Another one bites the dust

This is a sort of footnote to my last post in which I criticised science writer Tim Radford for propagating myths about the reception of heliocentricity in the sixteenth-century. Now a second truly legendary astronomer and science writer, John Gribbin, has turned up in the comments and shown that he also lives in the nineteenth-century, as far as history of science is concerned, when John William Draper and Andrew Dickson White created the myth of an eternal war between science and religion and presented Giordano Bruno and Galileo Galilei, alongside lesser lights such as Michael Servetus and Marco-Antonio de Dominis, as the scientific victims of Christian persecution.

Rushing in where angels fear to tread Gribbin sought to defend Radford’s honour with the following comment:

As a card-carrying pedant, I would point out that Tim says “ideas like that”, not “that idea”. Which makes Bruno relevant, whether you like it or not.

Now I appreciate Mr Gribbin’s attempt to help his friend and colleague but in doing so he has only displayed his own ignorance of the material. There was a very good reason why I ended my last post with the following tongue in cheek warning:

P.S. If anybody mentions either Giordano Bruno or Galileo Galilei in the comments I will personally hunt them down and beat them to death with a rolled up copy of The Guardian.

No modern historian of science, knowledgeable of the history of astronomy in the Early Modern Period, would follow Draper and White in viewing Bruno as a martyr of science. This is a myth that has been thoroughly debunked and which is, these days, usually only dug up by historically ignorant gnu atheists and others of that ilk, as a weapon with which to beat the Catholic Church around the head. As John Gribbin has walked straight into the trap we will just briefly examine why the Church committed Giordano Bruno to the flames.

A Dominican monk, Bruno came under suspicion of heresy and fled his Southern Italian monastery in 1576. He spent the next sixteen years wandering around Europe blowing his own trumpet, generally annoying people and pissing off the authorities, both civil and religious, wherever he went. Returning to Italy he landed, not unsurprisingly in the clutches of the Roman Inquisition. He was held prisoner and interrogated for seven years before being tried for heresy, found guilty, and executed by burning at the stake in 1600. The proceedings of his trial have disappeared so it is not known what exactly he was found guilty of but summary was discovered in 1940 and a list of the charges against him is known:

  • holding opinions contrary to the Catholic faith and speaking against it and its ministers;
  • holding opinions contrary to the Catholic faith about the Trinity, divinity of Christ and Incarnation;
  • holding opinions contrary to the Catholic faith pertaining to Jesus as Christ;
  • holding opinions contrary to the Catholic faith regarding the virginity of Mary, mother of Jesus;
  • holding opinions contrary to the Catholic faith about both Transubstantiation and Mass;
  • claiming the existence of a plurality of worlds and their eternity;
  • believing in metempsychosis and in the transmigration of the human soul into brutes;
  • dealing in magics and divination.

Now this list is not hidden away somewhere, I just borrowed it from the Wikipedia Bruno article, so Mr Gribbin could have consulted it himself. He would of course pounce on the sixth item on the list gleefully crying I told you so, but let us examine if he should be so sure of being right.

Given the fact that Bruno was accused of breaching almost every single central doctrine of the Catholic Church did this one point of highly speculative cosmology really play such a central role in his conviction and subsequent execution, I hardly think so. In fact I don’t think it played much of a role at all compared to his denying the divinity of Christ and the virgin birth. However there is more.

Bruno’s claiming the existence of a plurality of worlds and their eternity has little or nothing to do with Copernicus’ heliocentric theory the original statement for which Tim Radford claimed one could be condemned to the stake. Copernicus proposed a finite sun centred cosmos, Bruno speculated about an infinite universe filled with homogenously distributed infinite sun each with their own populated planets and no centre. The two proposals don’t have an awful lot in common. Copernicus expressly refused to enter the discussion as to whether the cosmos was finite or infinite, and never speculated about other inhabited planets. He, as a good Catholic cleric, would definitely have rejected an eternal universe as this contradicted the Creation. What about the two leading Copernican of Bruno’s own times? Kepler explicitly rejected Bruno’s infinite universe and infinite suns and in doing so brought the earliest known argument against Olbers’ paradox. Galileo simply ignored him. I think it is safe to say that the cosmological statements that were included in Bruno’s indictment were not ideas like Copernicus’ heliocentric theory, as claimed by Gribbin.

Gribbin’s claim also suffers from another problem. The reason why Bruno’s cosmological speculations were included in his indictment was very clearly theological and not scientific. As already mentioned if, as Bruno claimed, the universe were eternal then there could be no Creation, highly heretical. In fact this was one of the central reasons why the Catholic Church rejected the Greek philosophy of Atomism. Secondly if there were infinite populated worlds there would be serious problems with the doctrine of salvation through Jesus. If he was the only Son of God did he visit all of the infinite populated planets, simultaneously, one after the other? Or were there infinite Jesuses? Did he only save the earth? Then what about the other planets? A really tangled mess for the Catholic theologians! As with Galileo in 1615 if Bruno had had anything remotely like proof for his cosmology he might have had something he could argue with but he didn’t, all he had was pure unscientific, unsubstantiated speculation. As I sated in earlier posts Bruno’s cosmological speculations were anything but scientific and anything but accurate. As far as we know the universe is finite and not infinite, it had a starting point and will almost certainly have an end. There are neither infinite stars (suns) nor infinite planets and those that there are, are not distributed homogenously. To stylise Bruno as a scientific martyr, as Draper/White did in the nineteenth-century and as John Gribbin apparently still wants to do, boarders on the grotesque.







Filed under History of Astronomy, Myths of Science, Renaissance Science

29 responses to “Another one bites the dust

  1. As far as we know the universe is finite and not infinite, it had a starting point and will almost certainly have an end. There are neither infinite stars (suns) nor infinite planets and those that there are, are not distributed homogenously.

    The cosmological conventional wisdom changes every few decades, but the idea that the universe will “almost certainly have an end” went by the boards when it was discovered that the expansion of the (observable) universe is accelerating. (Cf “dark energy”). As for the infinity of the universe, the standard big bang model does indeed postulate a finite universe. However, the chaotic/eternal inflation of Linde and Guth is pretty popular among present-day cosmologists, and this does sport an infinite universe (or multiverse, if you prefer). Unfortunately, it’s very hard to imagine how these ideas could be tested observationally. Finally, the lack of homogeneity is indeed a feature of the observed universe.

  2. Koestler notes in a footnote that “It is surprising how indifferently scholars reacted to Bruno’s matyrdom, at least in Germany.” He then describes a correspondence between Kepler and a physician Brengger. Brengger asks Kepler what he thinks about Bruno’s plurality of worlds. Kepler replies that Tycho also believed that the stars were inhabited, and notes in passing that Bruno had been burned (actually 8 years previously). Why, inquires Brengger. Kepler explains, “He had asserted the vanity of all religions and substituted circles and points for God.” Brengger concludes that Burno must have been insane.

    I would say this strongly refutes the notion that Bruno was burned for his cosmological speculations.

  3. Here is a crude summary of the argument against the notion that Bruno was a scientific martyr.

    1. Most of the charges against Bruno were theological rather than cosmological.

    2. And in any case, his cosmological ideas weren’t exactly the same as those of Copernicus.

    3. And in any case, his cosmological ideas were wrong.

    4. And in any case (as Michael Weiss adds) he was thought to be insane by contemporary scientists.

    I’m afraid this sounds like kettle logic.

    Meanwhile, the Bruno fans seem to have got hold of the idea that because Bruno was burned at the stake, this proves that he was a more authentic and brave scientist than the others. This looks like science as Byron would have written it – in other words, a romantic myth.

    • I followed your link to its definition of “kettle logic”. Cute, but not really to the point.

      First question Thony tackles: could you be burned at the stake for ideas like the heliocentric hypothesis? He points out that Bruno’s cosmology differed considerably from the views of Copernicus and other Copernicans like Kepler. That’s the context for point (2) in your list. No one was burned for the heliocentric hypothesis per se.

      Point (3) is side issue; I don’t know why Thony included it (except maybe for its intrinsic interest). The present-day scientific verdict on Bruno’s speculations tells us nothing about the historical issues.

      Now we turn to a second question: was Bruno burned for his cosmological speculations? For this question, point (1) is crucial. Thony’s bullet list alone is strong evidence for a “no” answer. We have seven theological bullets and one cosmological one. Most of the theological points were third-rails at the time. Does anyone really believe that Bruno’s verdict would have gone the other way, if the cosmological bullet had been omitted from the indictment? To claim that Bruno was burned because of his cosmology is even less believable.

      My point (poorly summarized in your point 4) was really a footnote further supporting point (1). (In kettle logic, by contrast, the later points have to be inconsistent with the earlier ones.) It is essentially the testimony of a contemporary expert witness. Kepler is aware of Bruno’s cosmological views, but he doesn’t give this as the reason Bruno was burned, rather he cites theological reasons.

      Third question (raised by Richard Elwes): did Bruno’s immolation serve to intimidate contemporary scientific speculation? I won’t attempt an answer — this comment is long enough already. I just want to double-down on Elwes’s separation of this question from the question of why Bruno was burned.

      • laura

        It’s also worth pointing out that Bruno’s verdict would have gone the other way had he recanted. In fact, according to the histories I’ve read, he did recant in Venice. For bureaucratic reasons, the trial had to go through Rome and so, after a bureaucratic delay, Cardinal Bellarmine moved him there expecting him to repeat his recantation. But Bruno changed his mind and withdrew his recantation. As a result he was sentenced to burning.

        Of course, both arbitrary detention, forced recantations and burning are monstrous, deeply anti-intellectual activities. (Theocracy is bad! Repression of science is the least of it!) But they were hardly unique to the Catholic Inquisitions.

  4. The real historical issue is buried in all this stormy rhetoric over religion versus science. The application of new inventions made possible by the Renaissance reworking of classical methods of creativity threatened the control over society by an entrenched oligarchy which had its partisans across the waning medieval institutions. Some factions of that oligarchy responded by reaction, while yet others adapted and attempted to control the agenda of “science.”

    On the other side were extraordinary geniuses like Nicholas of Cusa who had a vision and plans for transforming society toward the model of a constitutional commonwealth where the endless wars over land, religion and resources could be overcome through peaceful scientific development.

    I hope your readers will explore Cusa’s works for themselves. In particular I would recommend On Learned Ignorance, Concordantia Catholica and De Pacei Fide.

  5. Well fine, but I can’t help feeling that an important point is being overlooked.

    For science to prosper people need to be able first to indulge in “pure unscientific, unsubstantiated speculation” without the threat of being murdered for doing it. Speculation comes first, then evidence follows (or not). So to that extent, it doesn’t especially matter whether Bruno’s martyrdom was for accurate or inaccurate cosmological theorising – the broader picture remains one in which the Catholic Church was aggressively intolerant of the sort of free-thinking about the universe (“ideas like that”) which is a prerequisite for scientific progress.

    Having said which, you may very well be right that Bruno’s cosmological theories probably played a comparatively small part in his indictment. All the same, if I put myself in the shoes of a 17th century thinker weighing up the merits of publicising my latest ideas, I’d like a bit more reassurance than “probably” and “comparatively small” when contemplating a course of action which may just possibly get me burned at the damned stake.

    • “it doesn’t especially matter whether Bruno’s martyrdom was for accurate or inaccurate cosmological theorising”

      You seem to have missed the point: there is zero evidence his kooky cosmology was an issue at all. Heliocentrism wasn’t heretical in any way at the time of his trial. And he got his idea about a multiplicity of worlds from Cusanus – a cardinal of the Church and one time Papal Legate. So not exactly some wild-eyed heretic.

      The myth of Bruno as a symbol of the Church’s supposed stifling of speculation about the cosmos depends on his cosmology being somehow heretical. It wasn’t. His theology, however, was – very much so. I know it kind of spoils the neat little fable, but Bruno was a common or garden variety of religious martyr, not a scientific one.

      • there is zero evidence his kooky cosmology was an issue at all

        If you believe that to be the case, you should take it up with Thony because that’s not what the post above argues. In fact it explicitly states that “Bruno’s cosmological speculations were included in his indictment”.

        The suggestion is then made that the reason for this is “theological and not scientific”, which I’m afraid I find a depressing line of argument, as it concedes from the outset philosophical ground I see absolutely no reason for scientists to abandon. In fact, rather than being an argument against kooky cosmology being a problem for the Church, it seems to make the case strongly that is was one: “if, as Bruno claimed, the universe were eternal then there could be no Creation, highly heretical”.

    • @Richard Elwes

      I’m afraid I find a depressing line of argument, as it concedes from the outset philosophical ground I see absolutely no reason for scientists to abandon.

      I want to clarify an issue here. Are we making value judgements, or trying to understand the historical situation as seen by the participants?

      I have nothing against either of these activities. I like to do both, myself. But they are very different. We don’t have to concede anything to the 17th C. theocratic perspective, philosophically speaking, to understand how it operated in the case of Bruno.

  6. Bruno clearly saw himself as a philosophical martyr, in the tradition of Socrates, rather than as a martyr for (what would later be called) science. He very clearly argued, both before and during the trial, for the pre-eminence of knowledge derived from the senses and from the powers of reason over knowledge from commonly received ideas or from a respected authority. This question of who decides on the truth and by what method we arrive at the truth was one of the major tensions in the trial, and one of the reasons that Bruno found himself unwilling to recant.

    Based on a reading of Bruno’s works and from the summary of the trial, the charge of heresy on the point of the infinite size and eternal existence of the universe resulted from Bruno’s use of theological argument to support these points. He argued that since God is supposed to be infinite and omnipotent, His creation should be something that reflects that omnipotence and infinitude, rather than a system of eight or nine crystalline spheres, centered on the Earth or the Sun; and ideally, it should be temporally unlimited as well, since God is timeless and unchanging.

    This mixture of mathematical-theological reasoning seems to have also produced several of the other heretical theories (which, I might add, Isaac Newton would later come to share, on a similar basis).

    That is, since one is the most perfect number, there can be only one God, and no Trinity. If no Trinity, no divinity of Jesus, and therefore no transubstantiation or virgin birth. If God is perfect and infinite and eternal, the Universe as His reflection must also be perfect and infinite and eternal.

    The strictly cosmological positions by themselves probably would not have been a sufficient cause to execute him. Even though there are eight charges listed, the Church tried, convicted and burned him on the totality of his beliefs; the whole set of them were seen as an integrated set of beliefs, not just freestanding propositions.

  7. Daniel

    What disturbs me most is not that they’re getting the stories of Bruno, Galileo, Hypatia et aliis wrong, but that their use of these names shows that they’re still operating off some Great Big List of Science Martyrs that had been finalized around *1880*. It’s not just that they’re warping these people to turn them into technocratic goody-two-shoes but that they really seem to think that no philosophy history of science or even art or magic written after 1910 is worth reading: their universe is that of Wells and Draper and maybe Bertrand Russell, Robert Ingersoll, or J.D. Bernal for the highbrow types. The ideas of Boas or Warburg or Seznec are so far beyond their comprehension all they can do is bark. The closest parallel I can think of is the US hyper-fundamentalist Jack Chick: none of his secondary sources were written after 1910, either. A mere mention of “Bruno” or “Galileo” not only distorts these figures into some two-dimensional Golden Books icons of an eternal struggle between innovation and reaction, it reveals that the user is basically thinking the thoughts of a late Victorian: it’s a worldview that lets some of them even insist, against all proof to the contrary, that Catholicism was (or even is) the biggest opponent to the theory of evolution.

    • This is all pretty strange and unsavoury.

      A distinguished scientist offers the entirely moderate (and – having surveyed the evidence presented so far – correct) opinion that Bruno is “relevant” to a previous discussion. In response Thony declares him to have bitten the dust, claims that he “lives in the nineteenth-century”, and accuses him of holding borderline “grotesque” opinions. Now Daniel likens him to a Christian “hyper-fundamentalist”, and says that all he can do is “bark”.

      What’s next? Shall we burn him at the stake?

      • “…offers the entirely moderate and – having surveyed the evidence presented so far – correct…”

        Strange, having surveyed the evidence presented so far I, and many others, find John Gribbin’s claim anything but correct and you have in no way shown it to be so.

        Before you react allergically to the above statement, it is a subjective opinion, exactly as was your comment that provoked it. Stating something is not the same as proving it and I can’t see where you have proved your claim.

      • But what is this “claim” that Jon Gribbin makes, which is so appalling, so desperately ignorant, and so urgently in need of debunking?

        Has he said that there is an “eternal war between science and religion”? Has he said that he views “Bruno as a martyr of science”?

        No. These are opinions you have hung around his neck. He simply said Bruno was “relevant” to a previous discussion, in which it was asserted that you could get burned at the stake for “ideas like [heliocentricism]”.

        And I claim that he is. Here are my arguments:

        a) One of the charges in his indictment concerned his cosmological speculations.

        This remains the case notwithstanding your attempts to explain it away as a minor charge compared to his views on the Virgin birth, etc., and Scott’s argument that he was martyred for “the totality of his beliefs”.

        I don’t don’t wish to dispute either of those arguments, they are probably correct. Nevertheless the fact remains that the Church, which had a completely free choice over what charges to level, opted to include his cosmological speculations. This bald, uncontested fact – remembering that I am simply seeking to establish that Bruno is “relevant” to the discussion, nothing more – is more than enough.

        b) The question now becomes Was Bruno’s cosmology “like” Copernican heliocentricism. I have already addressed this is a previous comment and I hold it is appropriate to take a much broader view of this question than the narrow interpretation you propose in your post. It is “like” it, insofar as it was a cosmological hypothesis fundamentally opposed to geocentricism. Again, I hold that that is more than sufficient.

        Your narrow reading is one in which the Church says “yes, you may speculate upon this, but never upon that“. Whether a particular hypothesis such as heliocentricism or the infinitude of the heavens comes under the heading of this and what is that may be of historical interest, but is ultimately peripheral to the big picture in which the Church insists upon its authority to make such pronouncements, finds that authority challenged, and responds with violence.

        If we are going to use phrases such as “martyrs for science” – and you are the only one to have done so – then the title should apply to those who have died (in part) for the right to think, investigate, and hypothesise freely about the universe. It should not be limited those who have been persecuted for making specific claims which have subsequently been vindicated by evidence.

      • “One of the charges in his indictment concerned his cosmological speculations. ”

        We don’t have his indictment. The item Thony referred to is a speculative reconstruction by the Italian scholar Luigi Firpo based on some notes from his earlier appearances before the inquisition in Venice. So he was certainly questioned about “the multiplicity of worlds and their eternity”, but we don’t know if he was condemned over these ideas.

        We do know that the idea that the cosmos was eternal was considered heretical. And we also know that he got his ideas about multiple worlds from Nicholas of Cusa. Nicholas of Cusa was not condemned for heresy over his ideas about multiple worlds or his speculation that they were inhabited by extraterrestrials. Nor was William Vorilong, who went further and contemplated whether these alien inhabitants of other worlds would have needed an alien Jesus Christ to redeem them or whether the Jesus who came to earth did the job for the aliens as well. William Vorilong was a respected theologian. Cusanus was made a Cardinal and a Papal Legate. Both remained unburned by religious nasty people.

        So while it makes sense that Bruno was questioned about his beliefs about multiple worlds in Venice, it can’t have been multiple worlds per se that were the problem. The issues lies in the words “… and their eternity”. Was this on the now lost indictment for his trial in Rome? We simply don’t know.

        ” the title should apply to those who have died (in part) for the right to think, investigate, and hypothesise freely about the universe”

        The title should actually be reserved for those who actually did something like actual science . Not mystical kooks like Bruno. It should also be reserved for those who were executed for something to do with the science they did. Not for a grab-bag of theological oddities. And that’s why Bruno is not relevant to the history of science, except as a footnote about crackpots.

      • Daniel

        Those might all be fair critiques–but my intent was not to paint Gribbin as an exponent of an insular, extremist technocracy by himself: what I was getting at was that his clichés come from a certain real strand of thought that does indeed believe that fin-de-siècle Whiggery is the be-all end-all of human thought. So even if he doesn’t hold to these notions, offhanded use of Bruno as shorthand for an eternal battle between dogma and inquisitiveness still propagates those notions (and erases everything that was actually going on).
        So I do in fact agree that Bruno, for all his, ah, extravagances, has a place in intellectual history–alongside Bacon, who meant it when he called for a New Atlantis, and Campanella, who was punished for summoning the goddess Venus into the Papal Apartments with hypolydian music and the appropriate gemstones with a full pardon and imprimatur. But automatically assuming that Bruno’s execution had a bearing on heliocentricity is already suspect, since it already sounds like centuries of agitation against Catholics. Assuming it had a bearing on heliocentricity and the size of the cosmos, AND not not covering all the already-intensively-researched heliocentrists and cosmic-infinitists (CUSA), just indicates a slack recycling of that hypothetical 1879 Big List o’ Science Martyrs. So if someone insists on pointing to cosmic infinity in a list of charges, they have to at least check if anyone else was charged with such.

  8. The first rule of Bruno studies is that everyone is wrong about Bruno. At least, everyone else.

  9. Pingback: Whewell’s Gazette: Vol. #13 | Whewell's Ghost

  10. Phillip Helbig


    “As far as we know the universe is finite and not infinite”

    You seem to be making a similar error, commenting on stuff outside your area of expertise. The answer to the corresponding question is that we do not know. What is clear is (assuming a trivial topology) that the universe is very close to spatially flat, which is the border between finite and infinite.

    An unrelated question (anyone who sees them as related hasn’t brushed up on his cosmology in the last 20 years or so) is whether the universe will expand forever. Current evidence is: yes. This is pretty certain.


    Which standard big-bang theory postulates a finite universe?

    • Phillip Helbig

      Just to be clear, the “geometry implies destiny” was never true in classical cosmology. Even in the 1920s finite models which expand forever were investigated. Only in the time between about 1950 and 1990, when people assumed that the cosmological constant was zero (or, towards the end of this time, when they assumed that the universe was (at least almost) exactly flat) could this simplification be made.

    • You are right about the topology, of course. but I was responding to Thony’s statement that the universe “had a starting point and will almost certainly have an end”, i.e., the Big Bang to Big Crunch model, the one which stops expanding and starts contracting at some point. The accelerating expansion pretty much puts paid to that.

      I was wrong to say that “the” standard big bang theory postulated a finite universe. I should have said “one of the big bang models popular before 1990” does that, namely those with Lambda=0 and Omega>1. I assume this is what Thony had in mind, since he appears to assume a Big Crunch. I was contrasting with more recent models which do suppose an infinite universe (or multiverse), harking back to my initial remark about the shelf-life of cosmological conventional wisdom. Sloppy phrasing on my part.

      As I said before, all this has no bearing on the historical questions.

      • Phillip Helbig

        “Lambda=0 and Omega>1”

        Yes, this would be spatially finite and have a big crunch. However, it was never really a popular model and was never supported by (even wrong) observations. Einstein did favour it for a while, because he wanted a finite universe because of Mach’s Principle and had given up on lambda after his blunder (actually, his blunder was not lambda, but his static universe).

      • John Wheeler also favored it; see “Our Universe: The Known and Unknown” in At Home in the Universe. The treatment in Gravitation is more circumspect.

        To the best of my recollection, theoreticians tended to like either Omega=1 or Omega>1 in the period in question, with of course Lambda=0. I seem to recall a post on sci.physics.research, in the late 80s, in which an observational astronomer severely chastised his theoretician collegues for these preferences, unsupported by observations, as you said.

        For example, Berry’s undergrad text Principles of Cosmology and Gravitation, 1989. He calculates the parameters using what he calls the “best” values of the data (his scare-quotes around “best”). He comes up with a negative Lambda and k=-1 (open universe). He is clearly uncomfortable with this, for he promptly turns to what he calls the “pure Einstein” view that Lambda=0. After a quick discussion of dark matter (or “missing mass” in his terminology), he recalculates, concluding that “Therefore the present data suggest a closed universe if the cosmical constant is zero, although k would be negative, and the universe open, if q_0 were less than 0.5, which is certainly not ruled out…”

        As for Lambda=0 being Einstein’s “greatest blunder”, Mario Livio has raised considerable doubt that Einstein himself ever called it that.

      • Phillip Helbig

        “To the best of my recollection, theoreticians tended to like either Omega=1 or Omega>1 in the period in question, with of course Lambda=0.”

        I wasn’t doing cosmology back then. 😦 After inflation came along, then Omega=1 reigned supreme. Some liked Omega>1 because (with lambda=0) it implied a spatially closed universe. (With lambda=0, it also implied a big crunch.)

        The famous paper by Gott, Gunn, Schramm and Tinsley argued for Omega<1.

        "I seem to recall a post on sci.physics.research, in the late 80s, in which an observational astronomer severely chastised his theoretician collegues for these preferences, unsupported by observations, as you said.”

        There were many such exchanges. One is documented by Dennis Overbye in Lonely Hearts of the Cosmos with, ironically, Schramm as the hidebound theorist, chastising a student for daring to do some simulations with Omega<1. Student: "But that's what Simon White did!" Schramm: "Simon White never understood inflation!"

        As late as the late 1990s, Rocky Kolb was still defending the Einstein-de Sitter universe, while observers like Ray Carlberg (and theoreticians like Peter Coles and George Ellis) pointed out that the evidence is for Omega<1.

        As for Berry (a really good book, by the way), the data simply weren't good enough to say much at all then.

        “As for Lambda=0 being Einstein’s “greatest blunder”, Mario Livio has raised considerable doubt that Einstein himself ever called it that.”

        AFAIK, the only source is a remark to this effect by Gamow in his autobiography My World Line. Gamow, of course, is not always a completely reliable source.

    • B'Rat

      The generalization used in these comments always baffles me.

      Yeah, according to General Relativity we can study the geometry of the Observable Universe. This by no means prove it does not constitute a special case of the possibly completely different enormous “everything” that could exist “outside” it, unless you assume a priori that “Well, it’ll be just the same”.
      This is, BTW, what permits ideas like “the Multiverse” to prosper, and to be called bad science, since by definition you can’t know anything about the “un-Observable Universe”.

      • I didn’t see anyone in these comments voicing an opinion on the actual state of the universe. Just discussing the various models that have have been popular among cosmologists during the past 50-odd years.

      • B'Rat

        What I see in these comments is a discussion on what cosmological models are favoured by physicists according to the “best” values of the data, in the context of asking oneself whether we can say that the Universe is finite OR infinite.

        In my understanding the big point is that all these speculations is Phillip Helbig’s “(assuming a trivial topology)“, that in this case I decline like “if whatever is beyond the Observable Universe is pretty much the same”.
        I suppose a possible analogy could be living in a 2-D universe and seeing that what we can observe around us has a positive curvature: are we on a sphere or is it just a bump in some other possibly infinite geometry? No way to know.

        I don’t think current observations of “dark matter” and “dark energy” can help us much. Even in the best case scenario in which we are able to confirm that they “exist” and characterize their current behaviour, what I get is that our understanding of them is somewhat analogous to pre-Newton celestial bodies mechanics: sure, we can describe how they behave, but we have no idea about why>.

        My two cents is that the limited speed of information put a pretty big nail on the coffin of our possibility of understanding the global attributes of our Universe; we might somehow bypass this by deeply understanding whatever happened with the Big Bang but (I hope to be proven wrong) I think it may be hardly ever possible.

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