Calendar System -Part I

Some of my friends in India were sincerely interested in having idea of the calendar system of the world. I am writing this post at their behest.

This post may be taken as Preface of the issue. It will be followed by a series of posts dealing with the issue in detail.      

A tryst with Dates -Notes on Calendar system of the world.


Since the very beginning of human civilization the fundamental question that had been nagging the human mind was the concept of time. At the most figurative level it was associated with cyclic order of sunrise & sunset or day & night. But at the same time it became associated with gradual but infinitesimally small phases of decay and eventual death of any element of nature, animate or inanimate, starting from its nascent stage of creation.  It is quite evident that at the tangible level the feeling of time arises due to relative motion of matter. Sun and Moon are changing its place or say moving round the earth and as a result there is cyclic order of day, night and season.  There arose the concept of ‘interval’ between two events whether between sunrise and sunset or between any two happenings. In this context there followed prolonged phases of astronomical and astrological realization in both Greek and Indian culture much before 4000 BC until they arrived at nearly accurate measurement of the changing length of day and night. But initial stage realizations were based on fallacy that sun moves round the earth. In India the first authentic document on astronomy is old ‘Surya siddhanta’. It was proposed in 285 AD but it was recompiled properly by Varahmihir in 5th century AD.  Incidentally 285AD was the year vernal equinox coincided with the beginning point of sidereal zodiac (that is Aries 0 degree). Though some people believe that old ‘Surya Siddhanta’ was based on an astronomical treaty of Ptolemy (A Greek astrologer in 2nd century AD), but majority think that it is exclusively of Indian origin.  We all know that in 17th century Galileo proposed Heliocentric theory contravening the earlier belief that earth is the center of universe. Around the same time telescope was devised. Around the same time in India Professor RangaNathan committee(Calendar reform committee) fixed old Surya Siddhanta which is being still followed in India. But even prior to that clocks, and several associated units as well, were devised which were based on the changing length and direction of shadow of a fixed erect object. Similarly night was divided into several parts. But all such instruments were standardization of convenience. In this respect oriental systems were much ahead of western system. This varied from zone to zone depending upon the climatic convenience and astronomical events. In Indian system several units for interval of time were devised as earlier as 6000 BC, followed by concept of week, month and year. In western system though the work on astronomy was going on since 4000 BC but the things took proper shape with the rise of Alexander  when he founded city of Alexandria in Egypt and encouraged work on Astronomy and Astrology. This was followed by Ptolemy in 2nd century AD. We will come back to the issue of several manmade and astronomical measures of time in subsequent section.


At the end of 19th century there came an incredible but interesting change in the concept of time and its measurement, as introduced by Einstein through Theory of special relativity.  It  was based upon certain derivations of his predecessors Minkowski, Lorentz and Poincare who considered space to be 4 dimensional, including the dimension of time. Einstein proposed that time is not absolute PLEASE SEE THE NOTES BELOW at the ending part of this post for further discussion on this issue.

We would discuss first the Western calendars and then Indian and Chinese calendar systems. In context of calendar system we often refer to  equinoxes. These are the points where celestial equator(earth’s equator extended into space) cuts across ecliptic( path along which sun appears to be moving around earth or otherwise). This point is ever changing due to precession of earth around an axis perpendicular to ecliptic. North point, or the point in course of northward journey of sun,  is called vernal equinox from where sun crosses on 22-23 March(Imagine geocentric view with earth axis standing as vertical ). On this day, duration of night and day is equal so next day onward span of day starts to increase. In western systems all astronomical measurements are done using this point as standard. This standard is called Tropical. This point is ever shifting backward in clockwise direction. Presently it is falling in line of sight with around 5 degree of Pisces constellation. Western system regards this point, which is of course changing its position in clockwise direction at an average rate of 50 second per year, as the beginning point of zodiacal belt. On the other hand in oriental/Indian customary system the beginning point of zodiacal belt is fixed. It starts at 0 degree Aries through which Sun , apparently, crosses in its northward journey on 13-14th April. This system is called sidereal system. (In western system Aries constellation is itself shifting backward and is always coinciding with vernal equinox position. This is very untenable proposition. So in western system there is no sidereal concept of year. We will come back to issue in brief in later section as to why do we call a system as ‘Tropical or ‘Sidereal’) Indian system has thrust on moon position whereas western system lays thrust on Sun’s position. Oriental systems (Indian, Islamic and Chinese) are called luni-solar(either luni-sidereal or luni-tropical) and western systems are purely Tropical. In oriental system cyclic lunar position is taken in consideration for monthly count and nomenclature. But speed of moon in not static but follows a pattern of definite variation from date to date which repeats itself after one lunar year. However, in India tropical system has been being followed for religious purpose since the time of Vedas. Sidereal is followed only for religious or astrological purpose. Tropical is preferred for calendar system. In Vedic period too the year used to start on vernal equinox day. Vedic seers were aware of shifting position, if not precession of earth, of vernal equinox. In Western system it was introduced by Greek astronomer Hipparchus in around 140 BC when he discovered processional motion



(The north-south axis of earth is inclined with perpendicular to ecliptic plane( or earth’s equatorial plane  is inclined to ecliptic plane) by around 23 degree. This is the reason for change in seasons on earth during the annual rotation. This axis also rotates around a normal perpendicular to ecliptic plane. This is called processional motion of earth. This motion is the reason of change in vernal equinox position. Regarding the exact duration for one full rotation of vernal equinox through all the 12 signs, it is a little controversial matter however roughly it can be taken as 360*72 years, i.e. 72 years/degree. But it is again controversial whether the axis makes one full rotation by 360 degree or oscillates around a mean position.)

So overall there are four types of units of time depending upon which different types of Calendar Systems have been developed in the world.

  1. a) Tropical
  2. b) Sidereal
  3. c) Lunar
  4. d) Luni-solar: Luni-sidereal and Luni-Tropical.

We will come back to all these issue in the ensuing relevant section. But it should be born in mind that these issues are primarily astronomical matters, not Astrological. Simply that Astrology is based upon these Astronomical concepts.



(Readers not having background in science may skip this section. The issues discussed here are time-old pleasantries but contextual. The real subject matter is too vast & complicated to be tackled through any such discussion. )

At the end of 19th century there came an incredible but interesting change in the concept of time and its measurement, as introduced by Einstein through Theory of special relativity.  It  was based upon certain derivations of his predecessors Minkowski, Lorentz and Poincare who considered space to be 4 dimensional, including the dimension of time. Einstein proposed that time is not absolute. However he started with certain postulates regarding light and its velocity, that velocity of light is constant irrespective of the motion of source and observer. Fundamentally this is because we see object, not light. Further this can be easily established with quantum concept of light. Einstein tried to establish that like all motion of rigid body, time is also relative. Meaning thereby it does not depend on only clock but also upon the relative velocity of frame of reference in which clock is located. For example when two trains are moving with different velocity then if clock is placed in one train then its time measurement for an event in the same train and for an event in the other train will be different even if the two events appeared to have occurred at the same time. He drew several conclusions on the basis of certain mathematical derivations proceeding on this line, such as: time passes faster for relatively slowly moving object.

Einstein started with two fundamental postulates and derived relativistic equation for both space and time in which velocity of light was taken as a constant for highest possible velocity. As said earlier, though these equations had been already derived earlier by Lorentz but Einstein derived the same independently and lent physical meaning to the same. There is paradigm of three concepts in this context.

1)Principle of relativity

2)Special theory of relativity

3)General theory of relativity

The prime concepts which Einstein added are as follows.

1)       A frame of reference, with respect to which position of body and time of an event is measured, is represented by a co-ordinate system. There are inertial (non-accelerated) and non-inertial (accelerated) frames of reference (F.R.).  All frames of reference which are either at rest or moving with uniform velocity with respect to space fixed static coordinate system are inertial frame of references, otherwise it is non-inertial frame of reference. Relativity of space in relation to or say inside one inertial frame of reference is ‘Principle of relativity”. Relativity of space & time as measured from two different inertial frame of reference is subject matter of ‘Special theory of relativity’. Relativity of space & time in relation to an inertial and a non-inertial frame of reference( Or both being non-inertial frame of reference) is called ‘General theory of relativity’.

2)       Normally if source, observer and a body in motion all remains confined to one inertial frame of reference then there is no relativity of time. Hence an inertial frame of reference is a co-ordinate system in which law of mechanics holds true without any relativistic consideration of time. That is to say law of mechanics is not concerned with the velocity of frame of reference itself provided the same is not accelerated in any way. The purpose of classical mechanics is to describe how   bodies change their position in space with time but inside only one inertial frame of reference. Newton’s laws of motion go to form basis for it. If a law of physics(say Newton law of motion) holds true with respect to one inertial frame of reference then it will hold true with respect to all inertial frame of references, so long as the event is confined to the one particular frame of reference. This is also put across as ‘Laws or Physics are invariant under change of inertial frame of reference’. This is ‘principle of relativity’.  Meaning thereby whatever relativity a motion of matter  is being subjected to with respect of one inertial frame of reference, this will also hold true  if the same event occurs inside and with respect to other inertial frame of reference.

3)        But if the space & time of the body in motion in one inertial frame of reference is measured with respect other inertial frame of reference then relativity of time, in addition to relativity of space, comes into picture. This goes to constitute ‘special theory of relativity” (Meaning of inertial frame, however, in General theory of relativity is a little different. In general theory of relativity a freely falling frame is regarded to be standard inertial frame of refrence. This is because even though the frame of reference is itself accelerated the body around it are moving with constant velocity with reference to the frame of reference ).

4) This can be resolved only if we assume that Velocity of light is a constant, so it does not depend upon the motion and frame of reference of source and observer. Meaning thereby velocity of light is not subjected to any relativity whatever may be frame of reference chosen OR the direction of propagation of light. As we have discussed that this is justified assumption if we keep in mind that we don’t watch light but object. Otherwise it can be shown that whole thing will come in conflict with principle of relativity as discussed above.

5) Time between two events may be different for observers from different frame of references, even if the observers are located on different/independent inertial frames of reference. Meaning thereby time is also co-ordinate of the frame of reference. Though concept of four dimensional space was already in place as proposed by Minowski and later on used by Lorentz in the course some electro-dynamical conclusions, yet Einstein independently argued in favor of the fourth co-ordinate, showing that the constant aspect of velocity of light in vacuum and accepting  time as fourth  co-ordinate are essential consequences of each other without sacrificing  the erstwhile Galilean principle of relativity. The most important thing was that a concept of ‘spacetime’ was introduced. This is different from the concept of space and time as used in defining simultaneity of two events in Gallilean-Newtonian frame of reference.

Einstein presented a detailed analysis of the issue discussed through several illustrations. The famous one is in relation to a person and a source of light on carriage of railway train, and a person watching the things from embankment that is static platform. The carriage and embankment are two inertial frames of reference.  With the help of these propositions he deduced relativistic transformation of space and time , same as Lorentz transformations. He further derived not only energy-mass equivalence relation but tried to show the implication of the relativity of time. That if there are two persons- one on earth and other in a spacecraft travelling with higher velocity near to that of light, then on return after a long time the person on earth will be much older than the person in spacecraft. I would pass my personal opinion on this issue in one of the ensuing paragraphs. There are two more issues in this context. First one is whether light have mass or not. As per Einstein the answer is no.  Of course there is effect of Gravity on light. But it not because light is having mass but because under the intense gravitational field of a body, the space itself stands curved and hence light appears to travel in curved path when it passes near the body. Practically energy and momentum of a body leaves an influence that causes curvature in space which manifests itself as gravity effect of the body.

The aforesaid conclusion was drawn by Einstein through his  next step called ‘General theory of relativity-1915’ proposed that relativity arises not only due to relative  motion of matter and time of event measured from different frame of reference, but it is there in relation to the relative movement between matter and space as well. Meaning thereby space is not a blank entity but may be regarded as field of force which interacts with earth or matter when matter moves with any kind of accelerated movement.

It appears that Einstein was trying to extrapolate certain metaphysical realizations into the realm of space & matter. At material plane whatever he derived are apparent phenomena. But in the realm of mind it is a reality.   So going a step further time appears to be associated with thought process as well. As said earlier, ageing or decaying process is inherently associated with time. So at the sublime level it was also realized as quantification of the process of passing from ‘ordered’ to ‘disordered’ state. The process was subsequently termed as Entropy. It is natural tendency of nature that left to itself everything wants to slide into disordered state starting from any possible ordered state. That is to say left to itself entropy increases. The process of change in entropy may also serve as a measure of time from the point of view of ageing process. So there is another aspect to time that is the feeling aspect. One span of clock time may be felt differently by different individual. We all know that it depends upon focus of mind. A more focused mind would feel time elapsing faster and entropy increasing relatively slower, hence this would increase longevity. Meaning thereby what is 1 year as per clock may be 6 months for one person and may be 1.5 year for other person. So an age of, say, 60 years would be age of 30 years for the first one and 90 years for the other one. So rate of change of entropy may be regarded to be inversely proportional to velocity of mind. But evidently any quantification in that regard is impossible. However one thing should be evident that concept of time, as implied in the motion of Sun, Moon, Earth and other celestial bodies, transforms itself into  feeling aspect of time. So any phenomena on inanimate plane in respect of time should have its counterpart on animate plane as well. But mixing the two may cause confusion. Maharishi Mahesh Yogi from India has attempted at the psycho-analysis with the help of Lagrangian and Hamiltonian tools of classical mechanics.  Though I don’t have any in-depth idea of the same but I think that probabilistic tools combined with quantum mechanics is the right answer.


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