The theory behind my username is quite simple. If you will just click the spoiler below...
Mathematics (from Greek μάθημα máthēma "knowledge, study, learning") is the study of quantity, structure, space, and change.[2] Mathematicians seek out patterns[3][4] and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. The research required to solve mathematical problems can take years or even centuries of sustained inquiry. Since the pioneering work of Giuseppe Peano (1858-1932), David Hilbert (1862-1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. When those mathematical structures are good models of real phenomena, then mathematical reasoning often provides insight or predictions.
Through the use of abstraction and logical reasoning, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that continues to the present day.[5]
Galileo Galilei (1564-1642) said, 'The universe cannot be read until we have learned the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth'.[6] Carl Friedrich Gauss (1777–1855) referred to mathematics as "the Queen of the Sciences".[7] Benjamin Peirce (1809-1880) called mathematics "the science that draws necessary conclusions".[8] David Hilbert said of mathematics: "We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules. Rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise."[9] Albert Einstein (1879-1955) stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality".[10]
Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, and practical applications for what began as pure mathematics are often discovered.[11]
Contents
[hide]
1 Etymology
2 History
3 Inspiration, pure and applied mathematics, and aesthetics
4 Notation, language, and rigor
5 Fields of mathematics
5.1 Foundations and philosophy
5.2 Pure mathematics
5.2.1 Quantity
5.2.2 Structure
5.2.3 Space
5.2.4 Change
5.3 Applied mathematics
5.3.1 Statistics and other decision sciences
5.3.2 Computational mathematics
6 Mathematics as profession
7 Mathematics as science
8 See also
9 Notes
10 References
11 Further reading
12 External links
Etymology
The word "mathematics" comes from the Greek μάθημα (máthēma), which means in ancient Greek what one learns, what one gets to know, hence also study and science, and in modern Greek just lesson.
The word máthēma comes from μανθάνω (manthano) in ancient Greek and from μαθαίνω (mathaino) in modern Greek, both of which mean to learn.
The word "mathematics" in Greek came to have the narrower and more technical meaning "mathematical study", even in Classical times.[12] Its adjective is μαθηματικός (mathēmatikós), meaning related to learning or studious, which likewise further came to mean mathematical. In particular, μαθηματικὴ τέχνη (mathēmatikḗ tékhnē), Latin: ars mathematica, meant the mathematical art. In Latin, and in English until around 1700, the term "mathematics" more commonly meant "astrology" (or sometimes "astronomy") rather than "mathematics"; the meaning gradually changed to its present one from about 1500 to 1800. This has resulted in several mistranslations: a particularly notorious one is Saint Augustine's warning that Christians should beware of "mathematici" meaning astrologers, which is sometimes mistranslated as a condemnation of mathematicians.
The apparent plural form in English, like the French plural form les mathématiques (and the less commonly used singular derivative la mathématique), goes back to the Latin neuter plural mathematica (Cicero), based on the Greek plural τα μαθηματικά (ta mathēmatiká), used by Aristotle (384-322BC), and meaning roughly "all things mathematical"; although it is plausible that English borrowed only the adjective mathematic(al) and formed the noun mathematics anew, after the pattern of physics and metaphysics, which were inherited from the Greek.[13] In English, the noun mathematics takes singular verb forms. It is often shortened to maths or, in English-speaking North America, math.
History
Main article: History of mathematics
Greek mathematician Pythagoras (c.570-c.495 BC), commonly credited with discovering the Pythagorean theorem.
The evolution of mathematics might be seen as an ever-increasing series of abstractions, or alternatively an expansion of subject matter. The first abstraction, which is shared by many animals,[14] was probably that of numbers: the realization that a collection of two apples and a collection of two oranges (for example) have something in common, namely quantity of their members.
In addition to recognizing how to count physical objects, prehistoric peoples also recognized how to count abstract quantities, like time – days, seasons, years.[15] Elementary arithmetic (addition, subtraction, multiplication and division) naturally followed.
Since numeracy pre-dated writing, further steps were needed for recording numbers such as tallies or the knotted strings called quipu used by the Inca to store numerical data.[citation needed] Numeral systems have been many and diverse, with the first known written numerals created by Egyptians in Middle Kingdom texts such as the Rhind Mathematical Papyrus.[citation needed]
Mayan numerals
The earliest uses of mathematics were in trading, land measurement, painting and weaving patterns and the recording of time. More complex mathematics did not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic, algebra and geometry for taxation and other financial calculations, for building and construction, and for astronomy.[16] The systematic study of mathematics in its own right began with the Ancient Greeks between 600 and 300 BC.[17]
Mathematics has since been greatly extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries continue to be made today. According to Mikhail B. Sevryuk, in the January 2006 issue of the Bulletin of the American Mathematical Society, "The number of papers and books included in the Mathematical Reviews database since 1940 (the first year of operation of MR) is now more than 1.9 million, and more than 75 thousand items are added to the database each year. The overwhelming majority of works in this ocean contain new mathematical theorems and their proofs."[18]
Inspiration, pure and applied mathematics, and aesthetics
Main article: Mathematical beauty
Sir Isaac Newton (1643-1727), an inventor of infinitesimal calculus.
Mathematics arises from many different kinds of problems. At first these were found in commerce, land measurement, architecture and later astronomy; nowadays, all sciences suggest problems studied by mathematicians, and many problems arise within mathematics itself. For example, the physicist Richard Feynman invented the path integral formulation of quantum mechanics using a combination of mathematical reasoning and physical insight, and today's string theory, a still-developing scientific theory which attempts to unify the four fundamental forces of nature, continues to inspire new mathematics.[19] Some mathematics is only relevant in the area that inspired it, and is applied to solve further problems in that area. But often mathematics inspired by one area proves useful in many areas, and joins the general stock of mathematical concepts. A distinction is often made between pure mathematics and applied mathematics. However pure mathematics topics often turn out to have applications, e.g. number theory in cryptography. This remarkable fact that even the "purest" mathematics often turns out to have practical applications is what Eugene Wigner has called "the unreasonable effectiveness of mathematics".[20] As in most areas of study, the explosion of knowledge in the scientific age has led to specialization: there are now hundreds of specialized areas in mathematics and the latest Mathematics Subject Classification runs to 46 pages.[21] Several areas of applied mathematics have merged with related traditions outside of mathematics and become disciplines in their own right, including statistics, operations research, and computer science.
For those who are mathematically inclined, there is often a definite aesthetic aspect to much of mathematics. Many mathematicians talk about the elegance of mathematics, its intrinsic aesthetics and inner beauty. Simplicity and generality are valued. There is beauty in a simple and elegant proof, such as Euclid's proof that there are infinitely many prime numbers, and in an elegant numerical method that speeds calculation, such as the fast Fourier transform. G. H. Hardy in A Mathematician's Apology expressed the belief that these aesthetic considerations are, in themselves, sufficient to justify the study of pure mathematics. He identified criteria such as significance, unexpectedness, inevitability, and economy as factors that contribute to a mathematical aesthetic.[22] Mathematicians often strive to find proofs that are particularly elegant, proofs from "The Book" of God according to Paul Erdős.[23][24] The popularity of recreational mathematics is another sign of the pleasure many find in solving mathematical questions.
Notation, language, and rigor
Main article: Mathematical notation
Leonhard Euler, who created and popularized much of the mathematical notation used today
Most of the mathematical notation in use today was not invented until the 16th century.[25] Before that, mathematics was written out in words, a painstaking process that limited mathematical discovery.[26] Euler (1707–1783) was responsible for many of the notations in use today. Modern notation makes mathematics much easier for the professional, but beginners often find it daunting. It is extremely compressed: a few symbols contain a great deal of information. Like musical notation, modern mathematical notation has a strict syntax (which to a limited extent varies from author to author and from discipline to discipline) and encodes information that would be difficult to write in any other way.
Mathematical language can be difficult to understand for beginners. Words such as or and only have more precise meanings than in everyday speech. Moreover, words such as open and field have been given specialized mathematical meanings. Technical terms such as homeomorphism and integrable have precise meanings in mathematics. Additionally, shorthand phrases such as "iff" for "if and only if" belong to mathematical jargon. There is a reason for special notation and technical vocabulary: mathematics requires more precision than everyday speech. Mathematicians refer to this precision of language and logic as "rigor".
Mathematical proof is fundamentally a matter of rigor. Mathematicians want their theorems to follow from axioms by means of systematic reasoning. This is to avoid mistaken "theorems", based on fallible intuitions, of which many instances have occurred in the history of the subject.[27] The level of rigor expected in mathematics has varied over time: the Greeks expected detailed arguments, but at the time of Isaac Newton the methods employed were less rigorous. Problems inherent in the definitions used by Newton would lead to a resurgence of careful analysis and formal proof in the 19th century. Misunderstanding the rigor is a cause for some of the common misconceptions of mathematics. Today, mathematicians continue to argue among themselves about computer-assisted proofs. Since large computations are hard to verify, such proofs may not be sufficiently rigorous.[28]
Axioms in traditional thought were "self-evident truths", but that conception is problematic. At a formal level, an axiom is just a string of symbols, which has an intrinsic meaning only in the context of all derivable formulas of an axiomatic system. It was the goal of Hilbert's program to put all of mathematics on a firm axiomatic basis, but according to Gödel's incompleteness theorem every (sufficiently powerful) axiomatic system has undecidable formulas; and so a final axiomatization of mathematics is impossible. Nonetheless mathematics is often imagined to be (as far as its formal content) nothing but set theory in some axiomatization, in the sense that every mathematical statement or proof could be cast into formulas within set theory.[29]
Fields of mathematics
An abacus, a simple calculating tool used since ancient times.
See also: Areas of mathematics
See also: Glossary of areas of mathematics
Mathematics can, broadly speaking, be subdivided into the study of quantity, structure, space, and change (i.e. arithmetic, algebra, geometry, and analysis). In addition to these main concerns, there are also subdivisions dedicated to exploring links from the heart of mathematics to other fields: to logic, to set theory (foundations), to the empirical mathematics of the various sciences (applied mathematics), and more recently to the rigorous study of uncertainty.
Foundations and philosophy
In order to clarify the foundations of mathematics, the fields of mathematical logic and set theory were developed. Mathematical logic includes the mathematical study of logic and the applications of formal logic to other areas of mathematics; set theory is the branch of mathematics that studies sets or collections of objects. Category theory, which deals in an abstract way with mathematical structures and relationships between them, is still in development. The phrase "crisis of foundations" describes the search for a rigorous foundation for mathematics that took place from approximately 1900 to 1930.[30] Some disagreement about the foundations of mathematics continues to the present day. The crisis of foundations was stimulated by a number of controversies at the time, including the controversy over Cantor's set theory and the Brouwer-Hilbert controversy.
Mathematical logic is concerned with setting mathematics within a rigorous axiomatic framework, and studying the implications of such a framework. As such, it is home to Gödel's incompleteness theorems which (informally) imply that any formal system that contains basic arithmetic, if sound (meaning that all theorems that can be proven are true), is necessarily incomplete (meaning that there are true theorems which cannot be proved in that system). Whatever finite collection of number-theoretical axioms is taken as a foundation, Gödel showed how to construct a formal statement that is a true number-theoretical fact, but which does not follow from those axioms. Therefore no formal system is a complete axiomatization of full number theory. Modern logic is divided into recursion theory, model theory, and proof theory, and is closely linked to theoretical computer science[citation needed], as well as to Category Theory.
Theoretical computer science includes computability theory, computational complexity theory, and information theory. Computability theory examines the limitations of various theoretical models of the computer, including the most well known model – the Turing machine. Complexity theory is the study of tractability by computer; some problems, although theoretically solvable by computer, are so expensive in terms of time or space that solving them is likely to remain practically unfeasible, even with rapid advance of computer hardware. A famous problem is the "P=NP?" problem, one of the Millennium Prize Problems.[31] Finally, information theory is concerned with the amount of data that can be stored on a given medium, and hence deals with concepts such as compression and entropy.
p \Rightarrow q \, Venn A intersect B.svg Commutative diagram for morphism.svg DFAexample.svg
Mathematical logic Set theory Category theory Theory of computation
Pure mathematics
Quantity
The study of quantity starts with numbers, first the familiar natural numbers and integers ("whole numbers") and arithmetical operations on them, which are characterized in arithmetic. The deeper properties of integers are studied in number theory, from which come such popular results as Fermat's Last Theorem. The twin prime conjecture and Goldbach's conjecture are two unsolved problems in number theory.
As the number system is further developed, the integers are recognized as a subset of the rational numbers ("fractions"). These, in turn, are contained within the real numbers, which are used to represent continuous quantities. Real numbers are generalized to complex numbers. These are the first steps of a hierarchy of numbers that goes on to include quarternions and octonions. Consideration of the natural numbers also leads to the transfinite numbers, which formalize the concept of "infinity". Another area of study is size, which leads to the cardinal numbers and then to another conception of infinity: the aleph numbers, which allow meaningful comparison of the size of infinitely large sets.
Many mathematical objects, such as sets of numbers and functions, exhibit internal structure as a consequence of operations or relations that are defined on the set. Mathematics then studies properties of those sets that can be expressed in terms of that structure; for instance number theory studies properties of the set of integers that can be expressed in terms of arithmetic operations. Moreover, it frequently happens that different such structured sets (or structures) exhibit similar properties, which makes it possible, by a further step of abstraction, to state axioms for a class of structures, and then study at once the whole class of structures satisfying these axioms. Thus one can study groups, rings, fields and other abstract systems; together such studies (for structures defined by algebraic operations) constitute the domain of abstract algebra. By its great generality, abstract algebra can often be applied to seemingly unrelated problems; for instance a number of ancient problems concerning compass and straightedge constructions were finally solved using Galois theory, which involves field theory and group theory. Another example of an algebraic theory is linear algebra, which is the general study of vector spaces, whose elements called vectors have both quantity and direction, and can be used to model (relations between) points in space. This is one example of the phenomenon that the originally unrelated areas of geometry and algebra have very strong interactions in modern mathematics. Combinatorics studies ways of enumerating the number of objects that fit a given structure.
\begin{matrix} (1,2,3) & (1,3,2) \\ (2,1,3) & (2,3,1) \\ (3,1,2) & (3,2,1) \end{matrix} Elliptic curve simple.svg Rubik's cube.svg Group diagdram D6.svg Lattice of the divisibility of 60.svg
Combinatorics Number theory Group theory Graph theory Order theory
Space
The study of space originates with geometry – in particular, Euclidean geometry. Trigonometry is the branch of mathematics that deals with relationships between the sides and the angles of triangles and with the trigonometric functions; it combines space and numbers, and encompasses the well-known Pythagorean theorem. The modern study of space generalizes these ideas to include higher-dimensional geometry, non-Euclidean geometries (which play a central role in general relativity) and topology. Quantity and space both play a role in analytic geometry, differential geometry, and algebraic geometry. Convex and discrete geometry was developed to solve problems in number theory and functional analysis but now is pursued with an eye on applications in optimization and computer science. Within differential geometry are the concepts of fiber bundles and calculus on manifolds, in particular, vector and tensor calculus. Within algebraic geometry is the description of geometric objects as solution sets of polynomial equations, combining the concepts of quantity and space, and also the study of topological groups, which combine structure and space. Lie groups are used to study space, structure, and change. Topology in all its many ramifications may have been the greatest growth area in 20th century mathematics; it includes point-set topology, set-theoretic topology, algebraic topology and differential topology. In particular, instances of modern day topology are metrizability theory, axiomatic set theory, homotopy theory, and Morse theory. Topology also includes the now solved Poincaré conjecture. Other results in geometry and topology, including the four color theorem and Kepler conjecture, have been proved only with the help of computers.
Illustration to Euclid's proof of the Pythagorean theorem.svg Sinusvåg 400px.png Hyperbolic triangle.svg Torus.png Mandel zoom 07 satellite.jpg Measure illustration.png
Geometry Trigonometry Differential geometry Topology Fractal geometry Measure theory
Change
Understanding and describing change is a common theme in the natural sciences, and calculus was developed as a powerful tool to investigate it. Functions arise here, as a central concept describing a changing quantity. The rigorous study of real numbers and functions of a real variable is known as real analysis, with complex analysis the equivalent field for the complex numbers. Functional analysis focuses attention on (typically infinite-dimensional) spaces of functions. One of many applications of functional analysis is quantum mechanics. Many problems lead naturally to relationships between a quantity and its rate of change, and these are studied as differential equations. Many phenomena in nature can be described by dynamical systems; chaos theory makes precise the ways in which many of these systems exhibit unpredictable yet still deterministic behavior.
Integral as region under curve.svg Vector field.svg Airflow-Obstructed-Duct.png Limitcycle.svg Lorenz attractor.svg Conformal grid after Möbius transformation.svg
Calculus Vector calculus Differential equations Dynamical systems Chaos theory Complex analysis
Applied mathematics
Applied mathematics concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. Thus, "applied mathematics" is a mathematical science with specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems; as a profession focused on practical problems, applied mathematics focuses on the formulation, study, and use of mathematical models in science, engineering, and other areas of mathematical practice.
In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics, where mathematics is developed primarily for its own sake. Thus, the activity of applied mathematics is vitally connected with research in pure mathematics.
Statistics and other decision sciences
Applied mathematics has significant overlap with the discipline of statistics, whose theory is formulated mathematically, especially with probability theory. Statisticians (working as part of a research project) "create data that makes sense" with random sampling and with randomized experiments;[32] the design of a statistical sample or experiment specifies the analysis of the data (before the data be available). When reconsidering data from experiments and samples or when analyzing data from observational studies, statisticians "make sense of the data" using the art of modelling and the theory of inference – with model selection and estimation; the estimated models and consequential predictions should be tested on new data.[33]
Statistical theory studies decision problems such as minimizing the risk (expected loss) of a statistical action, such as using a procedure in, for example, parameter estimation, hypothesis testing, and selecting the best. In these traditional areas of mathematical statistics, a statistical-decision problem is formulated by minimizing an objective function, like expected loss or cost, under specific constraints: For example, designing a survey often involves minimizing the cost of estimating a population mean with a given level of confidence.[34] Because of its use of optimization, the mathematical theory of statistics shares concerns with other decision sciences, such as operations research, control theory, and mathematical economics.[35]
Computational mathematics
Computational mathematics proposes and studies methods for solving mathematical problems that are typically too large for human numerical capacity. Numerical analysis studies methods for problems in analysis using functional analysis and approximation theory; numerical analysis includes the study of approximation and discretization broadly with special concern for rounding errors. Numerical analysis and, more broadly, scientific computing also study non-analytic topics of mathematical science, especially algorithmic matrix and graph theory. Other areas of computational mathematics include computer algebra and symbolic computation.
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects.[1] The temporal position of events with respect to the transitory present is continually changing; events happen, then are located further and further in the past. Time has been a major subject of religion, philosophy, and science, but defining it in a non-controversial manner applicable to all fields of study has consistently eluded the greatest scholars. A simple definition states that "time is what clocks measure".
Time is one of the seven fundamental physical quantities in the International System of Units. Time is used to define other quantities — such as velocity — so defining time in terms of such quantities would result in circularity of definition.[2] An operational definition of time, wherein one says that observing a certain number of repetitions of one or another standard cyclical event (such as the passage of a free-swinging pendulum) constitutes one standard unit such as the second, is highly useful in the conduct of both advanced experiments and everyday affairs of life. The operational definition leaves aside the question whether there is something called time, apart from the counting activity just mentioned, that flows and that can be measured. Investigations of a single continuum called spacetime bring questions about space into questions about time, questions that have their roots in the works of early students of natural philosophy.
Two contrasting viewpoints on time divide many prominent philosophers. One view is that time is part of the fundamental structure of the universe, a dimension in which events occur in sequence. Sir Isaac Newton subscribed to this realist view, and hence it is sometimes referred to as Newtonian time.[3][4] Time travel, in this view, becomes a possibility as other "times" persist like frames of a film strip, spread out across the time line. The opposing view is that time does not refer to any kind of "container" that events and objects "move through", nor to any entity that "flows", but that it is instead part of a fundamental intellectual structure (together with space and number) within which humans sequence and compare events. This second view, in the tradition of Gottfried Leibniz[5] and Immanuel Kant,[6][7] holds that time is neither an event nor a thing, and thus is not itself measurable nor can it be travelled.
Temporal measurement has occupied scientists and technologists, and was a prime motivation in navigation and astronomy. Periodic events and periodic motion have long served as standards for units of time. Examples include the apparent motion of the sun across the sky, the phases of the moon, the swing of a pendulum, and the beat of a heart. Currently, the international unit of time, the second, is defined in terms of radiation emitted by caesium atoms (see below). Time is also of significant social importance, having economic value ("time is money") as well as personal value, due to an awareness of the limited time in each day and in human life spans.
Ray Cummings, an early writer of science fiction, wrote in 1922, "Time... is what keeps everything from happening at once",[8] a sentence repeated by scientists such as C. J. Overbeck,[9] and John Archibald Wheeler.[10][11]
Contents
[hide]
1 Temporal measurement
1.1 History of the calendar
1.2 History of time measurement devices
2 Definitions and standards
2.1 World time
2.2 Time conversions
2.3 Sidereal time
2.4 Chronology
3 Religion
3.1 Linear and cyclical time
3.2 Numeric and Divine time
4 Philosophy
4.1 Time as "unreal"
5 Physical definition
5.1 Classical mechanics
5.2 Spacetime
5.3 Time dilation
5.4 Relativistic time versus Newtonian time
5.5 Arrow of time
5.6 Quantised time
6 Time and the Big Bang
6.1 Speculative physics beyond the Big Bang
7 Time travel
8 Judgement of time
8.1 Biopsychology
8.2 Alterations
9 Use of time
10 See also
10.1 Books
10.2 Organizations
10.3 Miscellaneous arts and sciences
10.4 Miscellaneous units of time
11 References
12 Further reading
13 External links
13.1 Perception of time
13.2 Philosophy
13.3 Timekeeping
13.4 Miscellaneous
[edit] Temporal measurement
Temporal measurement, or chronometry, takes two distinct period forms: the calendar, a mathematical abstraction for calculating extensive periods of time,[12] and the clock, a physical mechanism that counts the ongoing passage of time. In day-to-day life, the clock is consulted for periods less than a day, the calendar, for periods longer than a day. Increasingly, personal electronic devices display both calendars and clocks simultaneously. The number (as on a clock dial or calendar) that marks the occurrence of a specified event as to hour or date is obtained by counting from a fiducial epoch — a central reference point.
[edit] History of the calendar
Main article: Calendar
Artifacts from the Palaeolithic suggest that the moon was used to reckon time as early as 6,000 years ago.[13] Lunar calendars were among the first to appear, either 12 or 13 lunar months (either 354 or 384 days). Without intercalation to add days or months to some years, seasons quickly drift in a calendar based solely on twelve lunar months. Lunisolar calendars have a thirteenth month added to some years to make up for the difference between a full year (now known to be about 365.24 days) and a year of just twelve lunar months. The numbers twelve and thirteen came to feature prominently in many cultures, at least partly due to this relationship of months to years.
The reforms of Julius Caesar in 45 BC put the Roman world on a solar calendar. This Julian calendar was faulty in that its intercalation still allowed the astronomical solstices and equinoxes to advance against it by about 11 minutes per year. Pope Gregory XIII introduced a correction in 1582; the Gregorian calendar was only slowly adopted by different nations over a period of centuries, but is today by far the one in most common use around the world.
[edit] History of time measurement devices
Horizontal sundial in Taganrog.
Main article: History of timekeeping devices
See also: Clock
A large variety of devices have been invented to measure time. The study of these devices is called horology.
An Egyptian device dating to c.1500 BC, similar in shape to a bent T-square, measured the passage of time from the shadow cast by its crossbar on a nonlinear rule. The T was oriented eastward in the mornings. At noon, the device was turned around so that it could cast its shadow in the evening direction.[14]
A sundial uses a gnomon to cast a shadow on a set of markings which were calibrated to the hour. The position of the shadow marked the hour in local time.
The most precise timekeeping devices of the ancient world were the water clock or clepsydra, one of which was found in the tomb of Egyptian pharaoh Amenhotep I (1525–1504 BC). They could be used to measure the hours even at night, but required manual upkeep to replenish the flow of water. The Greeks and Chaldeans regularly maintained timekeeping records as an essential part of their astronomical observations. Arab inventors and engineers in particular made improvements on the use of water clocks up to the Middle Ages.[15] In the 11th century, Chinese inventors and engineers invented the first mechanical clocks to be driven by an escapement mechanism.
A contemporary quartz watch
The hourglass uses the flow of sand to measure the flow of time. They were used in navigation. Ferdinand Magellan used 18 glasses on each ship for his circumnavigation of the globe (1522).[16] Incense sticks and candles were, and are, commonly used to measure time in temples and churches across the globe. Waterclocks, and later, mechanical clocks, were used to mark the events of the abbeys and monasteries of the Middle Ages. Richard of Wallingford (1292–1336), abbot of St. Alban's abbey, famously built a mechanical clock as an astronomical orrery about 1330.[17][18] Great advances in accurate time-keeping were made by Galileo Galilei and especially Christiaan Huygens with the invention of pendulum driven clocks.
The English word clock probably comes from the Middle Dutch word "klocke" which is in turn derived from the mediaeval Latin word "clocca", which is ultimately derived from Celtic, and is cognate with French, Latin, and German words that mean bell. The passage of the hours at sea were marked by bells, and denoted the time (see ship's bells). The hours were marked by bells in the abbeys as well as at sea.
Chip-scale atomic clocks, such as this one unveiled in 2004, are expected to greatly improve GPS location.[19]
Clocks can range from watches, to more exotic varieties such as the Clock of the Long Now. They can be driven by a variety of means, including gravity, springs, and various forms of electrical power, and regulated by a variety of means such as a pendulum.
A chronometer is a portable timekeeper that meets certain precision standards. Initially, the term was used to refer to the marine chronometer, a timepiece used to determine longitude by means of celestial navigation, a precision firstly achieved by John Harrison. More recently, the term has also been applied to the chronometer watch, a wris****ch that meets precision standards set by the Swiss agency COSC.
The most accurate timekeeping devices are atomic clocks, which are accurate to seconds in many millions of years,[20] and are used to calibrate other clocks and timekeeping instruments. Atomic clocks use the spin property of atoms as their basis, and since 1967, the International System of Measurements bases its unit of time, the second, on the properties of caesium atoms. SI defines the second as 9,192,631,770 cycles of that radiation which corresponds to the transition between two electron spin energy levels of the ground state of the 133Cs atom.
Today, the Global Positioning System in coordination with the Network Time Protocol can be used to synchronize timekeeping systems across the globe.
In medieval philosophical writings, the atom was a unit of time referred to as the smallest possible division of time. The earliest known occurrence in English is in Byrhtferth's Enchiridion (a science text) of 1010–1012,[21] where it was defined as 1/564 of a momentum (1½ minutes),[22] and thus equal to 15/94 of a second. It was used in the computus, the process of calculating the date of Easter.
As of 2006, the smallest unit of time that has been directly measured is on the attosecond (10−18 s) time scale, or around 1026 Planck times.[23][24][25]
[edit] Definitions and standards
Units of time Unit Size Notes
yoctosecond 10−24 s
zeptosecond 10−21 s
attosecond 10−18 s shortest time now measurable
femtosecond 10−15 s pulse time of ultrafast lasers
picosecond 10−12 s
nanosecond 10−9 s time for molecules to fluoresce
microsecond 10−6 s
millisecond 0.001 s
second 1 s SI base unit
minute 60 seconds
hour 60 minutes
day 24 hours
week 7 days Also called sennight
fortnight 14 days 2 weeks
lunar month 27.2–29.5 days Various definitions of lunar month exist.
month 28–31 days
quarter 3 months
year 12 months
common year 365 days 52 weeks + 1 day
leap year 366 days 52 weeks + 2 days
tropical year 365.24219 days[26] average
Gregorian year 365.2425 days[27] average
Olympiad 4 year cycle
lustrum 5 years Also called pentad
decade 10 years
Indiction 15 year cycle
generation 17–35 years approximate
jubilee (Biblical) 50 years
century 100 years
millennium 1,000 years
exasecond 1018 s roughly 32 billion years, more than twice
the age of the universe on current estimates
cosmological decade varies 10 times the length of the previous
cosmological decade, with CÐ 1 beginning
either 10 seconds or 10 years after the
Big Bang, depending on the definition.
See also: Time standard and Orders of magnitude (time)
The SI base unit for time is the SI second. From the second, larger units such as the minute, hour and day are defined, though they are "non-SI" units because they do not use the decimal system, and also because of the occasional need for a leap second. They are, however, officially accepted for use with the International System. There are no fixed ratios between seconds and months or years as months and years have significant variations in length.[28]
The official SI definition of the second is as follows:[28][29]
The second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.
At its 1997 meeting, the CIPM affirmed that this definition refers to a caesium atom in its ground state at a temperature of 0 K.[28] Previous to 1967, the second was defined as:
the fraction 1/31,556,925.9747 of the tropical year for 1900 January 0 at 12 hours ephemeris time.
The current definition of the second, coupled with the current definition of the metre, is based on the special theory of relativity, which affirms our space-time to be a Minkowski space.
[edit] World time
Time keeping is so critical to the functioning of modern societies that it is coordinated at an international level. The basis for scientific time is a continuous count of seconds based on atomic clocks around the world, known as the International Atomic Time (TAI). Other scientific time standards include Terrestrial Time and Barycentric Dynamical Time.
Coordinated Universal Time (UTC) is the basis for modern civil time. Since January 1, 1972, it has been defined to follow TAI with an exact offset of an integer number of seconds, changing only when a leap second is added to keep clock time synchronized with the rotation of the Earth. In TAI and UTC systems, the duration of a second is constant, as it is defined by the unchanging transition period of the caesium atom.
Greenwich Mean Time (GMT) is an older standard, adopted starting with British railroads in 1847. Using telescopes instead of atomic clocks, GMT was calibrated to the mean solar time at the Royal Observatory, Greenwich in the UK. Universal Time (UT) is the modern term for the international telescope-based system, adopted to replace "Greenwich Mean Time" in 1928 by the International Astronomical Union. Observations at the Greenwich Observatory itself ceased in 1954, though the location is still used as the basis for the coordinate system. Because the rotational period of Earth is not perfectly constant, the duration of a second would vary if calibrated to a telescope-based standard like GMT or UT—in which a second was defined as a fraction of a day or year. The terms "GMT" and "Greenwich Mean Time" are sometimes used informally to refer to UT or UTC.
The Global Positioning System also broadcasts a very precise time signal worldwide, along with instructions for converting GPS time to UTC.
Earth is split up into a number of time zones. Most time zones are exactly one hour apart, and by convention compute their local time as an offset from UTC or GMT. In many locations these offsets vary twice yearly due to daylight saving time transitions.
[edit] Time conversions
The following time conversions are accurate at the millisecond level. Some are exact while others have differences at the microsecond level.
System Description UT1 UTC TT TAI GPS
UT1 Mean Solar Time UT1 UTC = UT1 - DUT1 TT = UT1 + 32.184 s + LS - DUT1 TAI = UT1 - DUT1 + LS GPS = UT1 - DUT1 + LS - 19 s
UTC Civil Time UT1 = UTC + DUT1 UTC TT = UTC + 32.184 s + LS TAI = UTC + LS GPS = UTC + LS - 19 s
TT Terrestrial (Ephemeris) Time UT1 = TT - 32.184 s - LS + DUT1 UTC = TT - 32.184 s - LS TT TAI = TT - 32.184 s GPS = TT - 51.184 s
TAI Atomic Time UT1 = TAI + DUT1 - LS UTC = TAI - LS TT = TAI + 32.184 s TAI GPS = TAI - 19 s
GPS GPS Time UT1 = GPS + DUT1 - LS + 19 s UTC = GPS - LS + 19 s TT = GPS + 51.184 s TAI = GPS + 19 s GPS
Sidereal time is the measurement of time relative to a distant star (instead of solar time that is relative to the sun). It is used in astronomy to predict when a star will be overhead. Due to the orbit of the earth around the sun a sidereal day is 4 minutes (1/366th) less than a solar day.
[edit] Chronology
Main article: Chronology
Another form of time measurement consists of studying the past. Events in the past can be ordered in a sequence (creating a chronology), and can be put into chronological groups (periodization). One of the most important systems of periodization is geologic time, which is a system of periodizing the events that shaped the Earth and its life. Chronology, periodization, and interpretation of the past are together known as the study of history.
[edit] Religion
Hindu units of time shown logarithmically
Further information: Time and fate deities
[edit] Linear and cyclical time
See also: Time Cycles and Wheel of time
Ancient cultures such as Incan, Mayan, Hopi, and other Native American Tribes, plus the Babylonians, Ancient Greeks, Hinduism, Buddhism, Jainism, and others have a concept of a wheel of time, that regards time as cyclical and quantic consisting of repeating ages that happen to every being of the Universe between birth and extinction.
In general, the Judaeo-Christian concept, based on the Bible, is that time is linear, beginning with the act of creation by God. The general Christian view is that time will end with the end of the world. Others suggest[who?] that time is like a ray, having a beginning but going on forever into the future.
In the Old Testament book Ecclesiastes, traditionally ascribed to Solomon (970–928 BC), time (as the Hebrew word עדן, זמן `iddan(time) zĕman(season) is often translated) was traditionally regarded as a medium for the passage of predestined events. (Another word, زمان" זמן" zman, was current as meaning time fit for an event, and is used as the modern Arabic and Hebrew equivalent to the English word "time".)
There is an appointed time (zman) for everything. And there is a time (’êth) for every event under heaven–
A time (’êth) to give birth, and a time to die; A time to plant, and a time to uproot what is planted.
A time to kill, and a time to heal; A time to tear down, and a time to build up.
A time to weep, and a time to laugh; A time to mourn, and a time to dance.
A time to throw stones, and a time to gather stones; A time to embrace, and a time to shun embracing.
A time to search, and a time to give up as lost; A time to keep, and a time to throw away.
A time to tear apart, and a time to sew together; A time to be silent, and a time to speak.
A time to love, and a time to hate; A time for war, and a time for peace. – Ecclesiastes 3:1–8
[edit] Numeric and Divine time
The Greek language denotes two distinct principles, Chronos and Kairos. The former refers to numeric, or chronological, time. The latter, literally "the right or opportune moment," relates specifically to metaphysical or Divine time. In theology, Kairos is qualitative, as opposed to quantitative.
[edit] Philosophy
Main articles: Philosophy of space and time and Temporal finitism
Two distinct viewpoints on time divide many prominent philosophers. One view is that time is part of the fundamental structure of the universe, a dimension in which events occur in sequence. Sir Isaac Newton subscribed to this realist view, and hence it is sometimes referred to as Newtonian time.[4] An opposing view is that time does not refer to any kind of actually existing dimension that events and objects "move through", nor to any entity that "flows", but that it is instead an intellectual concept (together with space and number) that enables humans to sequence and compare events.[30] This second view, in the tradition of Gottfried Leibniz[5] and Immanuel Kant,[6][7] holds that space and time "do not exist in and of themselves, but ... are the product of the way we represent things", because we can know objects only as they appear to us.
The Vedas, the earliest texts on Indian philosophy and Hindu philosophy dating back to the late 2nd millennium BC, describe ancient Hindu cosmology, in which the universe goes through repeated cycles of creation, destruction and rebirth, with each cycle lasting 4320 million years.[31] Ancient Greek philosophers, including Parmenides and Heraclitus, wrote essays on the nature of time.[32] Plato, in the Timaeus, identified time with the period of motion of the heavenly bodies. Aristotle, in Book IV of his Physica defined time as the number of change with respect to before and after.
In Book 11 of his Confessions, St. Augustine of Hippo ruminates on the nature of time, asking, "What then is time? If no one asks me, I know: if I wish to explain it to one that asketh, I know not." He begins to define time by what it is not rather than what it is,[33] an approach similar to that taken in other negative definitions. However, Augustine ends up calling time a “distention” of the mind (Confessions 11.26) by which we simultaneously grasp the past in memory, the present by attention, and the future by expectation.
In contrast to ancient Greek philosophers who believed that the universe had an infinite past with no beginning, medieval philosophers and theologians developed the concept of the universe having a finite past with a beginning. This view is shared by Abrahamic faiths as they believe time started by creation, therefore the only thing being infinite is God and everything else, including time, is finite.
Isaac Newton believed in absolute space and absolute time; Leibniz believed that time and space are relational.[34] The differences between Leibniz's and Newton's interpretations came to a head in the famous Leibniz-Clarke Correspondence.
Time is not an empirical concept. For neither co-existence nor succession would be perceived by us, if the representation of time did not exist as a foundation a priori. Without this presupposition we could not represent to ourselves that things exist together at one and the same time, or at different times, that is, contemporaneously, or in succession.
“
”
Immanuel Kant, Critique of Pure Reason (1781), trans. Vasilis Politis (London: Dent., 1991), p.54.
Immanuel Kant, in the Critique of Pure Reason, described time as an a priori intuition that allows us (together with the other a priori intuition, space) to comprehend sense experience.[35] With Kant, neither space nor time are conceived as substances, but rather both are elements of a systematic mental framework that necessarily structures the experiences of any rational agent, or observing subject. Kant thought of time as a fundamental part of an abstract conceptual framework, together with space and number, within which we sequence events, quantify their duration, and compare the motions of objects. In this view, time does not refer to any kind of entity that "flows," that objects "move through," or that is a "container" for events. Spatial measurements are used to quantify the extent of and distances between objects, and temporal measurements are used to quantify the durations of and between events. (See Ontology).
Henri Bergson believed that time was neither a real homogeneous medium nor a mental construct, but possesses what he referred to as Duration. Duration, in Bergson's view, was creativity and memory as an essential component of reality.[36]
According to Martin Heidegger we do not exist inside time, "we are time". Hence, the relationship to the past is a present awareness of "having been", which allows the past to exist in the present. The relationship to the future is the state of anticipating a potential possibility, task, or engagement. It is related to the human propensity for caring and being concerned, which causes "being ahead of oneself" when thinking of a pending occurrence. Therefore, this concern for a potential occurrence also allows the future to exist in the present. The present becomes an experience, which is qualitative instead of quantitative. Heidegger seems to think this is the way that a linear relationship with time, or temporal existence, is broken or transcended.[37] We are not stuck in sequential time. We are able to remember the past and project into the future - we have a kind of random access to our representation of temporal existence --- we can, in our thoughts, step out of (ecstasis) sequential time.[38]
[edit] Time as "unreal"
In 5th century BC Greece, Antiphon the Sophist, in a fragment preserved from his chief work On Truth, held that: "Time is not a reality (hypostasis), but a concept (noêma) or a measure (metron)." Parmenides went further, maintaining that time, motion, and change were illusions, leading to the paradoxes of his follower Zeno.[39] Time as an illusion is also a common theme in Buddhist thought.[40][41]
J. M. E. McTaggart's 1908 The Unreality of Time argues that, since every event has the characteristic of being both present and not present (i.e. future or past), that time is a self-contradictory idea (see also The flow of time).
These arguments often center around what it means for something to be "unreal". Modern physicists generally consider time to be as "real" as space, though others such as Julian Barbour in his book The End of Time, argue that quantum equations of the universe take their true form when expressed in the timeless configuration spacerealm containing every possible "Now" or momentary configuration of the universe, which he terms 'platonia'.[42] (See also: Eternalism (philosophy of time).)
[edit] Physical definition
Classical mechanics
\mathbf{F} = m \mathbf{a}
Newton's Second Law
History of classical mechanics · Timeline of classical mechanics
Branches[show]
Formulations[show]
Fundamental concepts[hide]
Space · Time · Velocity · Speed · Mass · Acceleration · Gravity · Force · Impulse · Torque / Moment / Couple · Momentum · Angular momentum · Inertia · Moment of inertia · Reference frame · Energy · Kinetic energy · Potential energy · Mechanical work · Virtual work · D'Alembert's principle
Core topics[show]
Scientists[show]
v
t
e
Main article: Time in physics
From the age of Newton to Einstein's profound reinterpretation of the physical concepts associated with time and space, time was considered to be "absolute" and to flow "equably" (to use the words of Newton) for all observers.[43] Non-relativistic classical mechanics is based on this Newtonian idea of time.
Einstein, in his special theory of relativity,[44] postulated the constancy and finiteness of the speed of light for all observers. He showed that this postulate, together with a reasonable definition for what it means for two events to be simultaneous, requires that distances appear compressed and time intervals appear lengthened for events associated with objects in motion relative to an inertial observer.
Einstein showed that if time and space is measured using electromagnetic phenomena (like light bouncing between mirrors) then due to the constancy of the speed of light, time and space become mathematically entangled together in a certain way (called Minkowski space) which in turn results in Lorentz transformation and in entanglement of all other important derivative physical quantities (like energy, momentum, mass, force, etc.) in a certain 4-vectorial way (see special relativity for more details).
[edit] Classical mechanics
In non-relativistic classical mechanics, Newton's concept of "relative, apparent, and common time" can be used in the formulation of a prescription for the synchronization of clocks. Events seen by two different observers in motion relative to each other produce a mathematical concept of time that works sufficiently well for describing the everyday phenomena of most people's experience. In the late nineteenth century, physicists encountered problems with the classical understanding of time, in connection with the behaviour of electricity and magnetism. Einstein resolved these problems by invoking a method of synchronizing clocks using the constant, finite speed of light as the maximum signal velocity. This led directly to the result that observers in motion relative to one another will measure different elapsed times for the same event.
Two-dimensional space depicted in three-dimensional spacetime. The past and future light cones are absolute, the "present" is a relative concept different for observers in relative motion.
[edit] Spacetime
Main article: Spacetime
Time has historically been closely related with space, the two together comprising spacetime in Einstein's special relativity and general relativity. According to these theories, the concept of time depends on the spatial reference frame of the observer, and the human perception as well as the measurement by instruments such as clocks are different for observers in relative motion. The past is the set of events that can send light signals to the observer; the future is the set of events to which the observer can send light signals.
[edit] Time dilation
Relativity of simultaneity: Event B is simultaneous with A in the green reference frame, but it occurred before in the blue frame, and will occur later in the red frame.
Main article: Time dilation
Einstein showed in his thought experiments that people travelling at different speeds, while agreeing on cause and effect, will measure different time separations between events and can even observe different chronological orderings between non-causally related events. Though these effects are typically minute in the human experience, the effect becomes much more pronounced for objects moving at speeds approaching the speed of light. Many subatomic particles exist for only a fixed fraction of a second in a lab relatively at rest, but some that travel close to the speed of light can be measured to travel further and survive much longer than expected (a muon is one example). According to the special theory of relativity, in the high-speed particle's frame of reference, it exists, on the average, for a standard amount of time known as its mean lifetime, and the distance it travels in that time is zero, because its velocity is zero. Relative to a frame of reference at rest, time seems to "slow down" for the particle. Relative to the high-speed particle, distances seem to shorten. Even in Newtonian terms time may be considered the fourth dimension of motion[citation needed]; but Einstein showed how both temporal and spatial dimensions can be altered (or "warped") by high-speed motion.
Einstein (The Meaning of Relativity): "Two events taking place at the points A and B of a system K are simultaneous if they appear at the same instant when observed from the middle point, M, of the interval AB. Time is then defined as the ensemble of the indications of similar clocks, at rest relatively to K, which register the same simultaneously."
Einstein wrote in his book, Relativity, that simultaneity is also relative, i.e., two events that appear simultaneous to an observer in a particular inertial reference frame need not be judged as simultaneous by a second observer in a different inertial frame of reference.
[edit] Relativistic time versus Newtonian time
Views of spacetime along the world line of a rapidly accelerating observer in a relativistic universe. The events ("dots") that pass the two diagonal lines in the bottom half of the image (the past light cone of the observer in the origin) are the events visible to the observer.
The animations visualise the different treatments of time in the Newtonian and the relativistic descriptions. At the heart of these differences are the Galilean and Lorentz transformations applicable in the Newtonian and relativistic theories, respectively.
In the figures, the vertical direction indicates time. The horizontal direction indicates distance (only one spatial dimension is taken into account), and the thick dashed curve is the spacetime trajectory ("world line") of the observer. The small dots indicate specific (past and future) events in spacetime.
The slope of the world line (deviation from being vertical) gives the relative velocity to the observer. Note how in both pictures the view of spacetime changes when the observer accelerates.
My nickname used to be Sid2dakid (everyone still calls me this) because my name is Sidney. I'M A GUY! I made up knowledge561 because there are a lot of dumb people where I'm from and I would always get good grades and know a lot about stuff. 561 is where I'm from.
My nickname used to be Sid2dakid (everyone still calls me this) because my name is Sidney. I'M A GUY! I made up knowledge561 because there are a lot of dumb people where I'm from and I would always get good grades and know a lot about stuff. 561 is where I'm from.
My MMA Career produced my nickname chaos , which is tattooed across the top of my back and Ninja is because my most completed martial art is ninjutsu so i use chaotykxninja as my username for every single site i use.
I think You think you think like me but thinking that you can think the way I think is a proof that you only think that you think the way I think while in reality you don't think the way I think......THINK ABOUT IT !
Re: What is your username?
My name is Talha and 52 is the no. of accounts i have on the Internet
mine is just random ......teachers used to call us PUNKs for nothing....and slowly it became a habit to add punk for making an account and it seems that punk wasnt used by lot in usernames and making a/c so thats the story....
try and knock me down but i'm still standing, try and knock me down but i'm still here, you may fade away but i won't disapear and i'm not going anywhere.
Re: What is your username?
My username is C WET... my first name is christian and my last name is sweat... ( yes like persperation )... anyway one of my army buddies one day just called me C WET and it stuck... soo i use it for alot of stuff now... my wife likes it too cuz well.. the 2nd half is a verb explaining how i get her.. if ya know what i mean...
My username is C WET... my first name is christian and my last name is sweat... ( yes like persperation )... anyway one of my army buddies one day just called me C WET and it stuck... soo i use it for alot of stuff now... my wife likes it too cuz well.. the 2nd half is a verb explaining how i get her.. if ya know what i mean...
did you saved her from drowning or something .....if another then my bad ....but it looks its pretty romantic hehehh ...cool cool
My username is C WET... my first name is christian and my last name is sweat... ( yes like persperation )... anyway one of my army buddies one day just called me C WET and it stuck... soo i use it for alot of stuff now... my wife likes it too cuz well.. the 2nd half is a verb explaining how i get her.. if ya know what i mean...
^^ Ofcourse dude... Well done
Originally Posted by PUNK
mine is just random ......teachers used to call us PUNKs for nothing....and slowly it became a habit to add punk for making an account and it seems that punk wasnt used by lot in usernames and making a/c so thats the story....
^^ Then everyone here can call you punk routinely, and you will not have any reason to get angry, lol.
Originally Posted by Talha52
My name is Talha and 52 is the no. of accounts i have on the Internet
^^ Wow.. Really? How do you manage
Originally Posted by chaotykxninja
My MMA Career produced my nickname chaos , which is tattooed across the top of my back and Ninja is because my most completed martial art is ninjutsu so i use chaotykxninja as my username for every single site i use.
^^ Did you learn ninja arts? I think they are lost in time. Or Are you just kidding.?