In measuring the existence of matter, scientists have come to speak about the half-life of a reacting substance in chemistry. It is stated that the half-life is not constant, but rather changes as of the extent to which the reaction itself has taken place. The half-life is the time required for half of the amount that is initially present to react. For example, at the end of one half-life, fifty percent (50%) of the originally existing atoms or molecules still remain present. Further, at the end of two half-lives, then, twenty-five percent (25%) remains in existence; and, at the end of three half-lives, twelve and one half percent (12.5%) would remain existent.

The concept of half-life is employed for describing only first-order relations, given that it is useful to employ the concept of half-life instead of a rate constant. While, for all other orders of reaction other than that of the first-order, the half-life is not actually constant, but rather changes depending upon the extent to which the reaction has occurred. And, although radioactive decay is not a chemical process as such, it does follow first-order kinetics, and therefore the rates of radioactive decay are frequently expressed in terms of half-lives of radioactive isotopes.

Chemists research the particular rates of chemical reactions in order to specify the conditions under which a given reaction may be caused to develop at a certain rate. The reaction rate law, by experiment, shows how the rate of a reaction has to do with the concentration of the reactants and other additional substances (catalysts). This involves the sequence of the steps by which the reactants become converted into products. This allows chemists to comprehend how chemical reactions develop at a molecular level. The study of chemical reaction rates (chemical kinetics) helps in understanding the chemistry thereof.

A rate lets us know how fast a quantity is changing or modifying over time. In either direction, then, a reaction rate is the given rate at which a reactant becomes consumed or, the given rate at which a product is formed out of that reactant. The rates of chemical reaction therefore depend upon the amounts/concentrations of the reactants, and the rate of a reaction is proportional to those concentrations raised to the powers of small integers. So, the rate law informs us as to how a reaction rate may depend upon a concentration. In that we have the rate law for a particular equation, and the rate constant (k) of the reaction itself. When the term of the equation is expressed to the first power, the rate law is said to be a first-order rate law, and the reaction may be referred to as a first-order reaction.

Now, the half-life (t_½) of a reactant is the time that is required for the concentration of a reactant to decrease by a factor of two (2). Within the field of chemistry, this is resolved as:

The manner in which this is stated, involves the expression, that the half-life for a first-order decomposition is independent of the initial concentration of the reactant.

Radioactive decay of the nuclei occurs at different rates, varying from a few millionths of a second, to even billions of years. Therefore, and significantly so, radioactive decay is independent of external factors (temperature and pressure), when considered under normal conditions of existence. The rate of radioactive decay processes may not be altered at least with present knowledge. And, it is this particular fact that makes the disposal of radioactive material so difficult to manage.

Thus, once more, the half-life of a radioactive isotope is represented by the time it takes one half of the sample of a particular isotope in question to undergo radioactive decay. And, the various radioisotopes have different half-lives. Whereby the half-life of a radioisotope is one of its singular characteristics and also reveals how quickly it might decay.

However, the one thing that has caught our eye in reviewing the characteristics of chemical reactions concerns the particular number that is employed for the computation of the concept of radioactive decay and that of half-life. In earlier essays, we have shown how within the Sothic calendar, the number/fractal 693 makes its encoded appearance (Cfr., Earth/matriX, Essay No.73). In this extract, we simply wish to draw attention to another significant coincidence, whereby a particular number/fractal encoded into the ancient reckoning system also shares a specific significance with another number of science.

It would be superficial, upon this isolated incident, to suggest that the ancients knew the constant number for computing the half-life of radioactive decay of the elements.

Yet, at the same time, we also witness how the particular half-life of Carbon 14 also represents, as of these computations, a maya number/fractal: 5760 years. Carbon 14 is employed for determining the age of organic material. Again, this simply represents another coincidence. Surely, the ancient maya did not choose such a relevant number/fractal for one of their reckoning categories as of the concept of the half-life of Carbon. This too must represent a mere coincidence. There could be no cognitive basis to their having chosen a particularly significant number/fractal as of the study of chemical reactions and the elements (carbon).

Yet, we may observe how the 693 number/fractal and the 5760 number/fractal do make their appearance once more within another field of science as established by today's standards. Obviously, the .693 number relates to the natural log of 2, which on most contemporary electronic pocket calculators is: .693147181. This would pose the possibility that the 693/fractal encoded into the Sothic Cycle calendar may have represented this particular function. That in itself would appear to be highly improbable. Yet, the coincidences continue to arise regarding the numbers/fractals of the ancient reckoning system and numbers/fractals/constants related to contemporary mathematics.