Leonardo da Vinci (Figure 1) is not usually known for his astrophysics. Yet this remarkable individual – the quintessential “Renaissance Man” – made quite a few pronouncements related to astronomy and astrophysics.
You may have heard that NASA recently determined that the space probe Voyager 1 crossed the heliopause and entered interstellar space on August 25, 2012. Figure 1 shows an image of the radio signal from the probe. The heliopause marks the boundary beyond which charged particles from interstellar space (ejected by previous generations of stars) are no longer deflected by particles from the solar wind. At about 12 billion miles from Earth, Voyager 1 became the first human-made spacecraft to have formally left the solar system.
Voyager 1 was launched on September 5, 1977, primarily to explore the planets Jupiter, Saturn, and their satellites. It continues to communicate with the Deep Space Network and to return data.
You may wonder why the fact that it has left the solar system (though not the influence of the Sun’s gravity) is significant. Indeed, from a purely scientific perspective, there isn’t much to expect from Voyager 1 in the future. The probe is not heading towards any particular star. The closest it will come to the first star it encounters will be about 1.6 light-years—and that will not happen for another 40,000 years. So it is hard to believe that the gold-plated audio-visual record on board the spacecraft will ever be found by an intelligent alien civilization. That record contains photos of lifeforms of Earth, a variety of scientific information, and various sounds. Nevertheless, there is something truly symbolic and inspiring in being first in any adventure in space exploration. Recall the commotion caused by the first artificial satellite, Sputnik 1, launched by the Soviet Union on October 4, 1957, or the excitement that accompanied the first person in space, Yuri Gagarin, in April 1961.
Of course, to date, nothing beats the landing on the Moon by the Apollo 11 astronauts on July 20, 1969, in terms of the emotions it evoked. Figure 2 shows the late astronaut Neil Armstrong on the Moon. I know of an entire generation of scientists who still cite the landing on the Moon as the single event that inspired them to choose a scientific career. Historical milestones are important. When Edmund Hillary and Tenzing Norgay finally conquered Everest on May 29, 1953 (Figure 3), there was clearly no immediate benefit to humankind. But these types of accomplishments demonstrate what humans can achieve when they put their mind and determination into the task.
Voyager 1 will probably not discover new worlds, but it has already taken the first step in interstellar travel for us.
In October 1604, the famous astronomer Johannes Kepler saw with his naked eye (and later observed in detail) what he thought to be a new star. In fact, what he saw was the explosion of an old star—a supernova. Over a period of centuries, there was no further historical record of a naked-eye supernova. Some jokingly said that this was because there hasn’t been a truly great astronomer since Kepler.
On February 23, 1987, however, something dramatic happened. Canadian astronomer Ian Shelton discovered a new supernova in our neighboring galaxy, the Large Magellanic Cloud, and that supernova was visible to the naked eye. According to tradition, since that was the first supernova (SN) observed in 1987, it was dubbed SN1987A (the second in any given year is denoted by the letter B, and so on). I personally remember the tremendous excitement that this supernova, a mere 167,000 light-years away (very near, by cosmic standards), caused. Soon, every telescope on the face of the Earth’s southern hemisphere (where it was visible) and in space was directed to it.
The initial observations delivered an immediate surprise. Based on the theory of supernova explosions, the expectation was that the exploding star should have been a red supergiant. Instead, previous observations of the precise location of the explosion revealed that the exploding star was a blue supergiant. Eventually, astronomers understood that the star had suffered severe mass loss during its evolution, making it more compact and hotter (and therefore blue).
Remarkably, one of the key predictions of supernova theory was readily confirmed. Supernova explosions occur when the dense core of a massive star collapses to form a neutron star (a very compact object, only about 12 miles in diameter), producing copious amounts of neutrinos in the process. Detectors, located deep underground in Ohio and Japan, indeed identified about a dozen of these elusive neutrinos as they passed through the Earth. This constituted an immense theoretical and experimental success.
After its launch, the Hubble Space Telescope also viewed SN1987A, and those observations revealed a mysterious structure of three rings (Figure 1). It took astrophysicists quite a while to understand their origin. Basically, mass loss from the star prior to the explosion formed an equatorial ring of material. An hourglass shape—in which the equatorial ring formed its “waist”— accompanied this, and fast-moving material expanding in a perpendicular direction formed the lobes. The outer rings mark the rim of the two lobes. The ultraviolet flash from the explosion heated all the rings, which consequently began to emit radiation.
In 2001, ejecta from the supernova eventually began colliding with the inner ring. The collisions still continue today, causing that ring to shine like a bracelet of pearls (Figure 2).
Supernova 1987A has given astronomers an unprecedented look at what can happen to a massive star before and after it explodes, though why we have not observed the radio pulses expected from a spinning neutron star is still a mystery. There are three potential explanations: (1) The pulsar is obscured by heavy dust. (2) The Earth is not in the line of sight of the beam of this radio “lighthouse.” (3) The collapsing core has, in fact, formed a black hole rather than a neutron star. Hubble, the Chandra X-Ray Observatory, and the Herschel Space Observatory continue to monitor the evolution of this supernova remnant, and there is no doubt that it will also be a target for the upcoming James Webb Space Telescope.
Supernovae eject into space elements needed for life, such as oxygen, phosphorus, and iron. SN1987A therefore provided us with a glimpse of our own beginnings.
If you’ll examine any list of the greatest mathematicians of all time, you’ll find that many of them were also interested in astronomy. More generally, quite a few were passionate about understanding the workings of the cosmos. For instance, it goes without saying that Newton and Archimedes (considered by many to occupy the top two spots on the list) contributed significantly to astronomy. Carl Friedrich Gauss (the third on most lists), developed (among other things) an elaborate method to calculate the orbit of the dwarf planet Ceres.
Henri Brocard (1845–1922) was not quite at the level of Archimedes, Newton, and Gauss (nobody was!), but he was nevertheless an accomplished mathematician and meteorologist, who spent the last years of his life in Bar-le-Duc, France, making extensive astronomical observations with a small telescope.
It appears, somehow, that those infatuated with the abstract, so-called “Platonic world of mathematical forms,” also frequently were bewitched by the heavens. Here, however, I want to concentrate neither on Brocard’s main, purely mathematical contributions (which were in the area of the geometry of the triangle; e.g., Figure 1), nor on his (more modest) contributions to meteorology and astronomy, but on a small, fascinating problem that he posed in articles written in 1876 and 1885.
For any whole number n, mathematicians denote by n! (called “n factorial”) the product of all the numbers up to and including n. That is:
n! = 1 × 2 × 3 × 4 … × n .
As it turns out, the different ways to arrange n objects in order is n!. For instance, you can arrange the three letters a, b, c, in 3! = 1 × 2 × 3 = 6 ways: abc; cab; bca; acb; cba; bac.
If you wonder in how many ways it is possible to arrange all 26 letters in the English alphabet, the answer is: 26! = 403, 291, 461, 126, 605, 635, 584, 000, 000.
What Brocard noticed was that in three cases, adding 1 to a factorial gave a perfect square:
4! + 1 = 24 + 1 = 25 = 52
5! + 1 = 120 + 1 = 121 = 112
7! + 1 = 5040 + 1 = 5041 = 712 .
He therefore asked the intriguing question of whether the same was true for any other numbers. That is, whether other whole numbers n and m exist, such that n! + 1 = m2. Pairs of numbers (n, m) that satisfy Brocard’s problem are known (for reasons that I must admit I don’t know) as Brown numbers.
Being unaware of Brocard’s query, in 1913 the famous Indian genius Srinivasa Ramanujan formulated the same question: “The number 1 + n! is a perfect square for the values 4, 5, 7 of n. Find other values.” In 1935, H. Gupta claimed that calculations of n! up to n = 63 gave no further solutions. It was only natural then for one of the most prolific authors of mathematical papers, Paul Erdös (Figure 2), to weigh in on this problem. Erdös is known for having collaborated with more than 500 mathematicians on a variety of joint papers. This productivity has led to the concept of the “Erdös number”—a measure of the number of steps needed to connect an author with Erdös. For instance, his direct co-authors have an Erdös number of 1, their co-authors on other papers have number 2, and so on. Incidentally, my own Erdös number is 4. Erdös conjectured that no solutions other than the above pairs (4,5), (5,11), and (7,71) exist. In 1993, Mathematician M. Overholt showed that if a weak form of another mathematical conjecture known as the “abc conjecture” holds true, then there is only a finite number of solutions to Brocard’s problem. In August 2012, mathematician Shinichi Mochizuki claimed to have proved the abc conjecture. However, Vesselin Dimitrov and Akshay Venkatesh pointed out an error in his proof in October 2012. Since then Mochizuki has posted a series of papers (the latest one just last month!) claiming to have corrected the mistake, but the jury is still out on those. Finally, in 2000 mathematicians Bruce Berndt and William Galway showed that no other solutions exist up to n equals one billion.
The ancient Pythagoreans believed that the entire universe could be explained by whole numbers. To their dismay, this turned out not to be correct. But whole numbers continue to intrigue many people (not just professional matheticians) even today, and to date, no mathematically rigorous answer to Brocard’s problem exists.
What did we know about the size and contents of our universe a hundred years ago? Very little. Even the proton, the nucleus of the simplest atom (hydrogen), was only discovered by Rutherford in 1917–1919. The neutron, the other occupant of the atomic nucleus, had to wait for its discovery until 1932, and the neutrino, the elusive particle that barely interacts with matter, was only discovered in 1956!
The size and structure of the cosmos were also a complete mystery to the astronomers and physicists of the beginning of the twentieth century. In fact, it was only in 1924 when astronomer Edwin Hubble unambiguously confirmed that there are other galaxies beyond our own Milky Way. Figure 1 shows a recent image of the Andromeda galaxy, M31, which was the first galaxy identified as being outside the Milky Way.
What do we know today about our universe’s dimensions and composition? Quite a bit, although much remains to be explored. Here is a concise inventory. While we don’t know the precise size of the universe, and it definitely may be infinite, the radius of the observable universe is about 46 billion light-years. One light-year is the distance that light travels in one year—approximately six trillion miles. For comparison, the distance to the Andromeda galaxy is “only” about 2.5 million light-years. The universe is about 13.8 billion years old. As far as we can tell, the universe is homogeneous (the same everywhere) and isotropic (the same in every direction) on its large scales. It is also geometrically flat. The average energy density in the universe is the equivalent of about 10-29 grams per cubic centimeter. About 73 percent of this energy density appears to be in the form of a rather mysterious, smooth, “dark energy,” which may represent the energy of the physical vacuum. About 23 percent appears to be “dark matter”—matter that does not shine light, but which can be detected through its gravitational influence. Ordinary (“baryonic”) matter constitutes only about 4 percent of the cosmic energy budget. According to the Standard Model of particle physics, there are 12 elementary particles (the most basic constituents of ordinary matter) that have a quantum mechanical spin of half a unit. These include six quarks (that are called: up, down, charm, strange, top, and bottom) and six leptons (electron, electron neutrino, muon, muon neutrino, tau, and tau neutrino). All of these are commonly grouped into three generations, the first of which includes, for instance, the up and down quarks, the electron, and the electron neutrino. In addition to the matter particles, there are force-carrying gauge bosons that include the photon (carrier of electromagnetism) the gluons (carriers of the strong nuclear force), and the W± and Z bosons (the carriers of the weak nuclear force). The latest addition to the list of elementary particles is the Higgs boson (discovered in 2012 and tentatively confirmed in 2013), which plays the crucial role of endowing all the other elementary particles (other than the photon and the gluons) with mass. Figure 2 presents the elementary particles of the Standard Model.
Intriguingly, there are theories that predict the existence of additional components to the above inventory, both in terms of contents (on the smallest scales) and structure (on the largest).
In one suggested extension to the Standard Model known as supersymmetry, every particle is supposed to have a yet-undiscovered partner. The leptons and quarks, for instance, would have sleptons and squarks, while the gluons would have gluinos. So far the Large Hadron Collider has not discovered supersymmetric particles, but it might still do so when it returns to operation at full energy.
On the cosmic scale, a more speculative idea is that of the multiverse—the proposal that our universe is but one member of a huge ensemble of universes. This speculation is based on insights gained from the concept of inflation—the brief phase of explosive expansion early on in the universe’s evolution, and from string theory. Certain otherwise perplexing properties of our universe (such as the value of the density of “dark energy”) may find an explanation if such a multiverse exists. String theory also suggests that in addition to the familiar three dimensions of space and one of time, our universe may have six or seven extra spatial dimensions.
To conclude, the last century has been absolutely phenomenal in terms of how much we have learned about our universe, but all signs are that the next one hundred years will be at least as exciting.
The heavens have always been a source of inspiration for poetry, music and the visual arts. The first chapter of the biblical book of Genesis already talks about the creation of the Sun, Moon and the stars. The ancient Babylonian, Chinese, North European and Central American cultures all left records and artifacts related to various astronomical observations. It was only natural then, that at the end of Medieval times, with the first signs of the Renaissance (in the fourteenth and early fifteenth centuries), the heavens would start making an appearance in important works of art. One impressive demonstration of the interest in astronomy was in the great Italian painter Giotto di Bondone’s fresco “the Adoration of the Magi” (Figure 1). The fresco was painted around 1305–06, and it features a very realistic depiction of a comet, representing the “Star of Bethlehem.” It is thought that the comet’s image was inspired by Giotto’s observations of Halley’s comet in 1301.
A second beautiful example of astronomy in art is provided by a famous illuminated manuscript. The three Dutch miniature painters known as the Limburg brothers created the Très Riches Heures du Duc de Berry book of prayers (Book of Hours), and it is currently considered to be one of the most valuable books in the world. The book was unfinished at the time of the death of the three brothers in 1416, and the work on it was completed by the painters Barthélemy van Eyck (possibly) and Jean Colombe (certainly). As Figure 2 shows, an attempt was clearly made to give an accurate representation of the night’s sky, even including meteors.
A third magnificent painting, the “Battle of Issus,” by the German painter Albrecht Altdorfer (Figure 3), may be the first painting in which the curvature of the Earth is shown as seen from above, from a great height.
Finally, I find the illustration of the Ptolemaic geocentric model by the Portugese cosmographer Bartolomeo Velho (Figure 4) extremely attractive. The illuminated illustration, “Figure of the Heavenly Bodies,” was created in France in 1568.
All of these works of art were being created shortly before or at a time when the Copernican revolution was about to forever change the view humans had of the cosmos and on their place within it. Far from being perfect and immutable, the heavens turned out to be part of an ever-evolving universe.
The tale of the discovery of Neptune, the eighth planet in the solar system (Figure 1) reads like a detective story.
The planet Uranus was discovered by astronomer William Herschel in 1781. Almost immediately, astronomers started to see deviations of its orbit from predictions made by Newton’s theory of gravitation. By the early 1840s, these deviations became substantial, leading a few astronomers to speculate that Uranus’s orbit might be perturbed by the presence of an unseen planet (alternatively, Newtonian gravity would have to be modified at large separations). In some sense, this was the first suggestion for “dark matter”—mass not detected through its light, but rather through its gravitational effects.
On June 1, 1846, the French mathematician Urbain Le Verrier published a calculation that explained the discrepancies by predicting the existence of a transuranian planet, and its expected location in the sky. Based on his prediction, the German astronomer Johann Galle and his student, Heinrich Louis d’Arrest, discovered Neptune just after midnight on the night of September 23, 1846. The new planet’s celestial longitude was just about one degree away from Le Verrier’s prediction! The excited Galle informed Le Verrier: “the planet whose place you have really exists.”
If the story would have ended here, this would have simply been a fascinating story of how sciences progress through theoretical predictions and observational verifications. This is, however, where the conventional plot started to thicken. According to the commonly told version, as soon as news of the discovery reached England, George Biddell Airy, the British Astronomer Royal at the time, realized that he had seen a similar prediction in the fall of 1845 on a note left at his house by a little-known English mathematician named John Couch Adams.
Adams had indeed been doing calculations for several years concerning the potential location of a new planet, and he briefly communicated his results to Airy and to James Challis, director of the Cambridge Observatory. However, the fact is, that the materials Adams provided to Challis and Airy were insufficient to convince the two to initiate an aggressive observational search. Only after Le Verrier’s prediction became known in England did Challis make an unsuccessful attempt to search for the planet suggested by Adams’ calculations. Nevertheless, following the announcement of the discovery of Neptune, a controversy arose between the English and French astronomical communities, with the English astronomers claiming that Le Verrier and Adams should share the credit for the prediction. The French initially reacted with suspicion, and the magazine L’Illustration even published a cartoon depicting Adams “discovering” Neptune in Le Verrier’s manuscript (Figure 2). The controversy eventually subsided after Airy presented certain documents which supposedly demonstrated that Adams had indeed produced predictions deviating from those of Le Verrier by only about one degree. The emerging consensus was, therefore, that Le Verrier and Adams should both be credited with predicting Neptune.
Amazingly, the story did not end there. Modern science historians, such as Neptune scholar Dennis Rawlins and astronomy historian Robert Smith, discovered that it was difficult to examine the details of the discovery of Neptune since the “Neptune file” containing Adams’ correspondence with Airy had gone missing from the library in the 1960s. In 1999, following the death of astronomer Olin Eggen, the file was discovered in his office in Chile, even though Eggen had previously denied having it. Eggen had served as chief assistant to the Astronomer Royal in Britain in the early 1960s, and apparently he was given the file—or he “borrowed” it (as well as other rare books)—for some research he was doing on Airy’s work. He then took the file with him to Australia and eventually to Chile.
Historian of science Nicholas Kollerstrom and his colleagues William Sheehan and Craig Woff have examined the file in detail, and in their view “the achievement [of predicting Neptune] was Le Verrier’s alone.” They based their conclusion on two main points. First, in successive calculations, Adams kept changing his prediction for the location of the putative new planet, once by as much as twenty degrees. Second, even though there is no doubt that Adams’ calculations were similar in nature, and at some level even in accuracy, to those of Le Verrier (both miscalculated Neptune’s distance from the Sun), Adams failed to convince his contemporaries to engage in an extensive search. Did, therefore, (in Kollerstrom’s words) “the Brits steal Neptune”? Maybe this is too strong a statement, but they certainly presented the evidence in a way that boosted Adams’ (and thereby Britain’s) claim for credit.
Scientists are only human after all.
The night sky, sprinkled with twinkling stars and the pale light of a silvery Moon, has fascinated humans since the dawn of history. But, why is it dark? If you think that the answer is: “Because you don’t see the Sun,” think again. While it’s true that we need the Sun not to be there, its absence is definitely not sufficient, as the following example demonstrates. Imagine that you are standing in the middle of a forest where all the tree trunks are painted white. If the forest is endless, you would see around you a uniformly white, continuous background, since a tree trunk would eventually interrupt every possible line of sight.
Similarly, if the universe were infinite, and filled identical stars, the night sky would glare with the brightness of the surface of a star. Instead, we see huge gaps of darkness separating the stars. Why is that? This puzzle has become known as “Olbers’ paradox,” named after the German physician and astronomer Wilhelm Olbers, who discussed it in 1823. This attribution is rather unfortunate, however, since Olbers was neither the first to ask this question, nor were his suggestions for how to solve it particularly valuable. Astronomer Edward Harrison extensively researched the history of this riddle, and he described his findings in the interesting book Darkness at Night.
The first person to record his wonder about the dark night sky was probably the Copernican astronomer Thomas Digges, who in 1576 suggested that the solution to the paradox lies in the fact that most stars could not be seen because “the greatest part rest by reason of their wonderfull distance invisible unto us.”
Unfortunately, while Digges seems to have understood that there was a problem, his proposed solution does not hold water. Take a universe that is uniformly filled with identical stars, and imagine that we divide space around the Earth into equally spaced thin spherical shells of increasing radius. A spherical shell that has twice the radius of another, contains four times as many stars (because its surface area is four times larger). Thus, even though each star in the more distant shell would indeed appear four times dimmer (the brightness decreases as the inverse square of the distance), the total light received from it would be the same as the total light received from the closer-in shell.
The next person to have been puzzled by the night’s darkness was the famous astronomer Johannes Kepler, who in 1610 wrote (in a letter to Galileo) that in an infinite universe filled with stars (Figure 1), “the whole celestial vault would be as luminous as the Sun.” Kepler’s proposed solution to the paradox—the universe has to be finite. This fell in line with Kepler’s religious beliefs that the entire universe was “for man’s sake.”
Edmund Halley (after whom Halley’s comet is named) also tried his hand at explaining the nocturnal darkness in 1720, but unfortunately his explanation was precisely the same as Digges’s, so it failed for the same reason.
Fascinatingly, the first person who seems to have anticipated elements of the correct explanation was not a scientist at all. It was the author and poet Edgar Allan Poe! In an essay entitled “Eureka: A Prose Poem,” published in 1848, Poe wrote:
“Were the succession of stars endless, then the background of the sky would present us a uniform luminosity, like that displayed by the Galaxy—since there could be absolutely no point, in all that background, at which would not exist a star. The only mode, therefore, in which, under such a state of affairs, we could comprehend the voids which our telescopes find in innumerable directions, would be by supposing the distance of the invisible background so immense that no ray from it has yet been able to reach us at all.”
In other words, Poe suggested that the universe has a finite age and therefore, because the speed of light is also finite, our observable universe has a horizon beyond which we don’t see stars. Poe’s qualitative solution was put onto solid mathematical ground in 1901, when physicist Lord Kelvin rigorously showed that in a universe that has a finite age, or one in which stars shine during a certain finite lifetime, the night’s sky should be dark.
Today we know that, in addition to the universe’s finite age, the cosmic expansion also contributes to the night sky’s darkness. Because of the fact that the universe expands, the energy of all the emitted radiation (including the background radiation—the “afterglow” of the Big Bang) has been reduced (redshifted) down to the low temperature of the cosmic microwave background (about 2.7 Kelvin; Figure 2).
Amazingly, the simple fact that the night’s sky is dark finds its explanation in the Big Bang theory—our universe is expanding and it has a finite age of about 13.8 billion years.
It all began in earnest on January 10, 2013, when I received an e-mail from composer and collaborative artist Paola Prestini. It started with a flattering line: “I am so intrigued by and love your blog!” she wrote. But then it got straight to the point: “I would like to create a Hubble song cycle or contemporary cantata for the mezzo soprano Jessica Rivera and the amazing ensemble ICE (International Contemporary Ensemble).” She added that she thought that the piece would get its strength from concepts related to the universe and Hubble imagery.
“Wow!” I thought to myself, “this would be fantastic.” After a few more exchanges and conversations via Skype, Prestini, librettist Royce Vavrek, and film maker Carmen Kordas came to Space Telescope Science Institute to meet with me on February 22nd. During the inspiring conversations that took place that day, we came up with the idea that the piece should somehow make a poetic connection between human life on Earth and the lives of the stars in the heavens. After all, stars are also born, they live, and they die. The time that was available to produce the complex multi-media piece was rather short, since Prestini and Manuel Bagorro, the Artistic Director of Bay Chamber Concerts, wanted the cantata to premiere in Maine on July 25, 2013.
We decided to symbolically anchor the Earth-based part of the lyrics on the agonizing experiences of a young woman struggling with a harsh reality. As Vavrek states in the introduction to the libretto: “Her footsteps tell stories.” The music and imagery for this section were partly inspired by the Japanese mythology-rich forest Aokigahara (Figure 1). Sadly, the historic association of this forest with demons has led to numerous suicides on the site. To connect the life (and death) experience of the young woman to the heavens, we used the ancient Peruvian geoglyphs known as the Nazca Lines (Figure 2 shows a satellite picture of such lines). Again in Vavrek’s words: “The woman walks in patterns, pictures emerge in the soil… She creates her own private Nazca lines, tattooing the Earth with her history.” The Nazca lines in Peru are believed to have been created between the fifth and seventh centuries, and they are thought (at least by some researchers) to point to places on the horizon where certain celestial bodies rose or set. In other words, they truly marked a direct astronomical connection between the surface of the Earth and the heavens.
In its conclusion, the Cantata completely intermingles the fate of the young woman with the ultimate fate of the stars (as is gracefully illustrated in Figure 3). The shapes in the sand and the constellations in the sky become one, mirroring the tortuous path of human life in the dramatic Hubble images of outbursts that simultaneously mark stellar deaths and the promise for a new generation of stars, planets, and life.
I have no better word to describe the fusion of Prestini’s music and Vavrek’s libretto with Kordas’s imagery than “mesmerizing.” I can only hope that the performance of the “Hubble Cantata” will travel extensively, to give as many people as possible the opportunity to emotionally experience its effect.
In one of the scenes of the movie Naked Gun 2 1/2, the camera pans across the wall in the “Loser’s Bar,” passing over pictures displaying major disasters. Among them are: the Hindenburg; the RMS Lusitania sinking; the 1906 San Francisco earthquake; and the Hubble Space Telescope! Indeed, between its launch in 1990 and the first servicing mission in 1993, Hubble was considered one of the greatest scientific blunders in history and was the target of numerous jokes. Its mirror, which was supposed to have been exquisitely polished, was ground to the wrong shape by about two millionths of a meter—enough to adversely affect the telescope’s anticipated sharper eye. That blunder should have undoubtedly been prevented through more rigorous testing. Nevertheless, I doubt there is anyone today who does not consider Hubble to be one of Science’s biggest success stories. Its original blurred vision inspired ingenious scientists, engineers, and shuttle astronauts to come up with a spectacular corrective action. The entire drama has only enhanced the popularity of this iconic telescope (Figure 1). The installation of corrective optics was enabled by the fact that Hubble was designed from the start as an ambitious and complex mission, one in which space-walking astronauts could exchange instruments and components.
Blunders are not only inevitable, they are an essential part of any innovative thinking process. If not for them, any creative enterprise might be wandering for much too long down too many blind alleys. I want to emphasize that this is not an advocacy for sloppy or careless procedures, but rather recognition of the fact that when there is potential for high return, outside-the-box ideas require taking calculated risks. In fact, the entire so-called “scientific method” is based on falsification—on finding out what doesn’t work—rather than on verification. In the words of the great philosopher of science, Karl Popper: “I shall not require of a scientific system that it shall be capable of being singled out, once and for all, in a positive sense; but I shall require that its logical form shall be such that it can be singled out, by means of empirical tests, in a negative sense: it must be possible for an empirical scientific system to be refuted by experience.”
Imaginative planning should also allow for the ability to take maximal advantage of serendipity; since some estimate, for instance, that nearly half of the discoveries leading to new medications have accidental origins. An excellent example is provided by the discovery of anti-depressants. One of the first of these, isoniazid, was actually developed as a drug against tuberculosis. Then, in an attempt to improve its effects, chemists synthesized some of its derivatives, only to discover a compound (iproniazid) that unexpectedly proved to be the key to pharmacologically treating mental depression.
Nature itself has learned this lesson—that serendipity and random errors (mutations) are part and parcel of evolution—billions of years ago. The fact is that extinction represents more than ninety-nine percent of all the species that ever lived. In this sense, our own existence is the result of multiple “errors.”
Tom Watson, who oversaw the growth of IBM for nearly half a century, recognized the importance of “brilliant blunders”—those mistakes resulting from bold ideas. In 1957, he said, “Let’s avoid being overly cautious, conservative, playing it safe. We should have the courage to take risks when they are thoughtful risks… We must forgive mistakes which have been made because someone was trying to act aggressively in the company’s interest.” Unbeknownst to Watson, he was describing here almost precisely the history of a blunder made by the famous physicist William Thomson (Lord Kelvin) in the nineteenth century (Figure 2). Kelvin was the person who made the first serious attempt to calculate the age of the Earth. Needless to say, the age of the Earth has implications for topics ranging from religious beliefs to geology and from astrophysics to Darwin’s theory of evolution. Kelvin’s calculation yielded about 100 million years—almost fifty times shorter than the value given by modern radiometric measurements. But his brilliant blunder literally opened the door to modern geochronology. Suddenly geologists realized that determining the age of the Earth is an essential part of what geology is all about. Furthermore, a detailed analysis of the reasons for Kelvin’s blunder (he neglected the fact that heat could be transported more efficiently by fluid motion), could have led to a more rapid acceptance of the notion of continental drift.
To conclude, taking calculated risks and embracing the possibility of blunders can lead to solutions and breakthroughs that may be entirely inaccessible to incremental processes. As playwright Samuel Becket once told an actor who had lamented that he was failing: “Go on failing. Go on. Only next time, try to fail better!”