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 taking place since their birth, on the individual’s level.

Heraclitus, 5th century BD, 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 thingsare 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”.(1)

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, wetbecomes dry, dry becomes wet”.This sort of mutual change presupposes the non-identity of the terms".(2)

Heraclites was pointing to the *objective* phenomenon of change, while his opponents were pointing to the theoretical system of logic, which *they* established. Their worry was about how would the “idea” of change fit within - or support - theirsystem of thoughts; how would the environment agree with their thinking. If identity of object A is fixed as A = A , then acknowledging the truth of change would - of course - lead to ‘contradiction’, because A is naturally destined to change.

The problem here 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, rocks and stones experience a change in their temperature, 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 authorityof Plato and Aristotle, who both disagreed with Heraclites views about the universality of Change.

Many intellectuals realised that following the “Authority” of past thinkers (such as Plato and Aristotle) leads to mistakes - and that the real authority in science should be acknowledged through direct observation and reason. This intellectual drive had its greatest expression in the rebellion of science in the 17th century, divorcing itself from stagnation of concepts imposed by past thinkers and demanding the actual proof as the criterion for validity of suggested concepts.

**The philosophical significance of the concept of “Rate of Change”**

The mathematical tool of Calculus paved the way for close examination of the mechanism operating in various natural phenomena, which display 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 equalling itself’.

Consider the function [y = e^t ]. The rate of change of this function is is equal to its derivative: dy / dt = d [e^t/ dt] = e^t

(which means that the “*rate of change”* of the function is *equal to the function itself!*).

Whether the change is about *growth* or - reversely - about *decline* of a certain phenomenon, the identity of this changing object stays always equal to its own speed of change.

(Source: A Journey into Mathematics “1089 and all that”, p.126, David Acheson, Oxford University Press)

This property of ‘*preserving own essence despite occurring changes*’ - has a philosophical significance in the field of Identity through the question: how can the identity of an object develop in time but still stays always itself; remaining the same.

In mathematical modelling, 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). Mathematics can offer philosophy a proof that an object can preserve its own essence of identity despite experiencing changes in time.

**The Certainty of Life and Death**

The phenomenon of *change* is specifically manifest in one’s own existence. Certainty becomes anchored here with the undeniable truth of life and death. Benjamin Franklin (1817) jokingly mentioned that *“In this world nothing can be certain, except death and taxes”* - and while tax evaders can enjoy part of this statement, the other part - concerning death - is quiet serious. The approach towards this serious matter differs greatly between individuals and cultures. For example, a Buddhist view on death points out that:

“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”. (3)

The processes we experience between birth and death of this present lifetime - are manifestations of the certainty of change, constantly 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 phenomenaare simply the two phases of Myoho, [the universal law of cause and effect].” (4)

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