, fortuitous or mystical about it, it is simply inevitable and required.

    If you are not convinced by the Anthropic argument then I beseech you to read J.D. Barrow & F.J. Tipler "The Anthropic Cosmological Principle" for a compelling and very tightly argued account of the theory.

    Consciousness is not what it thinks it is
    Thought exists only as an abstraction
  • Two murderers are in prison, and you chalk this up to persecution of Christians?

    I suggest you actually start studying Christianity as it was preached by Jesus, as opposed to the hate-filled legacy we have today. A good starting place would be John 8( Here [gospelcom.net] is a copy online so you don't have to dig your Bible out from under the "Focus on the Family" propoganda sheets.)

    Sometimes I am ashamed to call myself a Christian. Never afraid of persecution, just ashamed of the image many "Christians" have earned.

  • My background is in math but I do have a course in GR under my belt...

    Isn't the cosmological constant just a constant of integration? In a logical sense it doesn't need any explanation - you integrate and you have a constant left over whose value has to be measured!

    Cheers,
    Ben
  • With all the universe present (latent?) at the initial singularity, why didn't it just remain the Mother of all Black Holes ?
    I've seen two plausible answers to this; one is what I like to call the 'just because' theory; a quantum flip made the big bang, well, bang. I'm not fond of this theory as I don't understand how something can change its state without time being present.
    The other, cooler theory involves time loops. Relativity tells us that time can go backwards as long as the loop is closed, so its effects are never noticed. But if one of these time loops tried to loop back to before the big bang, weirdness would happen. This time loop would not only start the big bang, it would be the big bang.
    So the universe cloned itself. However wrong that theory may eventually turn out to be, I think it's cool and I really hope it's right.

    John Gribbin wrote about this in New Scientist last year; I can't find it in the online edition but the piece is recreated her e [auckland.ac.nz] (scroll down to In the Beginning 24 Jan 98 New Scientist).
  • Well, I am an armchair physicist all right. mea culpa. Though I hope I do better than most (such hubris!).

    You raise an interesting point and while I agree that most of philosophy is horseshit, ontology and epistemiology are a different matter as they are the only tools available for examining what lies beyond the scope of our instruments. Your assertions are far from meaningless.

    However I must still disagree with them.

    Quantum mechanics has been called the most successful physical theory of all time, by virtue of the number of predictions it has made which have been experimentally verified. But this is mot really the point.

    My understanding is that quantum theory is so abstract that it is qualitatively different to all other fields of human study. It is believed by many that quantum theory is the substratum which underpins not only the universe, not only all that which exists, but in fact all universes and all that could possibly exist in any sense at all, anywhere.

    So, to suggest that quantum is just another flawed "human" interpretation no better than theology is somewhat wide of the mark, IMO.

    However, I don't think there is a single person in the world who would seriously claim to understand quantum theory. It is, after all, an incomplete theory, and our current understanding must therefore be an oversimplification. All the same, if we ever manage to fill in the holes it will still be a quantum theory and I think the essential principles we use in quantum mechanics today will remain intact.

    There is one line of investigation I read about which seems to suggest that quantum theory might be an inevitable consequence of number theory. If true this would be an astounding result as it would mean that the universe is literally created out of mathematics. Maybe the entire cosmos follows inevitably from Bertrand Russell's simple method of constructing the set of natural integers. Wow!

    Consciousness is not what it thinks it is
    Thought exists only as an abstraction
  • it's still a bothersome question to those of us who are scientifically litterate and want to know: Where did it all come from?

    Perhaps you need to evaluate your question instead.

    In this case, he's given a fairly good explanation. While the question wasn't answered, the question was shown to have no meaning.

    You want to know where it all came from, and in this definition of the universe, it didn't come from anywhere. In all point of fact, the universe could be said to not to exist, except to the people living in it. :-)

    When you say that it's not fair to ask about "before", the answer may be mathematically corrrect, but it isn't really any more satisfying than attributing it all to some randomly selected tribal diety.

    This is true, but why do you assume that your question has any valid answer at all? Why does there need to be a "first cause" of sorts? Is it too much to ask that you accept the existance of the universe and move on? Perhaps it is...

    Do you prefer truth or satisfaction? In this case, it may not be possible to get both.

    ---
  • You're right, of course. I was inappropriately extrapolating from the purely local case PE ~ mgh (proportional to separation) and forgot that over significant distances PE=-G.m1.m2/r (*inversely* proportional to separation but with reversed sign). Somewhat counter-intuitive, but damn I should have remembered that. OK, put me in the sludge tank...:o\


    Consciousness is not what it thinks it is
    Thought exists only as an abstraction
  • Well, I can't for the life of me find it now, but a while ago when I was looking into the Omega Point theory, and transhumanism, I came accross a pretty good critique of Tipler and Omega Point theory by another rather eminent physicist, which basically said it was bunk, and that Tipler just created it to support his own personal/religious beliefs.
  • Well here's a link to a critique. While verbose and technical, it doesn't quite have the same dismissal as the article by the physicist which I cannot find:

    http://www.infidels.org/library/modern/graham_op py/tipler.html

I tell them to turn to the study of mathematics, for it is only there that they might escape the lusts of the flesh. -- Thomas Mann, "The Magic Mountain"

Working...