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Location of Julius Caesar’s Assassination to be Open to the Public!

by March 15, 2019

Move Aside Feral Cats! The ruins in the Largo di Torre Argentina are about to get a fashion make-over.
The location of the murder of Julius Caesar will soon be renovated, it has been recently announced. It was over 2,000 years ago on this day, The Ides of March, also known as March 15th, that famous Roman politician, General and historian was assassinated in the Theater of Pompey. Caesar was brutally stabbed to death 23 times by 60 members of the senate as a consequence of his growing power and influence. It was thought that he was a threat to the Republic itself, and yet, it was only after his death that the empire took hold.
Death of Caesar

Assassination of Caesar by William Holmes Sullivan, c. 1888, Royal Shakespeare Theatre

Now, the very interesting thing is that the location of this assassination is not where you might automatically think. Indeed, it was very ironic that Caesar died on the portico of a public work done by Pompey. (You may remember that Pompey, once Rome’s most accomplished general had, notably, been defeated by Caesar in a civil war and then murdered in Egypt by Caesar’s allies.)
You see, the Roman senate did not usually meet at Pompey’s Theater. Instead they had for centuries congregated at the Curia, or meeting house on the Comitium. Despite numerous fires, restorations and rebrandings, this was always Rome’s primary open air meeting location.
However, in 52 B.C. Publius Clodius Pulcher was killed by his political rival and his enthusiastic followers concluded that they needed to cremate Publius in the senate house, incinerating the entire place in the process.
Consequently, Caesar started constructing a new senate house. But while the ‘Curia Julia’ was being built, the senate moved temporarily to the Curia Pompeiana, part of Pompey the Great’s massive public theater.
The location of the death of Caesar, forever immortalized by historians and Shakespeare, was sadly covered up by the expansion of Rome and lost until the 1920’s. This is when the Italian dictator Mussolini undertook numerous archeological endeavors as part of a propaganda project to boost Italian nationalistic efforts, including uncovering the theater of Pompey and four temples. However, after World War II, many of these sites were left unattended… and recent economic woes have resulted in greater disrepair.
Roman Ruins

The current site of Caesar’s death, Largo di Torre Argentina

Fortunately the fashion house Bulgari, in a bizarre but exciting partnership, have decided to step in and contribute $1.1 million in funding the clean up and restoration. This isn’t even the first time… Bulgari has already paid $1.6 million to restore Rome’s Spanish steps. In fact, the city of Rome has been partnering with several luxury brands in efforts to preserve many of the iconic sites. For instance, fashion house Fendi aided the clean up of the Trevi Fountain while Tods funded half of the massive restoration of the Colosseum, which reopened in 2016.
With this unlikely source of revenue, we can expect a beautifully renovated walkways surrounding the ruins, which no doubt, will double as runways.

It’s Pi Time!

by March 14, 2019

The history of pie is both storied and interesting in and of itself. Did you know, for instance, that the Ancient Greeks are thought to have originated the pie pastry, as can be seen in Aristophanes’ plays (5th century BC), where there are mentions of sweetmeats including small pastries filled with fruit? Neither did I until today.
But that’s not what we are talking about, delicious as it sounds.
Instead, we are delving into a different pi, though it also shares some of its origins in Ancient Greece.
Yes, dear reader, we are investigating the captivating phenomena of a mathematical constant, the algorithm of which was devised by the brilliant (and perhaps evil) Archimedes around 250 BC.
While math may not peak your interest initially, the history and discovery of this unique irrational number should. And if nothing else, it might take you back to your old school days.
Think of it as a mathematical madeleine moment.
But first, let’s go over what exactly Pi is.
This curious number (of which the nerdist of memory masters like to repeat) was originally defined as the ratio of a circle’s circumference to its diameter. In other words, pi equals the circumference divided by the diameter (π = c/d). Conversely, the circumference is equal to pi times the diameter (c = πd). No matter how large or small a circle is, pi will always work out to be the same number.
Following me still? Well, it’s going to get tricker for a moment.
π is also an irrational number, and no, not like your mother in law. This means it can never be written as a fraction of two whole numbers, and it does not have a terminating or repeating decimal expansion. Essentially, there is no exact value, seeing as the number does not end. The decimal expansion of π goes on forever, never showing any repeating pattern. I’ll say it again for emphasis – it never repeats and it goes on forever.
I’ll just let the magnitude of that sink in for a moment.
Pi gif

Animation of the act of unrolling circumference of a circle having diameter 2, illustrating the ratio π.

Now, since π is irrational, all we can ever hope to do is get better and better decimal approximations… which is where the magnificent, albeit ultra nerdy, competition of reciting known numbers comes in.
Why Pi? Why not cake?
Good question, dear reader – I can tell you are hungry…. For knowledge. (waaa waaa)
Pi is called Pi because the 16th letter of the Greek alphabet, π (Pi), was employed as an abbreviation of the Greek word for periphery (περιφέρεια) which means circumference.
That was easy enough! Now, onto the history of this minxy little number.
Pi actually goes much further back that Ancient Greece. In fact, several ancient civilizations came up with fairly accurate values for π, including the Egyptians and Babylonians, both within one percent of the true value.
In Babylon, a clay tablet dated 1900–1600 BC has a geometrical statement that, by implication, treats π as 25/8 = 3.125. In Egypt, the Rhind Papyrus, dated around 1650 BC but copied from a document dated to 1850 BC, has a formula for the area of a circle that treats π as (16/9)2 ≈ 3.1605.
There is even a biblical verse where it appears pi was approximated:
And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it about. — I Kings 7:23 (King James Version)
Then, around 250 BC the Greek mathematician Archimedes created the first ever algorithm for calculating it. His system was so popular, it dominated the math scene for over 1,000 years, and as a result, π is sometimes referred to as “Archimedes’ constant”.
Around 150 AD, Greek-Roman scientist Ptolemy, in his Almagest, gave a value for π of 3.1416, which he may have obtained from Archimedes or from Apollonius of Perga.

Engraving of a crowned Ptolemy being guided by the muse Astronomy, from Margarita Philosophica by Gregor Reisch, 1508.

Later on in 480 AD, Chinese mathematicians used geometrical techniques to approximate to seven digits and Indian mathematics made it to about five in the 5th century AD. The historically first exact formula for π, based on infinite series, was not available until a millennium later, when in the 14th century the Madhava–Leibniz series was discovered once again in India.
Today we use algorithms based on the idea of infinite series from calculus, and our ever-faster computers allow us to find trillions of digits of π.
Now, while all this history is no doubt fascinating, these pages are dedicated to the Greeks and Romans! So let’s go back to Archimedes and his revolutionary technique.
First off, if you don’t know much about Archimedes, you should…and not only because he was likely a evil super-mind.

Archimedes Thoughtful by Fetti (1620)

Born in Syracuse on the island of Sicily in 287 BC, Archimedes was a Greek mathematician, scientist, mechanical engineer and inventor who is considered one of the greatest mathematicians of the ancient world. Among his many epithets, he is considered the father of simple machines, as he introduced the concept of the lever, the compound pulley, as well as inventions ranging from water clocks to the famous Archimedes screw.
He also designed devices to be used in warfare such as the catapult, the iron hand, and the death ray. In fact, Archimedes was one of the world’s first mathematical physicists whose inventions were actually applied to the physical world. (And there are fantastic re-enactments of these cruel creations. As seen here and here).

So it should be no surprise that such a mind was capable of figuring out the humble circle!

But how did it do it?

Archimedes used the Pythagorean Theorem to find the areas of two polygons. He then approximated the area of a circle based on the area of a regular polygon inscribed within the circle and the area of a regular polygon within which the circle was circumscribed. The polygons, as Archimedes mapped them, gave the upper and lower bounds for the area of a circle, and he approximated that pi is between 3 1/7 and 3 10/71.
Wait…. what? Let’s go over that again, but with pictures.
Basically, Archimedes observed that polygons drawn inside and outside a circle would have perimeters somewhat close to the circumference of the circle.
As described in Jorg Arndt and Cristoph Haenel’s book Pi Unleashed, Archimedes started with hexagons:
We start with a circle of diameter equal to one, so that, by definition, its circumference will equal π. Using some basic geometry and trigonometry, Archimedes observed that the length of each of the sides of the inscribed blue hexagon would be 1/2, and the lengths of the sides of the circumscribed red hexagon would be 1/√3.
The perimeter of the inscribed blue hexagon has to be smaller than the circumference of the circle, since the hexagon fits entirely inside the circle. The six sides of the hexagon all have length 1/2, so this perimeter is 6 × 1/2 = 3.
Similarly, the circumference of the circle has to be less than the perimeter of the circumscribed red hexagon, and this perimeter is 6 × 1/√3, which is about 3.46.

This gives us the inequalities 3 <π < 3.46, already moving us closer to 3.14. Archimedes, through some further clever geometry, figured out how to estimate the perimeters for polygons with twice as many sides. He went from a 6-sided polygon, to a 12-sided polygon, to a 24-sided polygon, to a 48-sided polygon, and ended up with a 96-sided polygon. This final estimate gave a range for π between 3.1408 and 3.1428, which is accurate to two places.

If I haven’t lost you, this was a revolutionary method, one that differed from the earlier approximations in a fundamental way.
Previously, the number was calculated in a very approximate way, usually by simply comparing the area or perimeter of a certain polygon with a circle.
Archimedes’ technique was new as it was an iterative process, one where you can get a more accurate approximation by repeating the process, using the previous calculation of pi to obtain a new, more correct number.
Now, some consider the celebration of Pi and its forever, never repeating decimals as an overblown party. But, we here at Classical Wisdom beg to differ. Any day that makes people stop and appreciate math and its marvels is certainly worthwhile… and I think we all know the late, great Stephen Hawking would agree, may he rest in peace.

The Hanging Gardens of Babylon

by January 25, 2019

By Jocelyn Hitchcock, Contributing Writer, Classical Wisdom
The mention of the Hanging Gardens of Babylon conjures up images of an oasis in the midst of a bustling city; a vibrant Eden of lush trees, shrubs, and vines supported with beautiful pillars and architecture. The gardens are thought to have been built by King Nebuchadnezzar II sometime in the 6th century BCE. While it is one of the seven wonders of the ancient world, its actual existence is quite contested, with three theories prevailing: (1) that the gardens were purely mythical and idealized in the minds of writers and travelers; (2) that they did exist, but were razed in the first century CE; and (3) that the “hanging gardens of Babylon” actually refers to a garden built in Nineveh by the Assyrian King Sennacherib.
Picture of Babylon Gardens

Artist depiction of the Hanging Gardens of Babylon.

Like many ancient marvels, our knowledge of the hanging gardens comes down to us via written record and subsequently should be taken with a grain of salt.
Diodorus Siculus wrote that the gardens were square, tiered, and made of 22 feet thick brick walls. He mentions that the terraces themselves resembled a theater, sloping upwards to a height of 20 meters. Strabo writes that the gardens were located by the Euphrates river, running through Babylon, and utilized complex irrigation to draw up water from the river to water the gardens. It is very likely that any classical writer focusing on the hanging gardens would have had to reference earlier works from the 5th and 4th centuries. Unfortunately, the earliest extant writing we have of the gardens comes to us in quotes from the Babylonian priest, Berossus, around 290 BCE.
Archeological site of the Palace

North Palace of Nebuchadnezzar II

Nonetheless, these authors provide us with a baseline of what these gardens may have looked like and where they may have been located. Gardens such as these would have required a great deal of resources to build and maintain, and so it is likely that they were located in or near the palace of Nebuchadnezzar II, if they existed at all. Extensive excavations of the palace of Nebuchadnezzar II has revealed gates, vaulted rooms, double walls, tablets, large drains, and a possible reservoir. Nothing has been produced though, either in the archaeological record or the written records, that corroborates the Greek description of the gardens of Babylon. Since the written records consist of an exhaustive list of Nebuchadnezzar’s achievements while king, if he built the gardens they would have surely been listed, but they are not.
Illustrations

Artistic Illustration of the Gardens of Babylon

What do we make of this lack of evidence? Did Greek authors just fall victim to hearsay without ever even seeing the gardens, having never existed at all? Or did they just exist perhaps at a different time and place?
The fact that the gardens are discussed in a wide variety of Greek sources, spanning hundreds of years, and the fact that gardens like the fabled one at Babylon were quite common and not out of the question, it is difficult to outright deny the existence of the gardens altogether.
One possibility is that the gardens were not in fact located in Babylon, but 350 miles north in Nineveh, the capital of Assyria. Recent scholarship from Stephanie Dalley claims to have found evidence in Nineveh texts of King Sennacherib that describes an “unrivaled palace” and a “wonder for all peoples.” Extensive aqueduct systems as well as water-raising screws have both been found in Nineveh and may have certainly provided the irrigation needs of such prominent gardens.
Rebuilt Gate

Nineveh – Mashki Gate

The confusion may be as simple as ancient geographers and authors attributing the name “Babylon” to several places, or just getting the kingdoms of Babylon and Assyria confused in the first place. Since the Greek and Latin texts we have on the hanging gardens all reference back to one another, using the same base sources, a mistake in one is unsurprisingly carried through them all.
Still, whether real or not, the very idea of the hanging gardens of Babylon was a prevalent one in the minds of the Greeks and Latins. The literary attention that persisted on the subject must have captured the imagination of Hellenistic Greeks and Romans of the empire, much like it does today.

Not Just Another Column

by December 7, 2018

What’s in a column? To the Ancient Greeks, the standing pillar was more than just a way to hold up the roof. Every section, from capital to base, was integral to the entire structure. It was a piece of art that followed very detailed specifications, an architectural order. In fact, you only need a fragment of molding to recreate a whole building.
The ancients weren’t just constructing a safe place in the rain, they were attempting to achieve perfection in architecture.
This meant nothing was left up to chance. It was never, Kyriakos – the average workman and heavy, choosing to put the pediment a “little the right”. The buildings were carefully designed using principles in harmony and symmetry and all overseen by a respected architect. The man in charge presided over every detail, from materials selected to choosing expert sculptors.
The order of the universe, believed so fervently by the Ancient Greeks, was reflected in the buildings themselves.
In fact, this is no exaggeration. The proportional ideals employed by these mathematical architects was the so-called Golden Mean, a ratio also found in natural spiral forms like Nautilus shells and fern fronds.
Here is the actual formula cherished by those men of yore:
Formula for the Golden Mean
Creating a perfectly proportional building had other desired consequences. It created an optical illusion. The end goal was, after all, how the building looked. They wanted perspective and concave results. Consequently, the major lines in the structure were rarely straight. This is most obviously seen in all the different columns’ profiles, whether they be Doric, Ionic or Corinthian.
But let us quickly review those three, very distinctive, major architectural systems, called orders.
Comparison of Ancient Greek Architectural Orders

Comparison of Ancient Greek Architectural Orders

The first and most primitive order is termed ‘Doric’. It is the serious, manly system that originated from wooden structures. It follows basic rules of harmony. Each column has to bear the weight of the beam laid across it. All the Triglyphs, or vertically channeled tablets, are arranged regularly. The columns themselves, short and stocky, stood initially without a base, and at a height of about six or seven times the diameter. The capital on the top of the pillar is basic.
The next architectural order is referred to as Ionic, due to its origination in Ionia (present day Turkey) in the mid-6th century BC. The southwestern coastline and islands of Asia Minor had been settled by the Ionic Greeks, who were distinguished from the Doric greeks by their Ionian dialect.
The Ionians’ more effeminate column design, however, proved popular amongst all the Greeks as evidenced by their construction on the mainland in the 5th century BC.
Ionic columns are most often fluted, and usually numbered at 24. This standardization was quite handy as it kept the fluting in a familiar, almost fragile, proportion to the diameter of the column… and at any scale. The system as a whole is characterised by its continuous freezes, and the scroll-like capitals, called volutes.
Corinthian Capital

Corinthian Capital

The third and final architectural order is termed Corinthian, from the ancient city of Corinth. It is the most elaborate and engraved system of architecture, distinguished by the stylized acanthus leaves and stalks found in the Corinthian capitals. These columns appeared much later and were more popular in subsequent periods than its own.
Overall, the disciplined and ordered approach to architecture was clearly effective … as it has been a major influence for the past two millennia. All three major architectural orders, Doric, Ionic and Corinthian can all still be seen in buildings, both public and private, throughout the world today.
But these systems of architecture did more than just beautified edifices globally. The western world also inherited from those brilliant mathematical architects the idea of a building as more than a space to live or worship. It can have another function: To be beautiful through harmony, balance and proportion.

Armillary Spheres: Following Celestial Objects in the Ancient World

by October 6, 2018

By Ḏḥwty, Contributing Writer, Ancient Origins
betrachtendem

Detail of Augustinus in betrachtendem Gebet. (1480) Sandro Botticelli. ( Wikimedia Commons )

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:
Astronomy


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

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.