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Intellectual history of time

History is not just an ordered set of singular events. It is a subtle underground movement in the minds, materials, and organization of a society. To comprehend history is not merely to know a given set of facts, but to know the factors, the state of the world and the mental state of the people that had inherited it at that moment, and not only statically but dynamically - the ebbs and flows of a social milieu like the moods of a personal friend - to understand that history has existed, not merely as a phantom, but as a complex and subtle reality that was felt intimately by its many voyagers.

Often, as remains the case today, "history" happens for the sole reason that it fails to be comprehended as such. For it is this, our inability to disassociate its affects from our most deeply felt and personal feelings, our failure to separate the convulsions of our minds and emotions from the flow of social information, from the sociology of knowledge and memetics, through which it becomes manifest. True history is something that we are immersed in, and it is by that very fact that it becomes history. Anything that effects us intellectually or emotionally is the progenitor of the collective behavior of our species, which then becomes our knowledge, which we pass down through tradition and culture.

It is for this reason that the very word history comes from the Greek word for investigation. There is no "history", just investigations (histories) of the past made by different people and left behind for others to read. For alas, no matter how advanced our technology, there is no way to be God and to be able to look back through time. We actually can only use technology to study the present, and make inferences about the past, and these inferences are necessarily faulty, for our science must by its very nature assume uniformity of processes, equality of time intervals, and other fictions that cannot be gotten around. For example, one can look at the Grand Canyon and "see" how it evolved over millions of years from the river flowing through it eating away at the rocks, or one can be God and see how what really happened was a gigantic flood that made the canyon in weeks, and left a little river at the bottom. It's the ultimate contradiction of history that catastrophes aren't subject to science, and hence the biggest history-makers are unrepeatable in a laboratory.

So, too, along with natural history, the history of ideas, including the way that we experience (socially) and measure time has evolved. By way of the changing tempo and structure of our lives through the passing generations, contorted by inventions, ideas, art, and altogether changing paradigms and philosophies, we have consistently found new ways to remedy time's obscure procession with our changing modes of measurement and interaction. Our conceived notions of time have developed in accordance with our art, our science, and our social infrastructure.

The intellectual history of time is a subtle progression that weaves through the collective experience of generations, as it weaves through each individual's emotional and intellectual lives.

At first, time was ripped from nature and turned into a monotonous and perfect citadel of periodicity and regularity. Was it the regular dripping of water, or the regular movement of heavenly bodies that gave primitive man his first concept of time? The regular return of the seasons, the death and rebirth of vegetation have not only been the basis of religion but of religious calendars which use either the moon or the sun cycle. Even today most modern people think of time via solar days and years. The intellectual attempt to look back in time by numbering the years is all but irresistible, even unavoidable. Nothing shocks the modern mind more than the thought that the day or the year has not always been the same length, or that the world might only be thousands rather than billions of years old. The debate continues today.

But time has burst religious confines. With Einstein's theory it became secularized. With quantum physics it ??, and now it has fully decentralized and lost altogether its regular, periodic form, endowing itself with a more complex and subtle beauty.

Irregular time

At one point in human history, time was, so to speak, irrelevant. The concept of time as we know it was absent from the human psyche, insofar as 'time' is a developed concept relating to a set of measurements that we use in our daily lives; insofar as it is a complex of ideas related to a set of practices and the sound of the word 'time' in our language, a language and a set of practices that at one point did not exist.

Early humans did not rely on time in the sophisticated sense that we do now. They hunted, gathered, and slept. The stars were but a passing curiosity, the cycles of light and dark an uncontemplated phenomenon, and the seasons might well have been random for all humans were concerned. They had the concepts of before and after, and they saw the days pass. They cared or knew little beyond this regarding time.

This was the pre-horticultural society[?] era; before agriculture was invented. With the invention of agriculture in the 3rd millennium BC, people relied heavily on the cycles of the season for planting and harvesting crops. Most humans came to live in settled societies. Over time, people came to associate changing patterns of the stars with the seasons. This was the beginning of calendars.

This early conception of time was based on the setting and rising of the sun. Only the learned could use astronomy to jiggle-in and jiggle-out days to make the lunar and solar calendars coincide, but even to them the idea of "10:14 A.M." or "6:23 P.M." would be unreachable - a sundial isn't that precise. It took centuries for technology to make time measurement accurate enough for seconds, milliseconds, microseconds, nanoseconds, picoseconds, femtoseconds, attoseconds to have a realistic meaning.

In 650 BC, when the water clock[?] was invented, time was first synchronized accordingly, so that in winter the hours were shorter and in summer they were longer.

Isochronous time

In 1502 AD came the pocketwatch[?]

?date? the clock tower[?](isochronous time straightened the roads, dualism of time and space- (the metric tensor, foreshadow relativity -this is actually when bars closed at 2:00))

With invention of the pendulum in 1657 came isochronous time, although the time was still adjusted to match what was thought of as 'natural time', the angle of the sun on the horizon. Isochronous time was seen as a problem more than a solution, because people's lives still revolved around the light needed to see. The acceptance of isochronous time had to wait until 1879 when the light bulb was invented.

But the clocks were still aligned with the rise of the sun. It took the steam enginge to completely divorce time from the sun. Invention of the locomotive in 1830, time had to be synchronized across vast distances in order to organize the train schedules. This eventually led to the development of time zones, and, of course, global isochronous time.



The isochronous clock changed our lives. The all-powerful business day revolved around it - the bars close at 2:00, and appointments were no longer 'within the hour', but on the hour, and five minutes was late (except if we're talking about a party). Time technology turned human life into a rigorous schedule, made humans part of a societal machine that used money as lubricant.

Relative time

The train wasn't finished altering the way we perceive time. In 1915, it would contort time like never before. It found its way into an essay regarding time, simultaneity, and the speed of light. This was Einstein's theory of relativity.

Chaotic time

In physics, the treatment of time is a quintessential issue because it amounts to a question of geometry. (See: philosophy of physics)

As our experience of time has changed with technological advances, new ways of thinking about time have become creatively more accessible. New concepts have been introduced, and new models have been inspired by our wonderment about the workings of our technology, as well as the new ways of interacting with our environment and eachother that technology has invoked. Some examples of this are: information theory, cybernetics, network theory[?], and emergence. These ideas contribute to our understanding of physics, and open up new areas of mathematical dialogue.

It is important to develop a thorough understanding of how the treatment of time in physics has evolved, in order to become sensitive to the contemporary influences which direct the progress of physics today. For, as Friedrich Nietzsche once said, "No stream is large and copious of itself, but is fed and guided by so many tributary currents. So it is with all intellectual greatness: it is simply a matter of pointing the way suggested by so many affluents, not whether one was richly or poorly gifted to begin with."

This survey seeks to elucidate the currents of history which have led us down the intellectual path we travel today, and those current which are still formulating in the hearts and minds of our generation. We hope that it may serve as a compass for those who seek new shores; we hope that it might "point the way" to fresh continents of understanding.

hash this to the above{

Communication technologies affect our perception of time by altering the way our nervous system experiences events that occur in space and time.

The tempo of experience alters the topology of information.

Which 20th century philosopher was it who said that time might only be man's sense that he isn't omnipotent, and can't change everything in the universe at once? For if he could, time would be irrelevant, since he could rearrange the universe to look like it was "an hour ago", and it would BE an hour ago.

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Newtonian physics and linear time

In 1665, when Isaac Newton invented the calculus to describe the motion of objects falling under gravity, the first mathematical/physical treatment of time began: linear time. (reversible physics) -universal clock.

$F= m\frac{\partial ^2d}{\partial t^2}$ (force)
$W= \int_{x_i}^{x_f}Fdx$ (work)
$a_g= \frac{m_1 m_2}{d^2 G}$ (acceleration due to gravity)
$E= \frac{1}{2} mv^2$ (kinetic energy)

Thermodynamics and the paradox of irreversibility

1824 - Sadi Carnot scientifically analyzed the steam engines

1st law of thermodynamics - the law of conservation of energy

2nd law of thermodynamics - the law of entropy

$E = ...$ (thermal energy)
$ds = ...$
$\frac{\partial ^2T}{\partial t^2} =\frac{\partial T}{\partial x}$

The Heat equation

$\frac{ du}{dt}=\nabla ^2 u$

Electromagnetism and the speed of light

Somewhere between 1831 and 1879, James Clerk Maxwell developed a combined theory of electricity and magnetism. These vector calculus equations which use the del operator ($\nabla$) are known as Maxwell's equations for electromagnetism, when a vacumm is assumed, they are as follows:

$\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{c\partial t}$
$\nabla \times \mathbf{B} = \frac{\partial \mathbf{E}}{c\partial t}$
$\nabla \cdot \mathbf{E} = 0$
$\nabla \cdot \mathbf{B} = 0$

where c is a constant that represents the speed of light in vacuum, E is the electric field, and B is the magnetic field.

The Wave equation

$\frac{ d^2y}{dt^2}=c^2 \nabla ^2 u$

Einsteinian physics and time

In 1875, Hendrik Lorentz discovered the Lorentz transformation, upon which Einstein's theory of relativity, published in 1915, is based. The Lorentz transformation states that the speed of light is constant in all inertial frames.

Einstein's theory of relativity uses Riemannian geometry, employing the metric tensor which describes Minkowski space: $[(dx^1)^2+(dx^1)^2+(dx^2)^2+(dx^3)^2-c(dt)^2)]$, to develop a geometric solution to Lorentz's transformation that preserves Maxwell's equations.

Einstein's theory was motivated by the assumption that no point in the universe can be a 'center', and that correspondingly, physics must act the same in all inertial frames. His simple and elegant theory shows that time is relative to the inertial frame, i.e. that there is no 'universal clock'. Each inertial frame has it's own local geometry.

$E^2 = m^2c^4+p^2c^2$ (atomic energy)

E = energy, m = mass, p = momentum, c = the speed of light

Quantum physics and time

The Fourier Transform

$F(s) = \int_0^{\infty} e^{-its}f(t)dt$

1926, Erwin Schrödinger, quantum wave mechanics

The Schrödinger equation

$ih\frac{\partial \Psi(\mathbf{r},t)}{\partial t} = -\frac{h^2}{2m}\nabla ^2 \Psi(\mathbf{r},t)+V(\mathbf{r},t)\Psi(\mathbf{r},t)$

describes the time evolution fo the wave function($\Psi$)

Dynamical systems and nonlinear time

This theory exploits the concept of nonlinearity, treating time as the fact of the presence of nonlinearity; of irreversibility. That is, time is nonlinearity. This theory creates a fascinating relation among time, state, information, and process.

In this perspective, one could say that time is a parameterization of a dynamical system that allows the geometry of the system to be manifested and operated on.

The most revolutionary product of this theory, is that in it, time is not assumed. Rather, time is an implicit consquence of Chaos. (i.e. nonlinearity/irreversibility[?])

Like Einstein's theory, this precludes the possibility of a universal clock. However, it goes even further, destroying the assumption of linear time, and presenting nonlinear time, which is an extension of the characteristic time[?], of a system. Time can actually be fractal, as Mandlebrot[?] shows in his book "Multifractals and 1/f noise", which introduces intrinisic time[?]. Intrinsic time is a more general form of characteristic time, with greater implications (e.g. allusions to topolopgy and 'intrinsic curvature', hinting at a nonlinear form of Special Relativity) The most profound implication of intrinsic time is that each 'system' (not to be confused with inertial frame) has it's own time, that may not be linearly related to the time of other systems.

Intrinsic time is 'real' because the given system only becomes mathematically amenable in it's intrinisic time. Intrinsic time is both physically measurable and physically meaningfull. It also enables greater scientific and technological progress.

These times all come into play in the process of non-dimensionalizing[?] (i.e. dimensional analysis), which is used extensively in physics. When one non-dimensionalizes a dynamical system, one is tacitly assuming that time "behaves" in a certain way. A summary of mentioned 'time's is as follows:

linear time - time that is involved in non-chaotic differential equations, and mutually, a geometry that consists of smooth manifolds.
nonlinear time - time that is involved in nonlinear differential equations.

characteristic time - time normalized to the relevant system
intrinsic time - characteristic time of a system of non-integral dimension.

Despite this theory's lack of articulation, in its embryonic youth it is breaking ground and tearing its way through what were once very difficult problems, opening up new insights in its wake. This is the exciting frontier of physics. Some physicists even go so far as to say that particle physics is dead, disreputing what they consider to be the perverted and outmoded reductionism that began with Democritus. (See: philosophy of science) One of the strongest mathematical arguments against particle physics is based on fractional brownian motion[?].

• A Brief Outline of History - H.G. Wells
• The Discoverers - Daniel J. Boorstein
• Theory Out of Bounds - Isabelle Stengers/Ilya Prigogine
• Order out of Chaos - Ilya Prigogine
• Multifractals and 1/f noise - Benoit Mandlebrot
• Understanding Media - Marshall McLughan
• Conversations on Science, Culture, and Time( Studies in Literature and Science) - Michel Serres; et al.
• The Structure of Scientific Revolutions - Thomas S. Kuhn

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