Apologetics Courses

Empirical sciences try to understand the way matter and energy function. Often such study depends upon the way an entity such as the atom is made up. Thus some understanding of the structure of the atom is needed to study the subject further. To do so they assume that the atom is made up if a massive core with electrons revolving around it. The properties of this structure are calculated, based upon known properties of electrons, protons, and the mathematics of circular motion.

Thus wherever there is an exceedingly complex entity, or something that is invisible, models are the way to study them. For example, the study of climate involves studying thousands of mutually dependant factors, many of which are not even properly known. Another example is the human language. Though speaking a language looks effortless, human language as an entity is an exceedingly complex phenomenon. Complex mathematical models are employed to study climate, human language and other such phenomenon on Super computers. It is the complexity of the model that demands such powerful machines. Much can be gained with the help of such models, yet models are not the final word in science. They are only an intermediate step in the scientific process of investigation.

Thus a Scientific Model is a representation of a complex entity or phenomenon, with this representation being an aid to a more objective understanding of what it represents. These representations or models can be of two types: qualitative and quantitative, or descriptive and mathematical. Each one has its own merits and demerits, and it will be profitable to know a bit more about them.

Qualitative/Descriptive Models: Models which are created based upon more verbal descriptions fall into this category. All of indulge in such model-based description. For example, all of us describe elephants and whales to those who have never seen them. This is model-making.

Scientific model-making is a bit more sophisticated. For example, Charles Darwin and followers spoke about the “survival of the fittest” and also “change through gradual adaptations”. There is no way to express these ideas in a quantitative manner. Consequently they cannot be measured or analysed using mathematics.

Qualitative or descriptive models are very attractive because they are easy to describe, and easy to visualize. No mathematics or abstract concepts are needed. However, their accuracy is difficult to analyse. Unless there is a way to quantity or express them in terms of mathematics, it is not possible to analyse them objectively.

The birth of the Solar System is a good example. All of us have heard in our school texts that originally there was only the sun. Then a massive body passed by, and its gravitational attraction was so strong that it putted out a lot of materiel from the hot and molten sun. This material broke up, began circling the sun, cooled down and became the planets of the solar system. There is a similar story about the formation of the moon. According to it, a massive stellar object exerted a great gravitational pull on the earth. Consequently, a piece broke away from the earth, and began circling it. That is moon. What’s more, there is a very large crater in the Pacific Ocean, a placer from where this piece could have broken away from the earth.

Both the above pictures look quite plausible, and that is why they are taught in School textbooks. Their power to depict complex phenomena in simple pictures is awesome and this is why descriptive models are so common and popular.

The greatest weakness of descriptive models, however, is their inability to yield to empirical or mathematical test. Only those models can be tested objectively that are quantitative in nature. A good example would be the two models from Astronomy mentioned above. Both of them look plausible, but once tested with the help of mathematical models they turned out to be unworkable. Today nobody takes them seriously.

Qualitative models do have a role to play, especially when they are the first stage in constructing a mathematical model of the same phenomenon. However, used by themselves they can totally mislead people because the human mind is adept at “imagining” many mental pictures which do not have a corresponding reality in the material world.

Quantitative/Mathematical Model: Mathematics has grown so fast in the last two centuries that today many physical phenomena can be represented accurately with the help of mathematical equations.

For example, the equation ax+by+c=0 represents an inclined straight line with as much accuracy as we wish. The equation V=u+at represents the final velocity of an object moving with an acceleration. Using calculus and other branches of higher mathematics, very complex phenomena can be represented mathematically.

The accuracy with which scientists these days predict astronomical phenomenon in the solar system is a good example of mathematical modelling and its success. Also, the way they are able to send spacecraft to moon and other solar objects and them back, all with split second accuracy in spite of the thousands pushes and pulls operating on the craft is another good example of the success of mathematical modelling.

The phenomenon under study is often represented in simple mathematical terms. Once this approximation yields an approximate result, more factors are added and the model is tested again. Several iterations finally yields models which are a satisfactory approximation of the reality.

This does not mean that today the scientists have successfully prepared mathematical models of all important phenomena. Not at all. The scientific study of nature is a never-ending quest, which throws out ten times more undiscovered phenomena at them as one mystery is solved. Thus there are numerous phenomena which defy such modelling, but what has been done so far is a great encouragement to those who study the unsolved questions of the Universe.

Models And Objective Truth: The qualitative and quantitative models are part of man’s attempt to study Nature and discover the underlying laws. However, the models do not represent the final truth.

All models are only approximations. They are proposed at the simple and simplified level, and then compared with the actual phenomenon. The model is then reject, modified, or refined based upon feedback. This way the model moves from a crude approximation to a highly accurate and complex mathematical construct.

The process of defining and then refining a model may go on for decades or even more. For example the current model of the atom is almost a century old, but refinements are still going on and the final model is nowhere in sight. What’s more, the discovery in the nineteen sixties of sub atomic particles known as quarks have shown that the structure of the atoms is incredibly more complex then what anyone could ever imagine, and that perhaps another century of additions and refinements will be needed to arrive art a comprehensive models of the atom.

The Use Of Models: Science and technology (including the social sciences) need to deal with numerous phenomena that are incredibly complex. Yet some kind of an approximate information is needed so as to handle that event or harness that phenomenon.

A good example is “Weather Forecast” with the help of models of climate. The most powerful super computers are employed for such studies, yet the results are far from perfect. Yet what these imperfect results yields are much more accurate than mere guesswork. They help agricultural scientists, town-planners, electric companies, and many such large institutions to plan their activities with some certainty. Such forecasts also help governments to plan import and export of agricultural commodities so that scarcity of foodstuff can be avoided.

Mathematical modeling helps technologists to come up with improved products that yield increasingly more reliable results. A good example is the CAT scanning machines which were invented only after a perfect mathematical model of scanning and reconstruction of the image was perfected first. The development of new medicines, new electronic gadgets, and even computers depends upon mathematical modelling.

Business that depend upon high-volume and high-traffic transactions depend heavily on mathematical modelling. A good example would be the operation of a credit card company. Their computers have to handle millions of transactions per second, and detect or control fraud, but computers can. They use fuzzy-logic (which is firmly based upon mathematical modelling) to detect the possibility of fraud, and catch the majority of people who true to cheat the system.

Thus mathematical modelling in science and technology helps physics, chemistry, engineering, medicine, economics, and even social sciences. In that way they are an important part of the modern scientific establishment.

The Scientific Status Of Models: A model is only an approximation. The qualitative models are an approximation only in appearance, and they may or may not have any correspondence with reality.

The quantitative models are closer to the truth, but how close they are depends upon how refined they are. However, no model (howsoever complex it might be) ever represents the phenomenon perfectly. Even the most complex and refined model is often only an approximation, and does not represent an established fact or law of science. Thus a scientific model is not admissible as an “evidence” in a legal inquiry.

When there are more than one model that try to explain the same phenomenon, one can compare them to see if one of them fits all the observations better than the other model. If there is no better fit, all models are considered equal. However if one fits the observations better it is considered a superior model. It is in this sense that the Creation Model is favoured by many over the Evolution Model.

Apologetics And Scientific Models: Since all models are approximations, the Apologist should keep reminding the audience that they are not “evidence”. While people are free to choose the better model, these models can be used only as an aid to study and understanding, and not as legal or scientific evidence in favour or against any statement. Models cannot be used to attack the Christian faith. At the same time, scientific models cannot also be used to establish the truth of the Christian faith.