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Infinity Foundation sponsored new book project titled:
"Kâla: Traditional Indian Time Beliefs in Relation to the Western and the Scientific"
by C. K. Raju, PhD


Part 1: Background

0. Why this book?

Time is very much an aspect also of the physical world. Many philosophers, however, have avoided questions about time in physics, as if the study of time can be neatly separated, like university faculty, into a metaphysical part suited for the philosophy department, and a physical part suited for the physics department!

As an example of the problems arising from this "territory-limitation" attitude, consider the case of the philosophy of science, which sets out criteria for separating physics from metaphysics, and hence seems to be itself as clear a case of metaphysics, as logic is a case of metamathematics. However, philosophers of science have overlooked that key criteria of a physical theory, such as refutability, internal consistency etc. involve implicit temporal assumptions about the real world. These assumptions are so very common everyday assumptions about the nature and structure of time, that they hardly seem to merit attention. Nevertheless, the unfortunate fact is that this mundane time is unacceptable in physics. This has led to the absurd situation where the contemporary philosophy of science is founded on temporal assumptions denied by current physics! Correcting this situation1 is not an easy task.

Whether or not one accepts this author's proposal (of a tilt in the arrow of time, which reformulates physics using mixed-type functional differential equations), the unavoidable conclusion is that for the study of time, a more holistic approach is appropriate.

This author has 'comprehensively reviewed'2 questions about time in physics. This author has also reviewed traditional Indian time beliefs in a series of articles3 for the Project of History of Indian Science, Philosophy, and Culture. Hence, this author is in the happy situation of being able to compare and contrast traditional time beliefs with current-day scientific beliefs.

The significance of such a comparative approach derives from the following.

1. The importance of time

Earlier expositions of time in Indian tradition have tended to elaborate on textual quotations relating to kâla. This does grave injustice to the importance of the subject.

(a) Time beliefs relate to the core religious values and the way of life.4

For example, the Upanishadic value of moksa, depends upon repeated rebirth, which makes sense only in the context of quasi-cyclic time.5 As a second example, the Buddhist Dhamma relates to paticca samuppâda (conditioned coorigination), as the Buddha himself stated.6 As a third example, the Islamic value of surrender to God was related by al Ghazâlî to ontically broken time.7 As a fourth example, the Christian doctrine of sin was constructed by Augustine using apocalyptic time.

(b) These time beliefs are primarily physical beliefs.

Thus, quasi-cyclic time and the associated notion of life after death, both, are refutable, hence physical beliefs. As a second example, the Buddhist idea, of locating causes in the past, also leads to a different physical theory, which is, however, more complicated to explain.8 As a third example, ontically broken time, exactly like the collapse of the quantum mechanical wave function, is contrary to Newtonian physics (though Newton himself strongly believed in occasional providential intervention). An important exception to this rule is Augustine's apocalyptic time, which is metaphysical. This exception is important because it has given rise to the predilection, in a long series of Western philosophers, to characterize as metaphysical the time beliefs underlying all religions. as metaphysical.

(c) Changes in these core religious values have often been brought about by rejecting as invalid the underlying physical beliefs about time.

For example, the Lokâyata rejection of quasi-cyclic time and life after death, in favour of mundane time, led to an Epicurean ethic. As a second example, present-day urban life in India is founded, from birth to death, on the belief that time is money, a belief that has been widely used by sociologists to characterise industrial capitalist societies;9 the temporal assumptions underlying this value principle, exactly like those underlying utilitarianism, contradict both quasi-cyclic time and Buddhist notions.10 As a third example, the rejection of quasi-cyclic time within Christianity, and its replacement with apocalyptic time, is a central point supporting Augustine's conception of heaven and hell and the related doctrine of sin, which sought to replace Origen's belief in equity and universal deliverance in the context of quasi-cyclic time. As a fourth example,11 al-Ghazâlî attacked the belief of the falâsifâ in the rational evolution of the cosmos by arguing that time is ontically broken (providence).

(d) Summary: Time beliefs are important because entire value systems, and the related ways of living, are premised on time beliefs. Changes in values and the way of life, whether in the past or the present, can be related to changes in time perceptions, as in Lokâyata, Buddhism, Christianity, Islam, utilitarianism, and present-day industrial capitalism.12 The value changes have typically proceeded by denying or rejecting the underlying time beliefs (which are usually physical beliefs).

2. Why a comparison?

Accordingly, in view of 1 (a), (b) and (c) above, it is interesting to know, from the viewpoint of current science, about the probable validity of the physical beliefs underlying traditional thought. However, a comparison between the two is not a simple matter. First, most of the time beliefs cannot be offhand rejected.

(a) Quasi-cyclic time, the basis of Upanishadic values, cannot be offhand rejected on the basis of current physics. Thus:

(i) The equations of Newton, Hilbert-Einstein, Schrödinger (or more generally Markovian evolution) necessarily lead to quasi-recurrence with probability one, under fairly general conditions, according to the Poincaré recurrence theorem,13 and its extensions to quantum mechanics. Classically, this requires the cosmos to be closed.
(ii) Whether or not the cosmos is closed is an open question. (Though my approach to the many-body problem, via the retarded functional differential equations of relativity, suggests that one cannot infer all that much missing mass from galactic rotation curves, the nature of the many-body problem has changed, so that one cannot so easily deduce whether or not the cosmos is closed, simply from a knowledge of the total mass of the cosmos.)

(b) Still less can one reject the Buddhist idea of locating causes also in the distant past. History-dependence (physical evolution according to retarded functional differential equations) rather than instantaneity (physical evolution according to ordinary/partial differential equations) appears to be the unavoidable route to future physics.

(c) Summary: Many of the traditional time beliefs cannot be rejected offhand.

3. The difficulties of a comparison

On the other hand, a deeper comparison of tradition with science is difficult because

(a) the core of religious values changes with time beliefs (thus time beliefs are emotionally supercharged),

(b) physical theory changes with time beliefs (e.g. from Newtonian physics to relativity), and

(c) even the criteria of an acceptable physical theory (falsifiability, internal and external consistency etc.) depend upon time beliefs.

Thus, ascertaining the physical validity of traditional time beliefs becomes an extremely difficult task. One must first sort out the present-day conflict between the temporal assumptions of the philosophy of science, and the temporal assumptions of the physical theory that the philosophy of science hopes to demarcate.

(d) Conclusion: Before deciding the physical validity of traditional time beliefs, one needs to compare time beliefs in the philosophy of science with the time beliefs in physical theory, and change one or the other or both. (This author has already proposed modifications of both physical theory and the criteria of the philosophy of science.)

4. Why a comparison? (continued)

There are other reasons for wanting to carry out a comparison.

(a) The past is inevitably viewed through filters of the present. Hence, an implicit comparison with contemporary beliefs is inevitable. Leaving this comparison implicit can be dangerous.

For example, Orientalists, who were sympathetic to Indian tradition, proceeded on the assumption that the then-prevailing Western and scientific beliefs were correct. Hence, they sought to find value in Indian beliefs by making Indian beliefs metaphysical and spiritual.14 This, as stated above, amounts to a gross distortion.

I have earlier criticized a similar tendency among contemporary scholars to bend, and even mutilate, Indian views to suit contemporary Western prejudices.

(b) Summary: The dangers of an implicit comparison can be avoided by making the comparison with contemporary beliefs explicit. "Contemporary" time beliefs really means Western and scientific time beliefs, so an explicit comparison with these time beliefs is necessary.

5. The difficulties of a comparison (language)

Beliefs about time are incorporated in the structure of the language; hence it is, for example, impossible to speak about some notions of time, like supercyclic time, in a simple way in Indo-European languages. (Indo-European languages assume that the before-after relation can be described by a two place relation: with supercyclic time, however, the before-after relation must be at least a four-place relation, so that certain pictures of time cannot be easily described in natural language.) On the other hand, most people are unfamiliar with formal languages, so it is hard to communicate to most people how the grammatical structure of the language shapes their thinking about supercyclic time. This has also contributed to the persistence over millennia of clearly erroneous arguments about time (see 6 b below).

6. The difficulties of a comparison (prevailing Western time beliefs)

(a) Western time beliefs are radically different.

Thus, the Western church cursed "cyclic" time to reject equity and immanence. Later on, this curse forced Christian rational theology to distinguish itself from Islamic rational theology, and led to the emergence of superlinear time, and the belief in the clockwork cosmos.

(b) This long-standing Western prejudice against "cyclic" time has confused present-day scholarly discourse on time, through repeated reiteration of Augustine's simplistic dichotomy between "linear" time and "cyclic" time, used to reject quasi-cyclic time by confusing it with supercyclic time. These confused arguments are incorporated also into current scientific theory, e.g. in Hawking's theory of singularities, or in the current debate on the Grandfather paradox of time travel.

(c) Western ways of dealing with time are also incorporated into the current-day philosophy of science.
Thus, the discord between the time beliefs of physics and of the philosophy of science has been treated exactly in the manner of the theological debate between "determinism" and "free will". Because Western theology had invested so heavily into the belief in God's omniscience and omnipotence, and also in the belief in a transcendent God who rewarded or punished human beings, it was compelled to argue that the two manifestly incompatible things were somehow compatible.

(d) Western ways of dealing with time are also incorporated into the present-day (urban) way of life based on the idea that time is money.

The compulsions of Christian rational theology which led to Augustine's apocalyptic time being converted to superlinear time, and the development of superlinear time through utilitarianism into the current-day belief in time as money is dealt with in detail in my book (The Eleven Pictures of Time).

(e) All these aspects of contemporary Western time beliefs lead to a quick rejection of any "deviant" time beliefs, such as quasi-cyclic time, the basis of the Upanisadic value of moksa (which is a central belief in Indian tradition, and hence must be studied, as emphasized also by Daya Krishna).

(f) Conclusion: A proper understanding of traditional Indian views on time requires that prevailing Western and scientific time beliefs also should be re-examined from both a scientific and cultural perspective.

This sweeping agenda has already been partly accomplished. The author's first book on time re-examined time beliefs from a scientific perspective, and the second book re-examined time beliefs from a cultural perspective. The arguments and conclusions of these books would be used as a background to the present book.

The organization of the proposed book is as follows.

Organization of the proposed book:

The above introduction is only a simplified summary of some of the complexities inherent in the subject.

To keep the proposed book self-contained, the key aspects of the necessary background material would be briefly summarised in Part I, and elaborated where needed in Part II, which would detail key aspects of Indian time beliefs. Part III would be an appendix relating to the measurement of time, and traditional clocks and calendars. This appendix would be a summary account, since a detailed account of the traditional calendar cannot be provided without getting into the history of mathematics and astronomy in India.

The first part has been briefly covered in the introduction above. The second and third parts are described in more detail below.

Part I: Background: Time in Physics and Philosophy

Part II: Mapping traditional Indian time beliefs

(a) Upanishads:

(i) âtman, quasi-recurrence, and moksa.
(ii) The distinction between quasi-cyclic time and supercyclic time, and the temporal dichotomy between "linear" and "cyclic" time which erases this distinction.
(iii) The possibility of quasi-recurrence in present-day science.

(b) Lokâyata:

(i) rejection of quasi-recurrence, and
(ii) the grounds thereof, and
(iii) how the grounds and conclusions differ from those of Augustine.
(iv) Mundane time, and the materialist ethic.

(c) Sânkhya-Yoga:

(i) Yoga sûtra on atomic time; present day possibility of discrete time.
(ii) the yogi and Laplace's demon.
(iii) Is direct perception of the future possible? Jung's synchronicity hypothesis.

(d) Buddhist:

(i) paticca samuppada
(ii) the reversed analogy of instant as cosmos, and rejection of âtman
(iii) history-dependence vs action by contact
(iv) Buddhist quasi truth-functional logic and its relation to quantum logic.

(e) Jaina:

(i) time measures, musical scales, and human perception,
(ii) syâdavada.

(f) Nyâya-Vaisesika:

(i) Nyâya sûtra and Vaisesika sûtra aphorisms on kâla;
(ii) the paradox of the absent present, and
(iii) action by contact.
(iv) Logic of discourse: Nayyayika misunderstanding of the Buddhist position.

(g) Advaita Vedanta:

(i) Sriharsa's Khandanakhandakhâdya, and attack on Nyâya.
(ii) Relation to McTaggart's paradox.

(h) Grammarians:

(i) Panini and Bhartrhari on time;
(ii) Patanjali's crow paradox.
(iii) The eleven tenses.

(i) kâla and tâla:

(i) time in the theory of Indian music.

(j) sûfî and bhakti: ontically broken time and providence.

Part III: Appendices

Appendix 1: Time measurement, and the calendar

(a) The early calendar: Vedânga Jyotisa

(b) The revised calendar (quick reviews):

(1) Surya Siddhanta
(2) Aryabhata
(3) Varahamihira
(4) Bhaskara
(5) Brahmagupta
(6) Later astronomers

(c) The post-independence revised calendar:

(1) Meghnad Saha committee report (Report of the Calendar Reform Committee).
(2) Tropical year vs sidereal year, and the case of the monsoons in India: from Euler to Saha and beyond.

Appendix 2: Time measurement and the clock

(a) Drowning time: the clepsydra.

(b) Shadowy time: the gnomon.

(c) Smelling time: incense sticks.

(d) Starry time: stellar transits.


1. C. K. Raju, Time: Towards a Consistent Theory, Kluwer Academic, Dordrecht, 1994. (Fundamental Theories of Physics, Vol. 64).

2. See, for example, James Woodward, "An Essay Review of C. K. Raju's Time: Towards a Consistent Theory (Kluwer Academic:, Dordrecht)", Foundations of Physics 26 (1996) 1725-1730.

3. (a) C. K. Raju, "Time in Indian and Western Traditions, and Time in Physics", in Mathematics, Astronomy, and Biology in Indian Tradition, D. P. Chattopadhyaya and Ravinder Kumar (eds), PHISPC Monograph Series, No. 3, ICPR, New Delhi, 1995, 56-93.

(b) C. K. Raju, "Time in Medieval India", in: Science, Philosophy and Culture: Multidisciplinary Explorations, Part 2 (D. P. Chattopadhyaya and Ravinder KUmar eds), PHISPC, New Delhi (1997), 253-78. Also in: History of Indian Science, Technology, and Culture, AD 1000-1800, A. Rahman (ed), PHISPC.Oxford Univ. Press, 1998, New Delhi. Reprinted in Indian Horizons, 46(4) (1999) and 47(1) (2000), 40-71.

(c) C. K. Raju, "Kâla and Dik", Commissioned article in P. K. Sen & P. K. Sen (ed), PHISPC volume in preparation. Presented at the volume seminar, New Delhi, 2001.

4. The thesis is fully argued out in C. K. Raju, The Eleven Pictures of Time: the Physics, Philosophy, and Politics of Time Beliefs, Sage, 2002. A preliminary account relating time-beliefs to values may be found in C. K. Raju, "Reconstruction of Values: the Role of Science", in: Cultural Reorientation in Modern India (Indu Banga and Jaidev eds), Indian Institute of Advanced Study, Shimla, 1996, 369-392.

5. C. K. Raju, "Time in Indian and Western Traditions, and Time in Physics", cited above, and C. K. Raju, The Eleven Pictures of Time, cited above.

6. C. K. Raju, "Time in Medieval India", cited above.

7. A detailed description of these terms, "conditioned coorigination", "ontically broken time" etc. may be found in, C. K. Raju, The Eleven Pictures of Time, cited above.

8. Technically, causes may be located in the past in a physical world evolving according to retarded functional differential equations, as explained in detail in my book, Time:Towards a Consistent Theory, Kluwer Academic, 1994.

9. E. P. Thompson, "Time, Work-Discipline and Industrial Capitalism", Past and Present, 38 (1967) 56-97; Lewis Mumford, Technics and Civilization, Harcourt Brace, New York; John Hassard, The Sociology of Time, Macmillan, London 1990; David S. Landes, Revolution in Time: Clocks and the Making of the Modern World, Harvard University Press, Cambridge, 1983, 59-66.

10. For a detailed account of the physical assumptions about time underlying these value principle, and for the "utilitarian fallacy", see The Eleven Pictures of Time, cited earlier.

11. Why the "naturalist fallacy", and the fact-value separation are irrelevant to the above examples, is explained in detail in my book on the Eleven Pictures of Time. Briefly, scholars have studied values, the point is to change them! The assumption underlying claims of the "naturalist fallacy" is that values ought to be deducible in the manner of logical deduction. On the other hand, in a statistical-empirical sense, for a large number of people, value changes may, in fact, be related to changes in perceptions of facts (and to an underlying "evolutionary ethic" that has remained roughly constant on a historical time scale of three thousand years). Facts are, therefore, relevant to understanding past changes of values, and to any enterprise of further changing them. It is another matter that the meta-value of logical-deduction is questionable even in mathematics. See, C. K. Raju, "Mathematics and Culture", in History, Culture and Truth, (eds) Daya Krishna and K. Satchidananda Murthy, Kalki Prakash, New Delhi, 1999, 179-93. Reprinted in Philosophy of Mathematics Education 11, available at http://www.ex.ac.uk/~PErnest/pome/art18.htm.

12. Once again, the thesis is fully argued out in The Eleven Pictures of Time, cited above, which also goes on to explore the ethical implications of the new physical proposal of a tilt in the arrow of time.

13. For an exhaustive analysis of this theorem, and the assumptions on which its proof is based, see, Time: Towards a Consistent Theory, cited earlier, Chapter IV and appendix. Or, see, C. K. Raju, "Thermodynamic Time", Physics Education (India) 9 (1992) 44-62.

14. This is a common strategy in Western theology, and this is exactly the strategy adopted by Heidegger vis a vis Nietzsche. Nietzsche understood the possibility of Poincaré recurrence/Markovian recurrence as physically inevitable, and based his philosophy on it. Heidegger thought that a whole philosophy could not be based on a physics, which was subject to change, so he moved these ideas to the plane of metaphysics.