HISTORY OF EARTH.

The history of Earth concerns the development of the planet Earth from its formation to the present day. Nearly all branches of natural science have contributed to the understanding of the main events of the Earth's past. The age of Earth is approximately one-third of the age of the universe. An immense amount of biological and geological change has occurred in that time span.

Earth formed around 4.54 billion years ago by accretion from the solar nebula. Volcanic outgassing probably created the primordial atmosphere, but it contained almost no oxygen and would have been toxic to humans and most modern life. Much of the Earth was molten because of frequent collisions with other bodies which led to extreme volcanism. One very large collision is thought to have been responsible for tilting the Earth at an angle and forming the Moon. Over time, the planet cooled and formed a solid crust, allowing liquid water to exist on the surface.

The first life forms appeared between 3.8 and 3.5 billion years ago. The earliest evidences for life on Earth are graphite found to be biogenic in 3.7-billion-year-old metasedimentary rocks discovered in Western Greenland and microbial mat fossils found in 3.48-billion-year-old sandstone discovered in Western Australia. Photosynthetic life appeared around 2 billion years ago, enriching the atmosphere with oxygen. Life remained mostly small and microscopic until about 580 million years ago, when complex multicellular life arose. During the Cambrian period it experienced a rapid diversification into most major phyla. More than 99 percent of all species, amounting to over five billion species, that ever lived on Earth are estimated to be extinct.Estimates on the number of Earth's current species range from 10 million to 14 million, of which about 1.2 million have been documented and over 86 percent have not yet been described.

Geological change has been constantly occurring on Earth since the time of its formation and biological change since the first appearance of life. Species continuously evolve, taking on new forms, splitting into daughter species, or going extinct in response to an ever-changing planet. The process of plate tectonics has played a major role in the shaping of Earth's oceans and continents, as well as the life they harbor. The biosphere, in turn, has had a significant effect on the atmosphere and other abiotic conditions on the planet, such as the formation of the ozone layer, the proliferation of oxygen, and the creation of soil.

Civilization

Throughout more than 90% of its history, Homo sapiens lived in small bands as nomadic hunter-gatherers. As language became more complex, the ability to remember and communicate information resulted in a new replicator: the meme. Ideas could be exchanged quickly and passed down the generations. Cultural evolution quickly outpaced biological evolution, and history proper began. Between 8500 and 7000 BC, humans in the Fertile Crescent in Middle East began the systematic husbandry of plants and animals: agriculture. This spread to neighboring regions, and developed independently elsewhere, until most Homo sapiens lived sedentary lives in permanent settlements as farmers. Not all societies abandoned nomadism, especially those in isolated areas of the globe poor in domesticable plant species, such as Australia. However, among those civilizations that did adopt agriculture, the relative stability and increased productivity provided by farming allowed the population to expand.

History of English

The History of English

The history of English is conventionally, if perhaps too neatly, divided into three periods usually called Old English (or Anglo-Saxon), Middle English, and Modern English. The earliest period begins with the migration of certain Germanic tribes from the continent to Britain in the fifth century A.D., though no records of their language survive from before the seventh century, and it continues until the end of the eleventh century or a bit later. By that time Latin, Old Norse (the language of the Viking invaders), and especially the Anglo-Norman French of the dominant class after the Norman Conquest in 1066 had begun to have a substantial impact on the lexicon, and the well-developed inflectional system that typifies the grammar of Old English had begun to break down.
The following brief sample of Old English prose illustrates several of the significant ways in which change has so transformed English that we must look carefully to find points of resemblance between the language of the tenth century and our own. It is taken from Aelfric's "Homily on St. Gregory the Great" and concerns the famous story of how that pope came to send missionaries to convert the Anglo-Saxons to Christianity after seeing Anglo-Saxon boys for sale as slaves in Rome:

Eft he axode, hu ðære ðeode nama wære þe hi of comon. Him wæs geandwyrd, þæt hi Angle genemnode wæron. Þa cwæð he, "Rihtlice hi sind Angle gehatene, for ðan ðe hi engla wlite habbað, and swilcum gedafenað þæt hi on heofonum engla geferan beon."

A few of these words will be recognized as identical in spelling with their modern equivalents—he, of, him, for, and, on—and the resemblance of a few others to familiar words may be guessed—nama to name, comon to come, wære to were, wæs to was—but only those who have made a special study of Old English will be able to read the passage with understanding. The sense of it is as follows:

Again he [St. Gregory] asked what might be the name of the people from which they came. It was answered to him that they were named Angles. Then he said, "Rightly are they called Angles because they have the beauty of angels, and it is fitting that such as they should be angels' companions in heaven."

Some of the words in the original have survived in altered form, including axode (asked), hu (how), rihtlice (rightly), engla (angels), habbað (have), swilcum (such), heofonum (heaven), and beon (be). Others, however, have vanished from our lexicon, mostly without a trace, including several that were quite common words in Old English: eft "again," ðeode "people, nation," cwæð "said, spoke," gehatene "called, named," wlite "appearance, beauty," and geferan "companions." Recognition of some words is naturally hindered by the presence of two special characters, þ, called "thorn," and ð, called "edh," which served in Old English to represent the sounds now spelled with th.
Other points worth noting include the fact that the pronoun system did not yet, in the late tenth century, include the third person plural forms beginning with th-: hi appears where we would use they. Several aspects of word order will also strike the reader as oddly unlike ours. Subject and verb are inverted after an adverb—þa cwæð he "Then said he"—a phenomenon not unknown in Modern English but now restricted to a few adverbs such as never and requiring the presence of an auxiliary verb like do or have. In subordinate clauses the main verb must be last, and so an object or a preposition may precede it in a way no longer natural: þe hi of comon "which they from came," for ðan ðe hi engla wlite habbað "because they angels' beauty have."
Perhaps the most distinctive difference between Old and Modern English reflected in Aelfric's sentences is the elaborate system of inflections, of which we now have only remnants. Nouns, adjectives, and even the definite article are inflected for gender, case, and number: ðære ðeode "(of) the people" is feminine, genitive, and singular, Angle "Angles" is masculine, accusative, and plural, and swilcum "such" is masculine, dative, and plural. The system of inflections for verbs was also more elaborate than ours: for example, habbað "have" ends with the -að suffix characteristic of plural present indicative verbs. In addition, there were two imperative forms, four subjunctive forms (two for the present tense and two for the preterit, or past, tense), and several others which we no longer have. Even where Modern English retains a particular category of inflection, the form has often changed. Old English present participles ended in -ende not -ing, and past participles bore a prefix ge- (as geandwyrd "answered" above).
The period of Middle English extends roughly from the twelfth century through the fifteenth. The influence of French (and Latin, often by way of French) upon the lexicon continued throughout this period, the loss of some inflections and the reduction of others (often to a final unstressed vowel spelled -e) accelerated, and many changes took place within the phonological and grammatical systems of the language. A typical prose passage, especially one from the later part of the period, will not have such a foreign look to us as Aelfric's prose has; but it will not be mistaken for contemporary writing either. The following brief passage is drawn from a work of the late fourteenth century called Mandeville's Travels. It is fiction in the guise of travel literature, and, though it purports to be from the pen of an English knight, it was originally written in French and later translated into Latin and English. In this extract Mandeville describes the land of Bactria, apparently not an altogether inviting place, as it is inhabited by "full yuele [evil] folk and full cruell."

In þat lond ben trees þat beren wolle, as þogh it were of scheep; whereof men maken clothes, and all þing þat may ben made of wolle. In þat contree ben many ipotaynes, þat dwellen som tyme in the water, and somtyme on the lond: and þei ben half man and half hors, as I haue seyd before; and þei eten men, whan þei may take hem. And þere ben ryueres and watres þat ben fulle byttere, þree sithes more þan is the water of the see. In þat contré ben many griffounes, more plentee þan in ony other contree. Sum men seyn þat þei han the body vpward as an egle, and benethe as a lyoun: and treuly þei seyn soth þat þei ben of þat schapp. But o griffoun hath the body more gret, and is more strong, þanne eight lyouns, of suche lyouns as ben o this half; and more gret and strongere þan an hundred egles, suche as we han amonges vs. For o griffoun þere wil bere fleynge to his nest a gret hors, 3if he may fynde him at the poynt, or two oxen 3oked togidere, as þei gon at the plowgh.

The spelling is often peculiar by modern standards and even inconsistent within these few sentences (contré and contree, o [griffoun] and a [gret hors], þanne and þan, for example). Moreover, in the original text, there is in addition to thorn another old character 3, called "yogh," to make difficulty. It can represent several sounds but here may be thought of as equivalent to y. Even the older spellings (including those where u stands for v or vice versa) are recognizable, however, and there are only a few words like ipotaynes "hippopotamuses" and sithes "times" that have dropped out of the language altogether.
We may notice a few words and phrases that have meanings no longer common such as byttere "salty," o this half "on this side of the world," and at the poynt "to hand," and the effect of the centuries-long dominance of French on the vocabulary is evident in many familiar words which could not have occurred in Aelfric's writing even if his subject had allowed them, words like contree, ryueres, plentee, egle, and lyoun.
In general word order is now very close to that of our time, though we notice constructions like hath the body more gret and three sithes more þan is the water of the see. We also notice that present tense verbs still receive a plural inflection as in beren, dwellen, han, and ben and that while nominative þei has replaced Aelfric's hi in the third person plural, the form for objects is still hem.
All the same, the number of inflections for nouns, adjectives, and verbs has been greatly reduced, and in most respects Mandeville is closer to Modern than to Old English. The period of Modern English extends from the sixteenth century to our own day. The early part of this period saw the completion of a revolution in the phonology of English that had begun in late Middle English and that effectively redistributed the occurrence of the vowel phonemes to something approximating their present pattern. (Mandeville's English would have sounded even less familiar to us than it looks.)
Other important early developments include the stabilizing effect on spelling of the printing press and the beginning of the direct influence of Latin and, to a lesser extent, Greek on the lexicon. Later, as English came into contact with other cultures around the world and distinctive dialects of English developed in the many areas which Britain had colonized, numerous other languages made small but interesting contributions to our word-stock.
The historical aspect of English really encompasses more than the three stages of development just under consideration. English has what might be called a prehistory as well. As we have seen, our language did not simply spring into existence; it was brought from the Continent by Germanic tribes who had no form of writing and hence left no records. Philologists know that they must have spoken a dialect of a language that can be called West Germanic and that other dialects of this unknown language must have included the ancestors of such languages as German, Dutch, Low German, and Frisian. They know this because of certain systematic similarities which these languages share with each other but do not share with, say, Danish. However, they have had somehow to reconstruct what that language was like in its lexicon, phonology, grammar, and semantics as best they can through sophisticated techniques of comparison developed chiefly during the last century.
Similarly, because ancient and modern languages like Old Norse and Gothic or Icelandic and Norwegian have points in common with Old English and Old High German or Dutch and English that they do not share with French or Russian, it is clear that there was an earlier unrecorded language that can be called simply Germanic and that must be reconstructed in the same way. Still earlier, Germanic was just a dialect (the ancestors of Greek, Latin, and Sanskrit were three other such dialects) of a language conventionally designated Indo-European, and thus English is just one relatively young member of an ancient family of languages whose descendants cover a fair portion of the globe.

History of Geometry.

Classic geometry was focused in compass and straightedge constructions. Geometry was revolutionized by Euclid, who introduced mathematical rigor and the axiomatic method still in use today. His book, The Elements is widely considered the most influential textbook of all time, and was known to all educated people in the West until the middle of the 20th century.
 
In modern times, geometric concepts have been generalized to a high level of abstraction and complexity, and have been subjected to the methods of calculus and abstract algebra, so that many modern branches of the field are barely recognizable as the descendants of early geometry.
 
The earliest recorded beginnings of geometry can be traced to early peoples, who discovered obtuse triangles in the ancient Indus Valley. Early geometry was a collection of empirically discovered principles concerning lengths, angles, areas, and volumes, which were developed to meet some practical need in surveying, construction, astronomy, and various crafts. Among these were some surprisingly sophisticated principles, and a modern mathematician might be hard put to derive some of them without the use of calculus. For example, both the Egyptians and the Babylonians were aware of versions of the Pythagorean theorem about 1500 years before Pythagoras; the Egyptians had a correct formula for the volume of a frustum of a square pyramid.
 
The ancient Egyptians knew that they could approximate the area of a circle as follows:

Area of Circle ≈ [ (Diameter) x 8/9 ]

The two problems together indicate a range of values for Pi between 3.11 and 3.16.
Problem 14 in the Moscow Mathematical Papyrus gives the only ancient example finding the volume of a frustum of a pyramid, describing the correct formula:

It is reasonable to expect that similar understanding would have been there in India." Dani goes on to say:

"As the main objective of the Sulvasutras was to describe the constructions of altars and the geometric principles involved in them, the subject of Pythagorean triples, even if it had been well understood may still not have featured in the Sulvasutras. The occurrence of the triples in the Sulvasutras is comparable to mathematics that one may encounter in an introductory book on architecture or another similar applied area, and would not correspond directly to the overall knowledge on the topic at that time. Since, unfortunately, no other contemporaneous sources have been found it may never be possible to settle this issue satisfactorily."

Modern geometry,

The 17th century

In the early 17th century, there were two important developments in geometry. The first and most important was the creation of analytic geometry, or geometry with coordinates and equations, by René Descartes (1596–1650) and Pierre de Fermat (1601–1665). This was a necessary precursor to the development of calculus and a precise quantitative science of physics. The second geometric development of this period was the systematic study of projective geometry by Girard Desargues (1591–1661). Projective geometry is the study of geometry without measurement, just the study of how points align with each other. There had been some early work in this area by Hellenistic geometers, notably Pappus (c. 340). The greatest flowering of the field occurred with Jean-Victor Poncelet (1788–1867).
In the late 17th century, calculus was developed independently and almost simultaneously by Isaac Newton (1642–1727) and Gottfried Wilhelm Leibniz (1646–1716). This was the beginning of a new field of mathematics now called analysis. Though not itself a branch of geometry, it is applicable to geometry, and it solved two families of problems that had long been almost intractable: finding tangent lines to odd curves, and finding areas enclosed by those curves. The methods of calculus reduced these problems mostly to straightforward matters of computation.

The 18th and 19th centuries

Non-Euclidean geometry[edit]

The very old problem of proving Euclid’s Fifth Postulate, the "Parallel Postulate", from his first four postulates had never been forgotten. Beginning not long after Euclid, many attempted demonstrations were given, but all were later found to be faulty, through allowing into the reasoning some principle which itself had not been proved from the first four postulates. Though Omar Khayyám was also unsuccessful in proving the parallel postulate, his criticisms of Euclid's theories of parallels and his proof of properties of figures in non-Euclidean geometries contributed to the eventual development of non-Euclidean geometry. By 1700 a great deal had been discovered about what can be proved from the first four, and what the pitfalls were in attempting to prove the fifth. Saccheri, Lambert, and Legendre each did excellent work on the problem in the 18th century, but still fell short of success. In the early 19th century, Gauss, Johann Bolyai, and Lobatchewsky, each independently, took a different approach. Beginning to suspect that it was impossible to prove the Parallel Postulate, they set out to develop a self-consistent geometry in which that postulate was false. In this they were successful, thus creating the first non-Euclidean geometry. By 1854, Bernhard Riemann, a student of Gauss, had applied methods of calculus in a ground-breaking study of the intrinsic (self-contained) geometry of all smooth surfaces, and thereby found a different non-Euclidean geometry. This work of Riemann later became fundamental for Einstein's theory of relativity.

 

It remained to be proved mathematically that the non-Euclidean geometry was just as self-consistent as Euclidean geometry, and this was first accomplished by Beltrami in 1868. With this, non-Euclidean geometry was established on an equal mathematical footing with Euclidean geometry.
While it was now known that different geometric theories were mathematically possible, the question remained, "Which one of these theories is correct for our physical space?" The mathematical work revealed that this question must be answered by physical experimentation, not mathematical reasoning, and uncovered the reason why the experimentation must involve immense (interstellar, not earth-bound) distances. With the development of relativity theory in physics, this question became vastly more complicated.

Introduction of mathematical rigor.

All the work related to the Parallel Postulate revealed that it was quite difficult for a geometer to separate his logical reasoning from his intuitive understanding of physical space, and, moreover, revealed the critical importance of doing so. Careful examination had uncovered some logical inadequacies in Euclid's reasoning, and some unstated geometric principles to which Euclid sometimes appealed. This critique paralleled the crisis occurring in calculus and analysis regarding the meaning of infinite processes such as convergence and continuity. In geometry, there was a clear need for a new set of axioms, which would be complete, and which in no way relied on pictures we draw or on our intuition of space. Such axioms, now known as Hilbert's axioms, were given by David Hilbert in 1894 in his dissertation Grundlagen der Geometrie (Foundations of Geometry). Some other complete sets of axioms had been given a few years earlier, but did not match Hilbert's in economy, elegance, and similarity to Euclid's axioms.

Analysis situs, or topology

In the mid-18th century, it became apparent that certain progressions of mathematical reasoning recurred when similar ideas were studied on the number line, in two dimensions, and in three dimensions. Thus the general concept of a metric space was created so that the reasoning could be done in more generality, and then applied to special cases. This method of studying calculus- and analysis-related concepts came to be known as analysis situs, and later as topology. The important topics in this field were properties of more general figures, such as connectedness and boundaries, rather than properties like straightness, and precise equality of length and angle measurements, which had been the focus of Euclidean and non-Euclidean geometry. Topology soon became a separate field of major importance, rather than a sub-field of geometry or analysis.

The 20th century.

Developments in algebraic geometry included the study of curves and surfaces over finite fields as demonstrated by the works of among others André Weil, Alexander Grothendieck, and Jean-Pierre Serre as well as over the real or complex numbers. Finite geometry itself, the study of spaces with only finitely many points, found applications in coding theory and cryptography. With the advent of the computer, new disciplines such as computational geometry or digital geometry deal with geometric algorithms, discrete representations of geometric data, and so forth.

Thats all Floks..!