As we learnt from the article "What is Science?" all scientific studies begin with doubts and conflicts between a theory and the available observations. The model based on the fundamental physical laws may be checked against the recorded observations. Smaller deviations mean a better model. Connection between a theoretical model and the real world comes from the observations. However, it is not, always, straightforward. Observer is a kind of model world, itself. It generates controversies regarding the interpretation. The usual requirement for a theoretical model is a prediction in terms of numbers. The numbers usually are not certain because of the approximations made during the computation. A theorist tries to understand nature by formulating a model on the basis of available knowledge.
Scientific models are mental pictures that account for observations in the outside world and predict new phenomena. In astronomy, for example, elements of a model interact to give it form. Geometry brings out a visual framework (shapes of the objects involved). Physics deals with the motion and the interaction of various parts. And aesthetics directs us to select the simplest and the most pleasing models from the many candidates.
A model, when accepted universally, becomes a theory. In everyday language, a theory is nothing more than a speculative guess. In science a theory is a group of related hypotheses that have been tested and supported by a great deal of evidence.
A new model presented to the scientific community
shall be seriously considered if:
a. It is internally consistent (i. e., mathematically sound).
b. It explains current observations.
c. It is verifiable by a variety of observations.
d. It predicts future observations.
e. It is changeable to match observations better.
For example, Dirac's theory of the electron was mathematically rigorous, it explained the observed electron spin and it predicted positive electron later discovered and named as positron. String theories are internally consistent and they explain a number of phenomena. However, they do not propose a test, which can be performed in the laboratory or observed in our environment. Therefore, some people have doubts about them.
Can one prove anything in science? No! One can only disprove a statement. A scientific statement is that statement for which an experiment can be devised to disprove it. A theory cannot be called absolutely correct or proving the observed results. All one may say is that a theory is usable under the given set of conditions. If the conditions change or new phenomena are observed the theory needs to be modified. Even the most established laws, e. g., " Newton's Law of Universal Gravitation" had to be modified when new logics and new observations were at our disposal.
If one generalizes from specific observations, one is said to be applying inductive logic. For example, the following line of argument is based on inductive logic. Water and oil are liquids. They flow and so all the liquids flow. If one obtains a particular result from a general law, one is said to be applying deductive logic. A line of argument that goes as the following is based on deductive logic. All liquids flow and water is a liquid. Therefore, it must flow. Pure sciences are inductive in nature. Applied sciences are deductive in nature. In applied sciences one develops a technology based on the general laws using the deductive logic. Mathematics is deductive in nature. Judicial rules of Islam are deductive in nature.
Science is the formulation of general laws applying mainly inductive logic. Engineering is modeling from the general laws to create practical systems. Technology is the implementation and the adaptation of a laboratory model to create a working system, which could be mass-produced. The tools to analyze, construct and optimize systems are called Operational Research. Operational Research makes use of mathematics, statistics, computer science and control theory along with a basic knowledge of the system to be dealt with.
One must be clear between the terms models and modeling. The former means study and critical analysis of the models developed by others whereas the latter means developing models of the systems found in our immediate surroundings. The essence of Applied Mathematics is modeling of the indigenous problems.
If one wants to be a scientist one must learn to reason, to see when one looks and to hear when one listens, to question how and why, to understand cause and effect.
Appeared in the NEWS International, Karachi, Technotalk Page, December 8, 1997
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