Math Is Fun Forum

  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2023-04-21 17:30:05

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 48,086

Time

Time

Summary

Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, to compare the duration of events or the intervals between them, and to quantify rates of change of quantities in material reality or in the conscious experience. Time is often referred to as a fourth dimension, along with three spatial dimensions.

Time has long been an important subject of study in religion, philosophy, and science, but defining it in a manner applicable to all fields without circularity has consistently eluded scholars. Nevertheless, diverse fields such as business, industry, sports, the sciences, and the performing arts all incorporate some notion of time into their respective measuring systems.

Time in physics is operationally defined as "what a clock reads".

The physical nature of time is addressed by general relativity with respect to events in spacetime. Examples of events are the collision of two particles, the explosion of a supernova, or the arrival of a rocket ship. Every event can be assigned four numbers representing its time and position (the event's coordinates). However, the numerical values are different for different observers. In general relativity, the question of what time it is now only has meaning relative to a particular observer. Distance and time are intimately related, and the time required for light to travel a specific distance is the same for all observers, as first publicly demonstrated by Michelson and Morley. General relativity does not address the nature of time for extremely small intervals where quantum mechanics holds. As of 2023, there is no generally accepted theory of quantum general relativity.

Time is one of the seven fundamental physical quantities in both the International System of Units (SI) and International System of Quantities. The SI base unit of time is the second, which is defined by measuring the electronic transition frequency of caesium atoms. Time is used to define other quantities, such as velocity, so defining time in terms of such quantities would result in circularity of definition. 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. To describe observations of an event, a location (position in space) and time are typically noted.

The operational definition of time does not address what the fundamental nature of time is. It does not address why events can happen forward and backward in space, whereas events only happen in the forward progress of time. Investigations into the relationship between space and time led physicists to define the spacetime continuum. General relativity is the primary framework for understanding how spacetime works. Through advances in both theoretical and experimental investigations of spacetime, it has been shown that time can be distorted and dilated, particularly at the edges of black holes.

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, and the swing of a pendulum. 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.

There are many systems for determining what time it is, including the Global Positioning System, other satellite systems, Coordinated Universal Time and mean solar time. In general, the numbers obtained from different time systems differ from one another.

Details

Time is a a measured or measurable period, a continuum that lacks spatial dimensions. Time is of philosophical interest and is also the subject of mathematical and scientific investigation.

Time and its role in the history of thought and action:

Nature and definition of time

Time appears to be more puzzling than space because it seems to flow or pass or else people seem to advance through it. But the passage or advance seems to be unintelligible. The question of how many seconds per second time flows (or one advances through it) is obviously an absurd one, for it suggests that the flow or advance comprises a rate of change with respect to something else—to a sort of hypertime. But if this hypertime itself flows, then a hyper-hypertime is required, and so on, ad infinitum. Again, if the world is thought of as spread out in space-time, it might be asked whether human consciousness advances up a timelike direction of this world and, if so, how fast; whether future events pop into existence as the “now” reaches them or are there all along; and how such changes in space-time can be represented, since time is already within the picture. (Ordinary change can, of course, be represented in a space-time picture: for example, a particle at rest is represented by a straight line and an oscillating particle by a wavy line.)

In the face of these difficulties, philosophers tend to divide into two sorts: the “process philosophers” and the “philosophers of the manifold.” Process philosophers—such as Alfred North Whitehead, an Anglo-American mathematician, scientist. and metaphysician who died in 1947—hold that the flow of time (or human advance through it) is an important metaphysical fact. Like the French intuitionist Henri Bergson, they may hold that this flow can be grasped only by nonrational intuition. Bergson even held that the scientific concept of time as a dimension actually misrepresents reality. Philosophers of the manifold hold that the flow of time or human advance through time is an illusion. They argue, for example, that words such as past, future, and now, as well as the tenses of verbs, are indexical expressions that refer to the act of their own utterance. Hence, the alleged change of an event from being future to being past is an illusion. To say that the event is future is to assert that it is later than this utterance. Then later yet, when one says that it is in the past, he or she asserts that it is earlier than that other utterance. Past and future are not real predicates of events in this view; and change in respect of them is not a genuine change.

Again, although process philosophers think of the future as somehow open or indeterminate, whereas the past is unchangeable, fixed, determinate, philosophers of the manifold hold that it is as much nonsense to talk of changing the future as it is to talk of changing the past. If a person decides to point left rather than to point right, then pointing left is what the future was. Moreover, this thesis of the determinateness of the future, they argue, must not be confused with determinism, the theory that there are laws whereby later states of the universe may be deduced from earlier states (or vice versa). The philosophy of the manifold is neutral about this issue. Future events may well exist and yet not be connected in a sufficiently lawlike way with earlier ones.

One of the features of time that puzzled the Neoplatonist philosopher Augustine of Hippo, in the 5th century CE, was the difficulty of defining it. In one current of 20th-century philosophy of language, however (that influenced by Ludwig Wittgenstein), no mystery was seen in this task. Learning to handle the word time involves a multiplicity of verbal skills, including the ability to handle such connected words as earlier, later, now, second, and hour. These verbal skills have to be picked up in very complex ways (partly by ostension), and it is not surprising that the meaning of the word time cannot be distilled into a neat verbal definition. (It is not, for example, an abbreviating word like bachelor.)

The philosophy of time bears powerfully on human emotions. Not only do individuals regret the past, they also fear the future, not least because the alleged flow of time seems to be sweeping them toward their deaths, as swimmers are swept toward a waterfall.

Prescientific conceptions of time and their influence:

The individual’s experience and observation of time

The irreversibility and inexorability of the passage of time is borne in on human beings by the fact of death. Unlike other living creatures, they know that their lives may be cut short at any moment and that, even if they attain the full expectation of human life, their growth is bound to be followed by eventual decay and, in due time, death (see also time perception).

Although there is no generally accepted evidence that death is not the conclusive end of life, it is a tenet of some religions (e.g., of Zoroastrianism, Judaism, Christianity, and Islam) that death is followed by everlasting life elsewhere—in Sheol, hell, or heaven—and that eventually there will be a universal physical resurrection. Others (e.g., Buddhists, Orphics, Pythagoreans, and Plato) have held that people are reborn in the time flow of life on earth and that the notion that a human being has only one life on earth is the illusion of a lost memory. The Buddha claimed to recollect all of his previous lives. The Greek philosophers Pythagoras and Empedocles, of the 6th and early 5th centuries BCE, whose lives probably overlapped that of the Buddha, likewise claimed to recollect some of their previous lives. Such rebirths, they held, would continue to recur unless a person should succeed in breaking the vicious circle (releasing oneself from the “sorrowful wheel”) by strenuous ascetic performances.

The belief that a person’s life in time on earth is repetitive may have been an inference from the observed repetitiveness of phenomena in the environment. The day-and-night cycle and the annual cycle of the seasons dominated the conduct of human life until the recent harnessing of inanimate physical forces in the Industrial Revolution made it possible for work to be carried on for 24 hours a day throughout the year—under cover, by artificial light, and at a controlled temperature. There is also the generation cycle, which the Industrial Revolution has not suppressed: the generations still replace each other, in spite of the lengthening of life expectancies. In some societies it has been customary to give a man’s son a different name but to give his grandson the same name. To name father and son differently is an admission that generations change, but to name grandfather and grandson the same is perhaps an intimation that the grandson is the grandfather reincarnate.

Thus, though all human beings have the experience of irreversible change in their own lives, they also observe cyclic change in the environment. Hence, the adherents of some religions and philosophies have inferred that, despite appearances, time flows cyclically for the individual human being too.

The human experience and observation of time has been variously interpreted. Parmenides, an Eleatic philosopher (6th–5th century BCE) and Zeno, his fellow townsman and disciple, held that change is logically inconceivable and that logic is a surer indicator of reality than experience; thus, despite appearances, reality is unitary and motionless. In this view, time is an illusion. The illusoriness of the world that “flows” in time is also to be found in some Indian philosophy. The Buddha and, among the Greeks, Plato and Plotinus, all held that life in the time flow, though not wholly illusory, is at best a low-grade condition by comparison, respectively, with the Buddhist nirvana (in which desires are extinguished) and with the Platonic realm of forms—i.e., of incorporeal timeless exemplars, of which phenomena in the time flow are imperfect and ephemeral copies.

It has been held, however—e.g., by disciples of the Greek philosopher Heracleitus—that the time flow is of the essence of reality. Others have held that life in the time flow, though it may be wretched, is nevertheless momentous, for it is here that people decide their destinies. In the Buddhist view, a person’s conduct in any one of successive lives on earth will increase or diminish that person’s prospects of eventually breaking out of the cycle of recurrent births. For those who believe in only one earthly life, however, the momentousness of life in the time flow is still greater because this life will be followed by an everlasting life at a destination decided by conduct in this brief and painful testing time. The view that life in time on earth is a probation for weal or woe in an everlasting future has often been associated—as it was by the Iranian prophet Zarathustra (Zoroaster; c. 600 BCE)—with a belief in a general judgment of all who have ever lived to be held on a common Judgment Day, which will be the end of time. The belief in an immediate individual judgment was also held in pharaonic Egypt. Both of these beliefs have been adopted by Jews, Christians, and Muslims.

Cyclic view of time in the philosophy of history

The foregoing diverse interpretations of the nature and significance of the individual human being’s experience and observation of time differ sharply from each other, and they have led to equally sharp differences in views of human history and of ultimate reality and in prescriptions for the conduct, both collective and individual, of human life. Thinkers have been divided between holders of the cyclic view and holders of the one-way view of time and between believers in the different prescriptions for the conduct of life that these differing views have suggested. Variations in the two basic views of time and in the corresponding codes of conduct have been among the salient characteristics distinguishing the principal civilizations and philosophies and higher religions that have appeared in history to date.

Environmental recurrences and religion

The cyclic theory of time has been held in regard to the three fields of religion, of history (both human and cosmic), and of personal life. That this view arose from the observation of recurrences in the environment is most conspicuously seen in the field of religion. The observation of the generation cycle has been reflected in the cult of ancestors, important in Chinese religion and also in older civilizations and in precivilizational societies. The observation of the annual cycle of the seasons and its crucial effect on agriculture is reflected in a ceremony in which the emperor of China used to plow the first furrow of the current year; in the ceremonial opening of a breach in the dike of the Nile to let the annual floodwaters irrigate the land; and in the annual “sacred marriage,” performed by a priest and priestess representing a god and goddess, which was deemed to ensure the continuing fertility of Babylonia. A cycle longer than that of the seasons is represented by the recurrent avatars (incarnations) of the Indian god Vishnu, one of the most popular deities of Hinduism, and in the corresponding series of buddhas and bodhisattvas (buddhas-to-be). Although the only historical Buddha was Siddhartha Gautama (6th–5th century BCE), in the mythology of the northern school of Buddhism (the Mahayana) the identity of the historical Buddha has been almost effaced by a long vista of putative buddhas extending through previous and future times.

In contrast to northern Buddhism and to Vaishnava (Vishnu-devoted) Hinduism, Christianity holds that the incarnation of God in Jesus was a unique event, yet the rite of the Eucharist, in which Christ’s self-sacrifice is held by Roman Catholic and Eastern Orthodox Christians to be reperformed, is celebrated every day by thousands of priests, and the nature of this rite has suggested to some scholars that it originated in an annual festival at the culmination of the agricultural year. In this interpretation, the bread that is Christ’s body and the wine that is his blood associate him with the annually dying gods Adonis, Osiris, and Attis—the divinities, inherent in the vital and vitalizing power of the crops, who die in order that people may eat and drink and live. “Unless a grain of wheat falls into the earth and dies, it remains alone; but, if it dies, it bears much fruit” (John 12:24).

The cyclic view in various cultures

The cyclic view of history, both cosmic and human, has been prevalent among the Hindus and the pre-Christian Greeks, the Chinese, and the Aztecs. More recently, the cyclic view has gained adherents in modern Western society, although this civilization was originally Christian—that is, was nurtured on a religion that sees time as a one-way flow and not as a cyclic one.

The Chinese, Hindus, and Greeks saw cosmic time as moving in an alternating rhythm, classically expressed in the Chinese concept of the alternation between yin, the passive female principle, and yang, the dynamic male principle.   When either yin or yang goes to extremes, it overlaps the other principle, which is its correlative and complement in consequence of being its opposite. In the philosophy of Empedocles, an early Greek thinker, the equivalents of yin and yang were Love and Strife. Empedocles revolted against the denial of the reality of motion and plurality that was made by his Eleatic predecessors on the strength of mere logic. He broke up the Eleatics’ motionless, and therefore timeless, unitary reality into a movement of four elements that were alternately harmonized by Love and set at variance by Strife. Empedocles’ Love and Strife, like yin and yang, each overlapped the other when they had gone to extremes.

Plato translated Empedocles’ concept from psychological into theistic terms. At the outset, in his view, the gods guide the cosmos, and they then leave it to its own devices. But when the cosmos, thus left to itself, has brought itself to the brink of disaster, the gods resume control at the 11th hour—and these two phases of its condition alternate with each other endlessly. The recurrence of alternating phases in which, at the darkest hour, catastrophe is averted by divine intervention is similarly an article of Vaishnava Hindu faith. In guessing the lengths of the recurrent eons (kalpas), the Hindus arrived, intuitively, at figures of the magnitude of those reached by modern astronomers through meticulous observations and calculations. Similarly, the Aztecs of Mesoamerica rivaled modern Westerners and the Hindus in the scale on which they envisaged the flow of time, and they kept an astonishingly accurate time count by inventing a set of interlocking cycles of different wavelengths.

Plato and Aristotle took it for granted that human society, as well as the cosmos, has been, and will continue to be, wrecked and rehabilitated any number of times. This rhythm can be discerned, as a matter of historical fact, in the histories of the pharaonic Egyptian and of the Chinese civilizations during the three millennia that elapsed, in each of them, between its first political unification and its final disintegration. The prosperity that had been conferred on a peasant society by political unity and peace turned into adversity when the cost of large-scale administration and defense became too heavy for an unmechanized economy to bear. In each instance, the unified state then broke up—only to be reunited for the starting of another similar cycle. The Muslim historian Ibn Khaldūn, writing in the 14th century CE, observed the same cyclic rhythm in the histories of the successive conquests of sedentary populations by pastoral nomads.

In the modern West, an Italian philosopher of history, Giambattista Vico, observed that the phases through which Western civilization had passed had counterparts in the history of the antecedent Greco-Roman civilization. Thanks to a subsequent increase in the number of civilizations known to Western students of cultural morphology, Oswald Spengler, a German philosopher of history, was able, in the early 20th century, to make a comparative study of civilizations over a much broader spectrum than that of Vico. The comparison of different civilizations or of successive periods of order and disorder in Chinese or in pharaonic Egyptian history implied, of course, that, in human affairs, recurrence is a reality.

The application of the cyclic view to the life of a human being in the hypothesis of rebirth was mentioned earlier. This hypothesis relaxes the anxiety about being annihilated through death by replacing it with a no less agonizing anxiety about being condemned to a potentially endless series of rebirths. The strength of the reincarnationists’ anxiety can be gauged by the severity of the self-mortification to which they resort to liberate themselves from the “sorrowful wheel.” Among the peoples who have not believed in rebirth, the pharaonic Egyptians have taken the offensive against death and decay with the greatest determination: they embalmed corpses; they built colossal tombs; and, in the Book of the Dead, they provided instructions and spells for ensuring for that portion of the soul that did not hover around the sarcophagus an acquittal in the postmortem judgment and an entry into a blissful life in another world. No other human society has succeeded in achieving this degree of indestructibility despite the ravages of time.

One-way view of time in the philosophy of history

When the flow of time is held to be not recurrent but one-way, it can be conceived of as having a beginning and perhaps an end. Some thinkers have felt that such limits can be imagined only if there is some timeless power that has set time going and intends or is set to stop it. A god who creates and then annihilates time, if he is held to be omnipotent, is often credited with having done this with a benevolent purpose that is being carried out according to plan. The omnipotent god’s plan, in this view, governs the time flow and is made manifest to humans in progressive revelations through the prophets.

This belief in Heilsgeschichte (salvational history) has been derived by Islam and Christianity from Judaism and Zoroastrianism. Late in the 12th century, the Christian seer Joachim of Fiore saw this divinely ordained spiritual progress in the time flow as unfolding in a series of three ages—those of the Father, the Son, and the Spirit. Karl Jaspers, a 20th-century Western philosopher, discerned an “axial age”—i.e., a turning point in human history—in the 6th century BCE, when Confucius, the Buddha, Zarathustra, Deutero-Isaiah, and Pythagoras were supposedly alive contemporaneously. If the axial age is extended backward in time to the original Isaiah’s generation and forward to the Prophet Muhammad’s, it may perhaps be recognized as the age in which humans first sought to make direct contact with the ultimate spiritual reality behind phenomena instead of making such communication only indirectly through their nonhuman and social environments.

The belief in an omnipotent creator god, however, has been challenged. The creation of time, or of anything else, out of nothing is difficult to imagine, and, if God is not a creator but is merely a shaper, his power is limited by the intractability of the independent material with which he has had to work. Plato, in the Timaeus, conceived of God as being a nonomnipotent shaper and thus accounted for the manifest element of evil in phenomena. Marcion, a 2nd-century Christian heretic, inferred from the evil in phenomena that the creator was bad and held that a “stranger god” had come to redeem the bad creator’s work at the benevolent stranger’s cost. Zarathustra saw the phenomenal world as a battlefield between a bad god and a good one and saw time as the duration of this battle. Though he held that the good god was destined to be the victor, a god who needs to fight and win is not omnipotent. In an attenuated form, this evil adversary appears in the three Judaic religions as Satan.

Observation of historical phenomena suggests that, in spite of the manifestness of evil, there has been progress in the history of life on this planet, culminating in the emergence of humans who know themselves to be sinners yet feel themselves to be something better than inanimate matter. Charles Darwin, in his theory of the selection of mutations by the environment, sought to vindicate apparent progress in the organic realm without recourse to an extraneous god. In the history of Greek thought, the counterpart of such mutations was the swerving of atoms. After Empedocles had broken up the indivisible, motionless, and timeless reality of Parmenides and Zeno into four elements played upon alternately by Love and Strife, it was a short step for the atomists of the 5th century BCE, Leucippus and Democritus, to break up reality still further into an innumerable host of minute atoms moving in time through a vacuum. Granting that one single atom had once made a single slight swerve, the build-up of observed phenomena could be accounted for on Darwinian lines. Democritus’s account of evolution survives in the fifth book of De rerum natura, written by a 1st-century-BCE Roman poet, Lucretius. The credibility of both Democritus’s and Darwin’s accounts of evolution depends on the assumption that time is real and that its flow has been extraordinarily long.

Heracleitus had seen in phenomena a harmony of opposites in tension with each other and had concluded that War (i.e., Empedocles’ Strife and the Chinese yang) “is father of all and king of all.” This vision of Strife as being the dominant and creative force is grimmer than that of Strife alternating on equal terms with Love and yin and yang. In the 19th-century West, Heracleitus’s vision was revived in the view of G.W.F. Hegel, a German idealist, that progress occurs through a synthesis resulting from an encounter between a thesis and an antithesis. In political terms, Heracleitus’s vision reappeared in Karl Marx’s concept of an encounter between the bourgeoisie and the proletariat and the emergence of a classless society without a government.

In the Zoroastrian and Jewish-Christian-Islamic vision of the time flow, time is destined to be consummated—as depicted luridly in the Revelation to John—in a terrifying climax. It has become apparent that history has been accelerating, and accumulated knowledge of the past has revealed, in retrospect, that the acceleration began about 30,000 years ago, with the transition from the Lower to the Upper Paleolithic Period, and that it has taken successive “great leaps forward” with the invention of agriculture, with the dawn of civilization, and with the progressive harnessing—within the last two centuries—of the titanic physical forces of inanimate nature. The approach of the climax foreseen intuitively by the prophets is being felt, and feared, as a coming event. Its imminence is, today, not an article of faith but a datum of observation and experience.

GettyImages-134043459-584c2c263df78c491e939046.jpg


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

Board footer

Powered by FluxBB