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Ptolemy, the Man who Reached the Stars

by May 17, 2019

By Mónica Correa, Contributing Writer, Classical Wisdom
The study of the earth, stars and space started millennia ago. With a lot of observation and subsequent writings, men such as Ptolemy built the foundations of our understanding of the universe that surrounds us.
Today we know that his name was, in fact, Klaudios Ptolemaios. He probably lived in or near Alexandria, Egypt during the times of the Roman Empire. Better known as Ptolemy, he made astronomical observations between the mid 120s and the early 140s of our era. Some have identified his method as Aristotelian, as while there are no records of his education, he regularly quotes Aristotle. This can give us hints regarding his methods.
From math and geography to music and optics, Ptolemy bequeathed us decades of work that are still a reference today.
Painting of Ptolemy

Ptolemy with an armillary sphere model, by Joos van Ghent and Pedro Berruguete, 1476, Louvre, Paris

Ptolemy’s Career
Sciences, as we know them today, have come a very long way. Over the centuries the broader categories have branched out into specific groups, which, of course affects the way we relate to ‘knowledge’.
According to Ptolemy, physics and theology are conjecture, while mathematics alone yields true knowledge and has the ability to contribute significantly to what we today consider the study of physics. This assertion was unprecedented in the history of ancient Greek philosophy.

Early Baroque artist’s rendition of Ptolemy

While reading his work, it’s important to remember that Ptolemy does not distinguish the terms astronomy and astrology as we do. What we call astronomy explains and predicts the configurations and movements of celestial bodies; what we call astrology studies and predicts physical changes caused by the powers emanating from celestial bodies. For Ptolemy, these were one and the same.
Ptolemy’s Known Work
Ptolemy lived in the second century C.E. in or around Alexandria and developed astronomical models that served as the western world’s paradigm in astronomy for approximately 1400 years. Lasting straight up to the Scientific Revolution, Ptolemy’s ideas have been arguably referred to longer than any one else’s.
Quite a bit of his work is fortunately extant; some exist in their original versions, while others are translations. Harmonics, Geographia and Almagest are the best kept today.
Geographia by Ptolemy

Geography by Ptolemy, Latin manuscript of the early 15th century

Ptolemy’s Harmonics is about music theory and the mathematics of music. It contains three books, though unfortunately the last three chapters, 3.14-16, no longer exist; only their titles remain.
Almagest is a systematic treatise in thirteen books in which Ptolemy deduces the structure and quantitative parameters of geometrical models for the heavenly bodies from empirical evidence, including specific dated observations. The Almagest uses models to derive tables for calculating the positions of the heavenly bodies on any given date, together with other phenomena, such as eclipses and planetary first and last visibilities. In Almagest, Ptolemy treats Hipparchus as his only legitimate predecessor in theoretical astronomy.
Almagest is so important because Ptolemy presents a series of astronomical models, which aim to account for the movements of the stars and planets, including the sun and moon. The models are both demonstrative and predictive, which was a breakthrough at the time.
Geometric models

Geometric construction used by Hipparchus in his determination of the distances to the Sun and Moon

Another known work is Optics, however, some scholars have questioned Ptolemy’s authorship of this book. There, he explains how the eye emits a visual flux in the form of a cone, which is resolvable into a collection of rays traveling in straight lines. As in the case of the Harmonics, sections of the Optics have disappeared.
In the book On the Kritêrion, Ptolemy examines the criterion of truth, the method by which humans gain knowledge, and the nature and parts of the human soul. Similar to Optics, some scholars have questioned Ptolemy’s authorship of this book. Others prefer the idea that this could be one of his first writings.
The books On the Elements and On Weights have also been attributed to Ptolemy, but are completely lost.
Ptolemy’s Legacy
While many of Ptolemy’s theories and ideas have been updated, his contributions cannot be understated. For instance, in Geographia, he acknowledged a spherical world and offered coordinates for over 6,000 places in the ancient world.
Unlike many other scholars, Ptolemy divided the world into 360 degrees, as well as into minutes and seconds. This could potentially give him credit for the first recorded treatise on geo-positioning.
Ptolemy's map

A 15th-century manuscript copy of the Ptolemy world map, reconstituted from Ptolemy’s Geography (circa AD 150), indicating the countries of “Serica” and “Sinae” (China) at the extreme east, beyond the island of “Taprobane” (Sri Lanka, oversized) and the “Aurea Chersonesus” (Malay Peninsula).

Of course, he did make a few mistakes. For instance, he exaggerated the length of the Mediterranean by about 30% and he ended his world in the middle of China. However, this can be forgiven as he only worked with astronomical observations without any sophisticated equipment.
Ptolemy’s works were later studied by Asian and Arabian cultures and as such, have survived until this very day. With them we are able to see and reflect on our path and evolution as humankind… as well as learn a little bit about our universe.

Aristarchus of Samos: Prophet of Astronomy

by April 24, 2019

In a recent article, I mentioned Galileo and his idea of heliocentrism. Heliocentrism is the idea that the Earth revolves around the Sun. It is opposed to the geocentric idea which claims that the Sun and other planets revolve around the Earth.
Galileo posed heliocentrism in the 17th century, and shortly after doing so, his life was threatened by the Church. The Roman Inquisition investigated the idea and claimed that a heliocentric model of the heavens was directly opposed to the Holy Scripture and was heretical in nature.
Thus, Galileo was forced to abandon the idea of heliocentrism on the threat of death.
As much as we might like to believe that we are at the center of the universe, and that everything revolves around us, that notion is quite simply false. My fiancé likes to remind me of this daily…
Just like many other revolutionary ideas, it should come as no surprise that the heliocentric model of astronomy has roots in ancient Greek philosophy.
One might think that since astronomy falls within the contemporary discipline of science, that it must fall within the ancient Greek discipline of science, but science, up until the 19th century, was simply known as natural philosophy.
Greek astronomy began sometime around the 5th century BCE and was rather sophisticated when one considers the lack of technology and scientific instruments available to the ancient Greeks.

Aristarchus of Samos (310 – 230 BCE)

Nearly 2,000 years before Galileo, Aristarchus of Samos posited the notion of heliocentrism. Aristarchus lived from 310 – 230 BCE. He was a mathematician, astronomer, and natural philosopher.
Aristarchus broke with the popular trend which adhered to the geocentric model of astronomy. Both Plato and Aristotle believed in and defended the theory of geocentrism.
To put it into perspective, arguing against Plato and Aristotle in ancient Greece would be akin to some contemporary scientist arguing against Albert Einstein or Charles Darwin. There is nothing inherently wrong with opposing their ideas, but you better have a pretty good argument for your opposition if you want to be taken seriously.

A 10th century AD copy of Aristarchus’ calculations regarding the relative size of the Sun, Earth, and Moon. (From left to right.)

Aristarchus capitalized on a few problems which plagued geocentrism. These problems included the brightness of planets and their apparent change in movement through the night sky, known as retrograde motion.
Although Aristarchus posed the heliocentric theory of the heavens, he also wrote an entire book of astronomy from the geocentric point of view. Scholars debate the implications of this, some claim that he only came to the idea of heliocentrism after writing his book on geocentrism. Others believe that it is possible that he abandoned the notion of heliocentrism because of its contradictory nature, and instead pursued geocentrism as the true theory of the heavens.
We could speculate about such matters to no end, so let us leave this aside and focus on what we know about Aristarchus.
Through the geometrical analysis of Earth’s shadow on the moon during a lunar eclipse, Aristarchus concluded that the Earth is probably smaller than the Sun. He also held an axiomatic principle which claimed that smaller objects orbit larger ones. Therefore, it would make sense that the Earth revolved around the Sun.

If this wasn’t revolutionary enough, Aristarchus also believed that the stars were distant suns, and that the universe was much bigger than previous astronomical models had predicted.
Most of this was denied legitimacy by mainstream Greek philosophy and mathematics. For instance, the only way Aristarchus could provide adequate proof for heliocentrism was through the idea that the Earth follows an elliptical orbit, rather than a circular one. This was a radical notion and not given much credit by his contemporaries.
Proof to his idea that the stars are distant suns could only be provided by observation via telescope. This is because of the phenomenon known as stellar parallax, which has to do with the movement of stars relative to one another as the Earth moves around the Sun. Stellar parallax is only observable using an instrument such as the telescope.
Like Democritus and his atomic theory of the universe, or the many theories of evolution posed by Anaximander, Empedocles, and Lucretius, Aristarchus’ mind was far beyond the available scientific or technological instruments that were required to prove such speculative theories.
It would take roughly 2,000 years for some of these paradigmatic ideas to gain observational proof.
One must ponder the source of such genius in ancient Greece, and wonder what other ancient theories we might find evidence for in the future…

Armillary Spheres: Following Celestial Objects in the Ancient World

by October 6, 2018

By Ḏḥwty, Contributing Writer, Ancient Origins
Astronomy is often considered to be one of the oldest branches of science. In many ancient societies, astronomical observations were used not only for the practical job of determine the rhythm of life, (e.g. the various seasons of the year, the celebration of festivals, etc.) but also for the philosophical exploration of the nature of the universe as well as that of human existence. Therefore, various instruments were invented to aid the important science of astronomy. One of these instruments was called the armillary sphere.
The Function of Armillary Spheres
An armillary sphere is an astronomical device made up of a number of rings linked to a pole. These rings represent the circles of the celestial sphere, such as the equator, the ecliptic and the meridians. Incidentally, it is from these rings that the name of this device is derived from (the word armilla is Latin for “bracelet, armlet, arm ring”).
Armillary spheres may be divided into two main categories based on their function – demonstrational armillary spheres and observational armillary spheres. The former is used to demonstrate and explain the movement of celestial objects, whilst the latter is used to observe the celestial objects themselves. Therefore, observational armillary spheres are generally larger in size when compared to their demonstrational counterparts. The observational armillary spheres also had fewer rings, which made them more accurate and easier to use.
Painting of Ptolemy

Ptolemy with an armillary sphere model. (1476) Joos van Ghent and Pedro Berruguete. ( Wikimedia Commons )

The Ancient Greeks and the Armillary Sphere
The armillary sphere is believed to have originated from the ancient Greek world. The inventor of this device, however, is less than certain. Some, for instance, claim that the armillary sphere was invented sometime during the 6th century BC by the Greek philosopher Anaximander of Miletus. Others credit the 2nd century BC astronomer, Hipparchus, with the invention of this device.
The earliest reference to the armillary sphere, however, is said to have come from a treatise known today as the Almagest (known also as the Syntaxis), written by the 2nd century AD Greco-Egyptian geographer, Claudius Ptolemy. In this treatise, Ptolemy describes the construction and use of a zodiacal armillary sphere, an instrument used to determine the locations of celestial bodies in ecliptic co-ordinates. Furthermore, Ptolemy also gives examples of his use of this device for the observation of stars and planets.
The Armillary Sphere in Ancient China
Interestingly, the armillary sphere was also being developed independently in another civilization – China (albeit possibly at a later date.) The armillary sphere is said to have appeared in China during the Han dynasty 206 BC – 220 AD.)
The use of such a device may be traced to the astronomer Zhang Heng, who lived during the second half of the Han Dynasty, i.e. the Eastern Han Dynasty (25 AD– 220 AD). Originally, the structure of these spheres was very simple, consisting of three rings and a metal axis that was orientated towards the North and South Poles.
However, over the centuries, more rings were added to the spheres so that different measurements could be taken. In the courtyard of the Ancient Observatory in Beijing, for example, one can see a full sized replica of an elaborate armillary sphere produced during the reign of a 15th century Ming emperor, Zhengtong.
Armillary Sphere in Asia

Armillary Sphere in the Ancient Observatory, Beijing, China. ( Wikimedia Commons )

Armillary Spheres in the Islamic World and Christian Europe
During the Middle Ages, knowledge for the production and use of armillary spheres passed into the Islamic world. The first known treaty on this device is known as Dhat al-halaq (translated as ‘The Instrument with the Rings,’) written by the 8th century astronomer, al-Fazari.
Many Muslim astronomers wrote about the armillary sphere, though with reference to Ptolemy’s work. It may be mentioned that clear references to demonstrational armillary spheres are absent from documents of the Islamic world, whilst there is a considerable amount of evidence for the use of the observational armillary sphere.
The armillary sphere is said to have been introduced into Christian Europe by Gerbert d’Aurillac (later Pope Slyvester II.) It is assumed that d’Aurillac acquired such knowledge from Islamic Spain. It has been suggested that by the Late Medieval period, the demonstrative armillary sphere became quite a common device in European universities, as treatises on the geometry of the celestial sphere was taught in many such institutions, thus making the armillary sphere an indispensable teaching tool.
Spanish Armillary Sphere

Spanish armillary sphere. (1582) Antonio Santucci. El Escorial Monastery, Madrid, Spain ( Wikimedia Commons )

The Eastern Roman Empire’s Legacy to Astronomy

by August 21, 2018

By Monica Correa, Contributing Writer, Classical Wisdom
Decades ago, the word “Byzantine” was used as a synonym for corruption and decadence, however, the period between 395 and 1453 was also one of great scientific progress.
Byzantium, later renamed Constantinople in honor of its founder, Constantine, was a land where Latin, Greek, Islamic and Jewish traditions mixed to create a new way to study Math, History, Science and Astronomy. Consequently, there were great discoveries by dedicated scholars, such as Claudius Ptolemy, Gregory Chioniades and Nicephoros Gregoras. The scholars of this period were committed to preserve and transmit the traditions and scientific knowledge of the ancient world.
According to some research done in the last two decades, Byzantine astronomers focused in three main topics:

Figure of the heavenly bodies — An illustration of the Ptolemaic geocentric system by Portuguese cosmographer and cartographer Bartolomeu Velho, 1568 (Bibliothèque Nationale, Paris)

1. Equinoxes and Eclipses
During the Byzantine era, the Astronomic model was geocentric, meaning the consensus view was that the earth was at the center of the solar system; however, most scholars were aware of some existing errors with regards to measuring the stars and planets.
Illustration of Ptolemy

Ptolemy (Source: Blanche Marantin and Guillaume Chaudiere, Paris, 1584

A gradual improvement of methods, such as better use of the astrolabe, culminated centuries later with the introduction of the heliocentric system, which correctly placed the sun at the center of our solar system. Gregoras, who lived between 1295 and 1360, understood the mechanism of eclipses, and he calculated all the solar eclipses of the millennium up to the 13th century. He also predicted future eclipses of both the sun and the moon, constructed a prototype astrolabe, and proposed reforms to the calendar, all of which led to great progress for human kind.
2. The shape of the earth
In the text The Schemata of the Stars, Chionades draws some diagrams for solar and lunar eclipses where the earth is spherical. This provides further evidence that the Byzantines (as well as several other cultures around the world at that time) considered the earth to be spherical.

Astrolabe (Source: Masoud Safarniya)

Some years later, when Gregoras refers to the Earth in his famous work Roman History, he uses the phrase ‘below the sun’. There, indirectly he accepts its spherical shape, and he also refers to its subdivision into parallel circles and continents.
3. Models for the sun, the moon and the five (known) planets
As mentioned previously, Byzantine models for the sun and the planets are geocentric. Essentially this means: for each celestial body it is necessary to introduce a system of spheres whose axes and rates of rotation are exclusive for them.
For Chionades, Mercury and Venus are inner planets and, as seen from the earth, appear to follow the sun because they are sometimes ahead and at other times trailing the sun.
Papal letter

The first page of the papal bull “Inter Gravissimas” by which Pope Gregory XIII introduced his calendar

Also, regarding Mercury, Chioniades makes an interesting remark concerning latitude. In his writings, he explains that among the five planets, four of them have their apogees (highest point) in the northern hemisphere of the globe, except for Mercury whose apogee is in the southern hemisphere. Was this the result of observations, or was he echoing an ancient tradition? We may never know, but this description of the latitudes survived after the introduction of the heliocentric system, with both Rheticus and Copernicus making similar observations.
Years later, a mixed model with Venus and Mercury rotating around the Sun, and all of them together rotating around the earth, was introduced by Heraklides of Pontus.
The legacy that lasts until today: Our Calendar
The writings of Gregoras are especially important; today we know Byzantine astronomy owes much of its progress to him. Aware of the mistakes made by his predecessors, in 1324 Nicephoros Gregoras proposed a correction to the calculation of the date of Easter, and to the Julian calendar itself.
At that time, his beliefs conflicted with his work, so he retired from public life and his work was discredited by the church.
The calendar as we know it today was implemented by the Italian, Pope Gregory XIII in 1582. Though the so-called Gregorian calendar was named in the Pope’s honor, it was not his invention.
Established on October 4, 1582, the new calendar solved the problem that the Julian year had 11 minutes and 14 seconds more than the solar year, which had a cumulative effect to the date of the spring equinox.
Despite the fact that Gregoras didn’t live to see it implemented, it’s one of the main contributions that Byzantine Empire bequeathed to us.