The Size of the World

24 November 2013


The Sloan Digital Sky Survey points to a large scale structure of the universe dominated by hyperclusters, which appear to be structures that exceed the upper size limit of structures as predicted by contemporary cosmology.

The Sloan Digital Sky Survey points to a large scale structure of the universe dominated by hyperclusters, which appear to be structures that exceed the upper size limit of structures as predicted by contemporary cosmology.

The world, we are learning every day, is a very large place. Or perhaps I should say that the universe is a very large place. It is also a very complex and strange place. J. B. S. Haldane famously said that, “I have no doubt that in reality the future will be vastly more surprising than anything I can imagine. Now my own suspicion is that the Universe is not only queerer than we suppose, but queerer than we can suppose.” (Possible Worlds and Other Papers, 1927, p. 286) In other words, human beings, no matter how valiantly they attempt to understand the universe, may not be cognitively equipped to understand it; our minds may not be the kind of minds that can understand the kind of place that the world is.

This idea of our inability to understand the world in which we find ourselves (an admirably humble Copernican insight that we might call metaphysical modesty, and which stands in contrast to epistemic hubris) has received many glosses since Haldane’s time. Most notable (notable, at least, from my perspective) are the evolutionary gloss, the quantum physics gloss, and the philosophical gloss. I will consider each of these in turn.

In terms of evolution, there is no reason to suppose that descent with modification in a context of a struggle for vital resources on the plains of Africa (the environment of evolutionary adaptedness, or EEA) is going to produce minds capable of understanding higher dimensional spatial manifolds or quantum physics at microscopic scales that differ radically from the macroscopic scales of ordinary human perception. Alvin Plantinga (about whom I wrote some time ago in A Note on Plantinga, inter alia) has used this argument for theological purposes. However, there is no intrinsic reason that a mind born in the mud and the muck cannot raise itself above its origins and come to contemplate the world in Copernican terms. The evolutionary argument cuts both ways, and since we have ourselves as the evidence of an organism that can raise itself from strictly survival behavior to forms of thought that have nothing to do with survival, from the perspective of the weak anthropic principle this is proof enough that natural selection can result in such a mind.

In terms of quantum theory, we are all familiar with famous quotes from the leading lights of quantum theory as to the essentially incomprehensibility of that theory. For example, Richard Feynman said, “I think I can safely say that nobody understands quantum mechanics.” However, I have observed (in The limits of my language are the limits of my world and elsewhere) that recent research is making strides in working around the epistemic limitations of quantum theory, revealing its uncertainties to be not absolute and categorical, but rather subject to careful and painstaking narrowing that renders the uncertainty a little less uncertain. I anticipate two developments that will emerge from the further elaborate of quantum theory: 1) the finding of ways to gradually and incrementally chip away at an absolutist conception of uncertainty (as just mentioned), and 2) the formulation of more adequate intuitions to make quantum theory more palatable to the human mind.

In terms of philosophy, Colin McGinn’s book Problems in philosophy: The Limits of Inquiry formulates a position which he calls Transcendental Naturalism:

“Philosophy is an attempt to get outside the constitutive structure of our minds. Reality itself is everywhere flatly natural, but because of our cognitive limits we are unable to make good on this general ontological principle. Our epistemic architecture obstructs knowledge of the real nature of the objective world. I shall call this thesis transcendental naturalism, TN for short.” (pp. 2-3)

I have previously written about McGinn’s work in Transcendental Non-Naturalism and Naturalism and Object Oriented Ontology, inter alia. Our ability to get outside the constitutive structure of our minds is severely limited at best, and so our ability to understand the world as it is is limited at best.

While our cognitive abilities are admittedly limited (for all the reasons discussed above, as well as other reasons not discussed), these limits are not absolute, but rather admit of revision. McGinn’s position as stated above implies a false dichotomy between staying within the constitutive structure of our minds and getting outside it. This is a classic case of facing the sheer cliff of Mount Improbable: while it is impossible to get outside our cognitive architecture in one fell swoop, we can little by little transgress the boundaries of our cognitive architecture, each time ever-so-slightly expanding our capacities. Incrementally over time we improve our ability to stand outside those limits that once marked the boundaries of our cognitive architecture. Thus in an ironic twist of intellectual history, the evolutionary argument, rather than demonstrating metaphysical modesty, is rather the key to limiting the limitations on the human mind.

All of this is related to one of the central problems in the philosophy of science of our time — the whole Kuhnian legacy that is the framework of so much contemporary philosophy of science. Copernican revelations and revolutions, which formerly disturbed our anthropocentric bias every few hundred years, now occur with alarming frequency. The difference today, of course, is that science is much more advanced than it was with past Copernican revelations and revolutions — it has much more advanced instrumentation available to it (as a result of the STEM cycle), and we have a much better idea of what to look for in the cosmos.

It was a shock to almost everyone to have it scientifically demonstrated that the universe is not static and eternal, but dynamic and changing. It was a shock when quantum theory demonstrated the world to be fundamentally indeterministic. This is by now a very familiar narrative. In fact, it is so familiar that it has been expropriated (dare I say exapted?) by obscurantists and irrationalists of our time, who point at continual changes at scientific knowledge as “proof” that science doesn’t give us any “truth” because it changes. The assumption here is that change in scientific knowledge demonstrates the weakness of science; in fact, change in scientific knowledge is the strength of science. Scientific knowledge is what I have elsewhere called an intelligent institution in so far as it is institutionalized knowledge, but that institution is formulated with internal mechanisms that facilitate the re-shaping of the institution itself over time. That mechanism is the scientific method.

It is important to see that the overturning of familiar conceptions of the world — some of which are ancient and some of which are not — is not arbitrary. Less comprehensive conceptions are being replaced by more comprehensive conceptions. The more comprehensive our perspective on the world, the greater the number of anomalies we must face, and the greater the number of anomalies we face the more likely it is that our theories will be overturned, or at least partially falsified. But it is the wrong debate to ask whether theory change is rational or irrational. It is misleading, because what ought to concern us is how well our theories account for the ever-larger world that is revealed to us through our ever-more comprehensive methods of science, and not how well our theories conform to our presuppositions about rationality. The more we get the science right, reason will follow, shaping new intuitions and formulating new theories.

Our ability to discover (and to understand) ever greater scales of the universe is contingent upon our growing intellectual capabilities, which are cumulative. Just as in the STEM cycle science begets technologies that beget industries that create better scientific instruments, so too on a purely intellectual level the intellectual capabilities of one generation are the formative context of the intellectual capabilities of the next generation, which allows the later generation to exceed the earlier generation. Concepts are the tools of the mind, and we use our familiar concepts to create the next generation of concepts, which latter are both more refined and more powerful than the former, in the same way as we use each generation of tools to build the next generation of tools, which makes each generation of tools better than the last (except for computer software — but I expect that this degradation in the practicability of computer software is simply the software equivalent of planned obsolescence).

Our current generation of tools — both conceptual and technological — are daily revealing to us the inadequacy of our past conceptions of the world. Several recent discoveries have in particular called into question our understanding of the size of the world, especially in so far as the world is defined in terms of its origins in the Big Bang. For example, the discovery of hyperclusters suggest physical structures of the universe that are larger than the upper limit set to physical structures by contemporary cosmologies theories (cf. ‘Hyperclusters’ of the Universe — “Something is Behaving Very Strangely”).

In a similar vein, writing of the recent discovery of a “large quasar group” (LQG) as much as four billion light years across, the article The Largest Discovered Structure in the Universe Contradicts Big-Bang Theory Cosmology states:

“This LQG challenges the Cosmological Principle, the assumption that the universe, when viewed at a sufficiently large scale, looks the same no matter where you are observing it from. The modern theory of cosmology is based on the work of Albert Einstein, and depends on the assumption of the Cosmological Principle. The principle is assumed, but has never been demonstrated observationally ‘beyond reasonable doubt’.”

This formulation gets the order of theory and observation wrong. The cosmological principle is not a principle that can be proved or disproved by evidence; it is a theoretical idea that is used to give structure and meaning to observations, to organize observations into a theoretical whole. The cosmological principle belongs to theoretical cosmology; recent discoveries such as hyperclusters and large quasar groups belong to observational cosmology. While the two — i.e., theoretical and observational — cannot be separated in the practice of science, it is also true that they are not identical. Theoretical methods are distinct from observational methods, and vice versa.

Thus the cosmological principle may be helpful or unhelpful in organizing our knowledge of the cosmos, but it is not the kind of thing that can be falsified in the same way that, for example, a theory of planetary formation can be falsified. That is to say, the cosmological principle might be opposed to (falsified by) another principle that negates the cosmological principle, but this anti-cosmological principle will similarly belong to an order not falsifiable by empirical observations.

The discoveries of hyperclusters and LQGs are particularly problematic because they question some of the fundamental assumptions and conclusions of Big Bang cosmology, which is, essentially, the only large scale cosmological model in contemporary science. Big Bang cosmology is the explanation for the structure of the cosmos that was formulated in response to the discovery of the red shift, which implies that, on the largest observable scales, the universe is expanding. It is important to add the qualification, “on the largest observable scales” because stars within a given galaxy are circulating around the galaxy, and while a given star may be moving away from another given star, it is also likely to be moving toward yet some other star. And, even at larger scales, not all galaxies are receding from each other. It is fairly well known that galaxies collide and commingle; the Helmi stream of our own Milky Way is the result of a long past galactic collision, and at some far time in the future the Milky Way itself will merge with the larger Andromeda galaxy, and be absorbed by it.

Cosmology during the period of the big bang theory (a period in which we still find ourselves today) is in some respects like biology before Darwin. Almost all biology before Darwin was essentially theological, but no one had a better idea so biology had to wait to become a science capable of methodologically naturalistic formulations until after Darwin. The big bang theory was, on the contrary, proposed as a scientific theory (not merely bequeathed to us by pre-scientific tradition), and most scientists working within the big bang tradition have formulated the Big Bang in meticulously naturalistic terms. Nevertheless, once the steady state theory was overthrown, no one really had an alternative to the big bang theory, so all cosmology centered on the Big Bang for lack of imagination of alternatives — but also due to the limitations of the scientific instruments, which at the time of the triumph of the big bang theory were much more modest than they are today.

As disconcerting as it was to discover that the cosmos did not embody an eternal order, that it is expanding and had a history of violent episodes, and that it was much larger than an “island universe” comprising only the Milky Way, the observations that we need to explain today are no less disconcerting in their own way.

Here is how Leonard Susskind describes our contemporary observations of the expanding universe:

“In every direction that we look, galaxies are passing the point at which they are moving away from us faster than light can travel. Each of us is surrounded by a cosmic horizon — a sphere where things are receding with the speed of light — and no signal can reach us from beyond that horizon. When a star passes the point of no return, it is gone forever. Far out, at about fifteen billion light years, our cosmic horizon is swallowing galaxies, stars, and probably even life. It is as if we all live in our own private inside-out black hole.”

Leonard Susskind, The Black Hole War: My Battle with Stephen Hawking to make the World Safe for Quantum Mechanics, New York, Boston, and London: Little, Brown and Company, 2008, pp. 437-438

This observation has not yet been sufficiently appreciated. What lies beyond Susskind’s cosmic horizon is unobservable, as anything that disappears beyond the event horizon of a black hole has become unobservable, and that places such matters beyond the reach of science understood in a narrow sense of observation. But as I have noted above, in the practice of science we cannot disentangle the theoretical and the observational, but the two are not the same. While our observations come to an end at the cosmic horizon, our principles encounter no such boundary. Thus it is that we naturally extrapolate our science beyond the boundaries of observation, but if we get our scientific principles wrong, anything beyond the boundary of observation will be wrong and will be incapable or correction by observation.

Science in the narrow sense must, then, come to an end with observation. But this does not satisfy the mind. One response is to deny the mind its satisfaction and refuse to pass beyond observation. Another response is to fill the void with mythology and fiction. Yet another response is to take up the principles on their own merits and consider them in the light of reason. This response is the philosophical response, and we see that it is a rational response to the world that is continuous with science even when it passes beyond science.

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Grand Strategy Annex

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Beyond the Big Bang

6 August 2011


The cover story on this month’s issue of Scientific American is Does the Multiverse Really Exist?, and the BBC has also had a story on the same, ‘Multiverse’ theory suggested by microwave background. Here is the opening paragraph of the Scientific American story:

“In the past decade an extraordinary claim has captivated cosmologists: that the expanding universe we see around us is not the only one; that billions of other universes are out there, too. There is not one universe—there is a multiverse. In Scientific American articles and books such as Brian Greene’s latest, The Hidden Reality, leading scientists have spoken of a super-Copernican revolution. In this view, not only is our planet one among many, but even our entire universe is insignificant on the cosmic scale of things. It is just one of countless universes, each doing its own thing”

It is typical for contemporary scientific thought to present this as a new idea, notwithstanding several thousand years of philosophical tradition investigating the infinity of worlds, as it is equally typical to cite a recent book on the topic rather than to acknowledge the theoretical underpinnings of the idea that go back to the earliest works of the Western tradition. I mentioned similar considerations not long ago in a post about Conformal Cyclic Cosmology.

The BBC story ‘Multiverse’ theory suggested by microwave background by Jason Palmer references the paper First Observational Tests of Eternal Inflation by Feeney, Johnson, Mortlock, and Peiris. Here’s the abstract of the paper:

The eternal inflation scenario predicts that our observable universe resides inside a single bubble embedded in a vast inflating multiverse. We present the first observational tests of eternal inflation, performing a search for cosmological signatures of collisions with other bubble universes in cosmic microwave background data from the WMAP satellite. We conclude that the WMAP 7-year data do not warrant augmenting ACDM with bubble collisions, constraining the average number of detectable bubble collisions on the full sky Ns < 1:6 at 68% CL. Data from the Planck satellite can be used to more definitively test the bubble collision hypothesis.

First Observational Tests of Eternal Inflation by Feeney, Johnson, Mortlock, and Peiris

This is from the second paragraph of the paper:

Eternal inflation is ubiquitous in theories with extra dimensions (string theory being the primary example) and positive vacuum energy. However, testing this scenario is extremely difficult since eternal inflation is a pre-inflationary epoch: any signals from outside of our bubble would naively appear to be stretched to unobservable super-horizon scales. While this is in general true, one prospect for probing this epoch lies in the observation of the collisions between vacuum bubbles. These collisions produce inhomogeneities in the inner-bubble cosmology, raising the possibility that their eff ects are imprinted in the cosmic microwave background

I find these recent developments in cosmology both welcome and troubling. It is welcome because the time in long overdue to give serious consideration to theories that do not limit the universe to that generated from the Big Bang (as cosmologists once limited the universe only to the Milky Way galaxy, and before that to our solar system), and it is troubling because the way in which these developments are presented confirms much that I have written recently about Fashionable Anti-Philosophy in science.

From the origins of the Big Bang model up until very recently, it was commonplace among scientists to assert that space and time began with the big bang, and that it was meaningless to speak of the big bang singularity as existing in space or time (this was called the “container theory” of space and time), since space and time (actually, spacetime) was generated by the big bang. To insist upon any other account marked you out as a philosopher and a fool who simply couldn’t understand the scientific concepts involved and the mathematics behind them.

Truly enough, from the point of view of observational cosmology it is meaningless to develop theories of things that can’t be observed, like the interior of singularities, what lies outside the light cone, or what happened before the big bang. But cosmology is not limited to observational cosmology, and physicists routinely theorize about things that can’t be observed, on the hope that they might someday be observed. The “standard model” of particle physics has been looking for the Higgs boson for years, and is hopeful that it will be found soon. But this is why we formulate hypotheses: so we have a research program that can focus on finding mechanisms that might explain the things that we can see.

The great scientific and mathematical revolution that supposedly made all this both possible and rational was the idea of the finite and unbounded universe that was bent around on itself, like the surface of the earth, so that even though there is no edge to the cosmos, that does not mean that it is infinite. There is no edge because there is no boundary, and there is no boundary because the universe is finite and unbounded. The elliptical geometry of Riemann, adapted by Einstein as the setting for General Relativity, gave a precise mathematical expression to this idea. But the advocates of the finite and unbounded universe carefully avoided explaining the distinction between intrinsic and extrinsic curvature, and with a little bit of ambiguity they were able to pretend that the universe was expanding into nothingness without giving an account of this nothingness.

A typical expression of this attitude, in the form of an aside, comes from J. J. Callahan, in discussing his motivation for writing his frequently cited paper, “The Curvature of Space in a Finite Universe” (Scientific American, Volume 235, Number 2, August, 1976). Callahan said the paper grew:

“…out of an attempt to explain Einstein’s concept of a finite but unbounded space to my nonscientific colleagues at Smith. They found it tough going, and some simply dismissed a finite universe as impossible, because Kant had done so when he studied the question 300 years ago.”

Apart from a misrepresentation of Kant, Callahan’s “non-scientific colleagues” are caricatured as mere simpletons who can’t hack mathematical and scientific ideas (it was “tough going” for them), and not people who had genuine intuitions of the how the universe is put together but were unable to express them with the same blinding simplicity of the big bang model producing a finite and unbounded universe.

I am not the only one to have noticed this systematic ambiguity in recent cosmology. I found this amusingly acerbic quote in The Ontology and Cosmology of Non-Euclidean Geometry:

“The closest we seem to have come to a more open consideration of these matters is when both Stephen Hawking and Karl Popper [Karl Popper, Unended Quest, Open Court, 1990; p.16] point out that Einstein, whether or not he successfully answered Kant’s Antinomy of Space, did not answer the Antinomy of Time: despite decades of everyone glorifying in the philosophical revelation of a finite but unbounded universe, they simply didn’t notice that the solution proposed for space didn’t work with time. It is to Hawking’s great philosophical credit that he faces this question squarely.”

The author here has been more charitable to Hawking than I would be, as Hawking has been prominent among those who have ridiculed what he sees as the simple-mindedness of philosophers in insisting upon answers to their questions about a universe with this geometrical structure. Morevoer, I would maintain that the “philosophical revelation of a finite but unbounded universe” doesn’t even offer a solution to the problem of space, much less time, much less spacetime.

So I am happy to see cosmologists extending their scope and trying to get outside the confines of the big bang model, but I continue to be distressed that they continue to ridicule the philosophical underpinnings of their own ideas, and that they will go through a lot of needless duplication of labor in coming up with ideas that have been worked through time and again. But, if you’re aiming at research dollars to build the latest, greatest superconducting supercollider, or the biggest and most sensitive radio telescope, it isn’t going to pull much weight with the grant writing committees or the grant granting institutions themselves to tell them you’ll be spending the next few years in a library reading old books in order to refine your concepts to the point that they might suggest a research program.

Physicists and cosmologists seem to belong to the Field of Dreams school of thought, pursuing a “if we build it, they will come” strategy in research, with “they” being discoveries, suitably celebrated in the headlines of newspapers.

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Grand Strategy Annex

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Several news stories have celebrated the twentieth anniversary of the launch of the Hubble Space telescope today (a pseudo-event, as it were, which is a useful pretext for reflection). It is an anniversary well worth celebrating. When Hubble was launched it was known that it would see farther and deeper into the cosmos than ever before. The past twenty years have been exciting times in cosmology. Many discoveries have been made that have greater advanced our understanding of the universe and our place within it.

It has already been more than ten years since the discovery that the expansion of the universe is speeding up rather than slowing down. This was a discovery made in part due to the sharp eye of the Hubble telescope. Prior to this discovery, big bang theories simply incorporated a “deceleration constant” into their equations, and the only question was presumed to be the speed at which the expansion was decelerating. Now that has all been overturned, and theoretical cosmology is still trying to catch up with the discovery. This is as close to a revolution as you get in Kuhnian “normal science” and it is but one idea substantiated by the Hubble telescope.

I find this revolution in cosmology to be very exciting, but of the memorable discoveries and images that have come from Hubble, my personal vote for the most important, and also the most moving, would go to the Hubble Deep Field and the Hubble Ultra Deep Field images. For these images the Hubble telescope was pointed at an “empty” bit of sky and exposed for a long time in order to register the very faint light of distant sources. The result shows us the universe of the cosmologist, with galaxies littering the sky like the stars of our own sky.

When we see this image we can understand, if only imperfectly, the cosmologist’s universe in which the basic unit of structure is not the star or the galaxy, but the group of galaxies, or even the cluster of groups or superclusters of galaxies. This image shows us how far we have come, in less than a century, from the theory of the “island universe” in which the Milky Way, as incomprehensibly vast as it is, was the only structure that constituted the universe. In other words, the image gives us an immediate and visceral (if not emotional) understanding of the Copernican principle, such that we do not occupy a privileged place in the universe. It is an unspeakable pretense to claim that one understands the size of the universe after one has contemplated the Hubble Ultra Deep Field image.

An image from the Hubble Ultra Deep Field (HUDF) sky survey.

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Grand Strategy Annex

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