The Origins of Science III: The Library of Alexandria

One of the seven wonders of the ancient world, the Lighthouse of Alexandria was commissioned by the first king of the Greek Ptolemaic Kingdom of Ancient Egypt Ptolemy I Soter (c.367-282 BCE), and built by Ptolemy II Philadelphus (280-247 BCE) at around the same time as the Great Library of Alexandria. It was estimated to have stood well over 100 m (330 ft) high. Only the Great Pyramid was taller. It stood on a small island on the western edge of the Nile delta, opposite the city founded on an isthmus by Alexander the Great in 332 BCE. It was later connected to the city by a mole (causeway). At its top, a mirror reflected sunlight during the day and a great fire was lit during the night. It was a beacon of light to sailors, but also to scholars whose thirst for knowledge brought them to the Great Library from afar.

The death of Aristotle in 322 BCE (and Alexander the Great a year earlier) marked the end of the Classical era, but also the start of the Hellenistic era. And in the Hellenistic era, scientific thinking flourished. Alexander's generals fought tooth and nail over the vast empire that he had left behind. Eventually, control of Egypt passed to Alexander’s general Ptolemy "the Saviour" (Soter). Ptolemy (like Alexander) had been taught by Aristotle and (like Alexander) appreciated the importance of acquiring knowledge. Perhaps this is partly why he (or his son, Ptolemy II) decided to add a great library to his palace complex in Alexandria – and encourage research activity.

The Library of Alexandria was not just any library; it was an important part of a large research institution, the Mouseion (which is where we get the word museum from). It was called the Mouseion because it was dedicated to the nine Muses. But in the Mouseion, the eight artistic muses were outshone by their one scientific sister: Urania, the Muse of Astronomy.

The precise origin story of the Mouseion and Library is not known. A member of the illustrious Lyceum, philosopher and statesman Demetrius of Phaleron, joined the royal court of Ptolemy I after fleeing Athens – and may have had a role in starting the Mouseion and Library. Another member of the Lyceum, the natural philosopher and atheist Strato, was brought over to Alexandria to tutor Ptolemy's son, the future Ptolemy II. Strato was a keen observer of natural phenomena (he worked out that falling objects accelerate) and believed that the universe comprises only matter and energy (i.e., neither supernatural entities nor eternal souls). Although Strato eventually left to become the third director of the Lyceum in Athens, under Ptolemy II the Mouseion and Library of Alexandria rapidly developed into the greatest centre of learning in the ancient world, and even outlived the Ptolemaic dynasty.

The exact layout of the Library is not known, but ancient sources describe it as being part of a large, richly decorated royal palace complex, close to royal gardens, and comprising a roofed walkway, a columned hall, shelves and shelves of papyrus scrolls, and a large communal dining hall where scholars (philologoi) routinely ate and shared ideas. It may also have contained private study rooms, residential quarters, and lecture halls. For example, archaeologists excavated the area and discovered what looks like numerous lecture halls, with central elevated podiums (presumably for the lecturer to stand on). This would make it arguably the world’s first university. 

A smaller library called the Serapeum (Temple of Serapis, a Graeco-Egyptian god) was later added to the Mouseion. It was said that the scholars had property in common (like a modern university), were provided with a salary, received free meals, free room and board, and free servants, and paid no taxes. Unlike the small communities of philosophers who met outside Athens' walls to discuss philosophy, the Mouseion was clearly a large, well-funded organisation of scholars dedicated to collecting knowledge from all over the ancient world and to generating new knowledge through research.

The scientific accomplishments that took place at Alexandria, or by physicists and engineers visiting Alexandria, are legion. For example, Philo of Byzantium (aka "Philo Mechanicus") gave experimental arguments in support of Anaximenes', Aristotle's, and Strato’s view that air was real. If you take an empty glass bottle and submerge it in water with its open mouth facing directly down, water will not move inside the bottle because the bottle will contain trapped air. If you tilt the bottle, air will escape (the bubbles) and water will move inside. Also, Hero (or Heron) of Alexandria described how to build a steam engine (albeit a weak one with no practical use). And the great mathematician and technologist Archimedes invented the screw-shaped water pump that is still in use today.

Few objects better demonstrate the ingenuity of Ancient Greek physicists, mathematicians, and engineers than the Antikythera mechanism. Discovered in a Roman shipwreck by sponge divers nearly two millennia after it had sunk off the coast of the Greek island of Antikythera (around 70-60 BCE), it is evidence of the world’s first known analogue computer. Although it had initially appeared to the divers as a single piece of rock with a single gear wheel embedded in it (left), researchers at Cardiff University used surface imaging and high-resolution 3D X-ray computed tomography to image inside fragments of the crust-encased mechanism and read the faintest inscriptions that once covered the outer casing of the machine. The study suggests that the device had 37 meshing bronze gears that enabled it to compute the movements of the Sun and Moon through the zodiac, to predict eclipses, and to model the irregular orbit of the Moon, where the Moon’s velocity is higher in its perigee than in its apogee. Machines with similar complexity did not appear again until the astronomical clocks of Richard of Wallingford and Giovanni de’ Dondi in the 14th century.

MEASURING THE EARTH

The Ptolemies also supported the leading mathematicians of the era. For example, Ptolemy I sponsored Euclid who wrote the most successful and influential textbook ever written, the Elements. It was required reading until the 20th century, by which time its content was taught through other school textbooks. But it was in the fledgling proto-scientific field of astronomy that the mathematicians of Alexandria contributed most. Before the Hellenistic era, astronomy was more astrology than astronomy; there was no distinction between the two. But within the walls of the Library, mathematics (geometry) was used to draw quantitative conclusions about the universe, such as the sizes of the Earth, Sun, and Moon, and the distances between them. How did they do that? Let’s take the size of the Earth as an example. In 245 BCE, Ptolemy III ("the Benefactor") brought Eratosthenes from the Academy at Athens to the Library at Alexandria. Eratosthenes soon became the new head of the Library, which is when he learned about a well in the city of Syene (now Aswan) in Upper Egypt where at noon on the summer solstice, the sun’s rays shone straight down the pit and cast no shadow, demonstrating that the sun was directly overhead. Now, by this period of time, Greek intellectuals believed that the Earth was spherical, partly because of some convincing arguments by Aristotle. By erecting a pole in Alexandria, Eratosthenes could use the shadow the pole cast to work out the angle of the sun’s rays at Alexandria on the summer solstice. It was about 7.2 degrees. Since the Earth is spherical, its circumference is 360 degrees. 360 divided by 7.2 equals 50. This means that the circumference (size) of the earth is the distance between Alexandria and Syene multiplied by 50. Eratosthenes hired someone to measure the distance between Alexandria and Syene. It's about 800 km (500 miles). According to Eratosthenes’ calculations, the (meridional) circumference of the Earth must therefore be about 40,000 km (25,000 miles). It’s actually 40,008 km. We do not know how accurately Eratosthenes measured the size of the Earth because he used the stadion as his unit of measure, not the kilometre or mile, and stadia were ~157.5 m long in Egypt and ~185 m long in Greece. Eratosthenes estimated that the circumference was 250,000 stadia. So, if he used the Egyptian stadion, then his estimate in kilometres would be 39,375 km. Not bad! In fact, whichever unit of measure Eratosthenes used (Greek or Egyptian), his estimate of the size of the Earth was far more accurate than the one Columbus used. Columbus thought the Earth was much smaller. Had Columbus known that the Earth was 40,000 km round, he would not have sailed west!

MEASURING THE HEAVENLY BODIES

As great as Eratosthenes was, perhaps the greatest mathematician astronomer of the Hellenistic age was Aristarchus of Samos (c.310-c.230 BCE). Aristarchus (known as “The Mathematician”) was a pupil of Strato (the natural philosopher who tutored Ptolemy II and became the third head of the Lyceum in Athens). Aristarchus was already a long-serving member of the Library by the time Eratosthenes arrived. He had used mathematics (geometry) to calculate the sizes of the Sun and Moon and their distances from the Earth, all relative to the diameter of the Earth. His results were way off. Nevertheless, his maths was impeccable. And this brings us to an important point. The difference between Hellenistic astronomers such as Aristarchus and today’s astronomers is not that their observational data were in error. Nor is it that they had inaccurate tools. None of our data or tools are 100% perfect. It’s that the Hellenistic astronomers never tried to judge their uncertainty. A very important part of science, including astronomy, is the use of statistics to estimate the uncertainty in a measurement. 

For example, based on his observation that when the Moon is half full, the angle between the lines of sight from the Earth to the Moon and to the Sun is 87 degrees (see figure below), Aristarchus used mathematics to calculate that the distance from the Earth to the Sun is between 19 and 20 times larger than the distance from the Earth to the Moon. Using modern trigonometry, we can calculate the figure to be 19.11. Aristarchus’ mathematical mind was brilliant! But the angle is actually 89.85 degrees, and therefore the distance is actually 390 (not 19) times larger. This is why we scientists take uncertainty so seriously. We can’t draw firm conclusions without it.

Let’s take a modern example: in 2000 astronomers observed a star they initially estimated to be a staggering 16 billion years old. After more careful observation, the figure was revised down to 14.46±0.8 billion years old. But how can this be when the universe is estimated to be only 13.8 billion years old? At first blush, it seemed to some members of the public that scientists should abandon their theories about the age of the universe and start again from scratch. But the central value of the estimate (14.46 billion years) is only part of the story. The measure of uncertainty (±0.8 billion) must also be taken into account. And the scientists estimated their uncertainty to be “±0.8 billion years". What this actually means is that the star had a 70% chance of being between 13.66 and 15.26 billion years old. This meant that there was a 30% chance that the star’s age was outside that range, and a 15% chance that it was even lower. So there was a good chance that its actual age was lower than the age of the universe. And this is why scientists always provide estimates of their uncertainty. It’s important for getting things right. And if they can’t provide an estimate (e.g., to the philosophical question 'Is the universe a computer simulation - yes or no?'), then they say that they can only speculate. This doesn't stop scientists from speculating or trying to estimate their uncertainty (see astronomer David Kipping’s attempt), but it does differentiate science from philosophical speculation. As it turns out, more detailed observations and more sophisticated modelling suggest that the star is actually 12±0.5 billion years old (Tang & Joyce, 2021), well within the age of the universe.

Although it did not occur to Aristarchus to work out the uncertainty in his estimates, he used mathematics and reason to measure the heavenly bodies and understand the cosmos as a natural phenomenon - an impressive feat! His calculations revealed that the sun is enormous and that the stars are extremely far away. From this, he correctly guessed that the huge sun is at the centre of the cosmos and the much smaller Earth revolves around the sun, a bit like how the smaller Moon revolves around the larger Earth. And he correctly guessed that the stars could be suns - but far away. Or to use modern terminology - our sun is just one of many stars.

MODELLING THE COSMOS: WHEN THE DATA DON’T FIT 

Aristarchus correctly guessed that the Sun was a star and that the Earth revolves around it, but he had no evidence to support this claim - and thus his idea never caught on. A century earlier, the highly influential philosopher Plato had assumed that the Earth was at the centre of the universe. Moreover, he believed that the motion of the heavenly bodies (the Sun, Moon, planets, and stars) around the Earth must be perfectly circular, uniform, and constantly regular. How could it be otherwise? A circle is beautiful. Movement should be smooth, not jagged. The universe, ordered. The beautiful perfect heavenly spheres should circle the Earth at a constant speed, he reasoned. But the movement of the planets in particular sometimes seemed highly irregular and did not match Plato’s expectations. In fact, the Greek word planet means ‘wanderer’, to reflect puzzlement that those lights moved across the sky in a pattern no shepherd or sailor could discern, unlike the predictable march of the constellations. For example, from the perspective of someone on Earth, Mars sometimes appears to reverse its direction of travel. But Plato was sure he could not be wrong, because he was arguing from what he thought were “first principles”. So he threw down the gauntlet and challenged the mathematicians to come up with a model of the cosmos that matched the data and his first principles (circular, uniform, and regular motions). 

His challenge was accepted. Plato’s contemporary Eudoxus of Cnidus (c.408-355 BCE) came up a mathematical model where the stars are carried around the Earth on a transparent sphere that revolves once a day, while the Sun, Moon and planets are carried around the Earth on transparent spheres that are themselves carried by other transparent spheres. The model did not fit the data. So, more spheres were added to the Sun, Moon, and planets by Eudoxus and others. The best and most influential version of this mathematical model was created by none other than Aristotle. The model still did not fit the data. But it was circular, uniform, and regular!

This brings us to another important point about science. When fitting models to data, the simpler the model, the better. And Plato's idea of how the model should look was simplicity itself! But the ideal model that Plato proposed did not match reality, so Eudoxus and others kept adding stuff (spheres) to the model to get it closer to reality. At one point, to explain the irregular motions of the planets, Eudoxus gave each planet four spheres! Each planet was attached to its innermost sphere, but each innermost sphere was attached to three other spheres! Adding stuff to a model to make it work is called “fine-tuning”. A little bit of fine-tuning is OK, because maybe we're missing something from our model that the fine-tuning is accounting for. But too much fine-tuning suggests that something is wrong with our current state of knowledge. Maybe heavenly bodies are not attached to myriad giant turning cosmic spheres! If a model needs a lot of fine-tuning, it’s probably wrong. But Eudoxus did not seem concerned that he had to fine tune his model to such an excessive extent...

To understand the highly irregular movements of the planets around the Earth, Eudoxus suggested that the motion of each planet is contingent on the rotation of multiple imaginary celestial spheres upon which it is fixed. The picture above contains just two spheres which rotate at the same rate but about two different axes. The outer (green) sphere is dragging the inner sphere around with it, while the inner sphere itself rotates in the opposite direction about its own axis (the black lines). Now imagine that the grey dot on the inner sphere is the planet Mars. From the perspective of someone on Earth (at the centre of the spheres), Mars seems to wobble back and forth. But in reality, Mars does more than wobble; it also drifts from West to East and occasionally even turns around and moves backwards! Thus, Eudoxus and others (e.g., Aristotle) had to add even more celestial spheres. For example, Eudoxus gave each planet four spheres - which is much too complicated to illustrate here! This is an example of fine-tuning. Fine-tuning is not always a bad thing. Sometimes it is necessary because we don’t have all the information we need. Take, for example, the cosmological constant. Over a century ago, Einstein presented a set of equations ('Einstein’s field equations') that became the framework of his theory of general relativity. The equations explain how matter and energy warp the fabric of spacetime to create the force of gravity. At the time, astronomers believed that the universe was fixed and unchanging. So when Einstein applied general relativity to the universe as a whole, he was shocked to discover that his theory predicted an unstable universe that would either expand or contract. He therefore added a term to his equations called "the cosmological constant” that ensured that the universe as a whole did not change. This is a bit like Eudoxus adding a sphere to his model (though of course, Eudoxus kept adding more and more spheres - and even then, his model did not fit the data!). A decade later, physicist Edwin Hubble discovered that our universe is not unchanging, and that in fact it is expanding! So Einstein realised that he did not need to have added that mysterious “cosmological constant” term to his equations. He called it his “biggest blunder” and got rid of it. In 1998, observations of distant supernovas showed that the universe is not just expanding; it’s expanding faster and faster! The unknown force behind the universe’s exponential expansion is called "dark energy". The “cosmological constant” has been reintroduced into Einstein’s field equations to account for this dark energy. But what is the cosmological constant or dark energy? It’s still a mystery, but many physicists suspect that it represents vacuum energy - i.e., the vacuum of space is not empty but comprises quantum fields like a vast dark ocean of fluctuating non-zero spacetime-expanding energy. The point is this: a little bit of fine-tuning may be necessary—at least temporarily—because we rarely have all the information we need. But too much fine-tuning would suggest that our model is so bad, it ought to be abandoned not saved.

According to Plato, the movement of the Moon around the Earth should be smooth, regular, and circular. But it isn't. For example, here is a composite photo of the position and phases of the Moon over a 28 day period. Each photo was taken at the same location each day. From this composite photo, the Moon's orbit certainly looks non-circular! Eudoxus tried to show that the Moon's orbit could be circular if the Moon were attached to two counter-rotating spheres (see above). Unfortunately, Eudoxus' model could not account for all of the Moon's movements - and it really struggled to explain the movements of the planets ("wanderers").

ASTRONOMY AT THE LIBRARY OF ALEXANDRIA

Could any of the researchers at the Library of Alexandria improve upon Aristotle’s model? As mentioned above, Aristarchus of Samos used mathematics to work out that the Sun was much larger than the Earth and all the other planets, and thus came up with the idea that the Sun is the “central fire” of the cosmos, and the Earth and planets revolve around it. He even argued that the Earth rotates about its axis once a day, which is remarkable - because we don’t feel the Earth moving beneath our feet, and if you throw something up into the air, it comes straight back down. The Earth does not seem to move. I don’t know why Aristarchus believed that the Earth rotates around its axis. I suspect it’s because the alternative (i.e., that stars infinitely far away rotate around the Earth) seems implausible; at such a distance, the stars would have to travel at an astonishing speed to circle the Earth every 24 hours. Aristarchus' model of the solar system predated Copernicus’ by about 1800 years. But as mentioned above, his arguments failed to convince the status quo.

The Library of Alexandria eventually fell into decline, particularly after the Romans had taken control of Egypt in 30 BCE. The Romans seemed to be less interested in knowledge for the sake of knowing. A part of the Library (or at least one of its storehouses) was even burned down at one point in 48 BCE, when Caesar’s soldiers set fire to the ships of Cleopatra’s brother, Ptolemy XIV, which were docked in the Alexandrian port. Nevertheless, research in the Library continued in some form or other, and in around 150 CE, a completely new model of the solar system was put forward - by Claudius Ptolemy (no relation to the Ptolemies who had ruled the city). Ptolemy made even more detailed observations of the heavens - and an enormous star chart. To fit a model to the data, he had to include something called "epicycles" (see below) and move things around a little (e.g., off-centre). The model no longer looked as neat and tidy as Plato wanted. But it did do a much much much better job of fitting the data than Aristotle’s. It was an admirable piece of mathematical modelling... which led to a schism in Western philosophy. Although there existed many different schools of philosophy and many different subdisciplines within philosophy, philosophy was philosophy. But now, philosophy itself was branching into two: philosophers and astronomers. For fifteen hundred years, natural philosophers (also translated as scientists or physicists) argued that “first principles” and thus Aristotle’s beautiful model of spheres trumps mathematics and thus Ptolemy’s uglier model. Reality reflects first principles, they argued. The astronomer-mathematicians did not agree. You cannot ignore the data, they said. They preferred Ptolemy’s convoluted model. Today, scientists know you need both. Like the natural philosophers of old, scientists make deductions from basic principles, but they also use mathematics in their work, and the basic principles are themselves expressed mathematically and are learned from observation, not from any assumptions about beauty, perfection and truth.

The great philosopher Plato argued that the motion of the heavenly bodies around the Earth must be perfectly circular, uniform, and regular. How could it be otherwise? Circles are perfect like spheres, and thus beautiful. And movement should be smooth, not jagged. But from the perspective of someone on Earth, the heavenly bodies (especially the planets) move irregularly and unpredictability. For example, Mars sometimes appears to reverse its direction of travel. To come up with a model of the cosmos that matches both observations and Plato's principles of circular, uniform, and regular motion, Ptolemy used "the epicycle” (the red circle in the picture above). In this model, planets such as Mars (the red dot) rotate around an imaginary point in space (the red circle), which in turn rotates around the Earth (the green dot); and this is why movement may look irregular (the blue line) when in fact, according to Plato, it is actually circular, uniform, and regular. However, Ptolemy's model still could not explain all celestial observations. To better fit his model to the data, Ptolemy introduced mathematical concepts such as the "equant" (see picture below). The equant is an imaginary point directly opposite to the Earth from another imaginary point called the "eccentric" (represented by the cross in the picture below). The introduction of the equant and eccentric, along with the epicycle, allowed Ptolemy to keep Plato's theory of uniform circular motion alive by stating that the path of heavenly bodies was uniform around one point and circular around another point. This is an example of fine-tuning a mathematical model to real observational data (see above). However, too much fine-tuning suggests that we are trying to shoehorn data into an inadequate model; it suggests something is wrong with our current state of knowledge. Perhaps the motions of the planets are not perfectly circular, constant, and smooth...?

CONCLUSION

Thus it was that in Ancient Greece astronomy and mathematics blossomed into something that resembled early science. The ancient Greeks did not just measure the heavens in order to predict the seasons and divine the future, etc., they measured the heavens to understand the cosmos. They measured the sizes of the Earth, Sun, and Moon, and the distances of the Sun and Moon from the Earth. For the first time, mathematics was being used to describe and understand the world. Although the Hellenistic Greeks had not quite worked out how to do science, and the complexity of the solar system defeated them, they had worked out that at least some aspects of nature could be described by mathematical naturalistic theories that agree with observation. Admittedly, we are still among the roots, but roots are not the least important part of the tree!

ADDENDUM

The Ptolemaic dynasty ended in 30 BCE with the death of Cleopatra and Rome’s conquest of Egypt. It was the beginning of the end of Hellenistic science. According to legend, Julius Caesar accidentally destroyed the Library of Alexandria when his army set fire to ships in the harbour in 48 BCE. But Caesar is likely to have burned down only a warehouse of books – the main Library seemed to still exist when Strabo visited it in around 20 BCE. So, why was there a decline in Hellenistic science? 

It seems that Rome was not interested in knowledge for its own sake, nor in the library as a status symbol, and thus the Library of Alexandria was largely neglected, which led to a dwindling of funds and gradual decline. The death blow to Hellenistic science, however, may have come with the decline of Rome and rise of Christianity from the fourth century CE. The sons of wealthy families seem to have been encouraged to join the Church to amass power. Bishops and presbyters were exempt from jurisdiction and taxation, and could wield enormous political clout. This was vividly demonstrated in Alexandria in 415 CE, when lector Peter, on behalf of Bishop Cyril of Alexandria, encouraged a mob of Christians to strip naked and slowly murder mathematician and philosopher Hypatia as she was travelling home in her carriage. It is thus clear that as the power of Rome declined, the Church came to rival even the governor in Alexandria. And even if the sons of wealthy families were not themselves politically ambitious, once Christian Emperor Justinian had closed the last great seat of learning (the Academy of Athens) in 529 CE, the only place for a bright young person to go for an education was the Church.

Furthermore, science may have become increasingly viewed as an ungodly distraction from the Christian spiritual path. In the 1st Century CE, the hugely influential Paul (the future St Paul) warned: “Beware lest any man spoil you through philosophy.” In around 200 CE, church father Tertullian asked, “What does Athens have to do with Jerusalem, or the Academy with the Church?” And the famous Christian theologian Augustine of Hippo (354-430 CE) asked, “What did it profit me that I could read and understand all the books I could get in the so-called ‘liberal arts’, when I was actually a slave of wicked lust?” Aristotle’s disinterested pursuit of knowledge (science) could have been seen as an existential threat to the Christian ministry.

Whatever the reason for the decline in Hellenistic science, the Lyceum was destroyed in 86 BCE by Roman general Sulla, the Library of Alexandria gradually dwindled away under Roman occupation (its last remaining part, the Serapeum, which by this time was no more than a place for philosophers to gather, was destroyed by Pope Theophilus in 391 CE), and the Academy at Athens was closed by Roman Emperor Justinian in 529 CE. It was the end of an era. But the beginning of another… the Islamic Golden Age.

Historical sidenote: Aristarchus was not the first to propose that the sun and stars were similar objects. The pre-Socratic philosopher Anaxagoras (c.500-c.428 BCE) is said to have brought philosophy and the spirit of scientific inquiry from the Greek city states in Ionian Asia Minor to Athens. His observations of meteorites led him to believe that objects may be loosened from the heavens and fall towards Earth. He realised what solar and lunar eclipses are. He believed that the Sun was a large blazing hot metal object, and that the planets were masses of stone that had been ripped away from the Earth and ignited by rapid rotation; the Moon, he said, was earthy, had mountains, and was inhabited; the stars, blazing hot stones. He believed the Earth was flat and floated on “strong” air; disturbances in the air sometimes caused earthquakes. Unfortunately, for having these ideas, Anaxagoras was charged for “impiety" in Athens, possibly for denying the existence of a solar and/or lunar deity. He fled to Lampsacus where he lived out the last years of his life. Upon his death, the citizens of Lampsacus are said to have erected an alter to “Mind and Truth” in his memory and placed over his grave the following inscription: “Here Anaxagoras, who in his quest of truth scaled heaven itself, is laid to rest."