Sunday, November 17, 2013

History mystery: Apollo’s Numbers – Part II

Apollo with Lyre
The special forms of lyre namely phorminx and the kithara were used more or less by professionals while the ordinary lyre was used for the social life due to its unsuitability of its softness for open air use. The strings of Hermes’ lyre vary but probably four strings were widely used originally and later on increased in number. The tetrachord or the four strings had to be tuned so that the first and the fourth strings could define the interval known as the fourth while the tuning of the other two strings seems uncertain. Towards 670 BC, the tetrachord got expanded with improvement by Terpander who added three strings to the original four strings while the last string of the original string acted as the double duty as well as the first string to the newly added strings together providing a new tetrachord. Mevsh or middle, being the common string, was considered the most important of all the seven strings. Based on standard pitch nowadays, A is considered as 440 vibrations per second and each lyre player tuned the strings to suit their own voice though whichever pitch was taken as fundamental for tonic or base note, the interval between the first and the fourth strings and between the fourth and seventh stings were called a fourth. The second, third, fifth and sixth strings were tuned according to the player and a number of varieties of tuning were used.

Performance was based solely on the ear and if the fourth and the fifth strings of tetrachord could conform to the interval of a fourth, the final results was the ear of the player that established it besides the fundamentals or tonic. Practitioners while committed to the interval of fourth as the basis for their instrument’s structure for performances had another larger interval demanding increased attention by way of octave. The string lengths were related to vibrations and shorter the string, greater was the number of vibrations resulting in higher tone. The Greeks had no means of measuring the vibrations of string but could measure its length and the common practice was to put the higher number first in a musical ratio though it was their custom to sing or play in descending scales while the custom presently is on ascending scales. Here the relationship between two tones is a ratio and the numbers are measured either on string length or vibrations, the ratio of which is called the interval between two tones. Intervals cannot be treated as string lengths and added but they may be combined. Combining ratio and intervals: When a numerical ratio is written as a:b, a, the first term is called the antecedent and b the second term is known as the consequent.

Pythagoras’s general principle has given illustration which shows that the interval which we call octave was defined by ratio 2:1 which means that if a string length was doubled it would define the tone of the octave below or if it was halved it would define the tone above. For scientific purposes, Pythagoras established the octave as the predominant interval and defined that it was the simplest string divisions and multiplications through doubling or dividing and the discovery in the use of the first two integers, 1 & 2, were the results of the most consonant of intervals. The next most natural consonants, the fifth, was defined by the ratio 3:2, and if a given string length is divided into three similar parts, the interval between whole string length and length of two of its part can be known as a fifth. With an interval of octave, it is possible to produce from a higher tone of the octave to a descending fifth which leaves the interval of a fourth i.e. `doh to fah’ and it is observed that an octave has been made up of fifth and a fourth. For the Greeks, the octave and the fifth were natural with pleasing sound to the human ear. In consideration of the lyre, the term octave is used but we do not have the scale eight tones but only seven tones due to the last tone of one string which did double duty as the first tone of the other tetrachord. Pythagoras used intervals to provide steps in the scale and he called a whole tone or just a tone and it was this interval which was used to separate the two tetrachords. With the given array of numbers representing the divided octave: 6 8 9 12 where 6:8 is the fourth and 6:9 is the fifth and the difference between them is the interval of 8:9 being a numerical expression of the whole tone of Pythagoras. Each fourth proposed by him should be divided into whole tones though the fourth will not contain the exact number of the whole tones and it will hold only two whole tones with a smaller interval left being close to a semitone or a half a whole tone with a calculated value of 234:256.

For example:

Let x:y be the left over interval

9:8 compounded with 9:8 compounded with x:y :: 4:3

Or 81:64 cp with x:y :: 4:3

Or x:y:: 4:3cp with 64:81

So x:y :: 256:24

On combining intervals; by multiplying we get

9/8 x 9/8 x 256/243 = 20736/15552 = 4/3 tone  tone   semitone   fourth, and the Pythagorean scale of one octave was made of following intervals -> tone, tone, semitone, tone, tone, tone, semitone, 

(first tetrachord)    (middle)     (second tetrachord) 

The arrangement was satisfactory with regards to the practical and ancient traditions of tetrachand though it was within the arithmetical musical division of the octave of Pythagoras. The division of tetrachand was in two whole tones as well as a semitone from which this system derived its name from those tones and was called the diatonic system. Scale or scales was the necessary base for tuning theory and diatonic scales were constructed mathematically or theoretically within the octave with the fifth and the fourth, while there was another method of constructing the scale with only the two intervals of an octave and a fifth, the method of which is known as the Spiral of Fifths. This had the advantage of being empirically tuned.

Friday, November 15, 2013

History mystery: Dravidian Maritime Knowledge

Maritime route
Maritime State of Tamil Nadu has an interesting history which dates way back to 6000 years ago which has been the cradle of the Dravidian culture. Trade relation resulted with the migration of people and developed into cultural relation with many neighboring countries. The Dravidians were the earliest people who build cities and engaged in extensive export and import business both through sea and land and by 7000 BC, camel trains trips were regularly done to distant Mesopotamia with Dravidian shipping pushing coastwise across the Arabian Sea to the Sumerian cities of the Persian Gulf and across the waters of the Bay of Bengal to the East Indies. The art of writing together with an alphabet was also imported from Sumeria by the seafarers and the merchants. The Dravidian centers of culture were in the river valleys namely the Indus and Ganges and along the three great rivers which flowed through the Eastern Ghats to the sea in the Deccan.

Moreover the settlements along the seacoast towards the Western Ghats had their prominence to maritime relationship with Sumeria. An ancient port having flourishing maritime trade namely, Mamallapuram or Mahabalipuram is located on the shore of the Bay of Bengal and was the chief sea port of the Pallavas ruling over South India during the 1st century BC to 8th century AD. It has been recognized as the site of the greatest sculptural and architectural achievement in India. It was during the reign of Narasimha Varman, that this seaport began to grow as a great artistic centre and Mamallapuram is now a world heritage site as well as a testimony of the early Dravidians style of architecture. Most of the well known dynasties namely Chola, Chera and Pandya which reigned during the 4th century had maritime trade with countries like Far East Burma, Java as well as other Indo Chinese region while the Pallava dynasty ruled during the 4th century.

During the Medieval Cholas reign, the Chola Navy grew both in size and stature and their Admirals were treated with prestige and respected in the society. Earliest record of naval function dates back to the 1st century in the Roman report which presently is known as Poombuhar, where a description is made on how the trade vessels were escorted by the King’s fleet to the natural harbor at the mouth of the river Kaveri. Activities on the existence of maritime is derived from some excavated wooden plaques portraying naval engagements in the location of the old city and some knowledge into the naval activities of the Cholas has been derived from Periplus of the Erythrean Sea. Description from this unknown author relates the activity of escort ships assigned to merchant vessels with valuable cargo where these early naval ships had a kind of rudimentary flame thrower or a catapult type of weapon.

Great ships like the Colandia were used by the early Cholas which was used to sail to the Pacific islands from Kaveripatnam as a center. With the rise of the Vijalaya dynasty the Chola navy took shape in the aftermath of the Chola power and during the Pallavas’ rule took control of the territories as well as the cultural and socio economic affairs thus inheriting dominance over trade and control over seas from the Pallavas. Serious efforts during the reign of the Pallava king, Simavishnu, was done to control the piracy in South East Asia, to establish a friendly Tamil regime in the Malay peninsula though this effort was only accomplished three centuries thereafter by the new Chola naval power. The Cholas also excelled in maritime activity and foreign trade spreading their influence towards China and Southeast Asia and an inscription dated 1088, was found in Sumatra in the Chola country which indicates that there was an active overseas trade during the Chola period. At the end of the 9th century, southern India progressed extensively in maritime and commercial activity especially with the Arabs and the Chinese and the Cholas having control over the west as well as the east coasts of peninsular India were at the forefront of all these ventures.

ancient shipbuilding
Their main trading partners were the Tang Dynasty of China, the Srivijaya Empire in the Malayan archipelago under the control of the Sailendras and the Abbasid Kalifat at Baghdad. Trading with the Chinese was a very profitable enterprise and the traders needed the approval from the king and the license from the customs force department for overseas voyages in trading. The duration for normal trade voyage required three legs of journey beginning with Indian goods of spices, cotton and gems shipped to China with the return journey with Chinese goods of silk, incense and iron which were brought back to the Chola ports. Some of these materials were used for local consumptions while the remaining cargo along with Indian cargo was shipped to the Arabs where this transfer involved material cargo to many ships before they reached the final destination.

Ancient Chola navy’s trade vessel designs were upgraded to boarding implements which changed throughout history and the later navy was a specialized force with built ships suitable for any type of combat. In addition to the regular navy namely the Kappal-Padai, they had many auxiliary forces which could be used for naval combat. The Army depended on the Naval-fleets for logistics and transportation. Besides this, the Chola Navy also had autonomous service, a core for marines as well as saboteurs who were trained pearl fishermen and dived to disable enemy vessels by destroying or damaging the rudder.

 The Chola would also undertake peace time patrol, escort trade conveys and friendly vessels. They would also undertake naval battle close to home ports and at high seas, establish a beach head or reinforce the army whenever the need arose, denied passage for allies of the state’s enemies and sabotage the vessels of the enemies. Their multi dimensional force prepared the Cholas to achieve the political, military as well as cultural control over their huge dominion. The supreme commander was the king or the emperor of the entire navy and military force.

Monday, November 11, 2013

History mystery: Shiva - God of Dravidians or Aryans?

Shiva - Pasupathi
There is much controversy about the Aryans and the Dravidians where some debate that the Dravidians were a race who were aborigines of Indian subcontinent while others say they migrated into India. The Aryans on the other hand migrated to India from Central Asia forcing the Dravidian towards the South. The physical character of the Dravidians were short in height, well versed with urban culture, of black complexion and were the followers of Lord Shiva while the Aryans who were well built, of white complexion, rural inhabitants, were the worshippers of nature. With constant fight going on between them, the Aryans pushed the Dravidians down towards the banks of the River Sindhu, southwards and settled in the Northern plains of India. There were lots of contradiction with the Aryan Dravidian race theory, the latest being that the Indus Valley civilization, the actual Saraswati valley civilization and the river Saraswati, the lifeline of the people had dried up which caused them to move out of that area to a more fertile East and South territory.

Shiva of Gandhara
As far as their belief was concerned, the advocates of invasion theory state that the inhabitants of Indus Valley were Saivites – Shiva worshippers and since Saivism is more prevalent among South Indians, the conclusion is that the inhabitants of Indus valley region could have been the Dravidians and worshippers of Shiva else Pasupathi. The Aryan Vaishnavites, the star calendar used by them was adopted from the Semito Dravidian Indus Valley Civilization since it is not referred in the Rig Veda or Avesta and before the Aryans came to India it was compiled when the Indus Valley was at its peak.

Hinduism is a subject with many interpretations and to some it may appear to be confusing. Contradictions are seen in every scripture in the world and Hindu scriptures also contain some contradictory ideas which have been stemmed from different ideas right from its development of primitive to the present religion. Hinduism, considered as a culture and way of life as well as a religion started around 3000 BC with the Indus River civilization and the Sindh Indo Pakistani region and the two cultures blended together to form the beginning of Hinduism with the Aryans of the north and Northwest regions of India and the Dravidians presumed to be of central Asian origin, of south India.

As Indra was Aryan war lord and all hymns have been dedicated to him, studies show that Shiva was a non Aryan king who fought the Aryans. Shiva worship is also known in the Vedic culture and is not only restricted to South India, but some of the important holy places for Saivites are also located in North India where the traditional holy residence of Lord Shiva is Mount Kailas which is situated to the far north. The ancient Dravidian worship, developed into a six fold religion and the worship of Sivalinka developed in different angles. There are various theories about the proper origin of the world Dravida which is a Sanskrit word and according to scholars could be the formation of the Tamil word while others say that the word Dravida may have originated from Sanskrit – Drava which could be related to water or sea and the root word for this is Drava in Sanskrit, signifying that the people of India lived nearer to the sea. The Tamils started using the word Dravida only in the 9th century AD in the context of the linguistics and the Tamil lexicon called Senthan Divakaram used Dravidam to denote Tamil.  The Dravidians are presumed to be the composers of religious treatises and hymns in Tamil language as well as the founders of magnificent and amazing stone temples all over India. They also prospered in many kingdoms and the temples established by them got religious importance by visitors of Hindu religious heritage.

They also influenced Hinduism which is evident especially in the South. Besides this, many elements of the Tantra are their heritage while many of the rites are traceable to their earliest culture and the Dravidians are the ones who have made their contribution to the philosophy of non dualism of Lord Shiva. They have contributed to the cult of Lord Shiva, the worship of Shakti, the Mother Goddess as well as the institution of Yoga and have given us several symbols connected with these gods and goddesses. The worship of Shiva in the form of a lingam or linga is depicted in various forms and one common form is the shape of a vertical rounded column. The meaning of Shiva is auspiciousness and linga means a symbol or sign and Shivalinga is considered as a symbol of the great God of the universe who is auspicious. Moreover Shiva also means – one in whom the whole creation sleeps after dissolution and linga – a place where created objects are dissolved during disintegration of the created world. According to Hinduism, since Shivalinga represents God himself, it is the same god that creates and sustains the universe. One of the famous Indian temples dedicated to Shiva is in Kashi, Varanasi where he is worshipped as Visvanath who is considered as the God of all lands and there are twelve jyotirlinga temples in various locations of the country. Temples featuring architecture mainly in the South have been the origins of the Dravidians. In South the famous Shiva temples are in Tiruvannamalai, Tirunaikaval, Srikalahasti and Chidambaram.

Other important temples of Shiva worship are Meenakshi Amman temple in Madurai, Brihadeeswarar temple in Thanjavur, and Nellaiappar temple in Tirunelveli. With regards to the Hindu culture, much of its basis has been the contributions of the Dravidians and the language adopted by them was Sanskrit. Moreover, they have also made contribution to important elements of the religious emphasis, the manners and customs, social structure, the arts which constitute the Hindu civilization. They have also given us many great philosophers like Shankar together with great products of artistic genius by way of dance and temple architecture and the sect known as Shaivism. Dravidian, the native Indian communities were the founder of Hindu religious and social systems. It was the Dravidians that had established a particular civilization known as the Dravidian civilization and according to some scholars, the speaker of proto Dravidian language were the founder of the Dravidian civilization. This civilization was presumed to be in existence much before the advent of the Indo Aryans in India. This pre Vedic civilization is the civilization of the people who spoke proto Dravidian language. The great mass of Dravidians deities, rites and superstitions had become a part of Hinduism and the Dravidians were very much involved as far as their religious rites were concerned and in most manners, there were links between Hinduism and the original Dravidian worship. According to some historians the proto Dravidians were part of a large Elamo Dravidian language while others were preceded in the subcontinent by Austro Asiatic people who were followed later by Indo European speaking migrants.

Other theories of Dravidian origin was propagated by Sir William Hunter who states that there were two branches of Dravidians namely Kolarians speaking dialects and the proper Dravidians which belonged to the Tamil section. While the first group entered India from north east, they occupied the northern part of Vindhya and this theory is considered obscure. Shaivism was indigenous while vaishnavism was imported and in earlier times both were competitive temporal philosophies. During the reign of Chalukyas’ rule in the peninsular towards 1000 to 2000 AD, there were instances of kings patronizing shaivism and prosecuting the vaishnavites and it was alleged that one of the Chalukya king, had removed the statue of Lord Vishnu from the Shiva shrine at Chidambaram and history relates that Shiva was the most revered deity of ancient India. Over a period of time, this competition between shavites and vaihnavites diminished and both of them merged to create Hinduism. Unless we take into account the food habits, folklores, dresses, traditions, customs and lingual dialects, the excavations of archaeological sites as well as the historical monuments do not relate the true tale of history making it an oral history besides written history. Based on the judgment of artifacts discovered only relates a disconnected and disconcerted information while most of the Indian history has been interpreted on the basis of potteries and metal works and the period have been assigned through a process of elimination. After the excavations at Harappa, ancient history has become prone to plenty of reasoning and arguments over Harappa being a pre Vedic or a post Vedic.

Wednesday, November 6, 2013

History mystery: Apollo’s Numbers – Part I

Many stories are told about the Greek scholar, Richard Porson who was born in 1759 and was educated at Eton and Trinity College, Cambridge and held the Regius Professorship of Greek till his death in the year 1809. He invited anecdotes and at times was ridiculed for his Dipsomaniacal conduct. Porson had a wonderful sense of humor which was invoked by the Trinity Combination Room which had the custom of permitting smoking during the twelve days of Christmas and one of the wittiest stories in connection with him was his habit of always taking toddy to bed.

Plato too enjoyed intellectual witticisms and Plato’s Ion dialogue is full of intellectual witticisms, with many references and allusions to Apollo, though his name is not mentioned. Ion in its eponymous term in connection to Ionians is related to Apollo. The dialogue Ion composed by Plato was about joke and riddle and in ancient Hellenic world it was assumed that every learned person would be familiar with the lyre and its basic theory and its tune. The rhapsode Ion had come from a festival of Asklepios, a city of Epidaurus which had a shrine of Apollo while Asklepios was another son and both were born out of wedlock. The festival had all the arts of music and Apollo presided over it.

Ion after winning the first prize in the competition got engaged with Socrates in a philosophical discussion where he admitted when asked by Socrates that his skill in performance recitation was limited to Homer and all other poets bore him. This puzzled Socrates which led him to solve the riddle of Ion’s limited expertise and informed him that art critics and judges of sculpture do not limit themselves to judge the work of single artist but criticize the art irrespective of the artist. To understand the dialogue Ion, one needs to read it which is a continual reminder of Apollo though he is not mentioned in it and the understanding is in the ancient tuning theory where the comprehension could probably be in the present acoustics or harmonics, though it is not concerned with composition or performance, on the contrary, it deals instead with arithmetical structure of the tones, scales and intervals connected in music.

Present musical instruments are made in terms of the historically developed tuning theory which is described with regards to the terms associated with it though the instrument does not explain the theory but embody and illustrate it. Modern musical terminology is the result of the long complicated history, details of which are not understandable. For those interested in tuning theory, the following brief preliminary details could be helpful. Platonist, Plutarch, who for twenty years of his life was a priest at Delphi and had taken an oath of secrecy, wrote with knowledge on what he could not reveal though he provided us with his helpful hints.

His most relevant hints are found in Isis and Osiris wherein he informs that sixty is the first of measures related to the heavenly bodies that is with science, astronomy and harmonics. Second being The E at Delphi, he goes on to tell us that Pythagoreans called five, the marriage number, stating that it is an attribute of the god Apollo and that it is confirmed by the importance of the number in music. He states that the right angled triangle – 3, 4, 5 is used in the Republic in formulating marriage number and 3 is the male number while 4 is the female number. The number 5 is in some ways like its father and mother since they are made up of 3 and 2 making 5 the human number.

The number sixty derived from the ancient Babylonian use of sexagesimals, is the base of all scientific work. The number five, an attribute of Apollo, an importance in music, together with sixty is the human number which is also designated with the letter E in the Greek alphabetized system of numerals and carved in wood, stone, metal in Apollo’s temple at Delphi. The combination of sixty and five results in 60 to the 5th power, 605 or 777,600,000, regarded as Apollo’s number, intimated by Plutarch though it is not certain and may have been known at Delphi.

This number is most important in tuning theory being the least number needed in tuning with spiral of fifths and coordinating the sexagesimal as well as decimal expression of tones involved and hence it is given the title of Apollo’s number. As per the ancient practice, the zeros have been omitted and we have 6 to the fifth power 65 or 7776.

The Ion has 7776 syllabus as per Plato’s joke and since Apollo being the whole of it, is not needed to be named in the dialogue and the joke is in the form of an enigma. People often became famous by solving and making up riddles which were obscene and Plato was obscure and could not be obscene. Apollo was thus connected with riddles while riddles were philosophy. Having musical knowledge, Plato knew the number 605 though it is not mentioned in the dialogues but 604 is mentioned in the Republic- Book VIII, the sovereign of better and worse births in the Critias – the foundation of the mathematical model of Atlantis. Dating back to ancient Greek tuning theory, the most clearly associated name is Pythagoras, born on the Ionian island of Samos, migrated to Crotona and later died in Metapotum in Magna Graecia (Italy) around 497.

 He was the first Greek who provided a scientific basis for music theory. Musical performers did not need the development of theory. Performers played either on aulos which were translated as flute, which was an impossibility, since it was a reed instrument and could be a single or a double reed or a form of the lyre. The greatly preferred instrument was the lyre by amateurs since it had the advantage over the aulos where the player could sing to one’s accompaniment and besides this it was also Apollo’s instrument who had accepted this as a gift from his younger brother, Hermes.

Sunday, November 3, 2013

Insight on the Concept of Mpemba Effect

Mpemba Effect

The Mpemba effect is the assertion that warmer water can freeze faster than cold water and is so named after a Tanzanian student, Erasto Mpemba from Africa. His first encounter with this phenomenon started in 1963 in Form 3 of Magamba Secondary School while freezing ice cream mix which was hot initially and his observation that it froze before the cold mix. On upgrading from his O level examinations, he went on to be a student of Mkwawa Secondary School in Iringa, Tanzania where the headmaster invited Dr. Denis G. Osborne from the University College, to conduct lecture on physics after which, Mpemba put forward a question asking why, when two similar containers with equal volume of water, one at a temperature of 35 degrees Cent; and the other at 100 degrees Cent; when placed in the freezer, the one with 100 degrees Cent; freeze first.

For this, Erasto Mpemba was ridiculed by his classmates as well as his teachers, but after initial confusion, Dr. Osborne experimented back at his workplace and confirmed Mpemba’s finding and the results were published in 1969. To understand the factors involved in how the water freezes will help to explain the Mpemba Effect. Here the temperature is the factor in water freezing and the temperature of water in the container is the average energy of its molecules where the heat of the water is defined as total amount of energy of its molecules. The heat depends on the content of the water and how many molecules are present in the container.
The change takes place when a container of water is placed in the refrigerator, in the freezer compartment, the water first cools and then freezes. When the temperature of the water drops down, the heat of the water – energy of the water molecules reduces and at this point, when the temperature reaches 0 degrees cent; the water changes from the liquid to a solid state. A point to be noted here is that the temperature of the water keeps dropping till it reaches freezing point and stays at 0 degrees cent; until the water becomes solid. When the water has turned into ice, its temperature can tend to be lower if the air temperature is lower. Most of the cooling is done through conduction, where the container is in direct contact with cold material namely the freezer shelf and gets cold thereby cooling the contents by conduction. Since metal is a good conductor, a metal container would quicken the cooling of water by conduction while wood is a poor conductor of heat.

Air which is in contact with the container as well as the water transfers heat to the cooler air through conduction which helps in lowering the temperature of the water. Convection is the transfer of energy through movement of currents of liquid which can be seen while heating a vessel of water on a stove, the effects which can also be seen on a cold windy day. Cold water being denser than warm water, will sink to the bottom of the vessel causing convection currents during freezing process and when the temperature reaches below 4 degrees cent; it tends to get less dense and float to the top till it finally freezes. Air convection also helps to move the cold air around so that the water gets cooled through air convention.

Evaporation is also another factor which helps the warm water to freeze quicker than cold water since the evaporation from hot or warm water is more, than in cold water and the during the evaporation process it carries some of the water resulting in less water to freeze in a particular container though it causes the temperature to drop due to heat loss in the warm container. Dissolved gases are another possible factor which has the effect of lowering the freezing point and water always has these impurities in the form of oxygen and carbon dioxide. As the water gets heated, the gases escape because they are less soluble in water at higher temperature and when hot water cools with less dissolved gas, it has a higher freezing point and freeze fast than the water which is not heated.

With the knowledge on the factors that are involved in the freezing process, it has been concluded that the Mpemba Effect takes place based on conduction, convection, evaporation, and dissolved gases. Another theory is that, frost can slow down the cooling process and if hot water is kept in the freezer in a container which is a good conductor of cold or heat, the heat of the container can melt away the frost that is collected on its surface including the ice at the bottom which when refreezes creates a good connection between the container and the surface. This provides a good conduction of cold than a container with cold water having frost on its surface as well as at the bottom, resulting in heat being drawn out from the warm container more quickly than with cold water in it. As the layer of frost at the surface can slow down the process of conduction of heat from the water, a layer on the surface on the upper side of the water can insulate water from colder air currents.