Alfred North Whitehead, a very renowned mathematician and philosopher, and a collaborator of Bertrand Russell in the work of Principia Mathematica, wrote a famous book, entitled Science and the Modern World³. The first chapter of the book deals with the origin of modern science. The thesis advanced in the book was that the growth of science practically coloured the European mentality and thereby strengthened itself by its most obvious application. He also added that Greece was the mother of Europe and that it was to ancient Greece one must took in order to find the origin of modern ideas which transformed Europe. We will thus follow the advice of Whitehead and begin with ancient Greece in our search. We will try to find out, in particular, in what way ancient Greek thought influenced the future.

There was an aspect of the ancient Greek Society which needs to be taken into account. Ancient Greek population was constituted by migrants who came in batches. They settled in different parts of Greece, Southern Italy and Asia minor and formed their own polity, the city states, so to say. The population belonged to many tribes, which were parts of a federal tribal group. An economic crisis visited Greece in the seventh century. The land of the poor was eaten by mortgages and annexed by their wealthy neighbours. It was felt that new laws had to be found for Greece for avoiding an impending chaos. The Oracle of Delphi sermoned that the lust of gain which had wrought the past trouble must come under rule and regimen⁴.

A new era dawned in the days of Solon. He sought to introduce the ideal of social equality into a state, torn by dissention of rich and poor. In this regard varieties of rules and acts were adopted.

Solon's work went much further. He put into operation the Greek conception of the rule of law, a constitutional scheme based on sovereignty, in which the officials naturally fell into their place as its servants. He made them responsible to a public court. He also admitted the poor Athenians to the assembly and gave them a voice in the election of their officials. Thus, in a way, a form of democracy, vigorous in many respects, was instituted in Athens which became the primary centre of intellectual activity. This aspect, completed with the fortunate appearance of a plethora of intellectuals, both by birth and migration, from other Greek City States, shaped the character of intellectual activity in Athens.

The system was highly unfavourable to the richer aristocratic class who could not aspire to find powerful positions in the new situation. The situation did not, however, prevail in all places where the migrant Greek population was settled. It did not prevail, in any case, where Ionic tribes were settled. In Ionic areas matters were relatively peaceful; a degree of prosperity also prevailed. In the Ionic Cities, thought and discussion played freely on all things in heaven and earth. The riddle of the physical universe, which was constituted by a variety of objects, and liable to changes, and yet presented an orderliness, bothered them. They speculated on these matters and advanced hypotheses freely.

Pythagoras, an Ionian, did not follow the line of thinking set by Thales and other Ionian philosopher/scientists who were searching physical unity behind the appearance of variety in the physical world. Pythagoras also searched for unity but found its basis in number which he thought was extended in space. From here, the Pythagoreans attained their idea of justice. The justice was considered a square number which was in perfect harmony because it was composed of equal parts. The state was considered just, so long as it was distinguished by equality of the parts, i.e. equality among members.

Pythagoras, in this manner, transposed the orderlines in the physical universe into a moral and political order system and brought about a change in the focus of speculation in ancient Greece. It helped the growth of political science by the application of the principle of natural philosophy to the state. The Pythagoreans also taught a definite theory of politics. The essence of that theory was the divine right of wisdom to rule the state.

The institution of democracy of a special form opened up activities in two directions. The Pythagorean idea of the right of wise persons to rule the state also worked in these directions. First, those who, on account of democracy feared loss of social position worked for entry into politics. Although what constituted wisdom was not known, nor was it defined in an appropriate manner, a general inclination for acquiring wisdom necessarily developed. The second activity followed from the need to acquire capacities to defend one self at the pepole's court, should the occasion arise. Good rhetoric capability was needed for this purpose. Individuals also needed capacities for arguing in a logical manner, more particularly, for establishing the meaninglessness of the prosecutors' position through arguments. But what could be the bone of contention in the courts and in the political arena, and what in particular could be a content of wisdom never came out.

Aristotle in his metaphysics held that all humans by nature desired to know. Thus a class of humans-philosophers or lovers of wisdomevolved whose activities ranked as the most choice worthy way of life. He also suggested that there should exist a science that enquired about the common principles and starting points of all special sciences which examined particular regions of things. This science Aristotle first called philosophy and wisdom; it began to be called metaphysics afterwards⁵.

Many other matters entered into Aristotle's Metaphysics but one could not find in it the content of wisdom which night help the Athenians escape distressful situations. The entry of sophists in the Athens scenario at this stage worked towards some solutions.

It might be understood that the sophists appreciated the scenario most clearly. The sophists did not belong to Athens, but migrated from other Greek States. They did not form schools, and moved from place to place for providing instruction and education to ones who so desired. Plato felt that they were professionals and earned money through work as teachers and that such was an abominable practice. Barker, however stated ‘that the sophists did take pay, though they left it to their pupils to fix the amount. He also added that it was not primarily, at any rate, for the sake of pay that they did so. There could also be other motivations for doing what they did, including one given below.

There is no doubt that Pythagoras, had an idea of a content of knowledge which qualified individuals to be rulers. This content was not made clear. The sophists also could note that the philosophical and the scientific propositions which were stated both by the Pythagoreans and the Ionian philosophers could never the empirically verified. Thus it was not also possible, generally, to grade the philosophers and scientists in order. Only one way could be found for ordering the intellectuals. It was that in intellectual disputes one might stand over all others if a question could be asked which had no answer, or answers given which could not be questioned.

Thus the sophists began giving instruction on rhetoric, debating skill, eloquence and art of communication which began to be valued highly by the aspiring politicians. In the process, the sophists evidently also involved themselves, for practical instructions, in debates, discussions and disputes, taking the views and ideas contained in propositions advanced by others.

It is also evident, that, without scope for empirical testing, debates and discussion on, and analysis of, propositions invariably raised issues of various sorts. As Barker said, the sophists were versatile; they did not leave unattended any aspect in the analysis of the propositions. Issues of grammar, origin of language, logic, nature of predication, significance of objects and their change, etc. were raised and discussed. Such discussions also entered into the literature which began to be formed at that time.

Most debates and discussions were centred on propositions related to change. Many ancient Greek intellectuals were apparently disturbed by a vision of continuous changes in the physical phenomena. Thus propositions were suggested stating that there could no change, or that changes were the order of occurrence. Plato, and for that matter most intellectuals of the time, also realized that in the framework of the intellectual activity, induced by the sophists, a debate on change might never by resolved. On the other hand, it could also be understood that the debates should continue and end in victory as proof of wisdom. Thus the Platonic theories related to the concept of idea, and perception, his distinction of appearance and reality and his epistemology, evolved as a crystallization of the ideology of the time.

The substantive elements in the contributions of ancient Greek authorities were ideas with respect to the natural order. The ancient Greek life was bound by customs, traditional laws and conventions. The life was fully ordered, in a way. On the other hand, the physical events, which also affected social life, did not apparently present an ordered pattern. This asymmetry in the behaviour of the physical and human world was a subject of discussion and presented a platform for exercise of the innate intellectual spirit possessed by them.

As we understand from the available literature a crystallization occurred in the discussions. It was that the physical and the human world were both under one order; reason and justice prevailed in the order of such events; the order was implicit and could not be perceived through the senses. It also followed that the order was universal, and determined fully the behaviour of individual natural units for all times. Belief in monotheism also followed.

The second aspect, which really has been a part of the above, related to epistemology. It began to be believed that the order could be known through exercise of reason and intellect by individuals, and by logical means. The manner in which Euclid presented his geometry substantiated the above proposition. The theorems were all logically derived from a few self-evident propositions. The results also proved that the observed facts could only be an approximation of reality, but never the reality. For example, the sum of three angles of a triangle, if measured from a drawing of a triangle, of many drawings, would never give exactly a hundred and eighty degrees (the logical and true value) but slightly different ones. The method adopted by Euclid has been called hypothetico-deductive method and we have in Aristotle a full elaboration of this logical method⁸.

Felix Klein, one of the outstanding mathematicians of the 20th century wrote a three volume work entitled elementary mathematics from an Advanced Standpoint which contained a volume on Geometry⁹. In this book he has anlayzed the content of Euclid's Elements, book by book. Klein referred to the dogma: that the Greeks had given a very substantial attention to Geometry and had set up there a system that could not be surpassed. Against this Klein asserted that although the Greeks worked fruitfully, not only in geometry but also in the most varied fields of mathematics, nevertheless the present day progress in these areas have gone beyond them everywhere and certainly also in geometry; that they failed in most things to get beyond what could be considered the beganning¹⁰.

Klein also added that in writing the elements Euclid never wished to compile a cyclopedia of the accumulated geometrical knowledge of this time, otherwise he could not disregard the entire portions of the theory of conics and of higher curves which the Greeks had started to treat extensively. He, therefore, expressed his feeling that in the writing of Elements there was a particular purpose, i.e., as a preparation of philosophic studies under the Platonic school. Thus the emphasis was placed on working out the logical connections and on setting forth geometry as a closed system, while all practical applications were laid aside.

Aristotle was Plato's student for many years and certainly imbibed his ideas in a considerable way. He also imbibed very definitely the Platonic ideas about Hypothetico-deductive method for acquiring knowledge. Aristotle built up his Logic which was based on such ideas. Euclid adopted this structure, in a general way, in the development and presentation of his Elements.

Amount the ideas which were absorbed by the Christian theology, principles of Aristotelian logic also entered. The ideas were studied extensively at the universities set up by the church and became the basis of scholastic philosophy which were developed in the universities. Scholarsticism ended with reformation in Europe. The most important progress in this line of thinking and work, thereafter, occurred in the area of symbolic and mathematical logic.

The belief that the Platonic Aristotelian logical method, as illustrated in the Euclidean geometry could bring out the truth, however, continued in one or other form and dominated some areas of intellectual activity. With the understanding that the success of the method is fully established in the geometrical area, further application of this method began to be made in the areas of arithmetic and analysis. It began to be understood that if the science of geometry could be built by logical means, other parts of mathematics could also be similarly developed. The logical basis of this development, and the directions in which progress occurred in this context are contained in an essay on Mathematics and the Metaphysicians by Russell¹¹. Russell himself also participated in this development and produced, in collaboration with A.N. Whitehead, a massive work entitled Principia Mathematica. The project was given up before completion, possibly for reasons which would be stated generally in the following pages.

Under this programme attempts to present mathematics as part of logic, and show the development of mathematics, which occurred over the ages, as extension of rules of logic, and product of operations of logical rules, has been made. This suggestion, took away the significance of the creative and imaginative work which, as also believed, contributed to bringing mathematics to the present state of excellence and respect for the certainty of its results. Thus the claims of the logisticians, as the proponents of the logical method in mathematics have been called, came under strong challenge by the practioners of traditional mathematics. D'Abro has provided a summary of the discussions, in his book, the Rise of New Physics in a chapter on controversies in the Nature of Mathematics¹². He has also given a short summary of the discussions in a chapter on Methodology of Science in another of his books, entitled The Evolution of Scientific Thought: From Newton toEinstein. As he wrote: ¹³ Of recent years, certain philosophers known as logisticians, Bertrand Russell in England, Courant in France, among others, have stressed the logical aspects of mathematics. The question is whether they have not overstressed it.

We also have a short discussion on the issue by Hermann Weil in his work on Philosophy of mathematics and Natural Science¹⁴. As he wrote: logistics has tried to build up the structure of modern mathematics, particularly arithmetic, in a framework of axiomatics, used in the construction of Euclidean geometry. Only a check of consistencies might bring out whether a system developed in this manner is correct or incorrect; there could be no empirical check as the structure can be expanded in all possible directions. Inconsistency in the system will show up in the form of contradictions, as has happened with the system developed by Cantor and others of his school¹⁵. Weil began his discussion on structure of Mathematics¹⁶ with a theorem proved by Godel. It showed that in any formal system, like the one developed by Hilbert, one can find:

1. artimetic propositions of comparatively elementary nature that are evidently true yet can not be deduced within the formalism, and

2. the formula that expresses the consistency of an axiomatic system is itself not deducible within the system.

Thus Weil concluded that true realistic mathematics should be conceived, in line with physics, as a branch of theoretical construction of the one real world, and should adopt the same sober and cautions attitude toward hypothetic extensions of its foundations.

We have, so far, prepared the ground for concluding that the intellectual activities conducted in Europe, including those in ancient Greece, might not have contributed to the burst of development in all spheres that occurred in Europe after the reformation. Interestingly, Whitehead in his study did not highlight any work before the reformation as having contributed to future European development¹⁷. He, however, argued that the middle ages, during which period, the church established itself as the dominant institution in Europe, was a long preparatory period for the following burst. Two features were highlighted. The first was the continuous stress in the theoretical literature on the orderlines of the universe and the evidences of regularities in the behaviour of physical events. The second was the work of the church which stressed the natural order and built up a faith in the mind of the people on the a priori character of such order.

One finds, thus, in Whitehead: the middle ages formed one long training of the intellect of Western Europe in the sense of order. The idea never for a moment lost its grip. It was pre-eminently an epoch of orderly thought, rationalist, through and through¹⁸. He also added how the habit of definite exact thought was implanted in the European mind by the long dominance of scholastic logic and scholastic divinity.

There has been, however, no support of history and facts to the ideas of Whitehead. No aspect of the middle age was carried forward to the modern age. The middle age was destroyed thoroughly under the renaissance and reformation movement and a new Europe emerged. During the middle ages, and also during the earlier days, particularly after the eclipse of Ionian physicists, natural order in the physical sphere was not stressed. The normal physical regularities like the succession of days and nights, the periodic movement of the moon and seasonal variation were taken for granted. Regularities which were not evident did not bother the individual. After Pythagoras, only in the sphere of social and political phenomena, natural order began to the stressed. The church extended the concept and worked for imposing a universal political order as part of the natural order under the control of the God and the Church. The universal order which the church worked for was fully broken under the impact of the renaissance and reformation movement; in its place many autonomous political units were formed. These worked for acquiring sovereign authority and a status that separated all units from each other.

The political and social institutions which directed life during the middle age were also destroyed fully and new institutions evolved. These were not universal but specific to individual political and social units. It was a major change.

The ancient Greek thought, with respect to natural order lost scientific significance altogether. It is said that St. Augustine baptized Plato; he and the church absorbed all platonic ideas except the part which held that the knowledge would be obtained through exercise of reason and intellect. The church held that the knowledge is revealed, and could never be obtained by other means. This belief of the church closed all scientific investigation; it also forbade presentation of ideas, contrary to the belief of the church and declared such as heretical¹⁹

Modern science is said to begin with the thesis by Copernicus; it was argued that the earth rotates around the sun, and not the other way round as under the Christian belief. Fear of ecclesiastical censure caused him to delay publication. At one stage Bruno was tried for his venture, into some speculations to which his acceptance of the new theory had led, and burnt alive by the sentence of the inquisition at Rome. Some times later the same tribunal forced the aged Galileo, who had supported the Copernicus thesis earlier, to detract as heretical the doctrine of the earth's motion²⁰

There above situation clearly indicates how the pursuit of scientific investigation was viewed during the late stages of the middle age. The universities which were established during the middle ages by the church did not also support education of science. The courses studied in the universities could be seen in two parts-ancient and modern- and covered seven arts. Three of these were elementary and formed the trivium and included Grammer, Logic and Rhetoric. The other four, called quadrivium, included Arithmetic, Geometry, Astronomy and Music. It was in these arts that the degrees in Arts were given at these universities.

Speaking generally, under the renaissance and reformation movement, a wholly new generation of scientists and philosophers worked to free humanity from the fetters of nature and to make nature's forces serve the ends that humanity desired. A distinctively new approach emerged with the works of Machiavelli, Martin Luther, Copernicus etc. Machiavelli initiated the approach to political life based on a bold unleashing of the passions and self-interest. Bacon transferred the lessons of machiavellism into study of nature. In effect, nature was divested of formal perfections and ceased to be an object of contemplative interest. Descartes, considered to be the founder of new philosophy and metaphysics, began by questioning the old Aristotelian metaphysics under which mind was simply receptive to form and was subject to the vicissitudes of nature or destiny and never the master of its fate. Descartes, considered to be the founder of new philosophy and metaphysics, began by questioning the old Aristotelian metaphysics under which mind was simply receptive to form and was subject to the vicissitudes of nature or destiny and never the master of its fate. Descartes introduced the concept of ‘I’ as a new sort of intelligence, one in which thinking is identical with doing, even with making²¹. In his works, the end of thinking was not remaining separate from the external world but appropriating the world and reconstructing it on the mind's own terms. This was echoing Bacon's view of forcing nature to answer the questions we put to it in experiments; later Kant took this approach still further.

Intellectual activities which also took shape as a part of the renaissance and reformation movement were focused at different ends. As stated earlier, the spirit of the middle ages and also the institutions which were associated with the middle age were severely attacked. A part of the intellectual activity was directed to providing ideas as to the new institutions which could be formed for supporting the build up of the modern age. The authors of the social contract theories worked towards the required structure of political institutions and ideologies. The literature which was produced in this context could not fall under scientific activities properly. This constituted, so to say, suggestions towards social engineering.

The most remarkable change occurred in the area of intellectual activities directed to scientific issues. Ancient Greeks never indulged in studies related to physical phenomena, their scientific speculations only led to further speculations in metaphysics and philosophy. Artistotle wrote a book on physics which was called Phusis. The word is translated as nature. In the ancient Greek use, the word had a confusing significance. The Ionians used it to represent the common substratum behind the variety of natural objects, i.e., the material substance. The word has also been used as the presentation of God in the world of phenomena, an instrument of control, so to say, working through the spread of inexorable laws of nature. In the physics by Aristotle, Phusis complemented his metaphysics. The concept of prime mover, all sorts of causes and the teleological aspects of change were provided in this book²². In the middle ages, under science people learnt these matters at the universities.

As has been discussed earlier Descartes changed altogether, through his work on metaphysics and philosophy, the focus of scientific studies. Descartes was a contemporary of Galileo and could be familiar with his work. He could also be familiar with the work by Kepler. Most importantly, he was himself a great mathematician and pioneered the development of analytical geometry. Thus, he was convinced about the capabilities of mathematics to pursue the changes in natural phenomena without bringing in Aristotelian concepts. Bacon had before him argued for empirical and inductive studies as means to acquire knowledge. With all the ideas and information before him, Descartes called for a new focus of scientific study, i.e., study of the external phenomena, objectively and analytically, whose potentialities had opened up as became evident from developments in the areas of physics, astronomy and mathematics.

Cartesian ideas were complemented by development of new ideas in epistemological aspects. The earlier theory of knowledge, as evolved in ancient Greece, was based on the Pythagorean idea of the divine right of wise persons to rule society. In course of varieties of discussions in ancient Greece, in which Platonists, Sophists and others were actively involved, it began to be understood that wise ideas could be deduced by logical means from intelligent premises, advanced a priori. The logic developed by Aristotle and illustrations of the method in Euclid's elements, substantiated the approach. Locke, who pioneered the new epistemology, argued, instead, that knowledge is obtained only through empirical observation.

The ideas of Aristotle again entered the scenario of thinking and queered the development of genuine empirical observation as a scientific method. Empirical observation as means of knowledge took the name of empiricism and began to be analyzed and discussed under philosophy. This culminated in Hume's skepticism; it was argued that causes of events, search for which was the object of investigation, could not be discovered though empirical observation. In a way, Netwon's theory of gravitation, which had appeared by that time, greatly supported the position taken by Hume: Kepler's three laws were developed, wholly, empirically. There were slight discrepancies in Kepler's figures with respect to observations. Newton's formula derived from his theory of gravitation, which had a priori basis, provided correct answers. It is another matter, and nobody pursued this, that Newton's formula, as shown by Max Born, could be derived from Kepler's three laws, using the mathematical tools possessed by Newton and to a large extent, developed by him²³.

Except physics, almost all other disciplines of scientific studies in the area of physical sciences are empirically based, within which the theories did not have a great role. In a large way, the prestigious position acquired by physics has been based on the uses of numbers which opened up application of mathematical methods. Geeting the numbers for operation by mathematical tools, involves empirical observation and measurement of physical magnitudes, which are correlates of qualities and properties of physical objects. In a classical work, N.R. Campbell has fully articulated the basis of research in the area of physics²⁴. He has also shown how theories come to be developed in a platform of extensive empirical measurement.

A change of great significant has also occurred in the process. The scientific workers belonging to the theoretical area still qualify as wise persons of the ancient Greek thinking process, and earn considerable respect, but the bulk of the scientific workers these days engage in pedestrain work of observation, classification, measurement and correlation. A new profession has emerged, in a way, and people get attracted into it depending on income prospects. The output of the scientific activities in the present times has been primarily information of various sorts. The information has found application progressively; it has entered in spheres of general engineering and production, medicine, including areas of public health, services, communication and even in area of sports, music and other entertainment based activities. In the process money has flown into the scientific activity and the flow has been increasing steadily causing steady increase in the size of professionals in this area.

Thus one finds that science, which in its ancient Greek heritage, was associated with metaphysics and philosophy, is now called jointly science and technology, S&T, for that matter. The pedestrain area of scientific activity, which is the core of S&T work, is also totally bereft of a priori ideas about nature, though such phrases as natural law and natural order, do come up now and then in the discussions.

In physics alone theoretical works abound. A wide variety of theories have been advanced and the theorists have received acclaims as wise persons as in the ancient times. Physics has also been a base for significant empirical work through experiments and in the process a large number of empirical laws have been discovered. The theories have formed an intimate relationship with the empirical research area. No theory could never be considered valid if it contradicted established empirical laws; on the other hand, most theories have been suggested as an explanation of empirical laws. We have a Plethora of examples in this area in a work by D'Abro²⁵. One notices that the respectability and the social significance of research in physics has been acquired primarily due to the close relationships between theoretical and empirical work. In the area of social science, this relationship has been absent totally with the result that the theories in this area could never improve our understanding of the social phenomena.

Discussion in the previous section has presented the necessary conditions for the change that occurred in Europe after the reformation. The change has been associated primarily with the progressive improvements in the standard and quality of life enjoyed by the European population (including those settled in United States, Canada and Australia). Steady improvement in technology, and its application to all social and economic activities have caused such a change. Capability for conduct of actions leading to improvement of technology has been possessed only by human individuals.

It is noted, in particular, that human beings and other animals differ in one respect very significantly. All animals act and react to the external world, and in the process, draw sustenance and escape peril. Other animals carry all the apparatus needed for this purpose in their bodies; only the human beings do not. Thus human beings, as a specie, are handicapped in their struggle for existence. They are, however, compensated by their natural propensity to develop technologies and use them for overcoming difficulties faced in their struggle for existence. This propensity enabled them, in the very early days of human civilization, to make small changes in the abundantly available stone pieces for use as weapons and tools and improve their chances for survival in a hostile environment. As more varieties of materials came to hand, this propensity further enabled them to produce better and improved tools for various uses²⁶.

The propensity mentioned above is a natural property possessed by all human individuals, in large or small measure. It belongs to the class of human qualities, like passions, emotions, creative abilities etc, which were highlighted during the renaissance and reformation movements. Under these movements giving opportunities for exercise of the basic human qualities was also highlighted.

A technology developed, at any point of time, rarely disappears and forms a part of the existing stock of technological knowledge. The propensity to develop technology is possessed in all ages by human individuals. Thus the stock of technological knowledge, considered, globally, can only increase over time. Contribution of individual societies in the global stock of technology might not, however, be proportional. In some societies generation of technological knowledge, during a period of time, could be rapid; at other periods it could be insignificant. Two features could be suggested for such asymmetry in the process of technological development.

Conditions which operate in nature are rigorous. All natural objects have limited lives as individual beings. Only as a collective body the nature is eternal. This character is obtained due to strong interdependence among the elements of the collection formed by for example human beings, other animals and organisms, forests, rivers, land surface, minerals and other resources, etc. The interdependence works physically in which qualities possessed by the individual natural objects have significance; consequently, if the objects are separated greatly in space, the force of interdependence becomes weak. Thus Nature survives eternally not as one body but as a collection of many bodies, which also live as independent collectives. On fulfillment of such conditions alone, nature as a whole, and individual sub-collections, acquire the life force and stability. Each collective is bounded but due to the life force it acquires it has infinite stretch in time.

In Europe, the Roman Empire with its universal aspirations worked against the natural process and did not allow natural collectives to evolve. Although the Roman Empire ended at some stage, the Catholic Church worked with the same universal aspiration and restrained evaluation of natural collectives. The break down of Europe into autonomous and closed sovereign states after the reformation opened up possibilities for development of natural collectives.

The life force, which such natural collectives acquire, is based on forces generated by the interaction among the qualities possessed by individual objects. Thus, it depends, so to say, on whether or not the effects of the qualities possessed by individual elements are restricted. With respect to human individuals, the pattern of rights and liberty enjoyed in a society determines the extent to which the basic human qualities are free to operate. The Roman Empire, and the following order which the church imposed, fully took away the rights of the individual. Under the renaissance and reformation movements the issues of individualism and of right and liberty of individuals were strongly highlighted. The new political and social institutions which began to be formed in different countries were particularly favourable to human rights. Thus, the two changes mentioned earlier succeeded in forming closed and autonomous natural collections in Europe. Possibilities of survival of these collections and of such development which are a part of survival, with support of their own life forces, also opened up consequently. These, however, formed only the necessary conditions for rapid technological development in Europe.

Sufficient conditions for the rapid and all round technological development in Europe depended on improvement in an altogether different direction. In the development of techniques during the ancient and middle ages such human qualities as hand skill and mental capabilities of individuals of sorts, particularly, understanding and appreciation of external features, played a critical role. Analytical tools came into use only rarely and in few places, which did not include Europe. Geometry developed in Europe significantly but not as an analytical support system.

As stated earlier, there occurred a great change in the character of European science after the Aristotelian metaphysics ceased to influence the minds of European scientists. Geometry, as developed by Euclid, also ceased to occupy the dominant position in sciences. The position was taken by physics; and the character of its initial development set the future direction for development of all other sciences.

The line of work in physics, which Galileo and Newton initiated, ended in development of, what has been Newtonian Mechanics. The name of the subject itself speaks of the character of ideas generated under the subject. The principles developed under this part of physics provided great support to mechanical and civil engineering works; it supported development of hydro statistics and hydrodynamics which had great scope for application. Further development in physics occurred keeping the possibilities of use as an analytical tool in mind, following the lines taken by classical mechanics. Development in other areas of sciences also followed similar lines; other sciences; chemistry led developments in chemical engineering; bio-engineering, bio technology, bio chemistry and many such engineering areas received principal support from researches in scientific areas. The scientific ideas which researches generated provided significant analytical support and built up the tempo of technological development.

In a way, the line of development in physics re-formed the sciences as a supporting system for engineering works and technological build-up. Behind this line of development, however, lay development in another area without which the line of development in physics could never be possible.

The matter is best illustated by drawing attention to a statement by Laplace; he is known to have told Napoleon that God is not a necessary hypothesis in natural sciences. He also highlighted the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position, as well as an absolute value, and the consequent ease which it has lent to all computations²⁶. Compiled with this development has been the bringing into use of algebra, the corner stone of modern mathematics. As Hogben says the transition to sythbolical algebra has been one of the most important things to understand in mathematics. Algebra and arithmetic together made mathematics a powerful tool for answering many sorts of analytical problems. More importantly, development of arithmetic and algebra enabled individuals to translate problems in mathematical terms and use mathematical knowledge for finding answers. Newtonian mechanics worked as rules for translation of engineering problems in mathematical language for use of mathematical tools.

Initial development in both these areas, i.e., arithmetic and algebra, on the lines giving them analytical capability occurred in India during the first 7/8 hundred years after the birth of Christ, and much before the reformation in Europe. Knowledge of these sciences reached Europe during the 13/14 century. In a way, it became available just at a time when re-formation of sciences began in Europe²⁷.

Use of the mathematical tools developed in India, provided, in a way, the European Scientists of the post reformation period capabilities to reconstitute sciences as analytical support for technology development. The end was achieved, and ground was prepared for the burst of technological improvement in Europe thereafter.

The paper has started with an understanding that after the renaissance and reformation in Europe many European states have achieved, in course of time, steady state of growth and development. Russell stated in an article on Rise of Science: Almost every thing that distinguished the modern world from the earlier centuries is attributable to science²⁸. Whitehead elaborated this idea²⁹ and also added that the ideas which transformed Europe had originated in ancient Greece. The paper is ostensively focused to finding the necessary and sufficient conditions for the achievement of steady state growth. A beginning has been made with the suggestion of Russell and Whitehead.

The analysis in the paper has brought out the following as having contributed to the achievement of a steady state developmental process in most European countries, including those which do not fall in Europe but are habitated by an European population. These are:

Two properties of human individual-creative Impulse and propensity to innovate-endowed by nature, have been highlighted in the discussion. The development which occurred in the area of science after the reformation could be the result of indulgence of these faculties by human individuals. Thus, in a way, an association has been brought out between state of progress achieved in Europe and the reconstitution of Europe as a collection of nature based collectives. An association has also been brought out between the natural process of birth and death and the steady character of the progress.

The renaissance and reformation movement has been taken, by and large, in a very narrow sense, as covering only political and religious aspects. It can be said, therefore, by way of a conclusion of the paper, that revolution in thinking about science, the romantic movement, and many similar others, also formed part of the renaissance and reformation movements which brought about the transformation in Europe. An appreciation of this point of view might also call for a need for renaissance and reformation movements in all areas which continue to be traditionally based.

References