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11 AUGUST, 2014

Ordering the Heavens: Hevelius’s Revolutionary 17th-Century Star Catalog and the First Moon Map

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How a visionary manuscript, completed by the first female astronomer of the Western world, survived three fires to become a beacon of scientific dedication.

On September 26, 1679, a fierce fire consumed the Stellaburgum — Europe’s finest observatory, built by the pioneering astronomer Johannes Hevelius in the city of Danzig, present-day Poland, decades before the famous Royal Greenwich Observatory and Paris Observatory existed. That autumn day, Hevelius — whose exquisite lunar engravings are considered the first true maps of the moon and who believed, long before it was established by scientific consensus, that the stars in the night sky were thousands of suns like our own — had retired to a garden outside the city, “feeling himself oppressed with great and unaccustomed troubles, as if presaging some disaster,” as a friend later recounted in a letter. In Hevelius’s absence, his coachman had left a burning candle in the stable and the wooden platform across the roofs of Hevelius’s three adjoining houses, upon which his fine brass instruments and telescopes were mounted, had caught aflame. As the fire raged on, the town’s people broke into the observatory trying to save Hevelius’s precious bound books, throwing them out the windows. Some survived, some were pilfered. His optical instruments and almost all of his bountiful unbound manuscripts perished.

Hevelius in his later years

Hevelius was sixty-eight when his observatory was destroyed. But despite having spent forty years building his own instruments, making groundbreaking observations with them, and engraving and printing his own books — fruits of labor most of which were consumed by the fire along with all his “worldly Goods and Hopes,” as he later wrote in a letter to the king of France — he refused to sink into bitterness and resignation. Instead, he set out to rebuild the observatory so he could return to observing the stars.

His resilience was in large part fueled by the miraculous salvation of one of his manuscripts — his fixed-star catalog, which contained the results of thousands of calculations of the positions of the stars made over decades of patient observation. The small leather-bound notebook was the sole manuscript to survive the fire, presumably saved by Hevelius’s 13-year-old daughter Katharina Elisabeth, the sole family member in Danzig at the time of the fire, who had a key to her father’s study. Half a millennium later, it was rediscovered. In 1971, it made its way to Utah’s Brigham Young University, becoming the one-millionth acquisition by the institution’s library. To mark the landmark event, the university published a slim volume titled Johannes Hevelius and His Catalog of Stars (public library) — an immeasurably engrossing chronicle of the life and legacy of Hevelius, the 300-year odyssey of his fixed-star catalog, and how it changed our world.

The manuscript of 'Catalogus Stellarum Fixarum,' Johannes Hevelius's fixed-star catalog

Hevelius was born in 1611, a year after Galileo had made his first observations with a telescope, at a time of blazing scientific breakthrough and controversy. His father, a successful merchant, pressed young Johannes to follow in his footsteps rather than pursue what he perceived to be the fool’s gold of the scientific revolution, and sent the nine-year-old boy to Poland to study Polish. (At the time, Danzig was part of the Prussian Confederation and Hevelius’s native language was German, something his father saw as an obstacle to doing trade.) When the boy returned at age sixteen, he pleaded with his father to allow him to continue his formal education. The old man eventually relented and young Hevelius quickly fell in love with mathematics, under the influence of his mentor, the acclaimed mathematician, astronomer, and polymath Peter Krüger. He also learned Latin, the language of most scientific publications and international correspondence, and under Krüger’s nurturing watch began learning to draw, engrave, and build rudimentary instruments out of wood and metal. As Krüger’s sight began deteriorating, he encouraged young Johannes to take an active part in the observation part of science.

When he was nineteen, Hevelius watched the total solar eclipse of 1630 and saw Saturn veil the moon in a rare lunar eclipse. He was filled with cosmic awe, but wasn’t ready, or didn’t yet know how, to translate this sense of purpose into a career in astronomy. Instead, he married the daughter of a distinguished businessman and settled into the comfortable life of a merchant. But in 1639, when Krüger was on his deathbed, he urged young Hevelius not to let his exceptional gift go to waste. Aware that his end was near, Krüger lamented that he would miss the rare solar eclipse about to occur later that year and exhorted Hevelius to take up the historic task of its observation.

Equipment used by Hevelius with a telescope to project an astronomical image onto a sheet of paper. This arrangement was used in his historic observation of the transit of Mercury on May 3, 1661.

His teacher’s dying words reawakened Hevelius’s forsaken but fiery love of astronomy. On June 1, 1639, he meticulously observed the solar eclipse, then decided to dedicate the rest of his life to understanding the cosmos. True to the notion that revolutionary discovery is the product of “the meeting of the right people at the right place with just the right problem,” Hevelius harnessed the fruitfulness of his timing — just as he chose to devote himself to astronomy, the telescope was revolutionizing the field and making possible discoveries never before imagined.

Hevelius's revolutionary map of the moon

Hevelius was particularly enchanted with the moon and made it the target of his first obsessive observations. Dissatisfied with the imprecise and vague drawings of its surface, he decided to complain the way all innovators do — by making something better. Turning his modest telescope to the moon and enlisting his talents as a draftsman and engraver, he set out to create a large, complete, delicately detailed map of its surface. But he quickly realized his telescope wasn’t up to the task — so he decided to build a better one himself. In 1647, after five years of methodical work fueled by this greatest talent — dogged patience — Hevelius published his magnificent maps under the title Selenographia.

One of Hevelius's exquisitely illustrated phases of the moon from 'Selenographia'

One of his first great admirers was the famed English traveler Mundy who, upon seeing the maps, marveled in his diary:

Of the Moone he hath Made above 30 large mappes, prints, or Copper peeces of the Manner of every daies encrease and decrease, deciphering in her land and sea, Mountaines, valleies, Ilands, lakes, etts., making in another little world, giving Names to every part, as wee in a mappe of our world.

Praise continued to pour in from all over Europe, but the greatest validation of the maps’ merit was the fact that they endured as the best moon maps for more than a century, despite the rapid progress of observational tools — assurance, perhaps, that what sets innovators apart from the rest aren’t their tools but their creative vision in using those tools and their unrelenting work ethic.

Encouraged, Hevelius set out to improve his observations, building bigger and better telescopes, with an unblinking eye on his most important project — the quest to revise the paltry star catalogs of the era. Star catalogs, Hevelius knew, were an essential tool for astronomers, enabling them to track the changes taking place in constellations — changes that would profoundly challenge the religious dogmas of the day, which depicted the universe as a static starscape laid out by a divine creator a long time ago. At a time when heliocentrism — the knowledge that the earth revolves around the sun, rather than vice-versa as the church claimed — was still a novel and controversial concept, proving that the universe was a dynamic ecosystem of bodies would be a major feat for science. But star maps had to be accurate and precise in order to reveal these changes.

So, in 1641, shortly after his thirtieth birthday, Hevelius began building his rooftop observatory. Three years into his work, the city of Danzig presented him with a gift — an astronomical instrument that had been stored in Danzig armory for many years, alongside firefighting equipment, the use and worth of which had remained unknown. A six-foot contraption known as an azimuthal quadrant, it had been envisioned by Krüger but remained uncompleted by his death. Once again, Hevelius’s mentor was shaping the course of his life, even from the grave — Hevelius completed the instrument, mounted it on his observatory tower, and began making observations with it. With its ability to measure the angular distances between neighboring stars, it became a key tool in the completion of his stellar catalog. Long before the invention of the meridian circle, Hevelius used his instrument to record coordinates according to what was essentially an equator line.

Hevelius and his large azimuthal quadrant, which he used to make many of the measurements in his fixed-star catalog

Over the sixteen years that followed, Hevelius expanded his observatory and equipped it with the best instruments he could build or acquire. His became Europe’s finest observatory.

But perhaps the most important event in Hevelius’s life and career was not one of science but of romance — or, rather, an exquisite fusion of the two. When he was 55, widowed for over a year, Hevelius married a young woman named Elisabeth Koopman, the daughter of an acquaintance of his, a Danzig merchant. Hevelius had known Elisabeth, many years his junior, since she was a child, when she had implored him to teach her astronomy. As a young woman, she had renewed her request, enveloping the now-revered astronomer with admiration and, soon, adoration. A German biography quotes her as exclaiming one night, while looking through Hevelius’s telescope:

To remain and gaze here always, to be allowed to explore and proclaim with you the wonder of the heavens; that would make me perfectly happy!

It was, essentially, a marriage proposal, which Hevelius gladly accepted. They were wedded at St. Catherine’s Church in 1663. Johannes was 52; Elisabeth was 17. Before recoiling in modern judgment, it’s important to note that such unions were far from uncommon at the time. But perhaps more importantly, they were often the only way for women, who were were barred from most formal education and scholarly work, to gain access to creative and intellectual pursuits through a kind of conjugal apprenticeship.

Hevelius and Elisabeth observing at the six-foot brass sextant

That is precisely what young Elisabeth, who had developed an active interest in astronomy at an early age, did. Hevelius saw in her a kindred mind, and they began making astronomical observations together as she mastered the craft. Nearly two centuries before Maria Mitchell, Elisabeth Hevelius essentially became the first Western female astronomer. All the while, she emboldened her husband — another biography cites her most frequent words of encouragement to him:

Nothing is sweeter than to know everything, and enthusiasm for all good arts brings, some time or other, excellent rewards.

In the years following their marriage, Elisabeth continued to observe the stars, but also gave birth to four children — a boy, who died in infancy, and three girls. All the while, she worked alongside Hevelius in completing the star catalog that had become the holy grail of his scientific career and his highest hope for a lasting legacy. In one of his books, Hevelius, who spoke highly of Elisabeth’s scientific skills and called her the “faithful Aide of [his] nocturnal Observations” in a letter to the king of France, included an engraving of the duo making an observation together.

With Elisabeth’s help, Hevelius published the first star maps in a planned series in 1673. The most extraordinary thing about them was that, as he explained in the preface, he had made most of the observations not with a telescope but with a naked eye — a practical method he favored, despite acknowledging the theoretical advantages of telescopes. It was a controversial statement in the golden age of telescopic studies, which caused a tumult among Europe’s astronomers, but Hevelius’s astounding accuracy spoke for itself and established him as the last and greatest of the naked-eye star observers.

Hevelius's comet drawings

Hevelius's comet drawings

But the fire that destroyed Hevelius’s observatory in 1679 nearly put a halt to his quest to catalog the stars. Desperate to resume his project, Hevelius wrote to French king Louis XIV, one of his longtime patrons, a lyrical and heartfelt plea for financial support. The letter stands as an exquisite exemplar of the art of asking, as well as the curious testament to how deeply religious piety permeated the minds of even the most dedicated scientists of the time:

Most Illustrious and mightiest King, most beneficent Lord: Your high Favour and incomparable Mercy have ever spurred me to scatter with diligence the Seeds of my Gratitude and to sow them in the Bosom of Urania, so that I have set in the Heavens nigh to seven hundred Stars which were not there aforetimes, and have named some of them after your Majesty. . .

But, alas, will this Fruit of the Labours of mine Age ever see the Light of Day? For no man knoweth what the Dark of Even bringeth. Woe and alas, how multitudinous the Misfortunes that embroil the Life of Man. All my worldly Goods and Hopes have been overturned in the Space of scarce an Hour.

Rumour of the dread Conflagration which hath destroyed my astronomical Tower hath no doubt already sped upon rapid Feet to Paris. Now I come myself hasting to Your Majesty as Herald of this great Woe, clad in Sackcloth and Ashes, deep distressed by this Visitation from Him Who judgeth all Things.

[…]

May the Windows of the Human Soul never again look upon such a conflagration as devoured my three Houses… if God had not commanded the Wind to turn in its Course, all of the Old City of Danzig would surely have burned to the Ground…

Saved by God’s Mercy were .. Kepler’s immortal Works, which I purchased from his Son, my Catalogue of Stars, my New and Improved celestial Globe, and the thirteen Volumes of my Correspondence with learned Men and the Crowned Head of all Lands.

But the cruel Flames have consumed all the Machines and Instruments conceived by long Study and constructed, alas, at such great Cost, Consumed also the Printing Press with Letters … consumed, finally my Fortune and the means which God’s Mercy had granted me to serve the Royal Science.

If such Damage should crush me to the Ground, I whose Locks are Hoary and who am not far from my Appointed End, could any reasonable Man cast Blame upon me therefor? Yet with the Aid of my many Friends I hope that I may restore my Specula observatoria, and implore you, Most Illustrious Monarch who have so often manifested Royal Munificence toward me, to breathe by some further Token of your Generosity new Life into the Work which may still lie before me. Then will I no longer bewail my cruel Misfortune, and yours, Noble Majesty, will be eternal Fame for all Posterity.

The king, moved, granted his request. But the most generous support came from the king of Poland, who granted Hevelius a yearly stipend of 1,000 Danzig gulden for the rest of his life. The astronomer thus went on to resume his observations and finish his publications.

In October of 1681, the French writer Jean-François Regnard visited the newly rebuilt observatory and marveled in his little-known diary not only at Hevelius’s prolific writings and his impressive proto-rolodex, but also at his sublime cross-pollination of art and science:

His works, the number of which exceeds all belief … are full of plates made with his own hand: he shewed us them all, besides fifteen large volumes, as thick as the Lives of the Saints, full of letters which the most learned men on the whole world had written to him on various subjects.

Map of the constellations from 'Prodromus Astronomiae'

But Hevelius remained preoccupied with the completion of his catalog of the stars, which had become his most consuming endeavor and his highest hope for legacy. Alas, he never fully attained it — at least not as a sole creator. On January 28, 1687 — the exact date of his 76th birthday — Hevelius died, having outlived the era’s life expectancy by decades. But Elisabeth, who had assisted him in the catalog all along, took it upon herself to finish Hevelius’s lifelong quest. She completed the book, dedicating it to the generous Polish monarch. The finished catalog included more than 600 new stars that Johannes and Elisabeth had observed, as well as a dozen new constellations, whose names, as given by Hevelius, astronomers still use today.

One of Hevelius's plates depicting a new constellation he discovered, the Lynx, named for the sharpness of vision required to see its faint stars

Hercules with the new constellation Cerberus

Elisabeth guarded the manuscript carefully until her death in 1693, at the age of 46. She left to each of her three daughters a complete set of Hevelius’s published works. The eldest, Katharina — who as a teenager had saved her father’s star catalog from the fateful fire — fittingly inherited a beautifully illuminated copy of the book, originally prepared as a gift for Louis XIV. But once Katharina married, her husband sold most of Hevelius’s prized books to a museum in Russia. The manuscript of the star catalog that had survived the fire was overlooked. Ironically, the greedy son-in-law didn’t think Hevelius’s magnum opus valuable enough to sell.

But the story of the star catalog and its miraculous survival doesn’t end there: In 1734, during the Saxonian-Russian siege of Danzig, artillery fire struck the son-in-law’s house and destroyed most of the property. One bomb fell directly into the room where Hevelius’s manuscripts and instruments were kept, destroying nearly all unbound manuscripts. But the star catalog somehow survived once more. Over the next two centuries, it made its way to the Danzig Institute of Technology. Then, as World War II broke out, the German administration evacuated the Institute’s library to a nearby village, where it was almost completely destroyed in the last days of the war. And yet the star catalog, by yet another stroke of mysterious fortune, survived its third assault by fire. This strange phoenix of science finally arrived at Brigham Young University in 1971, where it has remained safe from fire and brimstone in the decades since.

The manuscript of the fixed-star catalog featured in front of a copy of the posthumously published 'Prodromus Astronomiae' (1690), opened to the title page of the printed version of the printed star catalog

Complement engrossing out-of-print gem Johannes Hevelius and His Catalog of Stars with this modern-day field guide to naked-eye stargazing, then revisit pioneering astronomer Maria Mitchell’s wisdom on education and women in science.

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24 JULY, 2014

Astronomer Jill Tarter on the Ongoing Search for Extraterrestrial Life and How She Inspired Carl Sagan’s Novel-Turned-Film Contact

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The importance of playing the long game in life, be it extraterrestrial or earthly.

Astronomer Jill Tarter grew up taking apart and reassembling her father’s radios. She is the Bernard M. Oliver Chair for SETI Research — California’s institute of Search for Extraterrestrial Intelligence — and the inspiration for Jodie Foster’s character in the iconic 1997 film Contact, adapted from Carl Sagan’s novel of the same title. The recipient of two public service medals from NASA and the TED Prize, among ample other accolades, Tarter has spent nearly forty years searching the cosmos for alien life and advocating for the importance of that inquiry.

In this short video from NOVA, Tarter recounts how Sagan and Ann Druyan contacted her about the novel and explores the broader question of why the search for extraterrestrial life matters — and matters enormously:

In the book The Art of Doing: How Superachievers Do What They Do and How They Do It So Well (public library) — which also gave us this fascinating read on why emotional recall is the secret to better memory — Tarter speaks to the importance of playing the long game in the search for extraterrestrial life:

I don’t get out of bed every morning thinking, “Will I find extraterrestrial intelligence today?” But I do think every day, “How can I improve the search?” Fifty years of silence doesn’t mean SETI is a failure; it means we’re just getting started. We may not succeed tomorrow or next year or next decade or even next century, but a critical part of our job is passing on what we’ve learned to the future generations of cosmic scientists.

What a wonderful disposition toward life, extraterrestrial or earthly — to think how much more we could achieve and with what greater ease we could live if we only applied this to our everyday lives, from the search for love to the conquest of a project.

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23 JULY, 2014

The Universe, “Branes,” and the Science of Multiple Dimensions

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How a needle, a shower curtain, and a New England clam explain the possibility of parallel universes.

“The mystery of being is a permanent mystery,” John Updike once observed in pondering why the universe exists, and yet of equal permanence is the allure this mystery exerts upon the scientists, philosophers, and artists of any given era. The Universe: Leading Scientists Explore the Origin, Mysteries, and Future of the Cosmos (public library | IndieBound) collects twenty-one illuminating, mind-expanding meditations on various aspects of that mystery, from multiple dimensions to quantum monkeys to why the universe looks the way it does, by some of the greatest scientific thinkers of our time. It is the fourth installment in an ongoing series by Edge editor John Brockman, following Thinking (2013), Culture (2011), and The Mind (2011).

In one of the essays, theoretical physicist Leonard Suskind marvels at the unique precipice we’re fortunate to witness:

The beginning of the 21st century is a watershed in modern science, a time that will forever change our understanding of the universe. Something is happening which is far more than the discovery of new facts or new equations. This is one of those rare moments when our entire outlook, our framework for thinking, and the whole epistemology of physics and cosmology are suddenly undergoing real upheaval. The narrow 20th-century view of a unique universe, about 10 billion years old and 10 billion light years across with a unique set of physical laws, is giving way to something far bigger and pregnant with new possibilities.

Gradually physicists and cosmologists are coming to see our ten billion light years as an infinitesimal pocket of a stupendous megaverse.

Here, an inevitable note on a different kind of human narrowness: I am not one to advocate for a blind quota-filling approach, where there must be equal representation on all levels at all cost. And yet it’s rather disappointing to see only one female scientist alongside her twenty-two male peers. (One of the twenty-one essays has three authors.) To be sure, Edge itself is far from gender-balanced — one could rationalize that this is simply the state of science still — but the site’s vast archive, spanning fifteen years of conversations and essays, does feature a number of female scientists, which renders the 5% female representation in this collection editorially lamentable.

This gender gap lends double meaning to Susskind’s reflections on the progress of science in the twenty-first century as he notes: “Man’s place in the universe is also being reexamined and challenged.” Woman’s, evidently, is not.

And yet, it’s perhaps not coincidental that the sole female contributor is none other than Harvard’s Lisa Randall, one of the most influential theoretical physicists of our time, and her essay is the most intensely interesting in the entire collection. (Perchance Brockman considered its weighted quotient equal to several of the male essays combined. No, not really, but when the skies of equality get particularly cloudy, what is one to do but squint for silver linings?)

Lisa Randall (Photograph: Phil Knott)

Randall’s essay explores her work on the physics of extra dimensions of space, particularly the concept of “branes” — membrane-like two-dimensional objects that exist in a higher-dimensional space. (Randall illustrates this with the visual metaphor of a shower curtain, “virtually a two-dimensional object in a three-dimensional space.”) To understand why branes matter — more than that, why they are so infinitely interesting — we first need a primer on the physics of what is known as the “TeV scale.” Randall explains:

Particle physicists measure energy in units of electron volts. “TeV” means “a trillion electron volts.” This is a very high energy and challenges the limits of current technology, but it’s low from the perspective of quantum gravity, whose consequences are likely to show up only at energies 16 orders of magnitude higher. This energy scale is interesting, because we know that the as-yet-undiscovered part of the theory associated with giving elementary particles their masses should be found there… Back at the very beginning, the entire universe could have been squeezed to the size of an elementary particle. Quantum fluctuations could shake the entire universe, and there would be an essential link between cosmology and the microworld.

This ghostly playground of particles raises the question of whether “space and time are so complicated and screwed up that we can’t really talk about a beginning in time” — which brings us to string theory and its peculiar predicament. Randall writes:

The one thing that’s rather unusual about string theory from the viewpoint of the sociology and history of science is that it’s one of the few instances where physics has been held up by a lack of the relevant mathematics. In the past, physicists have generally taken fairly old-fashioned mathematics off the shelf. Einstein used 19th-century non-Euclidean geometry, and the pioneers in quantum theory used group theory and differential equations that had essentially been worked out long beforehand. But string theory poses mathematical problems that aren’t yet solved, and has actually brought math and physics closer together.

String theory is the dominant approach right now, and it has some successes already, but the question is whether it will develop to the stage where we can actually solve problems that can be tested observationally. If we can’t bridge the gap between this ten-dimensional theory and anything that we can observe, it will grind to a halt. In most versions of string theory, the extra dimensions above the normal three are all wrapped up very tightly, so that each point in our ordinary space is like a tightly wrapped origami in six dimensions. We see just three dimensions; the rest are invisible to us because they are wrapped up very tightly. If you look at a needle, it looks like a one-dimensional line from a long distance, but really it’s three-dimensional. Likewise, the extra dimensions could be seen if you looked at things very closely. Space on a very tiny scale is grainy and complicated — its smoothness is an illusion of the large scale. That’s the conventional view in these string theories.

The Cat's Eye Nebula, from 'Hubble: Imaging Space and Time.' Click image for more.

This is where Randall’s work on branes comes in as a promising contender for a better solution. She writes:

According to this theory, there could be other universes, perhaps separated from ours by just a microscopic distance; however, that distance is measured in some fourth spatial dimension, of which we are not aware. Because we are imprisoned in our three dimensions, we can’t directly detect these other universes. It’s rather like a whole lot of bugs crawling around on a big two-dimensional sheet of paper, who would be unaware of another set of bugs that might be crawling around on another sheet of paper that could be only a short distance away in the third dimension.

Of course, the concepts of multiple dimensions and parallel universes are far from new and can be traced as far back as another trailblazing woman in scientific thought, Margaret Cavendish, Duchess of Newcastle — her 1666 book The Blazing World features a heroine who passes into a world with different stars through a space-time portal near the North Pole.

Randall takes us into her own time machine to trace the history of multiple dimensions in contextualizing what makes branes so special:

People entertained the idea of extra dimensions before string theory came along, although such speculations were soon forgotten or ignored. It’s natural to ask what would happen if there were different dimensions of space; after all, the fact that we see only three spatial dimensions doesn’t necessarily mean that only three exist, and Einstein’s general relativity doesn’t treat a three-dimensional universe preferentially. There could be many unseen ingredients to the universe. However, it was first believed that if additional dimensions existed they would have to be very small in order to have escaped our notice. The standard supposition in string theory was that the extra dimensions were curled up into incredibly tiny scales — 1033 centimeters, the so-called Planck length and the scale associated with quantum effects becoming relevant. In that sense, this scale is the obvious candidate: If there are extra dimensions, which are obviously important to gravitational structure, they’d be characterized by this particular distance scale. But if so, there would be very few implications for our world. Such dimensions would have no impact whatsoever on anything we see or experience.

[…]

Branes are special, particularly in the context of string theory, because there’s a natural mechanism to confine particles to the brane; thus not everything need travel in the extra dimensions, even if those dimensions exist. Particles confined to the brane would have momentum and motion only along the brane, like water spots on the surface of your shower curtain. Branes allow for an entirely new set of possibilities in the physics of extra dimensions, because particles confined to the brane would look more or less as they would in a three-plus-one-dimension world; they never venture beyond it. Protons, electrons, quarks, all sorts of fundamental particles could be stuck on the brane. In that case, you may wonder why we should care about extra dimensions at all, since despite their existence the particles that make up our world do not traverse them. However, although all known standard-model particles stick to the brane, this is not true of gravity. The mechanisms for confining particles and forces mediated by the photon or electrogauge proton to the brane do not apply to gravity. Gravity, according to the theory of general relativity, must necessarily exist in the full geometry of space. Furthermore, a consistent gravitational theory requires that the graviton, the particle that mediates gravity, has to couple to any source of energy, whether that source is confined to the brane or not. Therefore, the graviton would also have to be out there in the region encompassing the full geometry of higher dimensions—a region known as the bulk—because there might be sources of energy there. Finally, there’s a string-theory explanation of why the graviton is not stuck to any brane: The graviton is associated with the closed string, and only open strings can be anchored to a brane.

Meanwhile, scientists haven’t studied gravity as intensely as they have other particles, largely because gravity is an extremely weak force. (It might not seem so every time you trip and fall, but as Randall points out, that’s because the entire Earth is pulling you down at that moment, whereas “the result of coupling an individual graviton to an individual particle is quite small.”) What makes branes especially intriguing is that including them into string theory allows us to contemplate, to use Randall’s technical term, “crazily large extra dimensions.” These, in turn, might explain why gravity is so weak — if its force is spread out across these gigantic dimensions, no wonder it would be this diluted on any one brane.

But it gets even more interesting — citing her work with Johns Hopkins scientist Raman Sundrum, Randall writes:

A more natural explanation for the weakness of gravity could be the direct result of the gravitational attraction associated with the brane itself. In addition to trapping particles, branes carry energy. We showed that from the perspective of general relativity this means that the brane curves the space around it, changing gravity in its vicinity. When the energy in space is correlated with the energy on the brane so that a large flat three-dimensional brane sits in the higher-dimensional space, the graviton — the particle communicating the gravitational force — is highly attracted to the brane. Rather than spreading uniformly in an extra dimension, gravity stays localized, very close to the brane.

René Descartes's 1644 model of the universe, from 'The Book of Trees.' Click image for more.

Randall’s discoveries get even more mind-bending. Outlining a finding that calls to mind the legendary Victorian allegory Flatland: A Romance of Many Dimensions (which in turn inspired Norton Juster’s brilliant 1963 book and film The Dot and the Line: A Romance in Lower Mathematics, she writes:

Conventionally, it was thought that extra dimensions must be curled up or bounded between two branes, or else we would observe higher-dimensional gravity. The aforementioned second brane appeared to serve two purposes: It explained the hierarchy problem because of the small probability for the graviton to be there, and it was also responsible for bounding the extra dimension so that at long distances, bigger than the dimension’s size, only three dimensions are seen.

The concentration of the graviton near the Planck brane can, however, have an entirely different implication. If we forget the hierarchy problem for the moment, the second brane is unnecessary. That is, even if there’s an infinite extra dimension and we live on the Planck brane in this infinite dimension, we wouldn’t know about it. In this “warped geometry,” as the space with exponentially decreasing graviton amplitude is known, we would see things as if this dimension did not exist and the world were only three-dimensional.

[…]

Because the graviton makes only infrequent excursions into the bulk, a second brane or a curled-up dimension isn’t necessary to get a theory that describes our three-dimensional world, as had previously been thought. We might live on the Planck brane and address the hierarchy problem in some other manner—or we might live on a second brane out in the bulk, but this brane would not be the boundary of the now infinite space. It doesn’t matter that the graviton occasionally leaks away from the Planck brane; it’s so highly localized there that the Planck brane essentially mimics a world of three dimensions, as though an extra dimension didn’t exist at all. A four-spatial-dimensions world, say, would look almost identical to one with three spatial dimensions. Thus all the evidence we have for three spatial dimensions could equally well be evidence for a theory in which there are four spatial dimensions of infinite extent.

So why does any of this matter, this “exciting but frustrating game” of speculation, as Randall elegantly puts it? For one thing, there might be subtle but important differences between these different dimensions and different worlds — for instance, black holes may not behave the same way in each of them. If energy leaks off a brane, a black hole might spit out particles into an extra dimension as it perishes. (If you’ve ever steamed a New England clam, you may have noticed it “spitting” water at you in its final moments — perhaps this is somewhat akin to what Randall describes.) Most importantly, multiple dimensions offer endless possibilities for the very structure of space. Randall writes:

There can be different numbers of dimensions and there might be arbitrary numbers of branes contained within. Branes don’t even all have to be three-plus-one-dimensional; maybe there are other dimensions of branes in addition to those that look like ours and are parallel to ours. This presents an interesting question about the global structure of space, since how space evolves with time would be different in the context of the presence of many branes. It’s possible that there are all sorts of forces and particles we don’t know about that are concentrated on branes and can affect cosmology.

Lisa Randall

So where does this leave us? Randall echoes Marie Curie’s famous words upon receiving her second graduate degree — a sentiment no doubt common to any great scientist who understands that not-knowing is the currency of meaningful work — and concludes:

In general, the problems that get solved, although they seem very complicated, are in many ways simple problems. There’s much more work to be done; exciting discoveries await, and they will have implications for other fields… It’s my hope that time and experiments will distinguish among the possibilities.

Randall’s essay is a spectacular, mind-bending read in its entirety, as are the rest of the contributions in The Universe. Complement it with Brockman’s compendium of leading scientists’ selections of the most elegant theory of how the world works and the single most important concept to make you smarter.

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