The Certainty of Change
The phenomenon of Change is expressed and witnessed by all people. Transience of all processes in nature is a readily available knowledge, which requires no proof. The observers themselves are manifestations of the unstoppable process of change in time, on the individual's level.
Heraclitus, 5th century BC, presented his observation about the nature of flux in all phenomena; however, his views were not well received:
“According to both Plato and Aristotle, Heraclitus held extreme views that led to logical
incoherence. For he held that /1/ everything is constantly changing and /2/ opposite things
are identical, so that /3/ everything is and is not at the same time. In other words,
Universal Flux and the Identity of Opposites entail a denial of the Law of Non-Contradiction”. (*)
Opposition to Heraclites' view was based on the argument that:
“If F is the same as G because F turns into G, then the two are not identical. And Heraclitus
insists on the common-sense truth of change: "Cold things warm up, the hot cools off, wet
becomes dry, dry becomes wet".
This sort of mutual change presupposes the non-identity of the terms". (**)
Heraclites was pointing out to a natural phenomenon of change, while his opponents were pointing to their own system of thinking, which they established. Their worry was about hHow would the “idea” of change fit within their system of thoughts? That was the “problem”, the phenomenon of change was creating!
The problem, of course, lies in the inflexible and incomplete definition of the Identity of objects: (A = A), a definition, which does not allow for the potential of change to take place. For example, many things are affected by temperature; water, metal, or rocks and stones: becoming warm under the sun and cool at night. Warm and cold are two opposing properties - but this fact does not create any contradiction in the identity of the object, which has the potential to manifest either state of temperature - depending on available conditions.
The prevailing tendency over hundreds of years in Western philosophical contemplation displayed loyalty - or attachment - to the authority of Plato and Aristotle, who both disagreed with Heraclites views about the universality of Change. The problem of mistaken conclusions, caused by following “the authority” rather than direct observation and reason - had to find its solution in the rebellion of science in the 17th century, divorcing itself from stagnation and fear from dominating authorities.
The philosophical significance of the “Rate of Change”
The mathematical tool of Calculus paved the way for close examination of the mechanism operating in various natural phenomena displaying growth (or decay) in time. For example, the rate of increase in population, the growth in bank interest rate, the rate of decay of radioactive materials, the rate of spread of disease, etc… all can be examined through differential calculus, and in the process, the rate of change of the mentioned processes manifests an exponential function ( e^x) studied in details by Leonhard Euler (1707 - 1783).
The essence of this function is that: at any moment in time, it changes in such a way that it keeps equaling itself.
The rate of change of ( y = e^t ) is equal to its derivative: dy / dt = d e^t/ dt = e^t (which means that the "rate of change" of the function is the function itself!).
Here is a function describing growth (and - reversely - decline) of a certain phenomenon, yet it is always stays equal to its own speed of change.
(A Journey into Mathematics “1089 and all that”, p.126, David Acheson, Oxford University Press, ISBN: 0 198516231)
This property of 'preserving own essence despite occurring changes' - has a philosophical significance in the field of Identity through the question: how can identity develop in time but stay always itself, the same. In mathematical modeling, any process (A), which manifests exponential growth or decline, as a function of time: A = A(t) – has its rate of change in time (dA/dt) equal to itself (A).
The Certainty of Life and Death
The phenomenon of change is specifically manifest in one's own existence. Eastern philosophy approached the quest for Certainty through observing “Life and Death”, as occurrences, which are beyond any doubt. Certainty becomes anchored here with the undeniable. Benjamin Franklin (1817) jokingly mentioned that “In this world nothing can be certain, except death and taxes” - and while tax evaders can find one part of this statement funny, the other part is quiet serious. The approach towards this serious matter differs greatly between individuals and cultures:
“Death makes room for renewal and regeneration. Death should therefore be appreciated,
like life, as a blessing....death [is] a period of rest, like sleep, by which life regains energy
and prepares for new cycles of living.
Thus there is no reason to fear death, to hate or seek to banish it from our minds”.(#)
Limiting our current observation, however, to the processes occurring between birth and death of this present lifetime - the certainty of change is at work at the background of all events. The truth of change is valid not only for individual entities but it governs all phenomena in the universe, according to Nichiren (1222 -1282):
"No phenomena - heaven or earth, Yin or Yang, the sun and moon, the five planets,
or any life-condition from Hell to [Enlightenment] - are free from birth and death.
Thus the life and death of all phenomena
are simply the two phases of Myoho, [the universal law of cause and effect]." (##)
(*), (**) Heraclitus, Internet Encyclopedia of Philosophy http://www.iep.utm.edu/heraclit/
(#) Death gives greater meaning to life, D. Ikeda
(##) The Ultimate Law of Life, Nichiren http://www.nichirenlibrary.org/en/wnd-1/Content/29