Human subtlety … will never devise an invention more beautiful, more simple or more direct than does nature, because in her inventions, nothing is lacking, and nothing is superfluous.
—Leonardo da Vinci
ith his small entourage in tow, at the invitation of the newly crowned Francis I, in 1516 Leonardo journeyed to Amboise, where he would spend his final three years. The belongings he had with him in that move included his treasured collection of books, two or three paintings, among them the Mona Lisa, and chests bursting with his papers. It has been estimated that he had produced 13,000 to 14,000 pages, less than a third of which have survived. He may have left some of the papers in Milan and Florence. But he must have retained a substantial portion of the original papers when he arrived, considering he still entertained notions of writing as many as “120 books.” The papers bound as notebooks or bundled together as loose sheets reveal the depth of Leonardo’s thoughts and the dizzying range of his interests, especially in science, mathematics, and technology. It is there that we find the evidence of his extraordinary talent for identifying critical questions regarding nature and the physical intuition to design proper experiments to answer these questions. There, too, we see his unflagging dedication to open-mindedness and intellectual honesty, quintessential assets for anyone engaged in scientific inquiry. For Leonardo there were no defined parameters, no boundaries. These manuscripts represent no less than detailed maps of previously uncharted territory in science and technology.
Leonardo’s early teacher, Verrocchio, had instilled in his apprentices the need to know anatomy, but the levels of investigation that Leonardo would undertake far transcended what he would need in order to inform his works of art. We know that in his own lifetime Leonardo’s patrons had little patience for his frequent retreats into science. The almost idolatrous admirer, the artist and biographer Giorgio Vasari, in 1550 singled out Leonardo and Michelangelo for the sublime quality and power of their works of art. But clearly he felt an obligation to explain that Leonardo’s artistic output had been limited because of what he described as Leonardo’s frequent “dalliance with science.” In writing that Leonardo “could have been a great scientist [if that was all he did],” Vasari revealed that he had little idea of the quality of Leonardo’s science. Could have been?
Leonardo’s work in science and technology might not have been known to us had the caretakers of the various manuscripts not begun to realize what they had on their hands. In the late nineteenth century, with the development of photography, there was a major effort to produce facsimiles, specifically of the Codex Atlanticus. But it was not until a hundred years later that high-quality facsimiles of the anatomical studies in the Codex Windsor appeared.
Unhappily, Leonardo’s inventions and scientific discoveries were to come to light long after so much that he had investigated was rediscovered independently, long after entire fields that he had invented were reinvented. One cannot avoid the nagging notion that some of the questions and methods that he introduced might have been handed down by word of mouth, or that some of the pages of his dismembered notebooks might have become available to others, considering how much of Leonardo’s manuscripts were lost. There were the detailed dissections and drawings of the human body that Vesalius undertook half a century after Leonardo. And there was also the fleeting annotation about the sun Leonardo left in a notebook—“The sun does not move”—the keystone of the Copernican heliocentric system. I have in mind also the experiments with the pendulum and with falling bodies that Galileo repeated with resounding success a century later. There is on one page of the Codex Atlanticus, admittedly with little explanation, a study of the reflection of light from a concave reflector mounted at the bottom of a vertical tube, with the angle of the tube completely adjustable. Are these the rudiments perhaps of a reflecting telescope, invented by Newton nearly two centuries later? Finally, I have in mind Leonardo’s conclusions in the Codex Leicester regarding the existence of geological strata chronicling the earth’s great age, and that fossils found in the strata represented once living animals.
The traditional view of the birth of modern science is that it dates from 1543 with the publication of two important books. There was the inspired treatise by Copernicus of De revolutionibus orbeum coelestium, arguing on behalf of a sun-centered universe. And the same year saw the publication of Vesalius’s first accurate anatomical atlas, De humani corporis fabrica. By the seventeenth century the scientific revolution was in full bloom with Galileo, Harvey, Boyle, Kepler, and especially Newton. Leonardo’s manuscripts, however, offer compelling reason to accept him as having foreshadowed modern scientific methodology by a full fifty years before Copernicus and Vesalius produced their works. Though Leonardo never disseminated his discoveries, it is not difficult to make a case for Leonardo being the first modern scientist, and indeed that theme is asserted in the title of a recent book.1
He kept two different kinds of notebooks. There were the daily notebooks containing an admixture of snapshot-like sketches of faces in the crowd, ideas for inventions, and mathematical calculations and doodling. He also included in these notebooks profound observations intermingled with the prosaic and the perfunctory. The sense one gets in viewing these pages is that of a broad cross-semination taking place among all the components of his world. The image evoked is of a circuit board with each site wired to all others, signals flashing between sites, until they pause and a finished idea emerges. Then they start all over again until the conception of another new idea.
In the second kind of notebook were the finished drawings, including the anatomical drawings produced from multiple angles, designs for machines replete with precise specs and operating instructions, drawings demonstrating the results of reflection and refraction, experiments in optics, and so on. The text, in vernacular Italian, was written in that otherworldly mirror text from right to left. At one level, there is of course the astonishing content, an unsurpassed artist illustrating unsurpassed science, recording it all in exquisite detail. But at another level, and in the vernacular of our time, even these manuscripts represent a masterpiece of sorts in the modern publisher’s art of layout drawings executed with clarity and precision, and text wrapped skillfully around the drawings, every last sheet a frameable piece of art.
The first attempt to put some order into the papers came from Melzi, a man of unremarkable intelligence and limited artistic talent, who proved to be well short of the Herculean task. Melzi spent fifty years of well-meaning travail trying to organize them, and achieved little success. According to Sherwin Nuland, Leonardo’s loyal assistant was able to assemble only 344 brief chapters into a collection, and unhappily even these remained in a state of confusion; none of it was ever to get published in Melzi’s lifetime.2 And the worst was still to come. Upon Melzi’s death in 1570 his nephew Orazio became heir to the wondrous collection. Orazio, a lawyer, proved to be a man of lesser wit than his uncle; moreover, he was entirely unencumbered by the devotion that his uncle had shown to his immortal mentor. He quickly lost all interest, losing some papers, selling others, and tragically dispersing the collection. Among those helping themselves to the treasure was the tutor of Orazio’s children. What and how much this man took and whether any of it remains among the surviving works will never be known.
Near the end of the sixteenth century the sculptor Pompeo Leoni managed to recover a large assortment of the manuscripts, and by cutting and pasting, grouped some of these into ten lots, or codices, with the rest remaining a potpourri of unrelated papers. The organizing principle of Leoni’s collation was general subject areas, but without any order in the dates in which the individual leaves were conceived. The collection was assembled for sale to Phillip II of Spain. Phillip, however, died in 1598 before even taking possession. Meanwhile, the manuscripts made the trip to Madrid, but with the failed sale Leoni returned to Florence, taking back with him only the Codex Atlanticus, dealing mostly with mechanical inventions. The rest he left behind in Spain.
The 1,119-page Atlanticus passed through the hands of various wealthy families, eventually finding its way into the Biblioteca Ambrosiana in Milan. A large part of the collection left originally in Madrid made its way to England. This included the corpus of the six-hundred-page Windsor collection, dealing with anatomical studies; a third group, the Codex Arundel, ended up in the British Museum; a fourth group of only seventeen pages, the Codex on the Flight of Birds, is in the Biblioteca Reale, Turin; a fifth group, Codex Forster, is owned by the Victoria and Albert Museum in London; a sixth group was purchased by a wealthy Oxonian, who subsequently bequeathed it to Christ Church, Oxford University, where it is periodically put on exhibition. Also included in the transfer to England was a seventh group of sixty-five sheets, the Codex Leicester, owned for centuries by the Leicester Family. The Codex Leicester was purchased from its English owners by the American industrialist, Armand Hammer, under whose ownership it became known as Codex Hammer. Then in the early 1990s this codex was purchased by Bill Gates at an auction of Hammer’s estate. With the change of ownership, the name of the collection reverted to the Codex Leicester.
The Gallerie dell’Academia in Florence, the Gallerie dell’Academia in Venice, the Uffizi in Florence, the Vatican Library in Rome, the Louvre in Paris, and the Institut de France all own collections of the manuscripts. The last institution listed owns both the Codex Ashburnham and the Codices of the Institut de France.
In 1651 a French publisher with deep reverence for Leonardo’s works culled from a jumble of Leonardo’s general writings just those pertaining to art. A critic at the time had characterized the notebooks as “a chaos of intelligence.” The publisher brought some organization to that chaos. After commissioning the French seventeenth-century artist Nicolas Poussin to illustrate the writings, he simultaneously published French and Italian editions of the Treatise on Painting—Traité sur la peinture and Tratatto di pittura.
Finally, in the 1960s a pair of volumes of Leonardo’s manuscripts was discovered in Spain, where they had been lost for 180 years in the Biblioteca Nacional. The caretakers of the collection had even pasted some of the “less useful” pages together in order to fortify others, then promptly misfiled the books. After painstaking restoration the glued pages were separated in the late 1960s and 1970s, and the 192 pages of the notebooks became available for study by Leonardo scholars as the Codices Madrid I and II. Volume I comprises Leonardo’s writings on classical mechanics; Volume II, a looser assortment of writings on mathematics and optics.
The mechanical designs of Leonardo can be loosely classified as machines for industrial engineering; machines for commercial application; tools for civil engineering; devices for locomotion on land, air and sea; and military engines for defense and offense. The mental inventions were sometimes accompanied by reflection on the fundamental science underlying the technology. How and why does nature behave as it does? The finite space that we can devote to reviewing the technical component of Leonardo’s legacy will allow only a partial inventory of these mostly mental inventions. We shall take a different tack and seek the wider connections among his endeavors rather than presenting a comprehensive catalogue. This approach should assist in understanding the immense value of Leonardo’s cross-fertilization of ideas, as well as his prescience, that genius for anticipating future science and technology. It will also serve to launch discussions of modern developments, some that Leonardo could have envisioned as extensions of his own, and others that even he could never have foreseen but would have found fascinating.
Leonardo’s preoccupation with the flow of rivers and the catastrophic movement of land (such as in earthquakes) now defines the fields of hydrology, geomorphology, seismology, and a host of other specialties within geology. In his early days in Florence he once wandered into a cave teeming with bats and the all-pervasive rancid mist repugnant even for spelunkers. He also came across the fossils of an extinct creature. The memories of those early encounters remained with him throughout his life; he contemplated the age of the earth, and became deeply skeptical of the time horizon for the age of the earth taught by the Church. He concluded that the earth was much older. He also wondered about the large-scale changes in the topography of the land as the overwhelming weight of the mountains bore downward. Those experiences are reflected in some of his paintings, as in the Virgin of the Rocks, where the background is provided by the cave with stalactites and stalagmites, permeated by the heavy mist. His geologic interests are also in evidence in the Mona Lisa, where the distant landscape includes a stream running through the undulating hills and valleys, all formed by the forces of nature.
Leonardo labored on the dynamics of vortices in water. The sketches in his notebooks of these circular, spiral, and cascading flow patterns would reappear in his paintings as gentle swirls in the hair of the subjects of his portraits. He preoccupied himself with problems of hydrostatics and hydrodynamics, examining the relationship between water depth and water pressure. Indeed, there is evidence that he anticipated discoveries made by his latter-day countryman Torricelli, and by the great Swiss family of scientist-mathematicians, the Bernoullis.3 He explained that it was the weight of the water that determined the pressure at different levels. His experiment in this instance called for holes of equal size drilled at different levels in a cylindrical water container. The water gushed out at different speeds from holes at different heights, revealed by the different ranges of the water’s trajectories, and was due to the pressure at different levels. He then extended this idea to explain the existence of different atmospheric pressures at different altitudes as evidence of the weight of the air itself. He designed variations of water pumps and made significant improvements in the hydraulic designs of Heron of Alexandria (first century A.D.)
Leonardo designed a side-wheel paddle assembly for propelling boats. In some versions of the design, a heavy flywheel builds up angular momentum and delivers the power uniformly to the paddles. The power is supplied by one or more people turning cranks. In the nineteenth century, with steam supplying the power, stern and side-wheelers were navigating the waterways, most prominently on the Mississippi River. Leonardo also designed a double-hull structure for ships that in the twentieth century became the standard design for oil tankers.
In the 1860s, during the American Civil War, the Confederate navy built the submarine the CSS H. L. Hunley, reminiscent of a design by Leonardo, powered by men cranking stern or side paddle wheels. By the early twentieth century, with diesel-powered engines, submarines became devastating engines of war.
Leonardo envisioned “floating shoes” that would allow an individual to walk on water, flotation rings that would keep him afloat, and he designed diving suits that would allow a submerged person to breath through hoses. He left behind drawings for equipment that could dredge silted waterways. One device consisted of a floating double-pontoon boat with vertically mounted rotating scoops, scraping silt and depositing it on a floating barge towed between the pontoons. This design is similar to the equipment used in the dredging of the Panama Canal at the turn of the twentieth century, except the latter was steam-powered.
Among his drawings is the design for a turbine to harness hydro-dynamic power. Water flowing or falling from a higher elevation rotates a turbine, which in turn drives other devices, such as mills, drills, and saws. With the harnessing of electricity in the nineteenth century, the turbine became a device to power the electric generator, which in turn provided the electrical energy to run the mills, drills and saws, and to run homes, cities, and factories.
In addition to countless designs for original devices, there are also present designs for “derived tools.” It is clear these are ideas that have been inspired by others’ inventions, but Leonardo’s versions rarely lack improvement over previous designs. There are his variations on the Archimedean screw—one design involving a single helical coil, another a pair of intertwined coils.4 The screws are turned by cranking a handle, raising the water uphill. In still another version a helical hollow coil wrapped around an axle is rotated manually with a crank.
Among the pages of the Codex Atlanticus are ideas for the mortar and the howitzer, shooting multiple cannonballs. The military engineering aspect aside, there is a subtle observation here of the inherent physics. That realistic depiction of the array of cannonballs reveals in their curvilinear motion the smoothly arched trajectories, a circumstance that no single cannonball frozen in space and time could reveal by itself. (This is in the manner of a stream of water propelled from the nozzle of a hose. No droplet alone frozen in space and time reveals the path as the stream itself does.) It is clear that Leonardo already had a more realistic understanding of the trajectory of a projectile than the instructors of natural philosophy (physics) who were still teaching Aristotelian physics in academic institutions. That archaic view, which prevailed into seventeenth century, had the projectile rising in a straight line at some oblique angle, and upon losing energy, plummeting vertically, the two straight lines of the rise and fall connected by a short semicircular curve. Among Leonardo’s drawings appears a set of trajectories of projectiles launched at different angles. These trajectories are recognizably parabolic in shape.5 In the parabola there exists a right-to-left symmetry about the midline, lacking in the trajectories depicted by the Aristotelians (Figure 10.1).
The mathematics describing the shapes of curves (analytic geometry) awaited formulation by Descartes a century later. Leonardo was unable to demonstrate the parabolic trajectories with mathematical rigor. Almost a century after Leonardo’s death Galileo established the exact trajectories of projectiles to be parabolic curves. Such measurements and calculations are revealed in one of Galileo’s lab books of 1608.6 In a first-year physics laboratory course in high school or college similar experiments are routinely duplicated by seeking the relationship between the vertical and horizontal distances projectiles travel.
Leonardo contemplated other weapons of much greater effectiveness, such as a machine gun. Multiple muzzles are arranged in splayed configuration and when fired spray projectiles in a wide horizontal plane. There is little chance of precision aiming with this weapon, depicted in the Codex Atlanticus, but then it is the scattershot effect that appears to be the goal. There is no evidence that the weapon was ever built in Leonardo’s time, but late in the nineteenth century the Gatling gun was invented with muzzles in a circular arrangement around a central axis.
Figure 10. 1. (top) Leonardo’s drawing of bursts of mortars, revealing smooth arched trajectories, Codex Atlanticus. (insets, left to right) Illustration from a military treatise published in the early seventeenth century reflecting the prevailing Aristotelian notion of a projectile’s trajectory. (inset, center bottom) Galileo’s discovery of the parabolic trajectory (1608). (inset, right bottom) Leonardo’s drawing of the trajectories of projectiles fired at a variety of angles
One is struck by the precision and detail in the drawings, and indeed in the transparency of their function. Every manner of spring, every manner of gear—worm gears, reducing gears, the variable transmission, and even the mechanism for converting reciprocating motion into circular (and conversely, circular into reciprocating) has been conceived and masterfully drawn, each a general solution awaiting a special problem.
In other instances solutions are presented for well-defined problems. There is, for example, the design of odometers to determine distances. For odometers he envisioned variations of a device reminiscent of a modern wheelbarrow that would be rolled along the path to be measured. There is a gearing down process with thirty revolutions of the main wheel resulting in one revolution of an intermediate wheel. Then thirty revolutions of the intermediate wheel result in one turn of the last wheel; followed immediately by the release of a bead into a collector. Even this collector/counter is arranged so that the beads form a regular array, which at a quick glance reveals the total distance covered by the odometer. For example, a 4-by-5 array of beads represents 30 × 30 × 20 = 18,000 revolutions of the main wheel of precisely known circumference. This apparatus is so simple and practical that Leonardo very likely constructed it to use in his civil engineering tasks.
It was mainly during his Milan years, from 1482 to 1500, that Leonardo’s thoughts ran to urban planning, revealing prescience regarding the communicability of diseases. He wrote about the intolerable squalor of certain sections of the city, and saw a threat of the spreading of “the seeds of plague and death,” perceiving a need for the population to be more uniformly spread out. To that end, he drew a plan to create a city of concentric circles of ten zones, and a zoning system that would distribute the population of 300,000 evenly among the ten zones. Unhappily his employer, the duke Ludovico Sforza, never saw fit to implement the plan, which, as Sherwin Nuland observes, could have served as a model for many European cities also suffering the tribulations of congested population densities. It was an idea of human settlement, ekistics, centuries ahead of its time.
In his original letter to Sforza seeking employment, Leonardo had offered his services as a military engineer—to build devices for defending walls as well as other devices to tear them down. His notebooks from this period reveal many of the proposed instruments of war having attained design stage, but rarely the level of production. There were shielded ladders and portable bridges to be used in attacking the enemy, or conversely, for retreating. There were cannons of unusual efficacy, among them a design to propel cannonballs with steam pressure. Also among the mental inventions in his arsenal was the design of a particularly grisly machine, a chariot-driven scythe that could mow down enemy soldiers (but as much a hazard to the attacker as the attacked). There was the design for a colossal bow that could breach fortified castle walls. The scythe is most likely derived from earlier Renaissance inventors, and indeed, the massive crossbow idea harks back to the Romans. Finally, Leonardo has the design of an improved trebuchet, the medieval war engine designed to catapult boulders or marble balls several hundred kilograms in mass into castle walls. The Mongol armies were known to have used the trebuchet to launch animal carcasses (and even plague-ridden human corpses) over city walls. This early application of biological warfare unhappily did not elude Leonardo, who also included in his notes the sketch of a trebuchet armed with its projectile: the carcass of a horse.
Operating a machine that is virtually invulnerable to the enemy while your warriors are attacking is a fantasy as old as the concept of warfare itself. Leonardo’s solution, an armored vehicle, prefigures the twentieth-century tank by more than four centuries. A gang of four men, providing power for the vehicle by cranking handles, does not make for efficient locomotion, but there is improvement in another design where he introduced oxen as the source of power. Once diesel-powered locomotion became available in the late nineteenth century, the feasibility of a tank blossomed fully in time for the First World War. It became an overwhelming offensive force in warfare through the twentieth century.
One device that was produced in his own lifetime following his design was the wheel lock. As a precursor to the flintlock, the wheel lock represents a significant development in the history of weapons, making possible portable guns—pistols, muskets, the blunderbuss, and ultimately the modern rifle. Leonardo’s designs for a door lock and a wheel lock both appear in the Codex Madrid; his designs for a variety of leaf and coil springs appear in the Codex Atlanticus.7 Springs and small connecting chains are used in cocking and releasing component parts. When a trigger is pulled, a cocked mainspring sets a steel flywheel spinning. A piece of iron pyrite, a flint, held in place by a small vise is brought into contact with the rim of the spinning wheel, resulting in the release of a stream of sparks. These ignite the gunpowder interposed in the barrel between the wheel lock and a bullet. Also required is a stock heavy enough to reduce the recoil when nestled in the gun-bearer’s shoulder, allowing the weapon to be held safely and comfortably, and aimed with ease. The necessary components of the rifle yield the common expression in English conveying the entirety of a system—“the lock, stock, and barrel.”
It is no surprise that Leonardo, who contemplated a variety of devices to harness energy, spent time designing a spring-driven horseless carriage. Leonardo’s crude sketch for the spring-powered cart appears in the Codex Atlanticus. As depicted, his machine would have lurched forward and traveled a short distance. Four hundred years later, after the discovery of the Otto cycle and invention of the gasoline-powered engine and the diesel engine the car became more than a viable means of transportation—it became indispensable. At the threshold of the twenty-first century the question is not whether such vehicles will be around into the distant future, but rather what will be their future sources of power—battery, fuel cells, hybrid?
In the book The Unknown Leonardo8 Ladislao Reti presents the marvels of the Codex Madrid, a pair of notebooks dating from Leonardo’s peak productive period, 1491 to 1505. This is a period coinciding with the years of his artistic masterpieces, the Lady with the Ermine, the Mona Lisa, and the Last Supper. The bicycle evolved during the nineteenth century—from a pair of wheels which a man straddled and took for a walk, to the unicycle, to a pair of wheels with varying sizes, and so on. There was experimentation with a small wheel in front and a large one in back, then vice versa, until the optimum general design finally emerged toward the end of the century. The modern bicycle—replete with two equal wheels, a handle bar, seat, pedals, a pair of gears and, connecting the gears, a chain-drive—dates to the 1890s, but the identity of its inventor depends on who is making the claim. According to French tradition Ernest Michaux, a blacksmith in Paris, created the first bicycle; according to the Germans it was Baron Drais von Sonnerbronn who had that honor. We are not in a position to resolve the debate. Or are we?
Leonardo’s Codex Madrid contains the vision of a bicycle, complete with two equal-sized wheels, a handle bar, a seat, pedals, a pair of gears and a connecting chain-drive.9 Displayed in the drawing is a tacit understanding of the mechanical advantage obtained from driving the smaller gear in the rear with the larger one in the front. Another figure appearing in the codex depicts the details of a bicycle chain complete with sprockets. Leonardo’s vision in this instance hurdled four centuries of technology, including the entire span of the Industrial Revolution.
Why should man not be able to do what the birds do?
—Leonardo da Vinci
Leonardo was in love with every facet of nature but reserved a special veneration for birds. He regarded birds as nature’s splendid flying machines. In their case form had followed function magnificently. He spent his life virtually fixated on the mechanics of the flight of birds, bats, insects, creatures all clearly heavier than air—and dreamed of human flight. He reasoned that if birds could fly, then with some help so could humans. His notebooks are filled with sketches of wings, their anatomy, their mechanical motion, and his own designs for a variety of ornithopters, pairs of strap-on wings resembling those of bats. His assistants may have been mortified by the notion that he might appear at work some morning and ask one of them to test-fly one device or another.
When Leonardo eventually concluded that achieving flight by flapping wings in the manner of birds was less than promising, he began to think of achieving elevation with a spinning helical foil. In his art, especially in the portraits, the helical shape had been used to create dynamism in his subjects. In the Archimedean screw it was used as a mechanical device to elevate water. He must have connected that shape and the memories of watching samaras descending gently from trees while spinning.10 Could the helical screw be rotated to achieve lift? Leonardo’s design for a helicopter called for a large helical foil, a massive screw, which would be powered by two (and in another version by four) men. A horizontal torque generated by cranking handles was converted into a vertical torque with one of the gear assemblies sketched out in his notebooks, operating in a manner reminiscent of the differential or rear end of an automobile.
Leonardo may have built miniature scale models of some of the inventions he had visualized, as it is generally believed he built models of the polyhedra presented in De divina proportione, but none have survived. Many of the machines he designed would have worked just as they were depicted. Others would have worked in principle, but not in practice. And others still would not have worked as they were conceived. The boat with side-paddles, the submarine, the car would not have had sufficient power if the energy came from humans exerting muscle power only. His aerial screw could never have generated sufficient “bite” powered by humans; moreover, it would have needed a stabilizer and a steering mechanism to become a practical flying machine. The Russian-American aeronautical engineer Igor Sikorsky claimed to have been inspired by Leonardo’s aerial screw when he created the first successful helicopter in the 1930s, powered by a gasoline engine with a stabilizing propeller in the rear.
Among the pages of the manuscripts there is an unusually rough sketch, a fleeting idea for a parachute, a pyramid-like four-cornered fabric structure and a man hanging from lines attached to each corner. An annotation by Leonardo explains its purpose: “If a man have a tent made of linen of which the apertures have all been stopped up, and if it be twelve braccia across and twelve in depth, he will be able to throw himself down from any great height without suffering any injury.” Even in our day we might find the design problematic, interesting, but unlikely to work as depicted, certainly unlike the billowing hemispherical sail, replete with a small stabilizing hole at the top, and the cords made of lightweight nylon that we are accustomed to. But in December 2000, five hundred years after Leonardo had created his sketch of a parachute, a National Geographic Society photographer captured the spectacle of a man sailing down from the skies above South Africa with a parachute created in the image of Leonardo’s own design and built to his specifications.
In 1500 Leonardo traveled to Florence for what would be a short second Florentine period. And although he was received with deference, he was not accorded the adulation of Michelangelo, the younger and exceedingly talented sculptor and painter who managed to finish projects. He came very close to relocating to Constantinople (today Istanbul), ostensibly to take up a position as court engineer similar to the one he had held in Milan, and to do a portrait of the Ottoman sultan Bayezid II. In his application for a job he had contemplated preliminary designs for a bridge over the Golden Horn, and a pontoon bridge across the far more expansive Bosporus. As events unfolded, however, Bayezid did not take him up on the offer, and Leonardo took instead a position in Urbino, under the patronage of the city’s new leader, Cesare Borgia.
There is a tradition among many in Istanbul that the father of Sultan Bayezid, the legendary Mehmed the Conqueror, had earlier invited Leonardo to Constantinople to paint his likeness. But with Leonardo being unavailable at the time, the commission had gone instead to an older contemporary, the Venetian Gentile Bellini, who made the journey to the Ottoman capital and produced the only known likeness of the legendary conqueror of the city. The portrait, created in 1480, a year before the Sultan’s death, is now in the National Gallery in London. It is certainly possible that Leonardo, then twenty-eight, could have been offered the commission, but there does not appear to be sufficient basis in fact to accept the story’s veracity.11
As for a bridge spanning the Golden Horn, a floating bridge was finally built 350 years later, and a pair of bridges spanning the Bosporus, five hundred years later (in 1973 and 1982, respectively). But Leonardo’s original design, combining function, structural strength and artistic elegance, but somewhat scaled down, was brought to fruition in 2001 in the far north—Ås, Norway.
Replicas of Leonardo’s mental inventions were ultimately created from the sketches that he left in his notebooks. The best known set of the replicas came in the late 1930s, when Benito Mussolini commissioned Roberto Guatelli, an Italian modeler/engineer, to create scale models from the sketches. Shortly after the replicas were completed they were shipped to Tokyo, where they were put on exhibition. But like so much else, they became victims of the war, destroyed during aerial bombing of the city. In 1951 IBM hired Guatelli to create a new set of replicas, finally completed in the late 1950s. The replicas are now owned by the Gallery Association of New York State (GANYS) and are lent out to museums and other institutions for display. Among Guatelli’s creations based on Leonardo’s drawings are the ornithopter, the parachute, and the aerial screw. Also there are the double-hulled ship, the paddle assembly for the side-wheeler boat, the mechanism for a water powered turbine, a transmission, variations of the odometer, a scale model of Leonardo’s tank, a printing press, the spring-powered cart (Leonardo’s automobile), an anemometer to measure wind velocity, and a hydrometer to measure moisture, among other inventions.
After the discovery of the two volumes of the Codex Madrid in 1967, Guatelli examined the books, uncovering the design of a machine closely resembling another sketch appearing in the Codex Atlanticus. Using the two designs in tandem, he created the replica of a machine that convinced him that he had a crude mechanical calculator on his hands. With thirteen gears connected in series, and a ratio of 10:1 between each pair of gears in sequence, Guatelli surmised that the machine was capable of registering up to 1012 (i.e., 100–1012). A panel of engineering faculty at MIT convened to study the machine and became convinced that the inherent friction between so many gears in series would render the machine unworkable as depicted, but that its intended function was that of a “ratio machine.” In 1971 Guatelli and chief assistant Joseph Mirabella, his stepson, left IBM and founded their own workshop in New York in order to continue producing replicas of Leonardo’s mental inventions.
Questions regarding the nature of time have baffled philosophers and physicists since ancient times, and it would have been surprising if Leonardo had not contemplated the problem. His concerns about the nature of time may have been fueled by his desire to build an accurate mechanical clock. But whether the concerns actually occurred to him in that order or in the reverse (i.e., pondering the nature of time, then addressing the engineering problem of designing a clock) may never be known. Over the ages scholars have grappled with notions of a circular time, with cosmic history repeating itself, and a linear time progressing irreversibly. The passage by Leonardo quoted at the beginning of Chapter 1, which compares the passage of time and a flowing river, is a reflection of the man’s interest in this enigmatic phenomenon of nature. His metaphor suggests that in his view time progressed according to the latter model. These prefigure twentieth-century cosmology’s debate between the validity of an always existing, steady-state universe versus an expanding universe that had a beginning in time (with a big bang). If the latter, will the universe keep expanding forever—making this a one-time universe—or will its expansion slow down and stop; and if this is the case, perhaps there would follow a collapse (a big crunch), followed by the endless repetition of the process. These are issues we shall examine later.
During his investigation of time and timekeeping, Leonardo examined the behavior of the simple pendulum. A weight is suspended by a string, and put into oscillation by being displaced to one side and released. The weight or pendulum oscillates back and forth, between a maximum displacement on one side (the amplitude) and the maximum displacement on the other. The period of the pendulum is defined as the time for the pendulum to go from one amplitude to the other and then to return to its original position, one full back and forth motion. The pendulum at its maximum displacement will momentarily stop before moving in the other direction, its maximum speed attained at the lowest point of its swing. In the ideal case, where air resistance is absent, the oscillation will continue unabated. In reality, air resistance creates a drag and eventually stops the oscillation of the pendulum. What is remarkable about the behavior of the simple pendulum is that the period of the oscillation turns out to be very nearly constant, even while the amplitude of the oscillation decreases.
Leonardo left a crude sketch of the simple pendulum. As it appears in the Codex Atlanticus, however, it has a confusing aspect to it. The pendulum is shown in successive images, but with the highest density of images occurring near the lowest part of the swing. If a modern strobe light were illuminating the swinging pendulum, the highest density of images would occur at the extreme points where the pendulum is in its slowest stage. Thus Leonardo appears in that sketch to be using greater density of images to represent the areas of greatest speed.
Leonardo’s notebooks also contain the rough sketch for a machine with a pair of flat springs twisted into shapes reminiscent of the horns of a water buffalo, and weights hanging from a pair of brackets on the machine’s sides. What Leonardo had in mind for this machine was a quandary until a German engineer replicated the machine recently, hoping to resolve the question of its purpose. It turned out to be the design for a mechanical clock driven by springs and fine-tuned with the adjustable weights.
Among Guatelli’s replicas is an apparatus to determine the curvature of the surface of the spherical earth, with a device somewhat evocative of the scheme used by the ancient Alexandrian astronomer Eratosthenes. With his technique of sighting a distant celestial body at two points on earth that are separated by substantial distance, Eratosthenes had measured the radius and circumference of the earth. Indeed, the notion of a flat earth was preposterous to Leonardo, even more so than an earth-centered universe. In speculations about the sun-centered universe he was echoing the sentiments of Aristarchus of Samos, another astronomer of antiquity (but a notion not to resurface until Copernicus published his book in 1543). The views of Aristarchus and Eratosthenes may or may not have been available to Leonardo. Never having received the sanction of the Church, these views were most likely not available in Italy, although the success of Columbus’s trip of 1492 had gone a long way toward confirming the shape of the earth prescribed by both scientists.
Whereas the dates of so many of Leonardo’s technical works have been obscured by Pompeo Leoni’s questionable sorting technique, the anatomical drawings can be traced mainly to two well-defined periods in his life when he is known to have undertaken such studies. His first Milanese period (1482–1500) saw some limited dissections of corpses, but more of animal carcasses than of human cadavers. Leonardo’s early beliefs had been shaped by the writings of the second century A.D. Greek physician Galen. He still accepted the Galenic view that blood originated from the liver, and a healthy body required a critical balance of the four humors—blood, black bile, yellow bile, and phlegm—together with the proper admixture of hot, cold, wet, and dry. His drawings of the heart of a calf and the embryo of a cow are exquisite in their detail, but not overwhelmingly significant for the understanding of the human machine, or that of any other mammal. He had little access to human cadavers in this period and his understanding is accordingly rife with errors.
Leonardo’s second Milanese period (1506–1513) turned out to be a time of bounty for his anatomical studies, and conversely, a time of austerity for his artistic productivity. Although the Mona Lisa may have been completed around 1507, few other works of art are known from the time. His new patron in Milan was the French King Louis XII, whose hegemony extended over Milan and who entered the city personally in 1507, shortly after Leonardo. For the inhabitants of the city the presence of the formidable French forces brought a life relatively secure from invasion at a time in Italy when the fear of invasion was one of the constants of life. Louis recognized Leonardo for his gifts and granted him regular compensation, allowing him to operate his own veritable “think tank.” There were seemingly no requirements to produce anything. Leonardo’s fertile imagination could explore untrammeled. For the first time in his life Leonardo had the opportunity to devote himself to his beloved science, unencumbered by the need to scrounge about for patronage.
A catalyst for his mastery of anatomy came with his meeting the prodigiously talented young anatomist, Marcantonio della Torre, who had recently transferred from the University of Padua to the University of Pavia. The former was one of the few Church-sanctioned seats of anatomical studies, including dissections, and the latter was aspiring to build up a program. The collaboration with della Torre, half his age, galvanized Leonardo’s intense dedication to the pursuit of knowledge. There is some disagreement among Leonardo scholars as to whether della Torre was the driver, directing Leonardo’s dissection procedures, or an equal partner deriving as much from Leonardo’s work as he contributed. A fair assessment five hundred years after the fact might be that della Torre indeed gave Leonardo’s methods of anatomical probing some structure, but that Leonardo—with his immense gifts of innovation, the dexterity of a supreme artist, and above all his independence of thought—took it from there. Just as he had always been a scientist doing art, here he was the artist doing science. The collaboration with della Torre, however, was to last no more than three or four years; in 1512 the young physician died, a victim of the plague.
The Leonardo scholar and professor of surgery Sherwin Nuland, to whom all scholars of Leonardo as an anatomist may safely defer, recounts a pair of back-to-back dissections that Leonardo performed. The first was carried out on a recently deceased old man who had claimed to be a hundred years old, on whom Leonardo was able to perform an autopsy almost immediately after death. Leonardo concluded that the cause of death was “a weakness through failure of blood and of the artery that feeds the heart and the lower members which I found to be very parched and shrunk and withered.”12 He found in a subsequent autopsy on a two-year-old child the same vessel to be clear of obstruction and the vessel walls to be supple. What Leonardo had described in the coronary arteries of the old man was “atherosclerosis of the aorta and perhaps even artery obstruction, hundreds of years before either was recognized by physicians.”13 The dissections he had performed on these two freshly deceased cadavers stood in dramatic contrast to others he had performed—mostly in fetid chambers—on cadavers in various states of decay, though also described copiously. The descriptive narrative, however, in those earlier cases is of less significance than the detailed anatomical drawings presented from multiple angles. Anatomical drawings of the female body that existed in the literature of Leonardo’s time could have been mistaken for schematic drawings of a frog’s anatomy (Figure 10.2).
One organ in the human body fascinated Leonardo beyond any other. His “window to the soul,” the eye, as the instrument of sight, had to be understood at all levels: its structure, its connections to other organs, and its precise operation as light traversed it. In order to understand the anatomy of the eye—this aqueous, mysterious organ—he had to perform minute dissections. But this is an organ uncommonly difficult to cut accurately because of its fluid interior. Leonardo invented the technique of holding the eyeball fixed in a glutamate formed by a hard-boiled egg (the eyeball would be immersed in egg white and hardboiled within it). The technique of embedding the eyeball in a coagulum such as paraffin for purposes of accurate slicing is routinely used today.14
Figure 10. 2. “The Great Lady,” Codex Windsor. Anatomical drawing of the female torso by Leonardo. (inset, upper right) Anatomical drawing of the female torso appearing in a contemporary work, Fasciculus Medicinae
Also to be mastered in this connection was the nature of light itself. Thus the anatomy (biology) of the eye was only half the story; it had to be augmented with the other half, optics (physics), which also required examination at a fundamental level. He studied the science of perspective, just coming into its own, and he made significant contributions. He recorded his observations on light falling on the sides of multifaceted polygons in order to understand the nuances of the shading, the scattering of light. This was invaluable for informing his paintings, especially the portraits. The faces of both the Virgin and the angel in the Virgin of the Rocks exude otherworldly and divine qualities because Leonardo was able to illuminate them with just the right light. The enigmatic visage of the Mona Lisa similarly reflects its creator’s surpassing mastery of light.
Studies in optics in the context of reflection and refraction of light are found in more than one codex—the Atlanticus, the Arundel, the Madrid II. On a page of the Codex Atlanticus (c. 1490) there is an entry, “making glasses to see the Moon enlarged,” proposing the idea of a refracting telescope, which was ultimately patented by the German-born Dutch optician Hans Lippershey in 1608. In a refracting telescope a pair of semiconvex lenses (a primary and a secondary) are used to magnify the object viewed, most of the actual magnification being performed by the larger primary lens. Less than a year later Galileo, having been presented approximate specifications of Lipershey’s marvelous invention by a close friend, created his own refractor (Plate 16, lower left).
One drawing that has fascinated me since I first came upon it several years ago in the Codex Atlanticus is a study of reflected rays from a concave mirror. On the same leaf also appears a cylindrical tube, possibly to house the concave reflector/mirror, and a hinged structure to allow the tube to be “aimed.” There is no annotation regarding that tube with the hinged base, but I cannot not help wondering—was Leonardo contemplating a rudimentary design for a reflecting telescope (Plate 16, upper left)? Finally, my suspicions regarding the purpose of that concave reflector’s function were further reinforced more recently when I came across an article.15 Almost a quarter of a century after his entry in the Codex Atlanticus referring to the possibility of a refractor, Leonardo had written: “[I]n order to observe the nature of the planets, open the roof and bring the image of a single planet onto the base of a concave mirror. The image of the planet reflected by the base will show the surface of the planet much magnified” (Codex Arundel, c. 1513).
In a successful reflecting telescope, the reflecting surface—the mirror—would have to be parabolic in its shape rather than circular for parallel light rays entering the tube all to be reflected to the focal point of the parabola. A small diagonal mirror located at the focal point would then gather these converging rays and reflect them all to an eyepiece. James Gregory in 1633 first described the correct structure of a reflecting telescope, but never constructed the apparatus. Then around 1668 Isaac Newton, after independently deriving the associated mathematics, created the first functional reflecting telescope. More than three hundred years later the Hubble Space Telescope (HST), a far more sophisticated version of the reflecting telescope, was placed into orbit by a space shuttle. Free of the obscuring atmosphere of the earth, the Hubble Telescope is able to peer into the distant edges of the universe (Plate 16, lower right).
Along with the telescope and the pendulum a number of Leonardo’s other concerns—the problem of friction between surfaces of moving bodies, the notion of center-of-gravity, and the behavior of bodies in free fall—are all concerns of physics. Leonardo designed a machine exclusively to study the phenomenon of friction, which is a practical problem, but does not rise to the level of fundamental physics. In one of his drawings (Codex Leicester) two men are seen on a seesaw in a manner suggesting the tacit understanding of balanced torques. In another drawing pairs of balls of different sizes are shown contiguously, hung from a nail in the ceiling. Depending on their relative sizes (presumably their weights), the center of gravity is identified by a vertical line—for two equal-size balls, the line passes through the two balls’ point of contact; when one ball is larger (more massive than the other), the line passes through a point inside the larger ball, the point of contact having shifted in the direction of the smaller ball. In still another set of drawings, Leonardo depicts the spherical earth with a concentric shell-like structure, explaining in his own words that heavier masses have gravitated toward the center of the earth, echoing the modern understanding of twentieth-century geophysics. As for the phenomenon of falling bodies, Leonardo first sowed the seeds but did not follow through to the harvest. One hundred years later Galileo established firmly the constancy of acceleration in free fall. More significantly, the problem led to Newton’s formulation of the universal law of gravitation, and ultimately Einstein’s general theory of relativity. That it would take Galileo, Newton, and Einstein’s entry into the fray, and the emergence of entirely new areas in physics and mathematics, to bring us to our present understanding attests to the problem’s importance. In the five hundred years since Leonardo framed his question there has been astonishing progress. But the final synthesis of the physics of the very large and the physics of the very small, a sort of Holy Grail of physics, still remains elusive. For the first time, however, the formulation of a “theory of everything” (TOE) seems within striking range. We shall devote the next two chapters to following the drama that brought us to this point in our understanding.