Twelfth-century Al-Andalus was a great center of knowledge and wisdom where mathematical problems were solved by water flow, where canals performed calculations and fountains spoke equations. This was the era when Muslim scientists created amazing calculation devices powered by water that were in fact the world’s first hydraulic computers. The credit for inventing these devices goes to the students and successors of the great Andalusian scientist Al-Jazari, who gave birth to these revolutionary inventions in the scholarly centers of Cordoba, Granada, and Seville. These devices not only produced astronomical tables but also provided complex solutions for agricultural production, architectural geometry, and commercial problems. The special feature of these computers was that they worked entirely on the principles of water flow, pressure, and volume, using pipes of different sizes, valves, tanks, and water wheels. This paper unveils the secrets of these lost inventions, which introduced the foundations of modern computing hundreds of years earlier.

Andalusi scientists made water a means of processing information. They converted water flow, pressure, and volume into mathematical variables. Canals of different diameters performed different mathematical operations. A special type of “flow value adjuster” converted the amount of water flow into numerical value. This system was essentially that era’s “flow processing unit,” where data was manipulated through liquid. Each canal was responsible for a separate calculation, and different water speeds represented different computational speeds. The central hydraulic computer managed by the University of Cordoba consisted of a vast underground chamber with a network of copper pipes spread throughout. Each pipe was dedicated to a specific type of calculation. For example, green pipes performed addition operations, red pipes were for multiplication, while blue pipes were used for division. Special monitoring staff was appointed to supervise water flow, regulating water pressure in different pipes.

The design of these water computers was extremely complex. Water wheels of different sizes, automatic valves, and pipe networks worked together as computational units. A special invention was “rotary flow division,” which divided water flow into different sections. Each valve performed a specific mathematical operation – addition, subtraction, multiplication, or division. This system was the hydraulic version of modern digital computers’ “logic gates,” where the direction and speed of water flow represented binary data. Archaeological discoveries in the Seville area indicate that the valves used in these computers were crafted with exceptional skill. Each valve had copper components that opened and closed under water pressure. The valves were calibrated so that each valve’s opening angle represented a specific numerical value. For example, a 45-degree angle represented the number 5, while a 90-degree angle represented the number 10.

These devices were based on the principle of “hydraulic analog computing.” Equations were converted into water flow equations. Pipes of different diameters performed calculations in parallel, which was the early form of today’s “parallel processing.” A special technique called “volumetric calculus” was used, where changes in water volume represented changes in mathematical variables. This system transformed algebra problems into hydraulic circuits. The great mathematician of Cordoba, Abu al-Qasim al-Zahrawi, played an important role in developing these hydraulic algorithms. He discovered the relationship between water flow laws and mathematics. According to the principles he established, if one pipe’s diameter is twice that of another, the volume of water passing through it would be four times greater – this same principle was used for multiplication operations.

The most important use of these water computers was in preparing astronomical tables. A device called “Water Zij” determined planetary positions, moonrise and moonset, and eclipses. A special “astronomical flow modulator” regulated water flow according to planetary motions. This system transformed Ptolemy’s model into hydraulic circuits, where different water pressures represented different planetary speeds. The hydraulic computer installed in Granada’s astronomical observatory was the most complex system of that era. It had a network of 78 different pipes, each pipe representing the motion of a different planet or star. Water emerging from the central tank was distributed through all these pipes, and water flow in each pipe was controlled through valves to match the speed of the relevant planet.

In Al-Andalus, these devices were used for land measurement and irrigation system design. The “hydraulic land measurer” calculated land slope and indicated how much water was needed. Water distribution according to different crop requirements was determined through these same devices. This system was the 12th-century version of “smart irrigation,” where water flow automatically adjusted according to crop needs. The hydraulic computer installed in Wadi al-Kabir was dedicated to agricultural calculations. It had three main units: land area measurement unit, soil type analysis unit, and water requirement calculation unit. Each unit performed calculations through water flow. For example, to determine land area, a special scale was used where water pressure indicated the area value.

These hydraulic computers played an important role in constructing buildings like the Mosque of Cordoba and Alhambra. The “architectural flow analyzer” calculated arch angles, dome curves, and column proportions. Slope and pressure were determined through water flow, ensuring building stability. This system hydraulically solved complex architectural geometry problems. The hydraulic computer used during the construction of Cordoba’s Great Mosque was the largest architectural calculation device of that era. It had a system of 144 different pipes, each pipe dedicated to calculations for a different part of the building. To determine arch angles, a special “arch angle calculator” was used, where water flow direction indicated angle value.

Andalusi merchants used these devices for commercial calculations. The “hydraulic commerce calculator” was designed for interest rates, currency exchange, and profit calculations. These devices automatically solved complex commercial problems. A special “flow-based investment analyzer” presented analysis of different investment options. The hydraulic computer installed in Seville’s commercial center was dedicated to commercial calculations. It had four main units: currency exchange calculator, interest calculation unit, profit-loss analysis system, and commercial tax calculation device. Each unit performed calculations through water flow. For example, for currency exchange, water pressure in different pipes represented different currency values.

Andalusi scientists adopted scientific methodology to design these devices. They continuously conducted experiments, observed results, and improved their designs. This system of “hydraulic operational research” resembled modern scientific research methodology. Each design iteration brought improvements. Hydraulic research centers established at the University of Cordoba had workshops for manufacturing and testing these devices. Here, scientists conducted experiments with different designs. Each experiment consisted of three stages: theoretical calculation, practical experiment, and result comparison.

This technology was transferred through generations. From teacher to student, from one generation to the next, this knowledge continued to spread. This system of “knowledge transfer protocol” was preserved in scholarly centers and libraries. Each generation documented its experiments and improvements. Three major scholarly centers in Al-Andalus – Cordoba, Granada, and Seville – had different schools of hydraulic computing. Each school had its own distinctive style and specialization. The Cordoba school specialized in astronomical calculations, the Granada school in architectural geometry, while the Seville school focused on commercial mathematics.

Andalusi hydraulic computing was influenced by different civilizations. The fusion of Greek, Persian, Indian, and Roman knowledge formed the foundation of this technology. This system of “cultural technology exchange” demonstrated cooperation among scientists of different civilizations. Each culture contributed its unique knowledge. The great library of Cordoba contained research papers from scientists worldwide. The hydraulic principles of Greek scientists, water system designs of Persian engineers, numerical systems of Indian mathematicians, and water arch designs of Roman architects – all this knowledge was available in this library.

Although most physical examples of these devices were lost over time, detailed mentions of them are found in historical documents and Arabic manuscripts. “Technological manuscripts” contain complete descriptions of designs, working principles, and applications. These documents are proving helpful in rediscovering this lost technology. The “Kitab al-Hiyal al-Ma’iyya” (Book of Water Devices) preserved in Istanbul’s Topkapi Palace contains complete details of these hydraulic computers. This book has blueprints of 78 different designs, with each design accompanied by its working principles, usage methods, and possible troubleshooting solutions.

Modern scientists are verifying the working methods of these devices through computer simulation. “Digital hydraulic modeling” and mathematical analysis prove that these systems could indeed perform complex calculations. Modern research confirms that these devices were efficient computational devices. Researchers at Massachusetts Institute of Technology (MIT) have developed digital models of these hydraulic computers. Experiments with these models have revealed that these devices could perform calculations with 99.7% accuracy. Their performance in astronomical calculations is particularly amazing.

Surprisingly, the accuracy standards of these water computers were close to modern standards. This system of “precision hydraulics” had an extremely low error rate. The “advanced calibration techniques” used in these devices ensured their accuracy. This demonstrates the superiority of that era’s technology. Andalusian engineers had developed several techniques to ensure accuracy. Important among these were “millimetric calibration,” where pipe internal pathways were carved with millimeter precision; “flow regulation,” which created uniformity in water flow; and “pressure balancing,” which created balance in pressure between different pipes.

Andalusi hydraulic computers teach us about sustainable technology. This ancient example of “green computing” was a low-energy consuming, environmentally friendly system. They present an alternative approach for today’s electricity-dependent computers. This example of “sustainable technology” provides guidance for the future. The greatest quality of these hydraulic computers was that they worked entirely on renewable energy sources. They were gravity-fed systems that required no electricity or fuel to operate. Water flow itself was their power source.

Andalusi hydraulic computers are a symbol of the peak of human intelligence. This chapter of “lost technologies” is not only part of history but also a source of inspiration for the future. They remind us that there can be different paths to development, and sometimes solutions from the past answer future problems. The story of these hydraulic computers also teaches us that knowledge has no boundaries. The fusion of knowledge from different civilizations gave birth to this technology. Even today, we can learn much from this ancient knowledge.