(This is an excerpt from my recent book, “The Elephant In The Room, The Denial of the Unconscious Mind.”)

The Thinking Man’s Cosmologist

Sean Carroll is a passionate, cutting edge cosmologist who happens to be a marvelous popularizer of his field. His From Eternity to Here aspires to do for cosmology what Richard Dawkins’ The Selfish Gene did for evolutionary biology. The book offers wonderful, imaginative pictures and analogies that force you to think, or engage with the beauty and mystery of cosmological complexity. It is obvious the author loves and has thought deeply about his subject and — more than anything — wants to communicate what he knows (like Richard Feynman). His presentation is strikingly original inasmuch as you can feel him reaching out to you (fittingly, his wife is an expert in educating the public on science).

Not surprisingly, he is deft when it comes to seducing the unsuspecting reader into thinking much more deeply than he or she is accustomed to. On more than one occasion I caught myself grumbling that I did not sign on for a book that was this much of a brain teaser. Yet, by the end — perhaps more than any of the many cosmology books I have read in the past ten years — I felt exhilarated by the sheer majesty of the cosmic puzzle that had been unfolded before me. In spite of myself I had to admire the audacity of the cosmologist’s visionary quest: intrepid voyagers who are willing to devote their lives to figuring out how the mysterious cosmic machine, that happens to be our universe, actually works.

One of the reasons I was so taken by Sean Carroll’s From Eternity to Here is that it never seemed to take the eternal questions for granted. He did not talk over the heads of his readers, down to his readers or at his readers. You felt, reading him, that he was speaking to you, raising questions that had always been in the background of your mind and after a while it seemed natural, in your mind, to speak back. Or at least I did. Thus when Sean Carroll jarred me with the provocative question:

“Why is it we can remember the past, but not the future?”….I somehow felt I needed to answer back and after mulling it over, I thought:

That’s like saying, why is it that I can always find pictures of myself showing how I looked in the past, but no pictures showing how I will look in the future? Or why is it that I can only take pictures of things that exist but not of things that don’t exist? Or of things that haven’t happened yet but are going to happen? We immediately see what the root of the confusion is: the past, by definition, refers to the retrieval of traces of things or events that have already occurred, while the future, again by definition, refers to possibilities that have not yet been and may not be actualized.

To therefore ask why we can remember the past but not the future is to commit what in logic is called a category error. It is a question therefore that is best answered by a logician and not a physicist. By contrast, to ask what prevents us from building a time machine that can travel forwards or backwards in time, is a question only a physicist could answer, and not surprisingly, it is a question that Sean Carroll discusses brilliantly in his book.

At another point, delving deep into the subtleties of time travel, Sean Carroll, referring to Einstein’s concept of space time as the fourth dimension, said, “basically, like most cosmologists, I’m an eternalist.” Which means, he explained, that events have already happened and are already waiting in their proper location in the universe’s fabric of space time for us to catch up.

It sounded like a fabulous idea, but the more I thought about it, the more I was puzzled. Does this mean that somehow, wondrously, any particular event in our lives — say this very day — is somehow fixed in space time, like a ghostly frozen diorama, waiting to be animated by our special presence? In what sense, I wondered, could a particular event have already occurred? Does that mean, in the same way that Brian Green referred to parallel universes, there is actually another world in which what is going to happen has already happened? Or is Sean Carroll referring to something like Plato’s realm of eternal ideas, existing in the abstract, of which we are but imperfect copies? Is Sean Carroll saying that we call and experience as real events are merely space time possibilities waiting to be actualized by our physical arrival? Or, is Sean Carroll referring primarily to space time locations, slices of space time already existing in the universe, in the sense that space and time, once the universe has started, can be said to exist (although evolving) but that — until we or some other configurations of matter arrive — are empty? Empty, that is, in the sense that we typically think of space and time as empty until something fills it? If so, then it would be space time emptiness and not filled space time that is eternal.

Since I could not know what was in Sean Carroll’s mind, the more I thought about it, the stranger it became. I tried to imagine, in earnest, what it would mean if all the events of our lives that we always had experienced as dynamically evolving in time, had actually already occurred, somehow frozen (and waiting for us) in the space time fabric of the universe. If that is literally true, doesn’t that mean that everything that happens to us — including all our choices, all the underlying molecular, atomic and subatomic events accompanying them, has already been determined? And if that is true, doesn’t that imply that strict determinism must hold all the way down to the subatomic realm (thus violating the canonical principle of quantum uncertainity)? Is saying one is “an eternalist” therefore equivalent to saying time doesn’t exist? Or is that merely saying time doesn’t exist now? Was there ever a moment when time did exist? If everything that occurs has already occurred, when did that great settling in place in space time happen? Was it right after the Big Bang? If time was not a factor, doesn’t that meant that there was no cause and effect, because cause and effect by definition imply an intervening time interval, howsoever infinitesimal?

Skeptical and puzzled though I continued to be, I have no doubt Sean Carroll, if here, could exhaustively and enthusiastically address my questions. My point simply is the highly specialized field of cosmology — the quest to scientifically explore the origin of the universe, with us in it — resonates profoundly on many levels. It is his gift and to his great credit that Sean Carroll can inspire so many questions in the reader, questions in one way or another that have been inscribed in the psyche eons ago by the hand of evolutionary biology — questions, even for world class cosmologists, that continue to grow.

So here in that skeptical, exploratory spirit, is another such question. Sean Carroll is discussing the enormous conceptual difficulties facing the would-be time traveler who aspires to “reverse time’s arrow.” Much as I wanted to follow him in his utterly fascinating but dizzying discussion, I could not picture what Carroll was talking about. What exactly is supposed to happen should we ever achieve the miraculous feat of reversing time’s arrow? Does this mean time reverses all at once, as it would if we suddenly revert to the way things were at some point in our immediate or distant past? Does reversing time, in other words, mean we skip all the intervening events between now and then, and simply arrive — via the space time magic of our hypothetical time machine — at the precise designated moment which we are trying to recapture? Or does it only mean that starting now — at the moment you start up your time machine — you travel sequentially backwards traversing every intervening moment between your starting time and your targeted past time?

The image that immediately suggests itself, of course, is the classic one of a movie running backwards. But if so, there is an immediate problem. It is one thing, using Newtonian mechanics, to imagine reversing the direction of a moving billiard ball. It is another to imagine reversing the direction of something as complicated as a human being. To continue the analogy of running a motion picture backwards: think of a man being shot, falling backwards; now, reversing the film, picture a man lying flat, miraculously returning to his standing position while the bullet, lodged in his chest, returns to the chamber of the gun in the shooter’s hand. Doesn’t that violate, or at least tweak, the known laws of how gravity and ballistics work? If everything were to really run backwards wouldn’t that introduce radically new relationships, if not laws, into physics?

So perhaps the image of a movie running backwards is the wrong one. Perhaps a better one would be a cloud chamber, the kind that is used to track the pathways of a particle in a cyclotron. Perhaps all that is meant is that if we could somehow manage to track every subatomic even in a particle that moves from point A to point B, we might then figure out how not to run everything backwards — but simply how to leapfrog back to the starting point for the particle at point A before it started its journey. It sounded a whole lot simpler.

New questions, however, arose. Never having seen a cloud chamber in person I had trouble holding the mental image of one in mind. I then thought of the famous example of the perfume bottle, an image used by Sean Carroll. There is a perfume bottle, unopened, standing on the dresser. We are asked to first imagine the exact location of the trillions of subatomic configurations underlying the overall molecular structure of the perfume bottle. We are told the perfume bottle is then opened, and over sufficient time, all of the molecules are dispersed. What are the chances those molecules could ever reassemble by themselves back into the perfume bottle in the exact way they were before it was opened? We are talking about the probability of this happening randomly. I imagined this to mean we wouldn’t give it any outside scientific help.

So I thought of just chance. I imagined a billiard ball, pushed by a sudden wind, rolling backwards. Does that count? Is that time’s arrow being reversed? Does time’s arrow being reversed mean that an entire event has to be reversed or can only a single aspect of it be reversed? Would that count?

How would an entire human being be reversed? Would we see a person’s age continuously being reversed, going from maturity back to the womb? In the case of the opened perfume bottle, would every molecule have to return to its original position or could just some of them? What about a chemist, a hundred years from now, with no foreknowledge accidentally preparing a new perfume bottle that just happens — purely by chance — to have the exact molecular structure of our century-old hypothetical perfume bottle? Does that count as time’s arrow being reversed? Or, does time’s arrow being reversed mean — almost immediately after the initial event has transpired? In other words, the bottle is opened, the perfume disperses, and then, incredibly but purely by chance, drifts back, reassembling into the bottle into its exact old position?

The most famous example of all, used by Sean Carroll, Roger Penrose and countless others, is that of several eggs being broken, scrambled, made into an omelet and then — although never before witnessed — somehow unscrambling and reforming itself into eggs, just as before. The example is used to demonstrate the Second Law of Thermodynamics: i.e., that entropy (disorder) always increases in a system. When the perfume is in the closed bottle it is contained in a very particular molecular arrangement, one unlike anything in its immediate environment. Opening the bottle sends the perfume scattering in every conceivable direction. The order is dispersed, diluted and so far as the perfume molecules are concerned, they are in a much more random, disorganized and therefore chaotic state. The same principle applies to the ice cubes being put into a glass of water. As cubes, the water is in a highly organized state (relatively low entropy). Once melted, the previous organization (as ice cubes) is gone and it has now become seemingly impossible to imagine, or ever actually witness, the process being reversed: in this case, for the water to randomly reform itself as ice cubes.

The great mathematical physicist, Ludwig Boltzmann, pointed to probability as being the ultimate explanation for the processes underlying the Second Law of Thermodynamics, which are thought to be pervasive in the universe. A system of matter is in a particular configuration, just one out of an unimaginable number of other possible permutations. The more organized that system is, the less likely it is that it could randomly recur without outside intervention. The perfume in the bottle, the water in the form of ice cubes, is therefore said to be in a comparatively low state of entropy (disorder): all that means is the existing state of organization needs to be protected — by the closed bottle in the case of the perfume and by keeping the frozen water (e.g., cubes) in a refrigerator. Remove the protection — open the perfume bottle without reclosing, drop the ice cubes into a much warmer liquid — and there is an immediate diluting of what once had been a relatively stable structure.

All this Boltzmann explained by the concept of probability. Since it is far less likely for randomly moving matter to wind up in an organized state than in a relatively chaotic one, it does not happen. Since it is less likely for us to be struck by lightning than not, we are almost never struck by lightning. Ditto for being attacked by a shark the next time you go swimming and ditto for being crushed by a falling tree the next time you take a walk through the forest. Boltzmann took this same kind of reasoning and applied it to the case of scrambled eggs randomly unscrambling themselves and winding up as the good old eggs they used to be. The odds of that naturally reoccurring are so astronomically low that we literally never see it happen. Note that Boltzmann is not saying that there is any existing law of nature that says this could not happen, just that it is almost so infinitely unlikely that it is as though there were a law prohibiting it.

Once again, I could not help but be filled by questions when I heard this. How, I asked myself, does Boltzmann know this? Isn’t probability established by a careful evaluation of past experience? Don’t expert handicappers meticulously study every nuance of every fact at their disposal before establishing provisional odds — odds that can immediately be revised at the whiff of a new or undisclosed piece of information?

Boltzmann is saying the reason we have never seen and never will see an omelet randomly turning back into its parent eggs is simply because of astronomically low probability. But aren’t examples of unimaginably improbable events — being eaten by a great white shark, being pronounced medically dead, yet returning to life — established directly by experience? Don’t top notch actuaries determine the likelihood of one in a million or one in a billion events by actually referring to actual verified experience?

So, just what experience, I wondered, does Boltzmann have that melted ice cubes can’t reform, that scrambled eggs can’t unscramble, and that totally dissipated perfume molecules can’t reassemble back to their former allure? But that is exactly the point according to Boltzmann. Things occur in nature because it is probable that they occur. When the odds are out of sight against something occurring, it either rarely occurs (being hit by lightning) or (so far as we’ll ever know) never occurs.

To take this just one step further, if I understand him correctly, Boltzmann is saying that given a universe of infinite space and time — in which anything that can happen will happen — it is certainly possible (or likely) that one time an omelet randomly will turn back into its parent eggs. You would only have to hang around until close to the end of time to witness such an unlikely event. But note, Boltzmann’s key idea — that there is a universe with infinite space and time — is not only unproven but unprovable. Even if true, no one can wait until the end of time because, by definition, there never can be an end to time. Therefore no one, not even a genius like Boltzmann, can possibly say what anyone would or would not experience in a future so incredibly distant. No one can therefore ever have the experience of seeing water turn back into ice cubes. No one can determine the level of improbability of that happening. No one, unless you are thinking of a supreme being, can prophesy what will or will not happen that far into the future. No one, even if they did witness such a miraculous spectacle, could say whether it was an instance of incredible chance or whether there was some unsuspected secret deterministic law at play forbidding such a thing. Finally, to be fair to the great Boltzmann, I’m just wondering if the Second Law of Thermodynamics (that entropy always increases) is more of a philosophical speculation rather than a sacred law.

In From Eternity to Here, Sean Carroll discusses Boltzmann brilliantly. Although he does not address the questions raised here directly, he may very well have compelling answers for them or it may be they are as yet not fully unresolved. My only point is that psychology, in particular the psychodynamic approach, can help clarify the confusion to which everyone (to some extent, even brilliant cosmologists) is susceptible when confronted with these age-old puzzles.

In regard to this I thought of Karl Popper, who famously said you could never prove a given scientific theory was true, but you could prove it was wrong. It therefore followed, said Popper, that the test of whether a particular hypothesis was scientific was whether it was falsifiable. If it wasn’t falsifiable, it wasn’t scientific. It was speculative, it was philosophical, it was creative, it was intuitive, it was even mind-blowing — but it wasn’t scientific. According to Karl Popper, then, if (astronomically) low probability is given by Boltzmann as the true explanation for why we never see time’s arrow reverse itself — i.e., the scrambled eggs unscramble, the melted ice cubes unmelt — then, in order for it to be considered a scientific theory, it would have to be falsifiable. How would you falsify the claim of probability as an explanation? You would either discover a hitherto undetected law which completely explains the supposedly random event, or you accumulate sufficient experience to show the estimate of (astronomical) low probability is wrong. In the case of time’s arrow reversing itself, that could entail, as mentioned, waiting if necessary for an eternity and observing that the hypothetical time’s arrow did not randomly reverse itself even once. That’s what it would take to completely rule out fantastically low probability as a viable explanation. But that, by definition, is impossible, which means Boltzmann’s explanation of low probability cannot be a scientific one. It can be a speculative mathematical, philosophical explanation, but not a scientific one.

Before leaving Sean Carroll, I want to mention just one of the many brain teasers he raises regarding hypothetical time travel. Having already asked why we can remember the past but not the future, he goes on to present the startling question of whether the future can ever determine the present? Can the effect ever precede the cause? We are asked (as a thought experiment) to consider the following fascinating, bizarre, but imaginable case: there is an infallible oracle — one who has never yet been proven wrong — who predicts that if and when a particular Fabergé egg drops and is broken, a certain person dies. Sure enough, the egg drops and the person, on cue, dies.

Sean Carroll then asks why did the Fabergé egg break? Did it break because it was dropped (cause preceding effect) or did it drop because the prediction said it would (effect preceding the cause)? Sean Carroll, if I understand him, is suggesting this would be an example of the future (the infallible oracle’s prediction) determining the present when the time arrives in which the egg drops (or is meant to drop).

To be honest, the more I thought about this, the less sense it made. It didn’t seem to logically follow. In order to demystify Carroll’s example of an infallible oracle (which no one has ever observed) — as a matter of fact, as investigators of paranormal phenomena know well, it is the hallmark of noted psychics that they are notoriously fallible — I thought of some much more garden variety psychics: the local tarot card reader, the fortune teller your friend swears by, the psychic who is on speaking terms with just about everyone (and sometimes their pets) who has ever died.

To be fair then, let’s imagine a fortune teller who happens to be very good at what she does. She is not always on target of course, but she has apparently made some very good predictions, and is right more often than wrong. How does she do it? Assuming she is not an out and out fake (which a surprising number of them are), but believes in what she is doing (as some of them certainly do), then typically she will bring herself to a receptive state (by any of countless means) and wait for a signal.

The signal, then, is really information, information about what would be called a paranormal phenomenon. The signal can come in the form of a vibration, of a kind of voice or, most often, of a kind of fuzzy picture. The picture could be the blurry outline of a not yet fully determined future, which is in the process of becoming, or it could be a direct communication from another reality, a present but generally inaccessible paranormal place. The fortune teller knows from a great deal of past experience if the signal is particularly compelling; more often than not it is conveying accurate information. So, she makes a prediction. She does exactly what all we non-fortune-telling ordinary people do when we live our lives. We make predictions, we calculate guesses about what is likely to happen to us all the time; and when and if they come true it is only because they were based on shrewd appraisal of the present situation, plus an informed understanding, based on our relevant history, of how we got to where we are.

The fortune teller who makes a prediction is doing the same thing. The only difference, of course, and it is a huge one, is that her prediction, in effect, is based on a paranormal hypothesis. She is saying, whenever she gets such a signal, the information it conveys (if properly decoded) tends to be reliable. If that is really what happens, and one day is scientifically validated, then that would of course be extraordinary. But all it would prove is that our gifted seer seemed to have some special relationship with a paranormal phenomenon. It would mean she had a heightened sensitivity to a special vibration, which carries important information about the future that the rest of us don’t have and that can’t yet be explained by conventional science. Where is the necessity to assume that the fortune teller had access to a time warp, a time tunnel — that she somehow traveled to the future, experienced an effect — and then came back?

A successful prediction is only to claim knowledge of the future, but it doesn’t imply experience of the future no matter how uncanny the possession of such knowledge seems. The professional seer does not claim to have visited the future, only to somehow know the future. The professional seer does not offer a scientific theory to explain how they do what they do. The professional seer says merely they do what they do because they have a gift. Part of their craft, of course, is to do everything in their power to dramatize the mysteriousness of what they do. They are well aware on some level (if not consciously, then unconsciously) that when knowledge of the future appears to be incomprehensibly, inexplicably precise, the ordinary person will tend to imbue the messenger of things to come with assorted supernatural powers.

I feel compelled, in terms of this book, to reiterate that it is the questions and not the answers that are important. They are questions that carry certain psychological meaning. They are rarely asked by non-specialists in the field, such as myself, not because they are not relevant, but because the mind tends to shut off when they are raised. That is because, as mentioned, we are creatures shaped by evolutionary biology to live in a mid-world that is not too big and not too small. It is hardly the world that contemporary cosmology is exploring. It is not the world that our so-called golden age of observational astronomy is hungrily mapping. It is not the world that Hubble and its successor Kepler are encountering as it peers into the far edges of our galaxy’s past.

Cosmologists are by no means immune to the paradoxes, the primal wonder of just what or where is our place in the cosmos. Reading Sean Carroll I became aware that I often could not tell where he was coming from. I could not tell when he was philosophizing, when he was just speculating, when he was engaged in cosmological hypothesizing or when he was doing hard and fast science. I wondered where he would draw the line if asked to define his own definitions of the parameters as he saw them between philosophy, metaphysics and cosmological science.

How would he explain the difference between what he is doing when he raises the hypothesis of a multiverse to explain the extraordinary fine-tuning we find at the moment of the Big Bang — and those who insist the only hypothesis which makes sense is that of an intelligent designer (ID)?

How would he answer the charges that the insistence of contemporary science on experimental proof for all such claims is just another form of faith? That the assertion that the ultimate basis of the cosmos is physical, that there is no such thing as a transcendental, non-materialistic origin, is itself without experimental proof?

Part of the problem is that cosmologists, who are part of the cosmos, are asking questions that are best answered by an observer who is outside of the cosmos. Since no such observer exists (within science), there is no one or no technological super-machine (which must always be within the cosmos) that can do this. In regard to whether time’s arrow therefore can reverse itself, we would need to step out of time or before time. We may never come close to doing that.

In terms of the Second Law of Thermodynamics — that entropy (disorder) always increases — it would help if we could peer behind the Big Bang, or look directly at the moment of the Big Bang. We might then be able to answer the question of whether the singularity which started everything was really so incredibly fine-tuned. We could answer the question of whether the hypothesized first point/atom of energy/matter that exploded was, for example, more or less organized and fine-tuned than perhaps the most intact object in our present universe: the human brain. We might answer the question of whether the large scale universe today, 13.7 billion years later, is really far more random and chaotic (less organized) than it was at that long-ago moment of creation. But we can’t.

The reader will see why, when Sean Carroll at one point said that Einstein’s General Relativity is “really based on a simple idea,” I could only balk. Why then is it so famously hard to understand? Sean Carroll is thinking perhaps of those iconic pictures — a boy riding ahead of a ray of light and looking back…a man in a falling elevator who cannot experience his weightlessness — that geniuses like Einstein often point to as a source of their inspiration. The difficulty does not lie in the picture, it comes in when the scientist attempts to translate the seemingly self-evident picture into the kind of rigorous quantification that can survive exacting predictions made in the messy real world.

Few books drive this point home as forcefully as David Mermin’s superb It’s About Time: Understanding Einstein’s Relativity, a work garnering accolades from no less than Brian Green and Peter L. Galison. Not satisfied with simple pictures, howsoever powerful, David Mermin searches for the underlying foundational principle that it illuminates. In an uncanny way, reading him, you get the sense that you are walking in the footsteps of Einstein — the creator — as he first dreamed up his revolutionary revamping of the then 250-year-old idea of space and time. Is this then the “aha” experience that Sean Carroll and so many others talk about? Well, maybe for them. For the rest of us there is instead a vivid impression of a shifting mosaic of interconnected details and obstacles, a baffling chaotic incubation that somehow gave birth to an admittedly great theory.

From a psychodynamic perspective, the meme of the simple great idea is an ad hoc construct meant to impose a soothing narrative arc on an unconscious context that is anything but simple. From the psychodynamic perspective, it is not a coincidence that the geniuses who manage to come up with these “simple great ideas” just happen to manifest extraordinary ability for complex thinking. From this richer contextual point of view, complexity and breathtaking simplicity are therefore linked aspects of a single process.

Think of a puzzle — say the picture of a racing horse — but in a thousand pieces of various dimensions. No one knows how to fit the pieces together or what the unifying picture would look like if it could ever be found. In this hypothetical example, the genius’ “great simple idea” would be: “the pieces will fit together if the picture is a horse!”

Note it is the genius who arrives at this idea because it is he who can simulate the countless permutations in his mind (like a computer) until he hits upon the very simple idea of a horse. The genius can have an epiphany of the unifying horse picture because he can tirelessly, mentally experiment with an incredible number of seemingly disparate elements, without retreating into hopeless confusion.

In other words, it is not enough to stumble upon a key idea, one must be able to envision how the new idea fits in with everything else that is already known (Richard Feynman famously referring to the “straight jacket” that the physicist wears: the new ideas must “not only be right, but it cannot contradict any known fact”). It may therefore be that the great simple idea comes at the end — not the beginning — of a complex process. It may be what will become the final piece of the puzzle at first is something constantly being modified by mental rotation and possible configurations — so that it more and more begins to resemble the eventual unifying idea — which, ready at last at the tip of the preconscious, presses for crystallization into consciousness (the aha moment). It follows the great simple idea will often come after much of the difficult complex thinking has been completed: e.g., Watson and Crick, at the very end of their historic quest for the secret of DNA, hitting on the idea of the double helix. Only a genius is likely to be able to do this, to have the confidence to “know” that the unifying key idea can be that simple because they, better than anyone, know the extraordinary hard work necessary to prepare for its final arrival.

Although obvious it is also worth saying. Simple ideas are easier to remember than complicated ones. Pictures are easier to assimilate than words. Great simple ideas that are in essence word pictures are easier to understand than great abstract ideas that are not word pictures (like Gregor Cantor’s idea of one infinity being bigger than another). We remember that Darwin was the father of the great idea that every living creature is evolutionarily united by common descent from a single ancestor. But almost no one wants to read his great taxonomic masterpiece on the evolutionary linkages of the barnacle family (Cirripedia) because it requires an attention to detail almost unrivaled in the history of biology. We remember Freud’s dramatic ideas of the Freudian slip, the repressed unconscious, the interpretation of dreams. But almost no one, not even the great psychoanalyst Erik Erikson, wants to read his amazing Project for a Scientific Psychology, a seminal attempt to model the neurodynamics of the human mind. We remember the apple hitting Newton on the head and the subsequent epiphany of an instantaneous attractive force between any two objects in the universe, no matter how far apart (e.g., the earth and the moon). But few are willing to read (or even try to read) his immortal masterpiece, The Principia, in which he almost single-handedly creates the modern discipline of mathematical physics.

Gerald Alper Author

God and Therapy

What we believe when

no one is watching

Author. Psychotherapist. Writing about psychology for all to read. I also interview scientists.