There is a continuous boggling debate among great thinkers if mathematics is a science in itself, but, one thing is generally accepted that sciences are articulated into the mathematical structure. The application of mathematics in the ancient times was focused more on understanding nature.

Ancient pioneers in science like Plato, Aristotle, Ptolemy etc. were all considered mathematicians and scientists in their attempts to capture the essence of nature through mathematical approximation of intuitive ideas, and descriptions of nature. Boyer (1949), said “The reliance on Mathematics to describe nature is the foundation on which sciences is built”.

Sciences and mathematics are standalone domains, science is characterized by definite procedures for formulation of problems and detailed techniques for solution. Mathematics, on the other hand, is an indispensable tool for procedure as well as essential language of description (Mitra, 2012) that rely more on logical deductions and support the validity and reliability of results of observations and measurements  of scientific experimental tests. In understanding Physics, it requires well-defined problem solving methodologies or algorithms (that should be mastered) to apply the basic mathematical concepts to fully understand the meaning of the basic concepts of physics that we observe in the real world (Boyer, 1949). Geometrical shapes and figures has no meaning unless ratios and proportions can be expressed in mathematical values.

In social and some ecological researches where results are expressed mainly in qualitative description are hard to analyze to establish relationships among variables unless quantitative values can represent the degree or level of perceptions being measured. Only then that data can be subjected to statistical analysis. Usually range are established for a given criteria and scores are approximated to a certain degree or level.

in this way, though not so exactly, results are expressed and understood by the field. Lastly, no field  of science has the liberty to be independent of mathematical process because the only measure of validity and truthfulness of science is the results of both observable and measurable data. Explain how numerical simulation and analysis (or computation) can bridge or increase in scope and range between the conventional experimentation and theory especially in regard to analysis of environmental problems, concerns and issues.

Conventional experiments are characterized by conducting test to measure changes which follows basic scientific methods. Usually variables are subjected to treatments and replications using a randomly selected subjects. The scientific methods involve processes of “systematic observation, measurement, and experiment, and the formulation, testing, and modification of hypotheses” (Oxford Dictionaries).

A general theory may be developed from a well supported hypothesis (Garland, 2015).On the other hand, numerical simulation contains algorithms and equations used to capture behaviors in creating computer system models.  The models that are then run in the program that contains these algorithms and equations is known as computer simulation. Simulation of a system is represented as the running of the system’s model. It can be used to explore and gain new insights into new technology and to estimate the performance of systems too complex for analytical solutions (Strogatz in Brockman, 2007).  At present, mathematical modeling of many natural systems in physics (computational physics), astrophysics, climate science, chemistry, biology, ecology, human systems in psychology, social science, and engineering are using computer simulations as a tool to visualize  predictive spatial and temporal scales of system behaviors.

Digital computer simulation helps study phenomena of great complexity ( Winsberg, 2010) such as weather and climate. Although there is an argument between experimentation and theoretical numerical simulation (computer simulation) which of them is most reliable and valid in the light of environmental science problems especially that variables are subject to dynamic variations and fluctuations, simulation is prone to “representation that fails to represent exactly” (Winsberg, 2010 reviewed by  Jerkert, 2012). The bridge between   conventional experiments and numerical simulation is that the experiment results  are used as the input to the creation of system model simulations.

Simulation worked to build good models of the target system, on the other hand, experiment is based on the object and the target that belong to the system itself (Winsberg, 2010 reviewed by  Jerkert, 2012). In a way, both experiment and simulation can be a part of each other, the later as the larger and bigger scale of the other. Simulation model can be  always compared with experimental results for validation and calibration to appreciate the real-time representations in 3 dimensional aspects of a system.

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