Einstein's Greatest Mistake

by David Bodanis

  In one sense, the expedition was a success, for Pigafetta did make it back to Spain nearly three years after setting out. But he was one of only 18 survivors from the original crew of 240, which was far from the goal of bringing everyone back with which the expedition and its backers had begun.

  At least the voyage started well. Magellan’s crew saw marvels along the South American coast: new sorts of humans never imagined in Europe; fish that could leap out of the water (“they fly further than a cross bow–shot”) yet were tracked by predators that followed their shadows and then seized and ate them when they splashed down, “which is a thing marvelous and agreeable to see,” Pigafetta wrote.

  But then the storms began, ferocious ones, and it was ages before Pigafetta could make the journal entry they’d all longed for: “Wednesday, the twenty-eighth of November, 1520, we came forth out of the said strait [at the southern tip of South America], and entered into the Pacific sea.”

  The prospects seemed excellent at first, for they encountered a great expanse of calm water. But the calmness went on, and on, with no landfall in sight ​—“We went fully four thousand leagues in an open sea”—and the men began to starve. “We ate old biscuit reduced to powder, and full of grubs,” Pigafetta wrote. “. . . We also ate the ox hides which were under the sails; also the sawdust of wood, and rats.”

  Under normal circumstances, the mariners would have found their way using the stars, but in the southern hemisphere there were few of the familiar constellations to navigate by, and certainly no guiding North Star. Looking up at the strange night sky, the sailors found that “there are to be seen . . . two clouds a little separated from one another, and a little dimmed.” These glowing clouds produced light “of reasonable bygnesse.”

  Was it a gift from God? Whatever the cause, these two mysterious glowing clouds held to the same relative position, night after night, eventually allowing the survivors to navigate their way home. Magellan himself didn’t make it—speared by natives in the surf off the Philippines—but these glowing beacons in the night sky were subsequently named in his honor, becoming known as the Large Magellanic Cloud and the Small Magellanic Cloud.

  Four hundred years later, Einstein would use those same Clouds to solve the conundrum of whether or not to go back to his original equation, as the Russian mathematician Alexander Friedmann had recommended. But that would not happen before the Magellanic Clouds were explored, and some of their mysteries teased out, by a second—if very different—sort of pioneer.

  In the 1890s, in an upstairs room of Harvard University’s respected observatory, banks of computers were used to analyze large glass photographic plates of the night sky. These computers were not electronic devices; rather, the word referred to the rows of young women seated at wooden tables on the observatory’s second floor. Their jobs were to measure details on the plates and tabulate neatly what they found.

  The observatory’s director, Edward Pickering, was proud of these human computers, whom he regarded in nearly mechanical terms: “A great savings may be effectuated by employing unskilled and therefore inexpensive labor, of course under careful supervision.” Just to be sure there was no dissension, he insisted that these women—some of the first female university graduates in America—not be trained in any mathematics that could tempt them to do the work of male astronomers. He also paid them very little, just twenty-five cents per hour, at a time when cotton mill workers got fifteen cents. His colleagues patronizingly came to describe the complexity of astronomical jobs in terms of “girl-hours” or, if the work was going to involve a great deal of tabulation, “kilo-girl-hours.”

  It takes two people, however, to make you feel bad about yourself: the one who slurs you, and you if you accept it. Few of the women accepted the men’s views of them, as a ditty they composed demonstrates. To the tune of “We Sail the Ocean Blue” from Gilbert and Sullivan’s H.M.S. Pinafore:

  We WORK from morn till night

  Computing is our DU-tee

  We’re FAITH-full and polite

  And our record book’s a BEAU-TY!

  The most indomitable of all the computers under Pickering’s supervision was Henrietta Swan Leavitt. No manipulative manager would keep her down.

  Pickering’s women weren’t supposed to be too educated, but Leavitt had attended the music conservatory at Oberlin College and had also obtained an A in calculus and analytic geometry at Radcliffe (then called the Society for the Collegiate Instruction of Women). She was perfectly capable of carrying out the dull tabulations that Pickering assigned her. Yet she was far from content with her station, and her curiosity would get her into trouble with Pickering—and eventually change the course of Einstein’s life.

  Leavitt experienced a special thrill whenever the carefully packed crates from distant Arequipa in the Peruvian Andes arrived at the Harvard observatory. That’s where the university had installed its great 24-inch photographic telescope, the most powerful instrument of its class in the world.

  At first Pickering had sent his own brother to Arequipa to run the telescope, but after he started mailing back reports about giant rivers and lakes on Mars—which no one else looking through the telescopes could see—Pickering replaced him with another male colleague. The region was dangerous—there were, as visiting Americans noted with the typical imperialist views of the time, half-breeds in Arequipa, as well as savages in the not-too-distant Amazon—and the 8,000-foot altitude was exhausting. Also, the work was complex. The idea that a woman could ever go to Arequipa, let alone operate the telescope, was never considered.

  Back in Boston, however, Leavitt had noticed something curious about the plates being sent from Arequipa, especially the ones that revealed details of the glowing Clouds that had guided Pigafetta and Magellan on their voyage. We’re used to our sun shining pretty evenly, at just about the same intensity day after day. But that’s because the layers of fuel in the sun burn fairly evenly. In some very different stars, the burning is highly uneven. Like a boiling pot, pressure builds up deep within and makes the “lid”—​the surface layer of the star, composed of shattered atoms—pop outward in long bursts of extra-brightness. That in a sense releases the pressure, so that the surface layer settles back down, and it then takes several hours or even days for the temperature to build back up and another burst of brightness to appear again.

  Henrietta Leavitt, probably 1890s

  In the smaller of the two Magellanic Clouds, Leavitt saw there were a great number of stars that burned like this. She found them by comparing plates that were taken days or weeks apart. Instead of shining with a steady fire like our sun, these distinctive stars glowed brightly at one time, then dimmed down before lighting up to shine brightly again a few days or weeks later. Since such throbbing stars had been originally identified in the constellation Cepheus, even before Leavitt began her work, they had been known as Cepheid variables.

  If it had turned out that these Cepheid stars oscillated randomly, Leavitt would have found only an unimportant curio in outer space. But she began to think about it. Whenever she sent out requests for more photographs of the Small Magellanic Cloud—forwarded by Pickering, of course, for he allowed no one else to contact the on-site director in the Andes—the photos that came back always showed there was a rich density of stars, more and more with every magnification. She speculated that the Cloud wasn’t anywhere near earth, but a cluster of stars at an immense distance from us.

  How far away was that cluster? Before Henrietta Leavitt, no one had been able to discover a yardstick with which to measure the farthest reaches of the universe. The problem is understandable if we think about how hard it is to tell much about a single flashlight that briefly glows “on” in a pitch-black pasture at night. A medium glow could be from a strong flashlight that’s far away—but it could, just as well, be from a weak flashlight that’s much closer. Leavitt’s great discovery was that it was actually possible to overcome this challenge when observing stars.

  What
Leavitt found, bent over her plates in the brick building outside Boston, was that she could sort the Cepheid variable stars like different types of flashlights. Imagine that the Small Magellanic Cloud was extremely far from us, like a very distant meadow. The Cepheid stars there would be like separate flashlights held by people standing scattered within that meadow. From our vantage point, they all could be considered approximately the same distance away.

  Leavitt noticed that some of the Cepheids pulsated slowly, over a ten-day schedule. Others pulsated more quickly, over a three-day schedule. Most important, the ones that pulsated slowly were a lot brighter in the photos from Arequipa. Since she was assuming that all of them were about the same distance from the earth, this meant the ones that pulsated slowly had to be pouring out more light than the ones that pulsated more quickly. As for our flashlights in the distant meadow, if the ones that flicked on and off more slowly looked brighter than the others, we could assume they really were brighter.

  By itself, that wouldn’t be enough to let us find the actual distance to the meadow. But suppose we managed to get our hands on one of those flashlights—say, a slowly pulsating one—and found that it poured out two watts of light. Now when we looked at the distant field at night and saw a flashlight pulsating just as slowly, we would know that its intrinsic power was also two watts. Depending on how dim it looked at that distance, we could estimate how far away it was.

  So it was with the Cepheid stars. And luckily, astronomers were able to measure one Cepheid that was much closer to the earth, at a known distance, and register how much light it actually was pouring out. That allowed Leavitt to work out a scale on her yardstick. If the newly discovered Cepheid pulsated on, say, a seven-day cycle, the Cepheids that pulsated on the same cycle in the far-distant Magellanic Clouds had to have the same intrinsic power. Depending on how dim that distant Cepheid looked compared to the near one, she could work out how far the Cloud actually was from the earth.

  It was wonderful for Leavitt to be able to do this, and when one star that she was working on seemed particularly unclear, she joked to a colleague, “We shall never understand it until we find a way to send up a net and fetch that thing down!” Yet Leavitt also knew that she wasn’t supposed to be doing this research. As one of her fellow computers wrote in a private note, “If we could only go on and on with original work, looking to new stars, studying their peculiarities and changes, life would be a most beautiful dream. But we have to put all that is most interesting aside.”

  Leavitt was skilled at finding ways around these obstacles, however. Once, she explained to Pickering that she had to be away from Massachusetts for a while at her father’s farm in Wisconsin, but that she would very much appreciate it if he could send her personal notebooks—all of them—so that she could continue to help. What she actually worked on, of course, he did not have to know.

  In 1906—when Einstein was still happily married to Marić and still trying to find a way out of the Patent Office—Leavitt put together her main findings in a paper titled “1,777 Variables in the Magellanic Clouds.” She explained how peering into the Magellanic Clouds had allowed her to create a yardstick with which to measure the universe—how her Cepheids oscillated on regular schedules, and how those schedules corresponded with their actual brightness.

  It was a magnificent achievement, and Pickering was furious. Leavitt was an underling, a computer, a mere woman. He tried putting her findings partially under his own name on papers or at conferences, but word was getting out. A Princeton astronomer, impressed, noted, “What a variable-star ‘fiend’ Miss Leavitt is. One can’t keep up with the roll of [her] new discoveries.”

  Pickering couldn’t bear it, and so he pulled Leavitt away from her work, explaining that she was to forget, entirely, about working on these so-called variable stars in the Magellanic Clouds. There was a thorough numbering of stellar coordinates near the North Star that he wanted her to start tabulating instead. It was work, admittedly, that other astronomers didn’t consider especially important, but Pickering was a punctilious man, and with these listings he felt that he could make his name.

  Leavitt repeatedly tried to get back to what she loved, and in 1912—the year Einstein was starting his collaboration with Grossmann on the mathematics for his theory of gravitation—she managed to publish a paper that gave even more details about how to use her Cepheid variables to measure true distances in the outer universe. After that insubordination, Pickering cracked down on Leavitt even more harshly. No more of the fresh plates coming from the Andes were to go to her, he decreed—not if they involved those damned Magellanic Clouds.

  Leavitt died in 1921 and never did get to travel to the observatory of which she’d dreamed. A year later, however, one of her colleagues among the computers made the trip for her. Pickering was no longer the director in Boston, and regulations had been slightly eased.

  Leavitt’s friend traveled by steamship to South America, took trains and horse-drawn wagons to continue inland, and finally reached the top of the valley that led to Arequipa. “In the distance,” a contemporary wrote, the city built of soft white volcanic stone appeared “to be a city of marble.” The colossal volcanic cone of El Misti was visible to the northeast, jutting nearly four miles into the sky; Pichu-Pichu could be seen to the east. The air was thin, but the woman had to go farther, for the observatory was high above the city. When she reached it, she was more than a mile and a half above sea level, high in the crystal-clear air of the Andes.

  The sun went down. The cool night began, and the stars—the brilliant, perfectly clear stars—began to appear. Afterward, Leavitt’s friend took out her journal and wrote, “Magellanic Cloud (Great) so bright. It always makes me think of poor Henrietta. How she loved the ‘Clouds.’”

  THIRTEEN

  The Queen of Hearts Is Black

  EINSTEIN WAS IN A HAZE of confusion after the fall of 1923. He’d been thrown by Friedmann’s unexpected paper suggesting that the original ideas in the raw G=T equation were right and the curvature of the entire universe could be changing. Clusters of stars and planets might end up sliding away from one another in what would become an infinite expansion. Or the opposite might occur, and the curvature might be flexing differently so that the ancient Hindu mythologies might prove to be true after all, and the entire universe was doomed to an endless cycle of contraction and expansion, as if we were somehow locked within an invisible sphere that deflated and inflated forever.

  Einstein had managed to push aside some of this haze, at least from his conscious mind, by pretending that what Friedmann had found was merely a mathematical possibility, of no real physical significance. But then, four years after Friedmann’s abortive visit to Berlin, and five years after Henrietta Swan Leavitt’s coworker made it to the mountains of Arequipa, that temporary reprieve ended.

  In 1927 Einstein was at a sequel to the Brussels conference he had first attended as a young man living in Prague. He was a hero now and had set aside any lingering concerns about his gravitational equation—or at least had tried to—so as to focus on other undertakings. Yet on one of the first days of the conference, an earnest, heavyset Belgian man in his thirties came up to him and said that he had a mathematical proof that the universe was expanding.

  Einstein and Lemaître, around 1930

  Physics professors, even those below Einstein’s level, frequently are bothered by cranks, and for Einstein this sort of thing happened all the time. He’d become good at polite but firm, immediate dismissals, and he needed that now in Brussels, where his focus was on new fields of study. But this man could not be so immediately sidestepped.

  Not only was Einstein’s interlocutor an official invitee to the conference—which suggested he at least had done graduate-level work in physics—but he was also wearing the stiff white collar and black woolen jacket that showed he was a Catholic priest. In fact, he was a Jesuit, part of an order that despite its dogmatic loyalty to the pope had been active in astronomy for centuries.r />
  Einstein let the pudgy man, Father Georges Lemaître, begin to explain. He had published a paper in a Belgian journal—had the Professor perhaps heard of it?—in which he had gone through the consequences of Einstein’s work, trying it with a range of values for Λ. The most interesting results arose when Λ was set to zero, so that the equation went back to its original, pure form of G=T.

  Decades later, remembering that encounter, Lemaître said that Einstein had commented favorably on how ingenious that and other details of Lemaître’s mathematical approach seemed to be. But those words were little more than the polite banalities of a famous figure trying to end a conversation, which Einstein quickly proceeded to do. Before Lemaître could finish, Einstein cut him off. Your calculations might be accurate, Einstein told him, “mais votre physique est abominable (but your physical insight is unacceptable).” And with that, Einstein set off to find a taxi that could take him to the lab of Auguste Piccard, the famed balloonist, whom he’d arranged to visit.

  Most people would have considered that the end of the conversation. But like almost all men of his age in Europe, Lemaître had survived the Great War, in his case having served as a trench digger, machine gunner, and finally artillery officer. Events such as the world’s most famous scientist walking firmly away from him and starting to close a taxi door in his face were to be considered opportunities, not rejections. The Jesuit accelerated and jumped in beside Einstein. Would the Professor care to hear how he had already taken that criticism into account?

  Whether the Professor wished to or not, a moving taxi is a difficult place from which to escape. Lemaître explained that in his paper—and oh, if Einstein had subscribed to the estimable Annales de la Société scientifique de Bruxelles, he would surely know all this—he’d given detailed experimental evidence showing that his conclusions were true.