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Throughout human history there have been worldwide events that have stimulated and defined civilization and culture. The relatively simultaneous development of art, craft, agriculture, building and materials technology, military strategy, and religion in disparate areas of the globe represent a form of cultural punctuated equilibrium. Throughout the continual process of investigation, discovery, and adaptation, creation mythology became the definitive cultural narrative in every society. Determining our origin and purpose are necessary pursuits in maintaining collective and individual identity, and restructuring that narrative has been an evolving chronicle since the Upper Paleolithic era 40,000 years ago. Star gazing remains an awe-inspiring activity and determining the motion of heavenly bodies became a priority throughout recorded history. Bone engravings from the Upper Paleolithic dating around 33,000 BCE (Before Current Era) calculate the total number of days throughout the phases of the moon.
The earliest cave drawings of apparent moon-month notation from around 9,000 BCE. The first image from Abris de las Vinas, Spain, shows a figure surrounded by spherical shapes that may indicate counting off nights of the quarter moon. The second image from Canchal de Mahoma, Spain, has 27 shapes that change from spheres to crescents and surround a central figure or other reference point.
Cave drawings, possibly of the sun, from La Pileta, Spain (circa 12,000 BCE)
Images from Lascaux cave in France (dated 17,000-27,000 BCE) show a graceful, sophisticated artistry
Although all organisms have complex social structures that promote group cohesion and survival, the human species is continually discovering and cataloguing information about the natural world. The accumulation of knowledge (and its ability to transform perception) constantly generates new cultural paradigms. Assimilation and adaptation of traditional social customs is characteristic of many cultural transformations. Life responds and adapts to internal, environmental, and social pressures - a new temple is built upon an old, an ancient myth acquires new interpretation, a new civilization evolves. This activity is organized upon the prime directive for all earthly organisms: The entirety of life is based on reproductive strategy. Central to this is controlling territory and resources to ensure survival of the group (genome). In the human species, this process is has been facilitated, contrived, and enforced by creation mythology and cultural narrative.
The artist must know not just the rules of perspective, but all the laws of nature. The eye is the perfect instrument for learning these laws, and the artist the perfect person to illustrate them. Leonardo da Vinci
As we probe deeper into the intricacy and complexity of nature, the scientist has developed instruments that surpass what the eye conveys. The language of mathematics is the language of Nature, and is perhaps the most powerful tool we have developed to describe our universe. Today, the pursuit of knowledge and understanding the parameters of Nature (through science and art) are the most powerful social tools that provide choice in direction and development.
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In the Beginning
Sumer was one of the earliest known civilizations with written language in the form of cuneiform tablets. The Sumerians arrived in the Tigris-Euphrates valley from Central Asia in approximately 5500 BCE and supplanted the existing settlements of the Ubaidians. Located in the southern part of Mesopotamia (now southeastern Iraq) this area is referred to as the "cradle of civilization" in the Eastern hemisphere. Art, crafts, architecture, mathematics, and religious expression flourished in Sumer.
Early Mesopotamian Astronomy "The Babylonian astronomers also served as priests who fostered the continuity of astronomical knowledge. But religion divorced Babylonian cosmology, the grand picture of the universe, from astronomy. In the cosmic picture, the gods created, ordered, and controlled the world. These divine functions were explained in religious myths. Because tables of astronomical cycles functioned strictly for predictions and lacked any geometric or physical framework, Babylonian astronomers could predict but not explain celestial motions in terms of physical causes. They never developed actual scientific models of the heavens, just records of their patterns..."
Sumerian mythology included the familiar theme of the Garden of Eden. Dilmun is the mythical divine garden wherein the ruling goddess Ninhursag cultivates eight plants (and condemns but ultimately forgives the transgressor Enki for stealing and eating some of them). The Sumerian word for rib, ti, means "to make live." Every aspect of the biblical Garden of Eden is appropriated from Sumerian narrative. These concepts, the Great Flood, and other biblical tales of Sumerian origin represented a cultural adaptation of the dominant narrative. The mythologies of early cultures initially reveal a universe created by a singular goddess, to a universe born of the Great Goddess and her male consort, to one created from the slain body of the Great Goddess by a male god, and finally, the demise of the goddess principle in the bible. This process was literally thousands of years in the making through constant manipulation and syncretism of the existing narrative. Consequently, the replacement of Pagan celebrations with Christian holidays helped to facilitate the acceptance and spread of Christianity. Every culture uses a variety of devices to proclaim and maintain its position in the world and cosmos. The proclivity to manipulate the geographical and sociopolitical environment is a hallmark characteristic of human activity, but the ability to develop complex symbolic systems that describe the mechanisms of nature is perhaps the ultimate intellectual achievement.
Ziggurat ruins at Chogha Zanbil, Iran
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From The School of Mathematics and Statistics at the University of St Andrews website:
It was an important task for the rulers of Mesopotamia to dig canals and to maintain them, because canals were not only necessary for irrigation but also useful for the transport of goods and armies. The rulers or high government officials must have ordered Babylonian mathematicians to calculate the number of workers and days necessary for the building of a canal, and to calculate the total expenses of wages of the workers...
The Egyptians were very practical in their approach to mathematics and their trade required that they could deal in fractions. Trade also required multiplication and division to be possible so they devised remarkable methods to overcome the deficiencies in the number systems with which they had to work. Basically they had to devise methods of multiplication and division which only involved addition.
The Moscow papyrus dates from Egypt about 1850 BC. The problems are mostly practical but a few are posed to teach manipulation of the number system itself without a practical application in mind. It also contains geometrical problems.
The first thing to understand about ancient Chinese mathematics is the way in which it differs from Greek mathematics. Unlike Greek mathematics there is no axiomatic development of mathematics. The Chinese concept of mathematical proof is radically different from that of the Greeks.
By the fourth century BC counting boards were used for calculating, which effectively meant that a decimal place valued number system was in use. It is worth noting that counting boards are uniquely Chinese, and do not appear to have been used by any other civilization.
Recent research paints a new picture of the debt that we owe to Arabic/Islamic mathematics. Certainly many of the ideas which were previously thought to have been brilliant new conceptions due to European mathematicians of the sixteenth, seventeenth and eighteenth centuries are now known to have been developed by Arabic/Islamic mathematicians around four centuries earlier. In many respects the mathematics studied today is far closer in style to that of the Arabic/Islamic contribution than to that of the Greeks...
Mayan mathematics
A common culture, calendar, and mythology held the civilisation together, and astronomy played an important part in the religion. Astronomy and calendar calculations require mathematics, and indeed the Maya constructed a very sophisticated number system. We do not know the exact date of these mathematical achievements but it seems certain that when the system was devised it contained features that were more advanced than any other in the world at the time...
This calendar sculpture depicts a Mayan God of Time carrying the burden of time on his back.
Read more about mathematics in various cultures
History of Astronomy From The Department of History and Philosophy of Science of the University of Cambridge
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After the decline and fall of the Roman Empire in 476 CE (Current Era), The last emperor (Romulus Augustus) was deposed by the German warrior Odoacer. The Catholic Church became a major unifying cultural influence after the Fall, and maintained a centralized administration through a network of bishops. It is no wonder that this remaining vestige of the glory of Rome became pivotal during the early European Medieval era (formerly regarded as the Dark Ages - approximately 476-1000 CE). The Christian Bible represented the irrefutable word of god - the ultimate trump card and signifier of ultimate authority. Further inquiry into the mechanisms of life was considered unnecessary with this definitive text. It was also improbable, given the state of affairs in the "civilized" Western world. The Church, Bible, and word of God maintained some semblance of cohesion and power on a fundamental level after the cultural turmoil of the Fall.
"When...the question is asked what we are to believe in in regard to religion, it is not necessary to probe into the nature of things, as was done by those whom the Greeks call phycisi; ... It is enough for the Christians to believe that the only cause of all created things...whether heavenly or earthly...is the goodness of the Creator, the one true God." From City of God, St. Augustine 415 AD
(So much for the prime directive of curiosity and discovery...obviously not an option for the intellectuals of the tribe).
During the European Medieval era, China invented paper, gunpowder, and the compass. The Chinese printed books using movable type in 1050 CE. They believed that the motions of the heavens and actions of people were inextricably linked, and royal astronomers watched for any celestial irregularities that might affect the emperor and kingdom. The result of this vigilance is a continuous record of astronomical events that included the appearance of a "guest star" in 1054 CE - the supernova explosion that created the Crab Nebula. This knowledge of constant astronomical transformation was in stark contrast to the Greeks, who believed the heavens were static. (The 1054 supernova event was virtually ignored in Western records).
Chinese paper making process / Compass / 1054 AD "guest star" (aka Crab Nebula)
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Also during Europe's Medieval era, Arabia achieved major advances in medicine, science, mathematics, and astronomy. Ibn al-Haytham, or Alhacen, (965–1039 CE) was a Muslim astronomer, engineer, mathematician, and scientist. He supported the heliocentric model of the solar system, established the use of scientific experiments, and invented the first pinhole camera (in addition to making other contributions to the principles of optics).
India devised the decimal numeral system, including the concept of zero, during the reign of the Guptas (320 to 600 CE).
However, the Ages weren't entirely Dark in Europe during this period - there was an emphasis on illustrating and writing manuscripts; innovations in architecture, painting, and crafts; and literacy was becoming a social force. By the High Middle Ages (1100-1300 CE) philosopher/theologians such as William of Ockham and Thomas Aquinas were discussing systems of logic, ethics, natural and political philosophy, and the relationship between faith and reason. Universities were being established, further eroding the authority of the church. In the Late Medieval Ages (1300–1500 CE) the conflict between the Holy Roman Emperor and the Pope concerned who would control Christendom in secular issues. The illiterate needed to know the stories in the bible, so churches began commissioning artists to represent these stories on the walls. By extension, the development of perspective in art is considered another catalyst for the Renaissance. A function of narrative is perception, and the rendering of geometric perspective in the early 14th century had a profound emotional and visual impact on the viewer.
A renewed interest in the art, philosophy, science, architecture, and education of classical antiquity stimulated a cultural transformation in the European Renaissance. It is important to note that the survival of classical Greek studies is the result of its preservation by the Muslim world from about the 8th Century. Greek ideals included order and linearity, and visual art was represented on a single plane in vase paintings and murals. When this convention was breached with the development of visual perspective in Florence, Italy, the viewer stood as an individual on a cultural precipice.
Giotto's skill in early perspective revolutionized the flat, two dimensional representation of imagery that dominated medieval manuscripts and painting. His interest and study of conic sections (the ellipse, parabola, and hyperbola) came from Archimedes via Euclid's lost work on these geometrical forms. The force of three dimensional perspective captured time and space in an accurate, eternal instant. This rendering of the spacetime continuum is obvious and ordinary now, but it was absolutely revolutionary and unprecedented in the purview of human experience at the time. Three hundred years later, Kepler would refer to Renaissance artists for his discovery of planetary motion. Six hundred years later, Manet would deconstruct perspective/reality as a prescient of Einstein's Special Theory of Relativity. But we're getting ahead of ourselves, so to speak.
Giotto greatly influenced Masaccio, (1401-1428) who was considered the first significant painter of the Renaissance.
The Tribute Money, Masaccio 1424
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| Michelangelo self portrait |
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| Pieta Michelangelo Buonarroti, 1498/9-1500 |
Sketch and image from the Sistine Chapel
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There is perhaps no other individual that personifies the transformative power of the Renaissance than Leonardo da Vinci: (1452–1519) scientist, mathematician, engineer, inventor, anatomist, painter, sculptor, architect, musician, and writer.
Leonardo's investigations into science and engineering were as prodigious and innovative as his art. He was constantly observing, recording, and inventing. His notebooks have 13,000 pages of drawing, notes, and inventions for flying machines, parachutes, and defense systems. Art and science were not viewed as separate disciplines, and his work combined art and natural philosophy (the objective study of nature). This contributed to the foundation of modern science.
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Printing Press
Printing was first conceived and developed in China and Korea. The oldest printed book using woodblock printing, a Korean Buddhist scripture, dates to 751 AD. The oldest surviving book printed using block printing, the Chinese Diamond Sutra, dates to 868. The movable type printer was invented by Bi Sheng in 1041 during Song Dynasty China. The movable type metal printing press was invented in Korea in 1234 by Chwe Yoon Eyee during the Goryeo Dynasty -216 years ahead of Gutenberg in 1450. By the 12th and 13th century many Chinese libraries contained tens of thousands of printed books.
In 1440, German goldsmith and inventor Johannes Gutenberg invented a printing press with technologies of paper, oil-based ink, and the wine-press to print books. Prior to this, the time-consuming process of pressing paper to inked woodblocks was used for printing in the Western world. This invention allowed the mass production of books and the resulting proliferation of ideas and ideologies.
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Nicolaus Copernicus (1473-1543) was a Polish polymath and the first European astronomer to formulate a modern heliocentric theory of the solar system. Aristarchus of Samos, a Greek astronomer and mathematician, proposed a Sun-centered Universe in the 3rd century BC (in addition to other astronomers throughout history). The heliocentric model was rejected by Ptolemy and Aristotle, and their geocentric theory became the "standard model" for 2000 years.
Copernicus published De revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres) in 1543. This concept was in conflict with the teachings of the Church, which stated the Earth was the center of the Universe, the Celestial Spheres held the planets, and Heaven existed beyond the Spheres. Contradicting the Bible was blasphemy, but the analytical train had left the station, and nothing on earth or in heaven could stop it.
Heliocentric solar system
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Although Copernicus had determined the proper description of the solar system, the Greek ideal form of the sphere plagued the idea of the movement of planets around the sun. It was not conceivable that god would create irregular shapes or motion that contradicted the perfection of the circle. The elliptical path of the planets was the discovery of Johannes Kepler (1571–1630) a German mathematician, astronomer, and astrologer. Kepler lived in an era when astrology and astronomy were not unrelated, and the church was reasserting authority with Counter-Reformation tactics of the Inquisition and censorship of prohibited books (Kepler's own mother was tried for witchcraft). Kepler served as Tycho Brahe's assistant and was then was appointed his successor as Imperial Mathematician, a position that included being Astrologer to Emperor Rudolph II. This was considered the most prestigious appointment in mathematics in Europe at the time. The division between fact and fantasy was a tenuous margin that manages to persist in the human frame of reference. Although the beauty and power of science eliminates unnecessary questions and simply 'wants the facts' - knowledge is power. Manipulation and appropriation of information for political agenda is inevitable.
Kepler developed the Platonic solid model of the Solar system in Mysterium Cosmographicum (1596) to explain the relative distances of the planets from the Sun in the Copernican System.
1. Planets move in orbits that are ellipses.
2. The planets move such that the line between the Sun and the Planet sweeps out the same area in the same area in the same time no matter where in the orbit.
3. The square of the period of the orbit of a planet is proportional to the mean distance from the Sun cubed.
An influence in Kepler's breakthrough was a German artist and mathematician, Albrecht Dürer (1471-1528). Dürer studied perspective and conic sections and wrote about them in 1525. He was a prolific artist mostly known for his woodcuts and engravings. Alberti wrote about problems in perspective in 1435, and discussed geometry and art as integral subjects. Kepler read books by written by artists to determine elliptical orbits and solved a centuries old problem.
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| Conic Sections |
Dürer self portrait (1500)
What distinguishes science from other disciplines is the scientific method. In Europe, it is credited to Galileo Galilei (1564 –1642) an Italian physicist, mathematician, astronomer, and philosopher. He improved the telescope and performed a variety of astronomical observations. In 1610, Galileo published an account of his telescopic observations of the moons of Jupiter, using this observation to argue in favor of the Copernican heliocentric model of the universe. This challenged the prevailing earth-centered Ptolemaic and Aristotelian models. The next year Galileo visited Rome to demonstrate his telescope to influential philosophers and mathematicians, and to let them see the four moons of Jupiter. In 1612, opposition arose to the Copernican system that Galileo supported, and the church condemned Galileo's model on the motion of the Earth as heresy. He went to Rome to defend himself, but in 1616, Galileo received a categorical admonition to neither advocate or teach Copernican astronomy. Scientific thought and analysis was in its infancy, and still struggles to survive under superstition, threat, and political device.
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| Galileo's drawings of the moon |
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| Galileo portrait by Leoni |
Galileo facing the Roman Inquisition, Cristiano Banti (1857)
The Renaissance was a period of tremendous insight and transformation in Europe after the Dark Ages. The innate human characteristics of curiosity, innovation, and triumph over all odds were restored through the study of Nature, the evolution of art, and through the power of objective analysis in science and mathematics. This enabled the distinction between the unknown and the unknowable. It is curious that those who lack the intellect to confront the exasperating intricacy of nature insist that everyone else should remain in the Dark Ages. They are their own best argument against evolution. Because of this insistence on ignorance, the current era can be characterized as the Dim Ages. The reader is encouraged to examine the patriarchal revolution and subsequent manipulation of cultural narrative.
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The Scientific Method developed by Galileo continued to be the guiding principle for scientists of all disciplines. The rigor of objective analysis combined with the power of mathematics created a new paradigm best characterized by two words:
PROVE IT.
The scientific method involves the following components:
- Pose a question about observed phenomena.
- Observation - a constant feature of scientific inquiry.
- Create a hypothesis that is consistent with what you have observed.
- Description of phenomena and process. Information must be reliable, repeatable, and relevant to the inquiry.
- Use the hypothesis to make predictions. Information must be valid for observations past, present, and future of given phenomena.
- Test those predictions by experiments or further observations and modify the hypothesis according to your results.
- Falsifiability, or the elimination of plausible alternatives. This is a gradual process that requires repeated experiments by multiple researchers who must be able to replicate results in order to corroborate them. This requirement, one of the most frequently contended, leads to the following: All hypotheses and theories are in principle subject to disproof. Thus, there is a point at which there might be a consensus about a particular hypothesis or theory, yet it must in principle remain tentative. As a body of knowledge grows and a particular hypothesis or theory repeatedly brings predictable results, confidence in the hypothesis or theory increases. (Obviously not a viable approach to those who seek to control the group through authoritative knowledge/power that can't be questioned. ie - hardware that resists the new software of continual inquiry).
For example, Newtonian gravity predicts that starlight will bend around a massive object, but the predicted effect is only half the value predicted by Einstein’s General Relativity postulates in his 1911 paper. Subsequently, during a solar eclipse, light deflection was observed by the change in position of stars as they passed near the Sun on the celestial sphere. The accuracy of the measurements was contested for fifty years until observations were made at the necessary radio frequencies that confirmed Einstein’s predictions.
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References:
Howard Bloom, The Lucifer Principle
Norriss Hetherington, Encyclopedia of Cosmology
C.L. Ruggles, Astronomy in Prehistoric Britain and Ireland
Leonard Shlain, Art & Physics
Lynn Margulis, E.O. Wilson, Nowak, Dawkins, Darwin, Gould....
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