How the Universe Got Its Spots: Diary of a Finite Time in a Finite Space

By Janna Levin

Is the universe infinite, or is it just really big? Does nature abhor infinity? In startling and beautiful prose, Janna Levin's diary of unsent letters to her mother describes what we know about the shape and extent of the universe, about its beginning and its end. She grants the uninitiated access to the astounding findings of contemporary theoretical physics and makes tangible the contours of space and time—those very real curves along which apples fall and planets orbit.

Levin guides the reader through the observations and thought-experiments that have enabled physicists to begin charting the universe. She introduces the cosmic archaeology that makes sense of the pattern of hot spots left over from the big bang, a pursuit on the verge of discovering the shape of space itself. And she explains the topology and the geometry of the universe now coming into focus—a strange map of space full of black holes, chaotic flows, time warps, and invisible strings. Levin advances the controversial idea that this map is edgeless but finite—that the universe is huge but not unending—a radical revelation that would provide the ultimate twist to the Copernican revolution by locating our precise position in the cosmos.

As she recounts our increasingly rewarding attempt to know the universe, Levin tells her personal story as a scientist isolated by her growing knowledge. This book is her remarkable effort to reach across the distance of that knowledge and share what she knows with family and friends—and with us. Highly personal and utterly original, this physicist’s diary is a breathtaking contemplation of our deep connection with the universe and our aspirations to comprehend it.

• Language: English
• Publisher: Princeton University Press
• Release date: Jan 10, 2023
• ISBN: 9780691232287

Book preview

PREFACE TO THE 2023 EDITION

I am rereading How the Universe Got Its Spots as though the diary was authored by someone else, which to some extent it was, if not by someone else entirely. I’m privy to the same recollections that are recounted in these pages, though mine are currently more diffuse, less immediate, and less accurate, permuted by time and experience. Though I’m disadvantaged by the erosion of those impressions and by the unconscious revision of personal history, I do have the advantage of hindsight. I am the future me, interpreting the past with a knowledge of things to come, reading the words of the former me, watching in the theater of my own mind as a representative of a prior self grapples with the uncertainty of immediacy. And I’m resisting revision.

I intended for incertitude to permeate the book. I pay homage to and have respect for the confidence of the classic scientific works by the accomplished and the lauded—it’s perfectly sensible for a renowned expert to share a lifetime of hard-earned knowledge, intuition, discovery, and acclaim. I have many such books on my own shelves. The authors wrote from the vantage of success and achievement. They knew the story’s end: Revelation. And though the tales were often thrilling, the discoveries monumental, and the understanding of the universe conveyed literally mind-altering, there was a vertical gulf between the author and the reader that I wanted to undermine. The certainty itself I wanted to undermine. I did not know my story’s end. Precisely because of my precarious status as a young, neoteric explorer, not yet secured in the ranks, I hoped to convey both the thrill and the anxiety of not knowing. I wanted to share with anyone who would listen not just revelations, though there are those in this book too, but also the fragile ideas—lavish ideas—that might otherwise be lost.

In writing this work, I stepped out of the conventional order dictated by unofficial, though not unspoken, rules to which successful scientists ought to adhere for smoothest ascent in academia: Get PhD, do postdoctoral research, do more postdoctoral research, get professorship, publish, publish, publish, stay in the lab for thirty-five years before emerging like Zarathustra coming down from the mountain. I realized quite early that a conventional path wasn’t actually available. Instead I saw an unscalable route cluttered by obstacles. I understand better now that life is the obstacles, there is no underlying paved way. The prospect of carving out a new byway through academia was intimidating, but even in my inexperience I knew that was the challenge demanded, or else I must relinquish the dream. This book was a first radical departure into untrodden terrain. I would write moment by moment, confessing all the while my own self-doubt. I would also find myself expressing a fair bit of irreverence, impulsiveness, impiety.

I included my personal exploits uninhibited because I anticipated they would be savagely cut once the editors got hold of the manuscript. I expressed those details in order to marinate in the mindset and set the tone, to establish intimacy, to keep me grounded in my own uncertainty so I wouldn’t slip into the cadence of an expert parsing out knowledge from some far-off vantage—a vantage I hadn’t yet earned. As you’ll see, those passages did not get cut, could not be cut really without doing violence to the structure. Whether or not I was entirely comfortable, the personal trip was integral to the scientific one.

The conceptual themes detailed here endure. We still do not know if the universe is infinite or finite, if there are extra, multiply connected dimensions, if nature executed an extravagant cosmic origami. Cosmologists have since confirmed suspicions that the expanding observable universe is roughly flat, that we cannot see all the way around a hypothetically compact cosmos. Still, the universe will reveal more and more beyond our present observable horizon over the coming centillion years. Though we won’t be here to see, light will reach our location from deeper into space and into time. We do not know whether spacetime stretches forever or wraps back onto itself, compact and finite. We might never know. The story may have no end.

This book changed my life, as though in the process of writing I had to unlock unexplored caves in my own mind that previously were not just inaccessible but unknown to me. The singular, dedicated intensity that is required to survive graduate school felt muscular, edifying, and as gratifying as reaching the summit after a harrowing climb. The singularity of focus was also brutal to sustain and inflicted significant collateral damage. I felt creatively bruised and suppressed. I had repressed the urge to write expressively in favor of mathematical research, concentrating on technical articles, which accommodate limited room to stretch. With How the Universe Got Its Spots, I had the inverted challenge to find a voice and a mood, to offer a visceral experience of the beauty of an austere cosmos.

Princeton University Press published the US edition in 2002, shortly after the original UK edition. I moved from England back to New York City as an assistant professor at Barnard College of Columbia University, with a baby and a husband. My trajectory had been unconventional and even seemingly hazardously misdirected, but each apparently confounding pivot was thoroughly considered. My research had shifted, and I began to build a small group with graduate students and postdocs focused on the elegance of black holes, from harbingers of chaos to beacons of light and gravitational sounds.

Nearly a decade later, I was invited to tell a story onstage at The Players iconic club in Manhattan for The Moth, a group dedicated to the art of storytelling. The rules are simple. Each story has to be true, autobiographical, oratory—no notes—and around ten minutes long. On that particular night, The Moth curated stories coproduced by the World Science Festival featuring scientists, including the founder of the human genome project, a hand-transplant surgeon restoring limbs to Iraqi veterans, a neuroscientist who discovered a gene for psychopathy (which he then discovered he carried), and a Nobel Prize–winning chemist—who had survived the Holocaust. And me. I felt ludicrous, almost panicked, to be on the roster. Sharing the stage with those accomplished scientists catapulted me back to that unassured, trepidatious, apprehensive youth who authored this book. I spent a solid hour stomping holes in the sidewalk around Gramercy Park to burn off my nervousness, practically to the final minute, as though I would come up the stairs, march straight onto the stage, and tell the story—at the urging of The Moth’s creative director, Catherine Burns—seeped in my personal affairs and inspired by this book, continuing on from the epilogue you’ll find on the final page of the volume. With Catherine’s unwavering direction, I told my story, nerves at bay. (At the time of this writing, the Moth story, along with How the Universe Got Its Spots, is under development in a film adaptation titled Mobius.)

I am a scientist immersed with artists and musicians, from the years recounted in this diary to the present. I write to you now with my feet propped up on the far side of a window covered in ivy, though it’s not the college. The former Pioneer Iron Works factory built in the mid-1800s loomed in a state of disrepair over a brutalist concrete storage yard on a remote Brooklyn corner overlooking the East River until the artist Dustin Yellin scrounged, pleaded, and magicked up the funds to procure the building. Dustin saw in the invaluable, aged brick and the mammoth wooden trusses a vivid utopian hallucination, a psychedelic, animated collage of artists and scientists that would come to fill the building with music and noise, provocations and discussions. Dustin, alongside founding artistic director Gabriel Florenz and a few neighborhood loyalists, lovingly transformed the structure, which a century ago survived a blaze, was rebuilt, took an unforgiving lashing during hurricane Sandy and the flood that followed, and most recently was struck by lightning, dislodging a singed brick off the defunct chimney that adorns the roof. When I first stepped into the energized but as-yet unfinished grand hall nearly a decade ago, it was as though every jagged, precarious redirect in my idiosyncratic trajectory—from Barnard to MIT to Berkeley to Cambridge back to Barnard and Columbia—had also led me here, to this building, to a particular gestating, abundant juncture. My arrival felt as inevitable as it had seemed improbable.

Gabe and Dustin would become powerful forces in my life and, I believe it’s not overstepping to say, I in theirs. I spent some months drifting around the rustic third floor, watching enthralled as exhibitions were built and demolished, finishing my own books to the soundtrack of laser cutters, hammering, rehearsals, welding, and the monotone beep of scissor lifts. Some nights I would stay late on that top floor, supine on a ragged brown couch that somehow had been hoisted over the catwalks and abandoned in an empty vast space that drew electricity from the more refined floors below. I shared the apparition of a coalescence of culture and science. I would call out to Dustin and Gabe that I had become an occupant of their collective hallucination, that we were going to build the world we wanted to live in, which became a sort of mantra for us. We are building the world we want to live in.

Pioneer Works is now a living, thriving, vibrant, eccentric cultural center, a magnet for vivacious artist and music residencies, concerts, singular exhibitions, and epic events that span social crises to the most abstract scientific endeavors. With generous philanthropic gifts, we converted that neglected third floor to Science Studios, and I became the Director of Sciences. During the crush of the recent plague, we launched Pioneer Works Broadcast, itself a work of art and science, a manifestation of Pioneer Works beyond the walls in virtual form, for which I am the editor in chief.

Whether as editor or writer, each time I experiment with prose I betray that I am besotted with nature. And each time I experiment, I struggle with the conflict between abstract truths that transcend culture, time, humanity itself and the distinctly personal, emotive, subjective pleasure found in language—spoken, written, mathematical. My peculiar navigation through the world has been steered by the tension between the lyricism of languages and the constraint of reality’s demand for respect.

There are days when I am a canonical university professor in an office flanked by overcrowded bookshelves on the walls and unstable towers of books on the floor. There are sheets of unlined paper nearly everywhere with calculations that refine increasingly neater as the ideas are worked and reworked until the paper deserves to be discarded or transcribed. I am grateful to be back in the classroom, and I feel a devotion to my students whose time with me is, by construction, transitory. I lose days to thoughts about black holes or the topology of extra dimensions or the nature of dark energy. There are other days I occupy the Science Studios at Pioneer Works, a space minimally decorated and carefully adorned by a few selected artworks, a piano, and a handmade, vintage-inspired bar. The two spaces deny being the product of the same psyche, yet they are.

I am often overwhelmed. I loathe when I complain. Sometimes I wish it was all simpler. Easier. Less demanding. But never—never—am I bored. I’m still trying to find my way. I no longer resent the obstacles. I pine for greater ease and less angst. I hope I will have the privilege of contemplating the universe quite a bit longer. I am still a student of nature and mathematics and words. I am grateful especially to you the reader for coming along on this compulsive exploration to understand, to contemplate our place, to be humbled and stretched beyond our presumed capacities. I am grateful to you for facing ambiguity. With any luck, this tale won’t end any time soon.

1

IS THE UNIVERSE INFINITE OR IS IT JUST REALLY BIG?

Some of the great mathematicians killed themselves. The lore is that their theories drove them mad, though I suspect they were just lonely, isolated by what they knew. Sometimes I feel the isolation. I’d like to describe what I can see from here, so you can look with me and ease the solitude, but I never feel like giving rousing speeches about billions of stars and the glory of the cosmos. When I can, I like to forget about maths and grants and science and journals and research and heroes.

Boltzmann is the one I remember most and his student Ehrenfest. Over a century ago the Viennese-born mathematician Ludwig Boltzmann (1844–1906) invented statistical mechanics, a powerful description of atomic behaviour based on probabilities. Opposition to his ideas was harsh and his moods were volatile. Despondent, fearing disintegration of his theories, he hanged himself in 1906. It wasn’t his first suicide attempt, but it was his most successful. Paul Eherenfest (1880–1933) killed himself nearly thirty years later. I looked at their photos today and searched their eyes for depression and desperation. I didn’t see them written there.

My curiosity about the madness of some mathematicians is morbid but harmless. I wonder if alienation and brushes with insanity are occupational hazards. The first mathematician we remember encouraged seclusion. The mysterious Greek visionary Pythagoras (about 569 BC–about 475 BC) led a secretive, devout society fixated on numbers and triangles. His social order prospered in Italy millennia before labour would divide philosophy from science, mathematics from music. The Pythagoreans believed in the mystical meaning of numbers and developed a religion tending towards occult numerology. Their faith in the sanctity of numbers was shaken by their own perplexing mathematical discoveries. A Pythagorean who broke his vow of secrecy and exposed the enigma of numbers that the group had uncovered was drowned for his sins. Pythagoras killed himself too. Persecution may have incited his suicide, from what little we know of a mostly lost history.

When I tell the stories of their suicide and mental illness, people always wonder if their fragility came from the nature of the knowledge – the knowledge of nature. I think rather that they went mad from rejection. Their mathematical obsessions were all-encompassing and yet ethereal. They needed their colleagues beyond needing their approval. To be spurned by their peers meant death of their ideas. They needed to encrypt the meaning in others’ thoughts and be assured their ideas would be perpetuated.

I can only write about those we’ve recorded and celebrated, if posthumously. Some great geniuses will be forgotten because their work will be forgotten. A bunch of trees falling in a forest fearing they make no sound. Most of us feel the need to implant our ideas at the very least in others’ memories so they don’t expire when our own memories become inadequate. No one wants to be the tree falling in the forest. But we all risk the obscurity ushered by forgetfulness and indifference.

I admit I’m afraid sometimes that no one is listening. Many of our scientific publications, sometimes too formal or too obscure, are read by only a handful of people. I’m also guilty of a self-imposed separation. I know I’ve locked you out of my scientific life and it’s where I spend most of my time. I know you don’t want to be lectured with disciplined lessons on science. But I think you would want a sketch of the cosmos and our place in it. Do you want to know what I know? You’re my last hope. I’m writing to you because I know you’re curious but afraid to ask. Consider this a kind of diary from my social exile as a roaming scientist. An offering of little pieces of the little piece I have to offer.

I will make amends, start small, and answer a question you once asked me but I never answered. You asked me once: what’s a universe? Or did you ask me: is a galaxy a universe? The great German philosopher and alleged obsessive Immanuel Kant (1724–1804) called them universes. All he could see of them were these smudges in the sky. I don’t really know what he meant by calling them universes exactly, but it does conjure up an image of something vast and grand, and in spirit he was right. They are vast and grand, bright and brilliant, viciously crowded cities of stars. But universes they are not. They live in a universe, the same one as us. They go on galaxy after galaxy endlessly. Or do they? Is it endless? And here my troubles begin. This is my question. Is the universe infinite? And if the universe is finite, how can we make sense of a finite universe? When you asked me the question I thought I knew the answer: the universe is the whole thing. I’m only now beginning to realize the significance of the answer.

3 SEPTEMBER 1998

Warren keeps telling everyone we’re going back to England, though, as you know, I never came from England. The decision is made. We’re leaving California for England. Do I recount the move itself, the motivation, the decision? It doesn’t matter why we moved, because the memory of why is paling with the wear. I do remember the yard sales on the steps of our place in San Francisco. All of my coveted stuff. My funny vinyl chairs and chrome tables, my wooden benches and chests of drawers. It’s all gone. We sit out all day as the shade of the buildings is slowly invaded by the sun and we lean against the dirty steps with some reservation. Giant coffees come and go and we drink smoothies with bee pollen or super blue-green algae in homage to California as the neighbourhood parades past and my pile of stuff shifts and shrinks and slowly disappears. We roll up the cash with excitement, though it is never very much.

When it gets too cold or too dark we pack up and go back inside. I’m trying to finish a technical paper and sort through my ideas on infinity. For a long time I believed the universe was infinite. Which is to say, I just never questioned this assumption that the universe was infinite. But if I had given the question more attention, maybe I would have realized sooner. The universe is the three-dimensional space we live in and the time we watch pass on our clocks. It is our north and south, our east and west, our up and down. Our past and future. As far as the eye can see there appears to be no bound to our three spatial dimensions and we have no expectation for an end to time. The universe is inhabited by giant clusters of galaxies, each galaxy a conglomerate of a billion or a trillion stars. The Milky Way, our galaxy, has an unfathomably dense core of millions of stars with beautiful arms, a skeleton of stars, spiralling out from this core. The earth lives out in the sparsely populated arms orbiting the sun, an ordinary star, with our planetary companions. Our humble solar system. Here we are. A small planet, an ordinary star, a huge cosmos. But we’re alive and we’re sentient. Pooling our efforts and passing our secrets from generation to generation, we’ve lifted ourselves off this blue and green water-soaked rock to throw our vision far beyond the limitations of our eyes.

The universe is full of galaxies and their stars. Probably, hopefully, there is other life out there and background light and maybe some ripples in space. There are bright objects and dark objects. Things we can see and things we can’t. Things we know about and things we don’t. All of it. This glut of ingredients could carry on in every direction forever. Never ending. Just when you think you’ve seen the last of them, there’s another galaxy and beyond that one another infinite number of galaxies. No infinity has ever been observed in nature. Nor is infinity tolerated in a scientific theory – except we keep assuming the universe itself is infinite.

It wouldn’t be so bad if Einstein hadn’t taught us better. And here the ideas collide so I’ll just pour them out unfiltered. Space is not just an abstract notion but a mutable, evolving field. It can begin and end, be born and die. Space is curved, it is a geometry, and our experience of gravity, the pull of the earth and our orbit around the sun, is just a free fall along the curves in space. From this huge insight people realized the universe must be expanding. The space between the galaxies is actually stretching even if the galaxies themselves were otherwise to stay put. The universe is growing, ageing. And if it’s expanding today, it must have been smaller once, in the sense that everything was once closer together, so close that everything was on top of each other, essentially in the same place, and before that it must not have been at all. The universe had a beginning. There was once nothing and now there is something. What sways me even more, if an ultimate theory of everything is found, a theory beyond Einstein’s, then gravity and matter and energy are all ultimately different expressions of the same thing. We’re all intrinsically of the same substance. The fabric of the universe is just a coherent weave from the same threads that make our bodies. How much more absurd it becomes to believe that the universe, space and time could possibly be infinite when all of us are finite.

So this is what I’ll tell you about from beginning to end. I’ve squeezed down all the facts into dense paragraphs, like the preliminary squeeze of an accordion. The subsequent filled notes will be sustained in later letters. You could say this is the story of the universe’s topology, the branch of mathematics that governs finite spaces and an aspect of space-time that Einstein overlooked. I don’t know how this story will play itself out, but I’m curious to see how it goes. I’ll try to tell you my reasons for believing the universe is finite, unpopular as they are in some scientific crowds, and why a few of us find ourselves at odds with the rest of our colleagues.

2

INFINITY

14 SEPTEMBER 1998

I’m on the train back from London – gives me time to write, this time about Albert Einstein, hero worship, idolatry and topology. Somebody told me he is reported to have said, ‘You know, I was no Einstein.’ He couldn’t get a job. His dad wrote letters to famous scientists begging them to hire his unemployed son. They didn’t. The Russian mathematician Hermann Minkowski (1864–1909) actually called him a ‘lazy dog’. Can you imagine? He worked a day job as a patent clerk and thought about physics maybe all the rest of his waking hours. Or maybe the freedom from the criticism of his colleagues just gave his mind the room it needed to

Reviews for How the Universe Got Its Spots

[dlmorrese · Rating: 3 out of 5 stars]

Musings on the shape, size, and nature of the universe...framed by a personal diary. It makes for an odd combination, but it does remind us that scientists are also all-too-human.

[cliffhays · Rating: 5 out of 5 stars]

Do you believe that the universe is infinite? In this book Levin gives a compelling argument that may cause you to reexamine that belief. It begins with the question "Is the Universe Infinite or Just Really Big?" and launches into a fascinating topological exploration of very large-scale phenomena (particularly the cosmic microwave background). The style, cleverness, and clarity with which she writes is unmatched by most authors today. Reading this will not only cause you to laugh outloud but will also allow your mind to grasp some highly technical and theoretical concepts that when presented in most other texts are largly unintelligible. For anyone who is interested in the workings of the universe at large I highly recommend it.

[criddick_3 · Rating: 3 out of 5 stars]

Interesting look into the life of a junior scientist. While providing glimpses into the chaotic life of the scientist, Levin also manages too provide very insightful looks at some of the tough mathematical and cosmological concepts. As a former math and physics major, I found her ideas refreshing and exciting.

[eduscapes · Rating: 5 out of 5 stars]

After listening to an interview with Janna Levin on the NPR program Speaking of Faith, I became interested in reading her books. Levin is an astrophysicist and author interested in sharing her interest in topics from quantum mechanics to a Theory of Everything.In the book How the Universe Got Its Spots, Levin uses a diary/letter style to explain contemporary theoretical physics in a way that is accessible to a layperson like me. She weaves the science through stories from everyday life. Her engaging writing style and excellent examples makes complex topics such as Einstein's theories easier to understand. It's interesting to learn how much we know and how much we still don't know about our universe. Is the universe finite or infinite? We really don't know.One of the most amazing aspects of the book is her interest in cosmic archaeology which examines the patterns of hot spots left over from the big bang. I was also fascinated by her explanations of topology and geometry of the universe. I've always been interested in the idea of more than three dimensions, but it wasn't until I read this book that I began to understand how these other dimensions might work. It's been nearly a decade since this book was written. I look forward to reading her newer, award-winning book titled A Madman Dreams of Turing Machines.Here's one of my favorite quotes from the book:“…there are no walls built in the human mind making some of us scientists and some of us artist. They are branches of the same tree, rooted in a common human essence. Maybe it’s out ability to step between the different disciplines, weaving strange loops all the while, that’s the core of our creativity.” (p. 193)

[librisissimo · Rating: 3 out of 5 stars]

Interesting juxtaposition of author's private life and professional work. Accessible explanations of astrophysical phenomena.

[ajburton · Rating: 4 out of 5 stars]

Janna Levin, a young and upcoming astrophysicist, leads the reader through a journey into the theories of cosmology and theoretical physics as she searches for clues to the structure of the universe. Is the universe infinite or just so big that it appears infinite to us? Her unique perspective from a topological view lends itself to possibly predicting the shape of the cosmic microwave background, thus showing the universe is finite and has a shape.Her thoughts are presented as letters she has written to her mother to explain her cosmological notions. This combined with her words about academia, her professional life, and her personal life make this book a unique and charming read. Do not expect many details regarding the many theories mentioned in the book, most are only dealt with from a conceptual or high level view.If you are interested in cosmology, or think you might be interested in cosmology, I would highly recommend this book.

[myfanwy_1 · Rating: 4 out of 5 stars]

I was recommended this book by the illustrious E. I paraphrase, but I think he described it as a book about cosmology and heartbreak. Janna Levin, is a leading young scientists in theoretical astrophysics and wrote this book in the form of a collection of explanatory letters to her mother. She peppers her descriptions of concepts in cosmology with occasional glimpses of her life, one composed of a series of dismal english apartments and constant travel.Cosmology is something that I have only the vaguest knowledge of. In my mind it's a sort of amalgam of pieces from Einstein's relativity and philosopher's questions of the nature of the universe. Levin does a remarkable job explaining it without making the reader feel dense. She describes the nature of infinity, and infinities which are larger than other infinities. She spends quite a bit of time on topology and topology in different dimensions, and she ends with a discussion of the universe and how we may one day perceive its finiteness, if it is indeed finite. I came away from the book with the sense that we are waiting for ripples of light from the shores of the universe, but of course there are no shores to speak of, are there?I'm quite sure I didn't understand all that was in this book. Nonetheless, this is an interesting book with just enough cosmology to whet the tastes of the uninitiated, like myself.

[workgman · Rating: 4 out of 5 stars]

i'm usually a fiction fan myself but my copy ended up with so many flags in it that i'm sure i will have to expand this portion of my library; i want to know more.