Posted: 01.08.2014

In the *Prologue*, light has been thrown on the necessity and utility of comparative studies in science and philosophy. I have also tried to refute a popular notion that science and philosophy being quite opposite to each other, there is no scope whatsoever for making their comparative studies. For this, I have gone through the views of some eminent scientists and on the basis of it I have shown that there is ample scope for such comparative studies and that it would prove fruitful for both science and philosophy.

The 'enigma' is a word which connotes an ambiguous or obscure statement or a dark saying meant to hide as much as it reveals. It, in fact, is a problem or riddle which is hard to solve. The Universe itself stands as an enigma before both the scientists and the philosophers. In the present work, three aspects of this enigma are tackled:

*What is the universe?**How big is the universe and what is its shape?**What is the age of the universe?*

The first question pertains to the metaphysical enquiry. In the **First Chapter**, an effort has been made to make a historical survey of the views of the western philosophers and modern scientists on the nature of reality in general and that of space and time in particular. Among the western philosophers Plato, Aristotle, Democritus, Descartes, Gassendi, Leibnitz, Locke, Berkeley, Hume, Kant, Russell and Margenau, and among the scientists Newton. Einstein, Eddington, Sir James Jeans, Hermann Weyl, Ernst Mach, Heisenberg, Reichenbach etc. are mainly discussed. This chapter also mainly deals with the concepts of space and time in the field of science before and after the discovery of the theory of relativity by Einstein. Moreover, an effort has been made to present the theory of relativity as explained in physics as well as its philosophical implications, as interpreted by different scientists.

The second and the third aspects pertaining to the enigma of the universe are related with astronomy, cosmology and cosmogony. The whole of the **Second Chapter** is devoted to purely scientific investigations about the shape, size and age of the universe. An extensive account of the new theory of expanding universe based on the red-shift has been given together with various possible models of the universe suggested by the scientists like Dr. George Gamow, Abbe Lemaitre, Hubble, Whipple, Prof. R. C. Tolman, Einstein, Eddington, Fred Hoyle, Hermann Bondi & Thomas Gold, Narlikar, Prof. Martin Ryle etc..

The whole of the **Third Chapter** is devoted to the meta-physical, cosmological and cosmogonical doctrines of the Jain philosophy. The whole chapter is divided mainly into three parts:

- First, a general discussion of the six dravyas (substances) together with the concept of sat (reality) is made and also ākāśa (space), kāla (time), dharmāstikāya (universal medium of motion) and adharmāstikāya (universal medium of rest) are discussed at length.

- Secondly, a complete account of the
*lokākāśa*(cosmic space) with respect to its size (dimensions at various parts of the*loka*) and total volume is given, together with the mathematical calculations of the shape and size of the loka. Also, an effort has been made to calculate the value of rajju, which is the astrophysical measure used in the Jain doctrine of Loka. Its exact value runs in many many light-years.

The main part of this research is to evaluate the mathematical efforts of the Shvetambara and Digambara ācāryas and evolve a precise value of the dimensions of universe as well as its volume and shape.

- Thirdly, a complete account of the cosmogonical doctrine of the Jain philosophy in terms of kālacakra, utsarpiṇī and avasarpiṇī and time-units such as palyopama and sāgaropama has been given.

The **Fourth Chapter "CRITIQUE"** contains a critical and comparative discussion of the various theories of western philosophers and scientists, mainly in the light of the doctrines of Jain philosophy. The main criterion of the critical examination is logic and also evidence, found in favour or against a particular theory or thought, is given to evaluate its consistency. Specially, the philosophy of science as presented by Eddington, Sir James Jeans etc. is elaborately discussed in the light of the Jain metaphysics and epistemology. Also, the views of materialism are subjected to sharp criticism on the basis of the available scientific arguments. In the end, the conclusions are drawn to present a consistent metaphysical theory of universe. In the same way, space and time as presented on the basis of the theory of relativity, the scientific concept of four-dimensional continuum, etc. are critically discussed and the difference of opinions amongst the scientists themselves is also made clear. Lastly, various models of the universe are compared and contrasted.

The whole work contains many Jain mathematical terms which require extensive computation in light of modern mathematical methodology. There are four appendices which are given with a view to include this.

The **First and the Second Appendices** explain in detail the space-units and time-units respectively used in the Jain philosophy. Incidentally, their co-relation with the modern units is also given.

The **Third Appendix** comprises my fundamental research in the theory of number as described in the Jain philosophical works. Mainly, it contains the computation of asaṃkhyāta (innumerable), which is altogether a new concept in mathematics, developed by the Jain philosophy. It is a category of numbers between numerable and infinite. After giving the scriptural definition of asaṃkhyāta and its various types, I have calculated it in the form of a mathematical series which proves the consistency of the middle category. It is a challenge to the modern mathematicians. Its importance lies, as we shall show below, in the concept of 'quantization of time'.

In the **Fourth Appendix**, firstly, the volume of the mṛdañgā-kāra loka as conceived by the Svetāmbara ācāryas and calculated by Vīrasenācārya (vikrama saṃvat 806-841, i.e., 750-785 A.D.) in the Dhavalā commentary is dealt with. Also, the discrepancy in the method adopted is made clear through modern mathematical method.

Finally, using the modern methodology of integral calculus, I have tried to find out the exact shape of the universe. This is my innovative research in this field. If it is true, it solves the problem of the shape of the loka, which has remained unsolved hitherto throughout the history of Jain mathematics. Also, it removes the discrepancy in the calculation made by the Śvetāmbara ācāryas. It is hoped that the new shape suggested by me would be unanimously supported by both the Digambara and Shvetambara traditions.

Fulfilling the requisite quality of modern research methodology, a complete Index of the words and names and a complete bibliography of the books used in the work have been given at the end.