IX:The ancient numerals of the Mighty Romans

IX.  The ancient numerals of the mighty Romans

   [Contd. A Journey to the Wonderland of Math. by Ajay Kumar Chaudhuri]

          

           We have heard many fascinating stories about ancient Rome and of mighty Roman emperors.Their ancient numerals also have importance even today and continues to be widely used,however,in certain formal  and minor contexts.For examples:on clock faces showing hours,coins,for inscriptions on corner foundation stones,generation suffixes such as Louis XIV,King George VI etc.

Let us have a glance at the ancient Roman civilisation before going to search for their numerals. The great ancient Roman civilisation is undoubtedly one of the mightiest and most influential of all cultures that came before and after.

Rome sprung up as a small, agricultural civilisation in the 10^th century BC from a small town in central Italy’s Tiber river in the 8^th century BC supposedly founded by the mythological twins Remus and Romulus. The traditional date of foundation of Rome is 21 April 753 BC. The origin of the city’s name “Rome” is thought to be after the name that of the reputed founder and the first ruler, the legendary Romulus. As the legend goes, Romulus and his twin brother Remus, apparent illegitimate sons of the Roman war god Mars and the descendants of the Trojan hero Aneas, were suckled by a she-wolf after being abandoned. After growing up they decided to build a city. The brother’s argued, Romulus killed Remus and then named the city Rome after himself.

Beginning in the 8^th century BC, ancient Rome grew up from a small town on central Italy’s Tiber River into an empire that at its peak encompassed most of continental Europe, Britain, much of Western Asia, Northern Africa and Mediterranean islands.  After 450 years of republic, Rome became an empire in the wake of Julius Caesar’s rise and fall in the first Century BC. The long and triumphant reign of the first emperor Augustus, began a golden age of peace and prosperity.

As the Roman empire grew, it became more and more difficult to rule from the city of Rome. To solve this problem, the Roman leaders decided to split it to two empires. Accordingly, one was the Western Roman Empire, to be ruled from the city of Rome itself, the other part was Eastern Roman Empire or Byzantine Empire which was to be controlled from the city of Constantinople, founded by Constantine the Great in 330 AD. At present we know this city as Istanbul, an important city of Turkey.

The fall of Rome generally refers to the fall of the Western Roman Empire. It fell in 476 AD. However, the Eastern Roman Empire or the Byzantine Empire ruled parts of the Eastern Europe for another 1000 years. The empire’s decline and fall by the fifth century AD was one of the most dramatic implosions in the history of mankind.

Ancient Rome was the progenitor of Western civilization. Among many legacies of Rome dominance are the wide spread use of Roman Language that derived from Latin such as Italian, French, Spanish, Portuguese and Romanian; the modern western alphabet, calendar and emergence of Christianity as a major world religion. Many more aspects of Roman civilisation worthy to mention are : Customs, law, technology, architecture, political system, military, literature, government and many factors and aspects of Western Civilisation are all inherited from Roman advancement.

In ancient Roman Society, women were accorded an important place. They enjoyed and shared almost equal right with Roman men and were provided similar opportunities to excel in education, business and trade.

‘Slavery’ is a contemptuous word to all of us now-a-days, as it grossly violets human rights, but in ancient Rome, slavery played an important role in society and economy. Romans, especially the rich ones depended greatly on their slaves for maintaining a luxurious lifestyle. Besides manual labour, slaves performed many domestic services and also be employed at highly skilled jobs and professions like the job of an accountant and physicians. Greek slaves in particular might be highly educated. Unskilled slaves or those sentenced to slavery as punishment, worked on farms, in mines and mills. Their living condition was brutal and their lives were short. They were considered properties under Roman law.

Roman Empire owed much of its achievements and grandeur to highly professional and disciplined Roman military. They achieved wonderfully in science and architecture at those days.

One of the greatest scientific feats of ancient Rome is the concrete roads. Nearly 30 military highways, all made of stone, exited in the great city. At one point, 372 roads connected 113 provinces. It helped greatly in efficient military operations and also in improvement in social life, thereby furthering civilisation.

Like art and other aspects of ancient Roman culture, early Roman architecture borrowed heavily from Greek architecture. However, they quickly adopted their own style and marveled in this field.

If you are to visit Rome, you could see many of the ancient buildings even today such as the Forum, the Colosseum and also many architectural marvels in domes like the Roman Pantheon, Circus Maximus and also famous aqueducts and bath like the Baths of Diocletian etc.

The Forum was at the centre of the city and the Roman public life was centred about it. This was a rectangular plaza surrounded by public buildings such as temples of gods and basilicas where commerce and other public functions could take place.Here many of the city’s major events, such as elections, trials, public speeches and triumphant processions were held. At the centre of Rome there were many other famous buildings like temple of Jupiter, the Colosseum, Circus Maximus, the Roman Pantheon and Pompe’s theatre.

The Colosseum is the largest amphitheater ever built and is one of the Seven wonders of the world. This is situated just east of the Roman Forum. As it is estimated, the Colosseum could hold between 30,000 and 60,000 spectators having an average audience of about 65,000. It was used for gladiatorial contest and public spectacles such as mock sea battles, animal hunt, executions, reenactment of famous battles and dramas based on classical mythology. Of all the functions held in the Colosseum, the gladiatorial contest was the worst adventurous, barbaric and most fearful. A gladiator was an armed combatant who entertained audience in the Roman Republic and Roman Emperors in violent, confrontations with other gladiators, wild animals like lion, tiger etc. and condemned criminals. Most were despised as slaves, schooled under harsh conditions, socially marginalised and segregated even in death.

Another architectural excellence of ancient Rome is the Roman Pantheon, the largest dome in the world for more than a millennium. It is the largest unreinforced solid concrete dome to this day.

The Circus Maximus was also a wonder of ancient Rome. It was a huge chariot racing stadium which could hold around 150,000 spectators. It was built on the land between Palatine and Aventine hills that two hills of the seven hills on which Rome was built.

Roman aqueducts and baths are example of wonderful advancement of ancient Roman technologies. The Romans constructed numerous aqueducts in order to bring water from distant sources into cities and towns, supplying public baths; latrines, fountains and private households. Waste was removed by complex sewage systems and released into nearby water-bodies, keeping town clean and free from effluent. Aqueducts also provided water for mining operations, milling, farms and gardens.

Romans also built many baths for public uses. Baths of Diocletian, named after the emperor Diocletian, was the largest and most impressive imperial baths. Of course you now could not find them in Rome. Parts of the structures were used for different purposes. The basilica of Santa Maria stands on the remains of the baths.

Roman art was an important aspect of ancient Roman civilisation. Roman art refers to the visual arts in ancient Rome and in territories of the Roman Empire. It includes architecture, painting, sculpture and mosaic work. At present luxury objects in metal work, gem engraving, ivory carvings and glass are sometimes considered to be minor forms of ancient Roman art. Sculpture was perhaps considered as the highest form of art by Romans, but figure painting was also very highly regarded. It is thought that the ancient Roman artists often borrowed from and copied Greek precedents; for much of the Greek sculpture known to-day is in the form of Roman marble copies. But also the Roman artists had their own contributions in art. A large body of ancient Roman Sculptures surviving from about first century BConwards, though little from before, but very little painting at all remains which may not be considered to be of the highest quality.

To have a glimpse at the ancient Roman paintings, let us go to the Villa of the Mysteries, a well preserved suburban Roman Villa on the outskirts of Pompei, Southern Italy. It is famous for the frescos in one room which are now probably the best known of the relatively rare survivals of ancient Roman painting. Like the rest of the Roman city of Pompei, the Villa was buried in the eruption of Mount Vesuvius in 79 AD and excavated from 1909 onwards. It is how a popular site of tourist visits to Pompei and forms part of UNESCO World Heritage Site at Pompei.

It has already been mentioned that the ancient Roman civilisation was one of the mightiest and most influential of all ancient cultures. In fact, ancient Rome was the progenitor of western civilisation but they had no substantial contribution towards mathematics. They invaded many kingdoms and countries including Greece. The Greeks at that time was much advanced in science, mathematics, art and philosophy than the Romans. Roman invasion of Greece was only for power, not for abstract mathematics. They killed Archimedes, the renowned Greek scientist, in 212 BC and thereby impeded the development of mathematics. On the other hand, the system of Roman numerals was too complicated for calculations. Actual counting had to be done on a counting board , an early form of abacus although the usage of Roman numeral system spread all over Europe and remained dominant  numeral system for more than five hundred years, yet not a single Roman mathematician is celebrated to-day. The Roman were more interested in using numbers to record their conquest and to count dead bodies.

Roman numerals follow the history of ancient Rome itself from its early stages at Latin Palatine Hill in the 8^th and 9^th century BC to its fall in the 2nd century AD from civil war, plague, civil apathy, rise of Christianity and Northern European powers.

There exist many theories as to the origin of the numerals; however it is widely accepted that Roman numerals are based upon a more ancient Etruscan system. Etruscans, who lived in central Italy before the Romans, developed their own numeral system with different symbols.

One theory of ancient Roman numerals is that of the Tally Sticks made of wood or bone. Tally sticks or some similar methods of simple recording had been in use long before founding of the Roman Empire. During ancient times merchants used tally sticks for recording business transactions. On tally sticks, single digits were represented with a single notch, where as a group of five was represented as either a standard or inverted V. To represent the value of 10, a tally stick simply crossed two single notches X.

An alternative to the tally stick theory is that Roman numerals are a representation of hand signals. The Roman numerals I, II, III, IIII represent the number of fingers held up during auctions when merchants would gather together and bid against each other, similar to modern day auction. This hand signal theory suggests that the Roman numerals is a direct representation of these hand signals. For larger numbers such as 5 or 10 merchants would hold up their hand with their thumb extended and their fingers together to represent 5 or arms crossed for 10, which are similar to V and X used in Roman numeral system.

Roman numerals are represented by seven different letters: I, V, X, L, C, D and M which represent 1, 5, 10, 50, 100, 500 and 1000 respectively. In fact, the Romans built their numerals based upon these Latin alphabets utilizing a series or combination of letters which represent numeric values. Roman numerals are an additive and subtractive system or more clearly, a system that add or subtract symbols in order to make corresponding numbers.

Roman numerals were usually written from largest to smallest , from left to right, this tells us that we must add the numerals together. However, this is not always the case. Romans didn’t like four of the same numerals to be written in row, so they developed a method of subtraction.

So, in Roman numeral system the number 2 will be represented by II which means two ones are combined together. Similarly 3 will be written as III, 12 as XII, that means 12=10+2 or X+II, 28 will be XXVIII, implies 28=20+5+3 as XX+V+III etc.

Likewise, by the subtractive system the number 4 will be 5 – 1 or IV, 29 will be written as 30 –1=IXXX, 90 as 100 – 10=XC etc. There are six instances where the Romans used subtraction, namely I can be placed before V(5) and X(10) to make the numbers 4 and 9.

X is placed before L(50) and C(100) to make 40 and 90.

C to be placed before D(500) and M(1000) to make 400 and 900.

A good example of the above rules, the representation of 1904, in Roman numerals

For 1904 = 1000+900+4 will be written as M+CM+IV or MCMIV

But it is difficult to write large numbers only with these Seven letters, the largest being M (1000). In fact, Roman rarely needed to write numbers larger than 3999 and that is why they never developed a system to overcome this problem, although a system was developed much later to do so.

The Roman number system flawed in many ways. The greatest of them was they had no idea of Zero (0) as a place holder yet, the word “nulla” meaning “none” in Latin was used by medieval computists in lieu of zero and sometimes represented by N, the initial letter of Nulla.

Though Romans used a decimal system for whole number, yet they used a duodecimal system for fractions. The reason behind it was that 12 has many divisors, like 2,3,4, and 6 while 10 has only two, 2 and 5. Divisibility of 12 makes it easier to handle the common fractions of 1/3 and 1/4 than does a system based on 10.

Romans used coins which were fractions from 1/12 to 12/12, the unit called “as”. They used a tally – like notational system based on twelfths and halves. One twelfths was called “uncia” which was indicated by a dot (.). These dots were repeated for fractions up to five twelfths. Six twelfths or one-half was abbreviated by S, the first letter of the word ”Semis”, meaning half. Uncia dots were added to S for fractions from Seven twelfth to eleven twelfths, just as tallies were added to V for whole numbers from six to eight.

Each fraction from 1/12 to 12/12 had a name in Roman times which corresponds to the related coins. Are you curious to know those names? It is given below. You will be surprised to discover the source of the English words “inch” and “ounce” from this table.

Table No. 8

Here one thing is to be noted that the arrangements of dots was variable and not necessarily linear. Five dots arranged like (∵) as on the face of a die are known as quincunx, derived from the name of the Roman fraction or Coin. The Latin words sextans and quadrans are the source of the English words Sextants and Quadrants. The list of Roman fractions above is not exhaustive.  There were other Roman fractional notations also.

Another usage of Minuscule or lower case letters of the Roman numerals was developed, well after fall of the Western Roman Empire, in Middle Ages and renaissance. Since that time lower case versions of Roman numbers have also been commonly used.  These numerals are as i, ii, iii, iv and so on.

Since the Middle Ages, a “j” has sometimes been substituted for the final “i” of a lower case Roman numeral, such as iij for 3 or vij for 7. Perhaps to signify the final unit to stop tampering and also to avoid misinterpretation of a number after it had been written on a document, j is used for the final i. We still find this practice in writing medical prescriptions.

Absence of Zero in Roman numerals hindered their advance in mathematics. The Romans probably didn’t use numerals for complete arithmetical operations due to its complexity. In this system the operation of multiplication and division are far too impractical. However, it is not impossible for addition and subtraction.

But before going to perform the operation of addition with Roman numerals, it is important to note that we don’t use the subtractive system of writing the numbers to be added. For example, the number four is not shown as IV but as IIII.

Let us take a simple case of addition of IX and XIII. Here we must first change IX to VIIII, as it uses subtractive principle. So, now we are left with  VIIII  + XIII. Now we can complete the sum just like we would if we were using Arabic numbers as shown below.

V I I I I         +  X I I I ――————— X V I I I I I I I

We arrange the numerals from biggest to smallest which gives XVIIIIIII. The next

step is to simplify IIIIIII to V which gives us VII and the sum as XVVII. This can further be simplified as XXII or 22, the required sum.

Similarly, in the process of subtraction we can’t use subtractive principle of writing the numerals. For example, let us subtract CCLXXI from CCLXXXXVIII or CCLXXXXVIII – CCLXXI. After cancelling the common characters CCLXX from both numbers, it gives   CCLXX XXVIII –  CCLXX I = XXVIII – I which can further be simplified as XXVII which the required result. In our Arabic numeral system, this problem actually is : to subtract 271 from 298. The required result is 298 – 271 = 27 or XXVII in Roman numerals.

Various uses of the ancient Roman numerals can still be seen in modern day. In fact they are all over the place!

Roman numerals are widely used to refer kings, queens, emperors and popes. For example, George V was the king of England to be called George. By using numeral we can easily distinguish between which King George we are talking about. Similarly, Queen Elizabeth-II or Pope Paul – VI refer to specific queen and pope respectively.

Many competitions such as in Olympic Games, use of the numerals to signify how many times the event have preceded the current one. For example, the Olympic Games in Brazil in 2016 will be the 31^st Games, so it will be the XXXI Games.

Roman numerals can often be found on buildings and monuments to illustrate the year of construction. Say, for instance, if we see the numerals MMIV have engraved on a building wall, we at once understand that the building was built in the year 2004.

Many movies use these Roman numerals to illustrate in which year the film was copyrighted or created. For an example : the movie ‘Gladiator’ was  copyrighted in the 2000. So it may have the numeral MM at the end of the credits or the film ‘Spartacus’ which was copyrighted in the year 1960 will have the numeral MCMLX.

A lot of clocks, even today, use Roman numerals to represent hours. We find frequently on the faces of clocks, for example, 3, 6, 9 and 12 o’clock are depicted as III, VI, IX and XII respectively.

Ancient Roman numerals can be found in so many real life situations. The list is not exhaustive, it goes on and on; at the beginning of books to number the pages before the book actually begins or within legislation to label sections, sub-sections etc. and even to refer to wars; such as WWI and WWII.
 Attribution:Table No.8----Ancient Roman Fractions
Creative Cosmos ( https://en.wikipedia.org/wiki/Roman_numerals#Fractions )
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