The institute for educational research and development
The Institute has initiated many innovative programs in such varied fields as Economics, Econometrics, Philosophy, Management, Education, Astronomy, Astrophysics, Social Science and Art & Culture. The activities of IERD are anchored to the Structural School of Thught, an alternative methodology developed by Professor Ranganath Bharadwaj in response to the deepening methodological crisis in education. Even though academic members of the Institute were working on certain basic concepts and pedagogic aspects of education since 1965, the Institution took a formal structure in 1990.
THe structural method
Dr. Ranganath Bharadwaj
As we are dealing with a new way of looking at phenomena, it would be fruitful if we present a comparative view of the present approach and the proposed methodology so that the reader may understand the origin and development of the method in a better perspective.
At the outset, it would be appropriate to elaborate the basics of the Newtonian method and the structural method.
Scientific investigations aim at studying phenomena and the various objects therein around us, ascertain their properties and uses so that we may use them to increase the standard of living of the people. Pursuing this objective, Sir Isaac Newton, then professor of mathematics in Cambridge University, UK, perceived that every object was differentiable (in a mathematical sense). Specifically, he postulates a functional relationship between an outcome and the inputs required for that. For example, consider the following function y=f(x,y,z).
In order to find out the impact of only one variable, say z, he advocated the following procedure involving analytical geometry.
He wanted to find out what happens to the output y if one of the variables, say z, is held constant. This procedure he thought would enable one to assess the contribution of z to y. Therefore the method involved in finding out what is called the derivative of the function at that point Q in fig1. As we know, every point on the curve is a number and may be written as a ratio such as a/b. In order to obtain the derivative of the function at the point, the procedure suggested is to find the limit of the ratio allowing b to tend to infinity and a remaining constant. This would lead to a continuous change in the value of the ratio and consequently it will become a point on some new curve with only 2 variables rendering the derivation of the derivative impossible.
The main problem in obtaining the derivative may be noted here.
Consider a point P in a 2 dimensional X-Y plane. The point is neither X nor Y. It is a new point formed by the combination of X and Y in terms of a common scale with definite proportions of X and Y in terms of that scale and hence having a specific location in that plane. It is a structure and not differentiable. To handle such entities we need to develop a different approach and it is the origin and development of that approach that we are discussing in this book. Newton named his method as differentiable method assuming that objects such as P are differentiable. As they are not differentiable but structural, I call the alternative method as the Structural Method.
In order to clarify this thought to myself, I imagined an X-Y plane and specified a point in the plane in Figure 4.
The point is neither X nor Y. It is a new entity; call it Z, which is composed of both X and Y measured in terms of a scale which is implicit at the origin. Fixed proportions of X and Y has given us the new point Z. It is not differentiable in the Newtonian sense. The actual example of Newton is in terms of a curve as shown in figure 5.
Given a function Y=f(x,y,z), we are required to find out the impact on Y as we hold one of the variables say z constant. Since the derivative is obtained at a point, let us try this exercise at a point P as indicated above. When we try to obtain the derivative at P, the curve will move away (see fig. 2). The point P may be represented as a ratio x/y. To obtain a derivative, it requires taking the limit of this ratio as y∞ and x remains constant. This will change the ratio continuously and therefore the value changes, thus making the process of obtaining the limit at that point impossible.
The above discussion clearly demonstrates that no phenomenon is differentiable. Every object we see around that is made by our effort or created by nature is a result of a combination of 2 or more things. The combination is not haphazard. It is in terms of a scale and in definite proportions of that scale. That is, it is a structure.
Sir Isaac Newton of Cambridge University perceived the nature of phenomenon differently. He thought it to be akin to a saucer containing dry fruits where you may take away one of them and add one that you may like i.e. phenomenon is differentiable (in the mathematical sense). However as we have seen, phenomenon is structural and not differentiable. Newton named his method as differentiable method; I call my method as Structural Method.