In the days leading up to Easter in 1900, a boat of sponge divers, forced to anchor near the small island of Antikythera, unknowingly made a historic discovery. At a depth of 60 metres, they found an ancient shipwreck containing remnants of a geared machine, later named the "Antikythera Mechanism." This remarkable device, dating back to around 80-50 BC, marks the beginning of the history of mechanical calculation.
Upon its recovery, the Antikythera Mechanism was examined by Valerius Stais, an archaeologist at the National Museum of Athens. Stais's study of the gears and inscriptions revealed the machine's purpose: not mechanical calculations, but the description of astronomical phenomena like moon phases, planetary positions, equinoxes, and seasons. This was achieved through a system of gears and dials replicating the numerical ratios of planetary movement.
In his 1959 paper "An ancient Greek computer," Derek J. de Solla Price further analyzed the mechanism. He argued that it was not a prototype, but a fully functional nautical device. This theory was supported by evidence of repairs made to the gears, even after 2000 years underwater.
Another early mechanical calculator is the abacus, a powerful device whose origins remain shrouded in mystery. The word "abacus" likely derives from the Greek "abax," meaning table or axis, or possibly the Hebrew "abaq," meaning sand or dust. Remarkably, some abacuses dating back over 2000 years have been preserved, highlighting their widespread use across diverse civilizations like the Mayans, Romans, Egyptians, and Chinese.
The invention of the abacus is lost in the mists of time, and its origins remain a mystery. The etymology of the word "calculus" stems from the Latin "calculi," referring to the small pebbles used in early abacuses. These pebbles were slid along rows of wires or grooves, enabling calculations.
Even today, in places like Japan, the abacus, known as the "soroban," is still widely used by schoolchildren, shopkeepers, and clerks. Requiring a certain dexterity, the soroban allows users to perform arithmetic operations with a speed comparable to modern pocket calculators. This enduring use highlights the abacus's lasting legacy as a powerful and efficient calculating tool.
Over the centuries, the historical development of early calculators has been closely intertwined with the evolution of mathematics. This progression has been marked by groundbreaking theoretical, logical, and analytical breakthroughs. These include the introduction of the concept of zero, the expansion of "number" to encompass fractions, decimals, real numbers, and complex numbers, and the development of infinitesimal calculus and mathematical analysis. These advancements not only enriched mathematical theory but also spurred innovations in calculating tools, shaping the trajectory of both fields.
In the annals of mathematics and mechanical calculation, the study of logarithms and their properties stands as a pivotal juncture. Formalized by Scottish mathematician John Napier in 1612, logarithms revolutionized complex calculations, simplifying multiplication and division. This breakthrough paved the way for Napier's invention of "Napier's bones" in 1614—a system of carved rods, often made of ivory, that facilitated calculations. By arranging these rods in specific combinations based on the numbers inscribed on them, users could effortlessly multiply and divide whole numbers by single-digit figures. This ingenious tool not only streamlined mathematical operations but also exemplified the symbiotic relationship between theoretical advancements and the development of mechanical aids to computation.
This historical interplay between mathematics and mechanical calculation, exemplified by Napier's work, underscores a common thread that weaves through the evolution of both fields. From the ancient Antikythera Mechanism, designed to predict astronomical phenomena, to the enduring abacus, still used in various cultures today, the quest to understand and manipulate numbers has driven innovation in both mathematical theory and the tools we use to calculate. The introduction of concepts like zero, the expansion of number systems, and the development of calculus have all spurred advancements in calculating devices, shaping the course of human history.
In 1622, building upon the groundbreaking work of John Napier, William Oughtred further expanded the realm of mechanical calculation. Recognizing the potential of Napier's logarithms to transform multiplication into addition, Oughtred conceived the slide rule—a revolutionary device that surpassed the capabilities of Napier's bones. This ingenious invention enabled swift calculations, extending beyond simple arithmetic to encompass algebraic and trigonometric operations with remarkable speed and precision, reaching up to the third decimal place. Oughtred's slide rule became an indispensable tool for scientists, engineers, and mathematicians, enjoying widespread use for several centuries. Its reign as the go-to calculating instrument continued until the advent of pocket calculators in the 1970s, which gradually supplanted the slide rule due to their compact size and increased computational power.
The slide rule's enduring legacy is a testament to its effectiveness and ingenuity. Its development marked a significant milestone in the history of mechanical calculation, bridging the gap between theoretical mathematical concepts and practical computational tools. Oughtred's invention not only simplified complex calculations but also democratized access to mathematical operations, empowering individuals across various fields to perform calculations that were once the exclusive domain of experts. The slide rule's impact on scientific, technological, and engineering advancements cannot be overstated, as it facilitated breakthroughs in areas ranging from navigation and astronomy to architecture and finance. Even in today's digital age, the slide rule serves as a tangible reminder of the remarkable ingenuity that has driven the evolution of calculating devices throughout history.
Thirty years after Napier's groundbreaking work on logarithms, a young French mathematician named Blaise Pascal made a significant leap forward in the field of mechanical calculation. In 1642, at the age of 21, Pascal invented the first mechanical calculator, known as the Pascaline. This ingenious device, designed to assist his father with his duties as a tax officer, could perform addition and subtraction operations with remarkable speed and accuracy.
The Pascaline was a marvel of engineering, featuring a series of interconnected gears and wheels that could be manipulated to represent and calculate numerical values. While its functionality was limited compared to modern calculators, the Pascaline marked a turning point in the history of computation, demonstrating the feasibility of mechanizing complex arithmetic operations. Today, approximately 50 Pascaline calculators are preserved in science museums worldwide, a testament to their historical significance and enduring legacy.
Pascal's invention was not without precedent. Many pioneers before him had attempted to create mechanical calculators, including the renowned Leonardo da Vinci. In a series of notes discovered at the National Museum of Spain in 1967, da Vinci described a machine with striking similarities to Pascal's design. These notes, which remained hidden for centuries, provided valuable insights into da Vinci's visionary ideas and his contributions to the field of mechanical calculation. The rediscovery of these notes allowed scientists to construct a working model of da Vinci's machine, shedding light on his remarkable ingenuity and foresight.
Following Pascal's groundbreaking invention, the quest to develop increasingly sophisticated mechanical calculators continued unabated for centuries, leading up to the advent of electronic calculators. In 1673, German philosopher and mathematician Gottfried Wilhelm Leibniz made a significant improvement upon the Pascaline by creating a new version capable of performing multiplication. This enhanced calculator, known as the Leibniz Wheel, was first exhibited in London and could execute all four basic algebraic operations, producing numerical results similar to the Pascaline.
Leibniz's contributions to the history of science extended beyond mechanical calculation. He also introduced the concept of binary representation, a fundamental system for representing numbers using only two digits (0 and 1). This innovation, initially an abstract mathematical theory, found practical application in the mid-19th century when George Boole rediscovered and utilized "binary calculus" to develop the algebraic foundation for electronic calculators.
The evolution of mechanical calculators from Pascal's Pascaline to Leibniz's Wheel and beyond demonstrates the iterative nature of innovation. Each advancement built upon the insights and achievements of its predecessors, gradually expanding the capabilities and complexity of calculating devices. This ongoing refinement paved the way for the eventual emergence of electronic calculators, which revolutionized computation by leveraging the power of binary logic and electronic circuits.
The historical trajectory of mechanical calculators also highlights the interconnectedness of seemingly disparate fields. Leibniz's work, for instance, bridged the gap between philosophy, mathematics, and engineering, showcasing the cross-disciplinary nature of scientific progress. The development of binary representation, initially a theoretical concept, ultimately found practical application in the realm of electronic computation, underscoring the unpredictable and often serendipitous nature of innovation.
Two centuries after the groundbreaking work of Pascal and Leibniz, mechanical calculation experienced further advancements, largely due to the contributions of Charles Babbage, an English polymath with a passion for mechanical design. In 1820, Babbage embarked on the development of the difference engine, a machine capable of solving polynomial equations. This invention is widely regarded as a precursor to the modern computer. Babbage's ingenuity earned him recognition from the Royal Astronomical Society, which awarded him its prestigious gold medal in 1822 for his paper titled "Note on the application of machinery to the computation of astronomical and mathematical tables." This early recognition underscored the significance of Babbage's work and its potential to revolutionize the field of calculation.
Unfortunately, the path from prototype to a fully realized engine proved far more arduous than anticipated. The design demanded an unprecedented level of precision and specialized machine tools to manufacture the intricate shafts, toothed wheels, and gears. While the imperfections in the mechanical components were not a critical issue for the small prototype presented to the Royal Astronomical Society, they posed significant challenges for the final version. Even the slightest faults had a cascading effect, leading to powerful vibrations, binding, and sudden system failures. After repeated unsuccessful attempts, government funding for the project was withdrawn, forcing Babbage to abandon his ambitious endeavor to build the difference engine.
In 1832, Babbage conceived a groundbreaking new type of mechanical calculator known as the analytical engine. This design exhibited an even closer resemblance to modern computers in its operational principles. Inspired by the Jacquard loom, a revolutionary weaving machine invented by Joseph Marie Jacquard in 1804 that used punched cards to create intricate patterns, Babbage incorporated a similar system into his analytical engine. Instructions would be fed into the machine using punched cards, allowing for programmable and automated calculations. Although the analytical engine never advanced beyond detailed drawings, Babbage's innovative technical solutions and the concept of using punched cards for input have had a profound and enduring influence on the field of calculator design.
Babbage's contributions extended beyond the realm of mechanical calculation, showcasing his keen analytical mind and foresight. One notable example is his insightful analysis of the mail system. Babbage astutely observed that the cost of calculating postage fees based on distance was disproportionately high compared to the actual cost of transporting letters. This realization led him to advocate for a revolutionary concept: a fixed postage rate regardless of the distance between sender and recipient. This principle, which we now take for granted, has made it possible to send letters anywhere within a country or region at a standardized cost, simplifying the postal system and making communication more accessible and affordable for everyone.
Augusta Ada Byron, daughter of the renowned poet Lord George Gordon Byron, was one of the few who recognized Babbage's exceptional intellect. She provided him with both intellectual and financial support, and even collaborated with him on a complex, albeit unsuccessful, system for betting on horse races, intended to fund the ambitious "analytical machine project." Ada Byron, a gifted mathematician in her own right, is often celebrated as "the first programmer in history." Despite her brilliance, she, like Babbage, found herself largely misunderstood and unsupported by her contemporaries. Babbage, isolated and disheartened, passed away on October 18, 1871. However, he left behind a significant intellectual legacy, including his memoir "Passages from the Life of a Philosopher," in which he recounted the origins of his fascination with calculators:
The earliest idea that I can trace in my own mind if calculating arithmetical tables by machinery rose in this manner: One evening I was sitting in the rooms of the Analytical Society at Cambridge, my head leaning forward on the table in a kind of dreamy mood, with a table of logarithms lying open before me. Another member, coming into the room, and seeing me half asleep, called out, “well, Babbage, what are you dreaming about?”, To which I replied, “I am thinking that all these tables ,while pointing to the logarithms, might be calculated by machinery. “
Wherever his spirit may reside, I hope Charles Babbage is aware that over a century after his passing, at the zenith of the personal computer age, a team of scientists rediscovered his designs and successfully constructed one of his visionary engines. In a fitting tribute to mark the bicentenary of Babbage's birth, the difference engine was finally built and unveiled at the Science Museum in South Kensington, London, on November 29, 1991. The completed engine functioned flawlessly, proving the validity of Babbage's concepts. Moreover, the Science Museum demonstrated that Babbage could have built the engine himself with the tools and technology available during his lifetime. The museum's project was not merely a technological feat but a vindication of a brilliant scientist whose ideas were too revolutionary for his era, and who was met with skepticism and derision by his contemporaries.
The idea of building a calculator based on punched cards was revived in 1890: the US census adopted a data encoding system with the punched cards devised by Hermann Hollerith, a German immigrant. In 1886, Hollerith founded the Tabulating Machine company, a small company, renamed International Business Machines that we call as IBM, 28 years later. Hollerith’s company was charged with producing the punched cards and reader for the US census. This technological tool which represents the “conjunction ring” between the early calculators of the 18th century and the electro mechanical calculators based on telephone relays of the early 20th century had become indispensable: increased birth rates had made a census data processing much more time consuming. In fact, Hollerith’s punched cards arrived just in time to prevent the United States from being overwhelmed with a huge and unmanageable amount of data. During the academic year 1882-83, Hollerith was teaching mechanical engineering at the Massachusetts Institute of technology, and he established the first link between the MIT and the history of computer science. The MIT itself was to become, several decades later, the setting where the first hackers explored the maze like world of computer circuits, and managed to transfer programming into a form of art.
The evolution of calculators reached a pivotal moment in 1936 Germany when Konrad Zuse, a visionary engineer from Berlin, embarked on a groundbreaking project with his friend Helmut Schreyer. Together, they began constructing the Z1, an electromechanical calculator that would be completed by 1938. Remarkably, Zuse conceived and developed this pioneering machine in his parents' home, foreshadowing the ingenuity and resourcefulness of the first American hackers who, four decades later, would establish "home laboratories" in Silicon Valley garages, transforming them into the birthplace of the modern computer industry.
The only non-mechanical component of Z1 is an electric engine, giving a “clock frequency” of 1 Hertz: calculations were performed by means of perforated tape which Zuse had made out of 35mm film recovered and recycled from the scrap materials of film industries. A copy of Z1 can be found in perfect state at Berlin’s Museum für Verkehr und Technik, the museum of transport and technology.
After this early machine, Zuse built a number of programmable calculators: the metal plates which characterised early models were replaced with telephone relays. The most advanced model of the Z series is Z4, which was started in 1942 and completed in 1945: Z4 is a colossus of 2.5 tons, with the surface of 20 square meters and 2200 relays. Konrad Zuse’s Z4 bridged the gap between two epochs: with a mix of mechanics and electricity, it anticipated the era of electronics, while at the same time closing the era of mechanical calculus, which had started from Pascal’s calculators three centuries earlier.