Where Did Time Get Lost?
Who Found It, Again?
Generally sought after, the ideas of perpetual motion, and transmutations of the abundant into more valued rare stuffs, dominated the thoughts of philosophers and scientists over most of early history. The merger of more complex mathematical modeling tools - and the concepts of equality and equilibrium - defined early systems. Nature's system has its own rules, although perpetual motion is forbidden, step-wise transmutation is continuous, through the nuclear decay process, as a statistical rate, a true Time-based function. Unless forced by Event-driven energy sources, these decay rates are measureably constant... and fuel our Universal Clock, from which we calibrate rates.
Natural Philosophers of Ancient Greek and Persian cultures created geometry and algebra, respectively. The two cultures invented symbolic codes so that they could share their measurements and insights. Clear desert skies, and few city lights made star-gazing a viable, interesting topic of debate... I can imagine the all night ghat chewing sessions in which the various mysteries of the night skies were pondered by our Persian ancestors... In fact, these were the original philosophers, leading eventually to Ptolemy of Alexandria, who in 140AD espoused the Geocentric Universe, in the Megalé syntaxis tes astronomias, later known as the Almagest. Ptolemy introduced trigonometric tables in his discussions of his concept of epicycles, to explain away the observed anomalies.
Nicolaus Copernicus (b1473-d1543) studied the solar system ... Posthumous publication of his De revolucionibus orbium coelestium, in 1543, "revolutionized" astronomy - although it upset "The Church" and its doctrines, created a major opening for Science to reinvest its explanatory powers, through mathematical communications.
There are two realistic methods for making progress in sciences, Inductive and Deductive (the first based on observations, the second based on axioms from previous experience - generating theorems). Despite long-running arguments - there are many unanswered questions. Science progresses by proving that one alternative solution has more validity than another. Surprises abound. Good scientists are rarely surprised when an old accepted theory proves to be false, given new observations.
By the late 16th century, the Scientific Method was truly defined by Galileo Galilei... and Progress takes TIME!
Galileo carried out systematic experiments in astronomy and physics, and encoded his observations and results in mathematical terms. Galileo also used geometry, a legacy of ancient Greek philosophers. He, too, clashed with the Roman Catholic Church over his support of the Heliocentric Theory.
The founder of modern philosophy, René Descartes, in the generation following that of Galileo, employed algebra - per the ancient Persians - to encode his thoughts and explorations of algebraic functions within x,y, z space, his important conceptual legacy for modern science.
In the 17th century, the great German philosopher and mathematician Gottfried Wilhelm Leibniz and the remarkable classical scientist Isaac Newton independently converged on the concepts of calculus, the language of "higher mathematics" that is used today. This allowed them the option of calculating speeds of interactive moving bodies, that resulted in changing rates of acceleration.
Their insight was that calculus allowed Time to become a component of general consideration. No matter what is being examined, measured, or estimated...
Time is Inexorable -
During the 18th and 19th centuries, Newton's Equations of Motion were transformed by a generation of great mathematicians exemplified by Pierre Laplace, Leonard Euler, Joseph Lagrange, and William Hamilton. They measured and then analyzed and described even more natural phenomena. These equations became the basis of a mechanistic paradigm in which it was posited that the world was a machine, a clockworks, and that everything was causal and deterministic.
During the 19th century, as more sophisticated observing tools were invented, the limitations of the Newtonian equations became apparent, and a new school of thinking evolved, greatly attributable the the physicist, James Clerk Maxwell.
Maxwell adopted a statistical method in his studies of the laws of motion of gases, resulting in a new science, statistical mechanics, which was to become the theoretical basis of thermodynamics.
Today, therefore, we have and employ two sets of analytical tools - deterministic equations, from Newton et al., and thermodynamics - from the subsequent statistical physical sciences. Both employ linear equations, as the nonlinear sets are too often insolvable, or extremely difficult.
We are well into transition from the 19th century clockworks world, on to a more complex non-linear world as we enter the 21st century.
Early 1900 scientists pushed knowledge of natural systems forward by using empirical measurements and systematic observations. The Scientific Method would finally cast out the wishful concepts of perpetual motion. However, these were too soon replaced by many other doubtful analogies.
For example, many 19-20th century economist's attempted to evaluate Work in non-energetic terms, using false physical metaphors, in order to shore up the unsure scientific basis of their efforts to forecast economic events, and explain the past.
It simply did not work... There were too many variables unaccounted for in most of these efforts.
Systematic applications of the Scientific Method help scientists both attain, and maintain credibility, although there are many modern instances when application of the so-called "best available science" has failed miserably in attaining its objectives. Loss of credibility is the inevitable outcome of such failures.
Natural resource management issues leap to mind when these topics are broached. The realistic question is what are important renewable resources, and which are the means for managing their removal rates. It is very difficult to identify any natural resources, living or non-renewable, that have been well managed.
In the final decades of the 20th century it has been recognized that due to the networking within animate systems, nonlinear phenomena dominate, and that inanimate interactions are also best described using nonlinear equations. These are very difficult to understand using only mathematical symbols. There seems to always be someone who has been at this impasse, and re-solved the problems by visual methods.
Enter Jules Henri Poincaré, one of the great mathematicians of the 20th century. Poincaré re-evolved the visual mathematical approach that is needed to communicate complex interactions and nonlinear systems behavior. His early explorations of topologies brought him to the doorstep of Chaos Theory, as he discovered patterns that are now called "strange attractors".
Also, early within the 20th century, Poincaré's contemporary, Albert Einstein, published his Theory of Relativity. For the next half century, physicists worked away on the issues of quantum theory and relativity, constantly barking their shins on complex abstractions. Their dilemma was such that many believed that any system that did not behave periodically would be unpredictable, or even more constraining, anything that is measured or observed creates its own cognitive reality.... Theories Abound!
Chaos, Feedback Loops, and Fractals are the new "Buzz". The one common denominator in these new areas of exploration of natural phenomena, and their encoding, is that these analyses are best communicated in visual form. Benoit Mandlebrodt's (1975, 1983) Fractal Geometry of Nature is a classic example of Science as Art.