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Posts Tagged ‘science’

27 JANUARY, 2015

The Absurdity of Infinity: Astrophysicist Janna Levin Explains Whether the Universe Is Infinite or Finite in Letters to Her Mother


“The simpler the insight, the more profound the conclusion.”

In 1998, while on the cusp of becoming one of the most significant theoretical cosmologists of our time, mathematician-turned-astrophysicist Janna Levin left her post at Berkeley and moved across the Atlantic for a prestigious position at Cambridge University. During the year and a half there, she had the time and space to contemplate the question that would eventually become the epicenter of her career — whether the universe is infinite or finite. What began as a series of letters to her mother, Sandy, eventually became an unusual diary of Levin’s “social exile as a roaming scientist,” and was finally published as How the Universe Got Its Spots: Diary of a Finite Time in a Finite Space (public library) — a most unusual and absorbing account of the paradoxes of finitude.

“I’m writing to you because I know you’re curious but afraid to ask,” Levin offers in the opening letter — a “you” that instantly becomes as much her mother as the person Virginia Woolf memorably termed “the common reader.” From there, she springboards into remarkably intelligent yet inviting explorations of some of the biggest questions that the universe poses — questions most of us contemplate, sometimes consciously but mostly not, just by virtue of being sentient participants in the chaos and enchantment of existence.

A 1617 depiction of the notion of non-space, long before the concept of vacuum existed, found in Michael Benson's book 'Cosmigraphics'—a visual history of understanding the universe. Click image for more.

In an entry from September 3, 1998, Levin fleshes out her ideas on infinity and writes with exquisite Saganesque sensitivity to the poetics of science:

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, spiraling 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.

Illustration from Thomas Wright’s visionary 1750 treatise 'An Original Theory,' found in Michael Benson's book 'Cosmigraphics'—a visual history of understanding the universe. Click image for more.

But having painted this bewitching backdrop for our intuitive beliefs, Levin sublimates the poet to the scientist, pointing out that however alluring these intuitions may feel, they are nonetheless ungrounded in empirical fact:

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, aging. 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.

A decade and a half later, Alan Lightman would come to write with a similar scientific poeticism about why we long for permanence in a universe defined by constant change. But however poetic the premise, Levin brings a mathematician’s precision to her “reasons for believing the universe is finite, unpopular as they are in some scientific crowds.” In another entry twelve days later, she writes:

Infinity is a demented concept…

Infinity is a limit and is not a proper number. No matter how big a number you think of, I can add 1 to it and make it that much bigger. The number of numbers is infinite. I could never recite the infinite numbers, since I only have a finite lifetime. But I can imagine it as a hypothetical possibility, as the inevitable limit of a never-ending sequence. The limit goes the other way, too, since I can consider the infinitely small, the infinitesimal. No matter how small you try to divide the number 1, I can divide it smaller still. While I could again imagine doing this forever, I can never do this in practice. But I can understand infinity abstractly and so accept it for what it is.

Pointing out that all titans of science — including Galileo, Aristotle, and Cantor — were besotted with the notion of infinity at some point, “each visiting the idea for a time and then abandoning the pursuit,” Levin notes that we can neither accept nor dismiss infinity on the basis of popular opinion alone. In early October, she writes:

Where in the hierarchy of infinity would an infinite universe lie? An infinite universe can host an infinite amount of stuff and an infinite number of events. An infinite number of planets. An infinite number of people on those planets. Surely there must be another planet so very nearly like the earth as to be indistinguishable, in fact an infinite number of them, each with a variety of inhabitants, an infinite number of which must be infinitely close to this set of inhabitants. Another you, another me. Or there’d be another you out there with a slightly different life and a different set of siblings, parents, offspring. This is hard to believe. Is it arrogance or logic that makes me believe this is wrong? There’s just one me, one you. The universe cannot be infinite.


I welcome the infinite in mathematics, where … it is not absurd nor demented. But I’d be pretty shaken to find the infinite in nature. I don’t feel robbed living my days in the physical with its tender admission of the finite. I still get to live with the infinite possibilities of mathematics, if only in my head.

Illustration by Lisbeth Zwerger for 'Alice in Wonderland.' Click image for more.

Understanding the infinite — both as a mathematical possibility and an impossibility of the physical universe — might be more a matter of coming to terms with infinite simplicity than with infinite complexity. In an entry from early February of 1999, Levin echoes Margaret Mead’s famous proclamation about clarity and writes:

I try to find a simple expression for my ideas. I figure if there is none, the ideas must be wrong. When I first started to work on topology I wondered about complex properties of spaces and didn’t take my own suggestions seriously until I realized the simple way to ask the question: is the universe infinite? Einstein’s simplest insights were profound. The simpler the insight, the more profound the conclusion.

In the remainder of How the Universe Got Its Spots, which is unbearably beautiful in both intellectual elegance and stylistic splendor, Levin goes on to explore questions of quantum relativity and freewill, death and black holes, spacetime and Wonderland, and more. Complement it with Levin on science, free will, and the human spirit, then revisit Alan Lightman on how dark energy explains why we exist and treat yourself to this poetic primer on the universe written in the 1,000 most common words in the English language.

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19 JANUARY, 2015

The Paradox of Intellectual Promiscuity: Stephen Jay Gould on What Nabokov’s Butterfly Studies Reveal About the Unity of Creativity


“There is no science without fancy, and no art without facts.”

The history of human culture is rife with creators hailed as geniuses in one domain who also had a notable but lesser-known talent in another — take, for instance, Richard Feynman’s sketches, J.R.R. Tolkien’s illustrations, Sylvia Plath’s drawings, William Faulkner’s Jazz Age illustrations, Flannery O’Connor’s cartoons, David Lynch’s conceptual art, and Zelda Fitzgerald’s watercolors. Only rarely, however, do we encounter a person who has contributed to culture in a significant way in both art and science.

No one, argues Stephen Jay Gould — perhaps the greatest science-storyteller humanity has ever had, a man of uncommon genius in the art of dot-connecting — better merits recognition for such duality of genius than Vladimir Nabokov, a titan of literary storytelling and a formidable lepidopterist who studied, classified, and drew a major group of butterflies, and even served as unofficial curator of lepidoptery at Harvard’s Museum of Comparative Zoology.

In a spectacular essay titled “The Paradox of Intellectual Promiscuity,” found in his altogether indispensable final essay collection I Have Landed: The End of a Beginning in Natural History (public library), Gould uses Nabokov’s case to make a beautiful and urgently necessary broader case against our culture’s chronic tendency to pit art and science against one another — “We have been befogged by a set of stereotypes about conflict and difference between these two great domains of human understanding,” he laments — and to assume that if a person has talent and passion for both areas, he or she can achieve greatness in only one and is necessarily a mere hobbyist in the other.

Gould writes:

We tend toward benign toleration when great thinkers and artists pursue disparate activities as a harmless hobby, robbing little time from their fundamental achievements… We grieve when we sense that a subsidiary interest stole precious items from a primary enterprise of great value… When we recognize that a secondary passion took substantial time from a primary source of fame, we try to assuage our grief over lost novels, symphonies, or discoveries by convincing ourselves that a hero’s subsidiary love must have informed or enriched his primary activity — in other words, that the loss in quantity might be recompensed by a gain in quality.

Nabokov's drawing of 'Eugenia onegini,' named for Aleksandr Pushkin's novel in verse, Eugene Onegin, which Nabokov translated. The illustration appeared on the endpaper of 'Conclusive Evidence,' Nabokov's autobiography.

But Gould argues that neither lamentation of such “intellectual promiscuity” detracting from the primary endeavor nor the manufactured comfort of believing that one domain enriched the other is an appropriate response to Nabokov’s two great loves, literature and butterflies. Gould unambiguously annihilates a common misconception about the great author:

Nabokov was no amateur (in the pejorative sense of the term), but a fully qualified, clearly talented, duly employed professional taxonomist, with recognized “world class” expertise in the biology and classification of a major group, the Latin American Polyommatini, popularly known to butterfly aficionados as “blues.”

No passion burned longer, or more deeply, in Nabokov’s life than his love for the natural history and taxonomy of butterflies. He began in early childhood, encouraged by a traditional interest in natural history among the upper-class intelligentsia of Russia (not to mention the attendant economic advantages of time, resources, and opportunity).


The reasons often given for attributing to Nabokov either an amateur, or even only a dilettante’s, status arise from simple ignorance of accepted definitions for professionalism in this field.


Nabokov loved his butterflies as much as his literature. He worked for years as a fully professional taxonomist, publishing more than a dozen papers that have stood the test of substantial time.

That he received an annual salary of merely a thousand dollars during his six years at Harvard’s zoology museum and worked under the vague title Research Fellow shouldn’t be used as evidence of Nabokov’s amateurishness — in making a larger point about the rich history of people working on what they love for little or no pay, Gould points out that several esteemed curators at the museum during his own tenure worked as volunteers for the symbolic annual salary of one dollar. In one of his many spectacular, almost outraged asides — Gould’s signature intelligent zingers — he drives home the point that there is little correlation between merit and prestige:

Every field includes some clunkers and nitwits, even in high positions!

Returning to the two camps of explaining Nabokov’s dual giftedness — and parallel talents in general — Gould writes:

In seeking some explanation for legitimate grief, we may find solace in claiming that Nabokov’s transcendent genius permitted him to make as uniquely innovative and distinctive a contribution to lepidoptery as to literature. However much we may wish that he had chosen a different distribution for his time, we can at least, with appropriate generosity, grant his equal impact and benefit upon natural history… However, no natural historian has ever viewed Nabokov as an innovator, or as an inhabitant of what humanists call the “vanguard” (not to mention the avant-garde) and scientists the “cutting edge.” Nabokov may have been a major general of literature, but he can only be ranked as a trustworthy, highly trained career infantryman in natural history.

Even Nabokov’s butterfly drawings, Gould points out, were great but far from masterworks of natural history illustration, especially in comparison to the work of such visionaries as butterfly-drawing grand dame Maria Merian.

One of Maria Merian's pioneering butterfly drawings. Click image for more.

Here, we are reminded of another perilous pathology of our culture — in the cult of genius, as in any cult, we leave no room for nuance; mere greatness is not good enough — one must lay a claim on grandeur. This is perhaps the most extreme testament to how perfectionism thwarts creativity.

But despite his mere greatness at lepidoptery, Nabokov regarded his time at the zoology museum as the most “delightful and thrilling” in his adult life — so creatively electrified was the author there that his years at Harvard even produced history’s most epic and entertaining account of food poisoning. But his love of butterflies began much earlier. In fact, one of the very first things Nabokov wrote in English, at the age of twelve, was a paper on Lepidoptera. The only reason it wasn’t published was that it turned out the butterfly in question had already been described by someone else.

This remark, which Gould makes rather in passing, made me wonder whether the incident instilled in young Vladimir an early reverence for attribution of discovery. As Gould later notes in another passing mention, Nabokov frequently voiced annoyance with scientists and science-writers not attributing discovery — not acknowledging the person who discovered and named a butterfly species. Therein lies a broader, and rather timely, lament about our culture’s failure to honor discovery as a creative act and a subset of scholarship — such a scientist, after all, doesn’t invent a species, for it already exists in nature, but discovers it, names it, and contextualizes it in the canon of natural history. It is no coincidence that Nabokov’s own role at the Harvard Museum of Comparative Zoology was that of curator, for this is the task of the curator — to describe, arrange, and contextualize what already exists in such a way as to shed new light on its meaning, to discover and un-cover its significance and place in the canon of ideas.

Embedded in this act is also a lineage of discovery, similar to the “links in a chain” metaphor Pete Seeger used for creativity: I learned of Nabokov’s pet peeve about discovery thanks to Stephen Jay Gould — perhaps the greatest curator of scientific ideas the world has ever known, the greatest contextualizer of such ideas in the popular imagination — and you learned of it via me, and the person you tell about this will learn of it via you. All of us are links in the evolutionary chain of ideas, much like each butterfly species discovered is a link in the evolutionary chain of natural history. This is why Richard Dawkins, in coining the word meme, used a metaphor from evolutionary biology to describe how ideas spread: “Just as genes propagate themselves in the gene pool by leaping from body to body via sperms or eggs, so memes propagate themselves in the meme pool by leaping from brain to brain.”

But back to Nabokov: His dedication to the integrity of discovery prompted him to write a short poem titled “A Discovery” in 1943:

Dark pictures, thrones, the stones that pilgrims kiss
Poems that take a thousand years to die
But ape the immortality of this
Red label on a little butterfly.

It might also be why he was so passionate about the integrity of detail. In a motto that calls to mind Susan Sontag’s memorable assertion that “a writer is a professional observer,” Nabokov instructed his literature students:

Caress the details, the divine details. In high art and pure science, detail is everything.

Butterfly drawing by Nabokov, August 1958 (Courtesy of Nabokov Museum)

In this, Gould finds the reconciliatory unity between Nabokov’s two great loves and how they communed with one another:

Although time spent on lepidoptery almost surely decreased his literary output, the specific knowledge and the philosophical view of life that Nabokov gained from his scientific career directly forged (or at least strongly contributed to) his unique literary style and excellence… Perhaps the major linkage of science and literature lies in some distinctive, underlying approach that Nabokov applied equally to both domains — a procedure that conferred the same special features upon all his efforts.


Among great twentieth-century thinkers, I know no better case than Nabokov’s for testing the hypothesis that an underlying unity of mental style (at a level clearly meriting the accolade of genius) can explain one man’s success in extensive and fully professional work in two disciplines conventionally viewed as maximally different, if not truly opposed. If we can validate this model for attributing interdisciplinary success to a coordinating and underlying mental uniqueness, rather than invoking the conventional argument about overt influence of one field upon another, then Nabokov’s story may teach us something important about the unity of creativity, and the falsity (or at least the contingency) of our traditional separation, usually in mutual recrimination, of art from science.

Therein, Gould argues, lies the only true solace in the accusation of “intellectual promiscuity.” Debunking the two false explanations of the Nabokov paradox — that “lepidoptery represented a harmless private passion, robbing no substantial time from his literary output” and that “his general genius at least made his lepidoptery as distinctive and as worthy as his literature” — Gould writes:

Nabokov’s two apparently disparate careers therefore find their common ground on the most distinctive feature of his unusual intellect and uncanny skill — the almost obsessive attention to meticulous and accurate detail that served both his literary productions and his taxonomic descriptions so well, and that defined his uncompromising commitment to factuality as both a principle of morality and a guarantor and primary guide to aesthetic quality.

Science and literature therefore gain their union on the most palpable territory of concrete things, and on the value we attribute to accuracy, even in smallest details, as a guide and an anchor for our lives, our loves, and our senses of worth… Of all scientific subfields, none raises the importance of intricate detail to such a plateau of importance as Nabokov’s chosen profession of taxonomic description for small and complex organisms. To function as a competent professional in the systematics of Lepidoptera, Nabokov really had no choice but to embrace such attention to detail, and to develop such respect for nature’s endless variety.


The universal and defining excellence of a professional taxonomist built a substrate for the uncommon, and (in Nabokov’s case) transcendent, excellence of a writer.

Young Vladimir and Véra Nabokov by Thomas Doyle from 'The Who, the What, and the When: 65 Artists Illustrate the Secret Sidekicks of History.' Click image for more.

But Gould’s most important point of all has little to do with Nabokov and everything to do with the toxic mythologies of creativity to which we, as a culture and as individuals, subscribe:

An ancient, and basically anti-intellectual, current in the creative arts has now begun to flow more strongly than ever before in recent memory-the tempting Siren song of a claim that the spirit of human creativity stands in direct opposition to the rigor in education and observation that breeds both our love for factual detail and our gain of sufficient knowledge and understanding to utilize this record of human achievement and natural wonder.

No more harmful nonsense exists than this common supposition that deepest insight into great questions about the meaning of life or the structure of reality emerges most readily when a free, undisciplined, and uncluttered (read, rather, ignorant and uneducated) mind soars above mere earthly knowledge and concern. The primary reason for emphasizing the supreme aesthetic and moral value of detailed factual accuracy, as Nabokov understood so well, lies in our need to combat this alluring brand of philistinism if we wish to maintain artistic excellence as both a craft and an inspiration.


If we assign too much of our total allotment to the mastery of detail, we will have nothing left for general theory and integrative wonder. But such a silly model of mental functioning can only arise from a false metaphorical comparison of human creativity with irrelevant systems based on fixed and filled containers — pennies in a piggy bank or cookies in a jar.

Gould ends by exhorting us:

Let us celebrate Nabokov’s excellence in natural history, and let us also rejoice that he could use the same mental skills and inclinations to follow another form of bliss.


Human creativity seems to work much as a coordinated and complex piece, whatever the different emphases demanded by disparate subjects-and we will miss the underlying commonality if we only stress the distinctions of external subjects and ignore the unities of internal procedure. If we do not recognize the common concerns and characteristics of all creative human activity, we will fail to grasp several important aspects of intellectual excellence-including the necessary interplay of imagination and observation (theory and empirics) as an intellectual theme, and the confluence of beauty and factuality as a psychological theme-because one field or the other traditionally downplays one side of a requisite duality.


I cannot imagine a better test case for extracting the universals of human creativity than the study of deep similarities in intellectual procedure between the arts and sciences.

No one grasped the extent of this underlying unity better than Vladimir Nabokov, who worked with different excellences as a complete professional in both domains.


Nabokov broke the boundaries of art and science by stating that the most precious desideratum of each domain must also characterize any excellence in the other — for, after all, truth is beauty, and beauty truth.

Gould seals this beautiful truth with a line — an exquisite, ennobling, oft-cited line — from one of Nabokov’s interviews:

There is no science without fancy, and no art without facts.

I Have Landed remains one of the finest tapestries of thought ever woven in the history of science storytelling. Complement this particular thread with Nabokov on inspiration, censorship and solidarity, what makes a great writer, what makes a great reader, and his sublime love letters to his wife.

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19 JANUARY, 2015

How Jane Goodall Turned Her Childhood Dream into Reality: A Sweet Illustrated Story of Purpose and Deep Determination


A heartening testament to the power of undivided intention.

“One should want only one thing and want it constantly,” young André Gide half-observed, half-resolved in his journal. “Then one is sure of getting it.” More than a century later, Werner Herzog wrote passionately of the “uninvited duty” that a sense of purpose plants in the heart, leaving one with “no choice but to push on.” That combination of desiring something with inextinguishable intensity — which begins with letting your life speak and daring to listen — and pursuing it with steadfast doggedness is perhaps the single common thread in the lives of those we most admire as luminaries of enduring genius. It is also at the heart of what it means to find your purpose and live it.

As a lover of illustrated biographies of cultural icons — such as those of Pablo Neruda, Julia Child, Albert Einstein, and Maria Merian — I was thrilled to stumble upon a wonderful take on the early life of one of my greatest heroes, Jane Goodall, and how she came to live the dream that bewitched her at a young age. In Me…Jane (public library), celebrated cartoonist, author, and animal rights advocate Patrick McDonnell tells the story of how the seed planted by a childhood dream blossomed, under the generous beams of deep dedication, into the reality of a purposeful life.

McDonnell’s protagonist is not Jane Goodall the widely influential and wildly revered elder of science and peace — one of a handful of people in history to have both the titles Dame and Doctor, and the subject of a very different illustrated biography — but little Jane, the ten-year-old girl who decided that she was going to work with animals in Africa when she grew up and, despite her family’s poverty, despite living in an era when girls were not encouraged to live the life of science or adventure, despite nearly everyone telling her that it was impossible, turned her dream into reality.

With simple, enormously expressive illustrations and an eloquent economy of words, McDonnell — creator of the beloved MUTTS comic strip — begins at the very beginning: that fateful day when little Jane was given a stuffed monkey named Jubilee.

Jane and Jubilee became inseparable, and she shared with him everything she loved — especially the outdoors. Together, they watched the birds and the spiders and the squirrels fill the backyard with aliveness.

At night, Jane and Jubilee read books to better understand what they saw.

One day, tickled to find out where eggs came from, they snuck into grandma’s chicken coop and observed the miracle of life.

It was a magical world full of joy and wonder, and Jane felt very much a part of it.

Jane liked to climb her beloved beech tree with Jubilee on her back, then sit perched on its branches reading and rereading Tarzan, imagining herself in place of that other Jane, wild and filled with wonder amid the jungles of Africa.

That dream soon became an all-consuming desire not just to go to Africa but to live there, trying to understand the animals and help them.

Every night Jane tucked Jubilee into bed and fell asleep with that dream, until one day — and such is the genius of McDonnell’s elegantly simple message of the dreamer’s doggedness — she awakes in a tent in the Gombe, the seedbed of what would become a remarkable career and an extraordinary life of purpose.

Goodall herself — who founded the heartening youth-led learning and community action initiative Roots & Shoots — writes in the afterword:

We cannot live through a single day without making an impact on the world around us — and we have a choice as to what sort of difference we make… Children are motivated when they can see the positive results their hard work can have.

Me…Jane, which received the prestigious Caldecott Honor and is a spectacular addition to these great children’s books celebrating science and scientists, is an emboldening treasure from cover to cover. Complement it with Goodall on science and spirituality, her answers to the Proust Questionnaire, and her own little-known children’s book, then treat yourself to “Dream Jane Dream” — a magnificent homage to Goodall by jazz singer-songwriter Lori Henriques:

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