Concept and measurements of Time- DGP Arun Upadyay IPS (Rtd)
It is in continuation of my notes on era and geography of Asuras & Devas. There was a hint on ancient chronology on which a self styled Physicist Ravindra Kaul started abuse by words Indian (common derogatory word in Kashmir), Ṛgveda (for him, it is Rigged, correct spelling is abuse) Hanuman Chālīsā, Rudrākṣa without showing any knowledge of physics. 2 years back somebody had abused me with words-Gita and Gita Press. By his boasting of being the greatest physicist without having written a single paper, even educated persons may be misled that Time can have no other meaning.
In modern Physics, Time is used in many senses-(1) As a dimension (or extra time like dimensions), (2) Flow of time-similar to concept of dimension, (3) Interval of time-definition of its unit.
Ernest Mach was the first to analyze philosophy of time space and universe. Albert Einstein developed his idea and methods of Riemann geometry of manifold to explain universe as 4-dimensional space-time continuum. While space dimensions extend in positive and negative directions up to infinite distances, time can only move forward. But mathematical equations are symmetric for all 4 dimensions and some persons talk about journey into past. There was a famous sci-fi ‘Time-Machine’ by H. G. Wells describing a machine which can take us in past. So far, this is not feasible to make such a machine. It also violates the law of cause & effect. Suppose, a person visits in past and kills his father or grandfather as infant-then how he is born and existing, Or somebody goes 300 years back and unites Indian kings against Mughals and British invaders and frees India. It will lead to a parallel world vastly different from real world seen today. Theory of infinite universes is something like that.
Flow of time was analyzed by Arthur Eddington in 1928 who defined many types of ‘Arrows of Time’. Summary of these theories can be found in ‘Universe Around us’ by J B. Narlikar (OUP) or a popular book ‘Brief History of Time’ by Stephen Hawkins.
There are 2 main concepts or arrows-(1) Thermodynamic arrow of Time-Second law of thermodynamics has many parallel statements. One statement is that no natural process is reversible. Its implication is that Entropy or Disorder of a closed system always increases with any process of change. Disorder is measured by addition all permutations of components (atoms, molecules also) and its logarithm is called Entropy. Both are very large numbers impossible to calculate or measure. In Shannon’s Theory of Communication-Entropy or disorder is a measure of noise. In practical view, no state of an object comes back. (a) By shaking sugar in water, it will be dissolved. No amount of further shaking will separate them again. One author on Thermodynamics has estimated that by shaking a mixture of sand-sugar in glass, probability of its separation will be ones in many billion times the age of universe. (b) A child can grow, become adult and old. But an old cannot become child again. (c) Smoke can disperse into air. It can never come back to fire. (d) Mango can become ripe but not back to unripe or flower stage.
(2) Mechanical arrow of time- It is used in mechanics and is measure of velocity. It is measured by time period of cyclic processes. Natural cycles of time are day, month, year and time units are with reference to those periods as multiples or components. In Physics, we use the same time in Electromagnetic arrow of time. But they cannot be same-in mechanics speed is relative to observer, but speed of light (electromagnetic wave) is same for all observers. This is a philosophical contradiction not resolved till today (see Brief History of Time).
Due to 2 types of measurable times, all 10 versions of 10-dimensional string theories or 2 forms of M-string theories, we use a time dimension as in GTR (General theory of relativity). Another is time-like dimension. All string theories are mathematical equations only with no concept of individual dimensions. In GTR also, time dimension differs from 3 dimensions of space in that Time is unidirectional increasing in future only. Space dimensions extend to infinity in positive and negative directions also.
Measure of Time is in 2 ways-(1) Unit of Time-interval, (2) Elapsed time since a particular point in terms of basic units of time. In experiments, elapsed time can be from any point. For human calendars, it starts from a particular epoch and count of year-month-das from that. Year-month are measured in 2 ways-solar days/years, lunar day/month.
Definition of time-In Physics, second is defined as 86400 parts of a solar day (from local sunrise to sunrise or more accurately from mid-night to next midnight). In mathematics, mid-night system is preferred as it is same for all places on same longitude. There are 2 errors in this definition also. Day length changes seasonally-axial rotation components is same, but component (4 minutes) due to relative motion of 1 degree of sun changes due to elliptic shape of orbit. Another error is that axial rotation of earth is slowing down due to tidal friction, ¾ part by moon attraction and remaining by sun. To make it more specific, second was defined as 86400 part of mean solar day in year 1900 of Gregory calendar.
When it became possible to measure atomic property more accurately, second was defined as the duration of 9, 192, 631, 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.’ (1967). Both the measures are technically different but match within limits of experimental error.
Another definition can be based on speed of light when it was possible to measure it accurately by Kerr-cell method. Here, metre is defined as the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.’ (1983). If metre is taken as standard, this can be a definition of second.
Continuous measure of time from a particular epoch is calendar, which can be solar or a combination with lunar motion as observed from earth. Here, the preferred unit is day as all calculations are based on day-count (ahargaṇa in Indian astronomy). Large astronomical distances are measured in light year = distance travelled by light in 1 year.
In India, Vedic texts relate 4 aspects of Puruṣa with 4 types of Kāla (Time).
Puruṣa (as in Puruṣa Sūkta) means any object within a Pura (structure within a boundary surface). It can mean Man (including woman) and any structure or complete universe. Man is a conscious being which can think and act accordingly. The whole Universe or its Creator also is a conscious being called Puruṣa. Here, consciousness is called Chetanā. Chit = point space. Citi (City) = arrangement or design of point spaces. Chetanā = Agent which can do Chiti-चितिरूपेण या कृस्नं एतद् व्याप्य स्थिता जगत्, नमस्तस्यै, नमस्तस्यै, नमस्तस्यै, नमो नमः। (दुर्गा सप्तशती ५/८०) In Universe, Puruṣa is whole or visible parts of Universe or its creator. Uniform homogeneous source is called ‘Rasa’ out of which only ¼ is used in creation of world, remaining ¾ is always in original undisturbed form-पादोऽस्य विश्वा भूतानि, त्रिपादस्यामृतं दिवि (पुरुष सूक्त, ३
Puruṣa has 4 aspects out of which one is beyond description as there is no distinction (Bheda) in its parts. Other 3 are defined as Kṣara, Akṣara, Avyaya-
गीता, अध्याय १५-द्वाविमौ पुरुषौ लोके क्षरश्चाक्षर एव च। क्षरः सर्वाणि भूतानि कूटस्थोऽक्षर उच्यते॥१६॥
उत्तमः पुरुषस्त्वन्यः परमात्मेत्युदाहृतः। यो लोकत्रयमाविश्य बिभर्त्यव्यय ईश्वरः॥१७॥
(1) Kṣara Puruṣa-All objects within a boundary are Kṣara = decaying). This is physical form of objects which always decays.
(2) Akṣara Puruṣa-Though all objects decay, there unseen (Kūṭastha) name or identity and functions remains the same throughout its life. This aspect is Akṣara.
(3) Avyaya Puruṣa-As part of a system, nothing changes. The complete system or world structure is called Avyaya. Its controller is called Īśvara.
(4) Parātpara Puruṣa-Overall Universe or ultimate reality has no distinction in time or space, so it is beyond description, called Parātpara.
Same object has all 4 aspects, first of which has form and decaying. Other 3 are formless and successively more permanent. Our aim is to move from Mṛtyu (transient) to Amṛta (मृत्योर्मा अमृतं गमय), so we first observe real universe forms then move to 3 stages of unseen reality. Unity is later realization- एकत्वं अनु-पश्यतः (ईशावास्य उपनिषद् २)
Kāla (Time) is perception of change. Here also, perception of the smallest or the largest is beyond our imagination, so that aspect is Parātpara Kāla. All types of Kāla explained in Bhāgavaat Purāṇa part 3 chapter 11. Here also length units are defined as per velocity of light which can be units of time if length unit is taken as standard. Definitions of Gītā are given below-
कालोऽस्मि लोक क्षयकृत्प्रवृद्धो । (गीता ११/३२)
कालः कलयतामहम् । (गीता १०/३०)
अहमेवाक्षयः कालो धाताहं विश्वतोमुखः (गीता १०/३३)
Sūrya siddhānta (1/10) defines 2 types-Nitya Kāla (eternal time) which decays world, so it is called Mṛtyu (death) also. Other is called janya (creative-in cycles of yajña which creates) which has 2 types-Mūrta (perceived), Amūrta (beyond perception). ).
सूर्य सिद्धान्त (१/१०)-लोकानामन्तकृत् कालः कालोऽनयः कलनात्मकः।
स द्विधा स्थूल सूक्ष्मत्वात् मूर्तश्चामूर्त उच्यते॥
(1) Nitya Kāla (Eternal time)-Thermodynamic arrow of time-unidirectional change.
(2) Janya Kāla (measure of creative cycles)-Natural cycles of production or Yajña are day, month, year and time units are defined in terms of them. This is calculated in physics (Kalanātmaka). Since we have not resolved mechanical and electromagnetic time, Bhagavān calls him as Kāla which is most difficult in all calculations (Gītā 10/30).
(3) Akṣaya Kāla-Time of a complete system. Measure of running time by calendars.
(4) Parātpara Kāla-Beyond perception and description.
These correspond to 4 Puruṣa-
Niitya Kāla-Kṣara Puruṣa
Janya Kāla-Kṣara Puruṣa
Akṣaya Kāla-Avyaya Puruṣa
Parātpara Kāla- Parātpara Puruṣa
Universe as a whole has 10 dimensions. First 5 dimensions describe mechanical universe. So, there are 5 basic units of measurement corresponding to 5 Mā-Chhandas-Mā, Pramā, Pratimā, Anumā, Asrīvi. Remaining 5 dimensions are different stages of Chiti and describe Chetana (conscious) world. So there are parallel words-Daśa (10), Daśā (state, condition), Diśā (direction). Knowledge of 10 dimensions is 10 mahā-vidyā. 10 dimensions are-
0-Point
1-Line (Rekhā)
2. Surface (Pṛṣṭha)
3, Volume (Stoma, Āyatana, Āyu)
4. Matter-This is not a dimension in GTR which terms matter as curvature of space-time.
5. Time- Nitya Kāla-eternal time
6. Puruṣa-Within structures, creator of order or design.
7. Ṛṣi (String)-Links between any 2 points or objects. Of 7 types-4 fundamental forces of nature (body of symbolic bird-Suparṇa), 2 symmetry (wings), one anti-symmetry (tail).
8. Nāga or Vṛtra (limiting bodies within curved boundary)-similar to concept of limited dimensions in Calabi geometry).
9. Randhta (Defect)-Changes in levels of density, energy which cause creation-janya Kāla.
10. Ananda or Rasa-Same as point dimensions.
Complete description of World can be in 6 ways-from 5 to 10 dimensions-giving rise to 6 Darśana (visions) loosely translated as philosophy. Its representation in word will also need 6 types of Darśa-Vāk (visible word = script). Script is on a surface of 2 dimensions, so its components (letters) are square of dimension numbers-equal to elements of Darśana-
1. Sānkhya- 5x5 elements-Roman script of 25 letters
2. Śaiva-6x6 elements-Hebrew, Latin, Russian, Gurumukhi (with Om).
3. Marut (7x7)-Devanāgarī
4. Kalā (8x8)-Brāhmī
5. Vijñāna (8+9) square-36x3 Vowels, 36x5 consonants, 1 om used in Veda.
6 Sahasra- Many thousand letters beyond Vyoma (Tibbet) in China.
Surya Siddhānta describes 9 types of time units parallel to 9 stages of creation from abstract source. Formative stages are mixed called Varāha (boar or cloud). That is meaning of 9th cloud. All 9 units are defined differently. They can be converted to each other, but it has experimental errors.
सूर्य सिद्धान्त (१४/१)-ब्राह्मं दिव्यं तथा पित्र्यं प्राजापत्यं च गौरवम्।
सौरञ्च सावनं चान्द्रमार्क्षं मानानि वै नव॥ Nine Indian Time-units-
(1) Brahma-Time period of creation from formless (avyakta) to forms is called a day of Brahma or Kalpa. In same period of time, creation dissolves into avyakta (Gītā 8/17,18). Day of Brahma has been defined as of 1000 yugas in Gītā, purāṇas, Sūrya-siddhānta etc. Each yuga is of 12,000 divya-years, 1 divya-year = 360 solar years. Thus, 1 day of Brahmā = 432 crore years.
(2) Prājāptya-Prajāpati started yajña (Gītā 3/10), so prājāpatya period is period of galaxy from where creation started. Rotation period of galaxy is called Manvantara of about 31.68 crore years. Present stage is 7th manvantara. This has been called 7th day in Bible. After 4, 5th days sun, moon, earth were created. So, day cannot mean here rotation of earth or even of sun. This is rotation of first creation galaxy. Modern estimate of period of sun revolution around center of galaxy is 20-25 crore years.
(3) Divya year is of 360 solar years, arrived in 3 ways. This is approximate period of revolution of imaginary planet at 60 AU (or average rotation of about 60,000 Balakhilyas at same distance), called Aloka (dark) boundary of 100 crore yojana diameter, This has been called parivarta yuga in Vāyu, Matsya purāṇas, which is cycle of historic changes. Third view is that north-south motion of sun is like day-night cycle. This cycle of 1 year is 1day (divya).Taking round number 360 for days in a year, divya year is of 360 years.
(4) Guru scale-In period of 60 years Saturn and Jupiter complete integral revolutions-2 and 5. Alternatively, Angirā-effect (upward convection due to radiation pressure takes 60 years to complete (Aitareya Brāhmaṇa 18/3/17,Taittirīya Br, 2/2/3/5-6)
(5) Pitar māna- Synodic revolution of moon in 29.5 days is called 1day of pitars. Varāha is 15 ahargaṇa or 4,096 times earth size-that is parjanya. Intermediate level is pitar, 64 times earth size called pitar. Moon orbit is 61 times earth size. So pitars of human beings also reside on outer region of moon. Our bright half of month is night of pitars and dark half is their day.
(6) Sāvana māna-Sunrise to next sunrise is sāvana or civil (practical) day. 1 month = 30 days, 1 year = 12 months.
(7) Solar-Apparent revolution of sun around earth is yea (sidereal). 1/12th part is 1 month (1 rāśi = 30 deg. Movement).1 day is 1 deg. movement.
(8) Lunar-Synodic revolution of moon around earth is a lunar month.5 angas of pañchānga are defined from moon and sun—Tithi = (M-S)/12deg., 1tithi = 2 karaṇa, yoga = (M+S)/13.3.Nakshatra is average daily motion of moon. Vara (day) is cyclic naming of days.
(9) Nakshtra (sidereal)-Axial rotation of earth with respect to fixed stars is sidereal day of 23 hours 56 minutes. Month, year have 30 and 360 days.
Micro units of time-Śatapatha Brāhmaṇa (12/3/2/1,5) divides mean day length of 12 hours successively by 15 parts into units named as muhūrtta (48 minutes), kṣipra, etarhi, idānī, prāṇa, aktana (or, ana), nimeṣa, lomagartta, svedāyana. It is stated that stars (nakṣatra) in galaxy (Brahmāṇḍa) are like its loma-gartta (roots of skin hairs). Number of lomagartta in a year (Samvatsara) is equal to the number of stars in a galaxy, so this unit of time is called lomagartta which is equal to muhūrtta x 15 (-7) = about 80.000 parts of a second. Similarly its 15th part is svedāyana equal to about 11,20,000 parts of a second. In this time light travels about 270 meters. Rain drops (sveda) move (ayana) about same distance without breaking or joining, so this time unit is called svedāyana. Estimate of number of stars in galaxy was done after 1985 which is correctly estimated in Śatapatha-Brāhmaṇa to be 10 (11). Logic of division by 15 is given that ratio of earth orbit to earth size is same as ratio of Tapah-loka (visible universe) and galaxy, both equal to 2 (15).
Seven Yugas-By joining two cycles of time, a yuga is formed. Munīśvara in his astronomy text Siddhānta Sārvabhauma has stated 5 yugas.
It is in continuation of my notes on era and geography of Asuras & Devas. There was a hint on ancient chronology on which a self styled Physicist Ravindra Kaul started abuse by words Indian (common derogatory word in Kashmir), Ṛgveda (for him, it is Rigged, correct spelling is abuse) Hanuman Chālīsā, Rudrākṣa without showing any knowledge of physics. 2 years back somebody had abused me with words-Gita and Gita Press. By his boasting of being the greatest physicist without having written a single paper, even educated persons may be misled that Time can have no other meaning.
In modern Physics, Time is used in many senses-(1) As a dimension (or extra time like dimensions), (2) Flow of time-similar to concept of dimension, (3) Interval of time-definition of its unit.
Ernest Mach was the first to analyze philosophy of time space and universe. Albert Einstein developed his idea and methods of Riemann geometry of manifold to explain universe as 4-dimensional space-time continuum. While space dimensions extend in positive and negative directions up to infinite distances, time can only move forward. But mathematical equations are symmetric for all 4 dimensions and some persons talk about journey into past. There was a famous sci-fi ‘Time-Machine’ by H. G. Wells describing a machine which can take us in past. So far, this is not feasible to make such a machine. It also violates the law of cause & effect. Suppose, a person visits in past and kills his father or grandfather as infant-then how he is born and existing, Or somebody goes 300 years back and unites Indian kings against Mughals and British invaders and frees India. It will lead to a parallel world vastly different from real world seen today. Theory of infinite universes is something like that.
Flow of time was analyzed by Arthur Eddington in 1928 who defined many types of ‘Arrows of Time’. Summary of these theories can be found in ‘Universe Around us’ by J B. Narlikar (OUP) or a popular book ‘Brief History of Time’ by Stephen Hawkins.
There are 2 main concepts or arrows-(1) Thermodynamic arrow of Time-Second law of thermodynamics has many parallel statements. One statement is that no natural process is reversible. Its implication is that Entropy or Disorder of a closed system always increases with any process of change. Disorder is measured by addition all permutations of components (atoms, molecules also) and its logarithm is called Entropy. Both are very large numbers impossible to calculate or measure. In Shannon’s Theory of Communication-Entropy or disorder is a measure of noise. In practical view, no state of an object comes back. (a) By shaking sugar in water, it will be dissolved. No amount of further shaking will separate them again. One author on Thermodynamics has estimated that by shaking a mixture of sand-sugar in glass, probability of its separation will be ones in many billion times the age of universe. (b) A child can grow, become adult and old. But an old cannot become child again. (c) Smoke can disperse into air. It can never come back to fire. (d) Mango can become ripe but not back to unripe or flower stage.
(2) Mechanical arrow of time- It is used in mechanics and is measure of velocity. It is measured by time period of cyclic processes. Natural cycles of time are day, month, year and time units are with reference to those periods as multiples or components. In Physics, we use the same time in Electromagnetic arrow of time. But they cannot be same-in mechanics speed is relative to observer, but speed of light (electromagnetic wave) is same for all observers. This is a philosophical contradiction not resolved till today (see Brief History of Time).
Due to 2 types of measurable times, all 10 versions of 10-dimensional string theories or 2 forms of M-string theories, we use a time dimension as in GTR (General theory of relativity). Another is time-like dimension. All string theories are mathematical equations only with no concept of individual dimensions. In GTR also, time dimension differs from 3 dimensions of space in that Time is unidirectional increasing in future only. Space dimensions extend to infinity in positive and negative directions also.
Measure of Time is in 2 ways-(1) Unit of Time-interval, (2) Elapsed time since a particular point in terms of basic units of time. In experiments, elapsed time can be from any point. For human calendars, it starts from a particular epoch and count of year-month-das from that. Year-month are measured in 2 ways-solar days/years, lunar day/month.
Definition of time-In Physics, second is defined as 86400 parts of a solar day (from local sunrise to sunrise or more accurately from mid-night to next midnight). In mathematics, mid-night system is preferred as it is same for all places on same longitude. There are 2 errors in this definition also. Day length changes seasonally-axial rotation components is same, but component (4 minutes) due to relative motion of 1 degree of sun changes due to elliptic shape of orbit. Another error is that axial rotation of earth is slowing down due to tidal friction, ¾ part by moon attraction and remaining by sun. To make it more specific, second was defined as 86400 part of mean solar day in year 1900 of Gregory calendar.
When it became possible to measure atomic property more accurately, second was defined as the duration of 9, 192, 631, 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.’ (1967). Both the measures are technically different but match within limits of experimental error.
Another definition can be based on speed of light when it was possible to measure it accurately by Kerr-cell method. Here, metre is defined as the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.’ (1983). If metre is taken as standard, this can be a definition of second.
Continuous measure of time from a particular epoch is calendar, which can be solar or a combination with lunar motion as observed from earth. Here, the preferred unit is day as all calculations are based on day-count (ahargaṇa in Indian astronomy). Large astronomical distances are measured in light year = distance travelled by light in 1 year.
In India, Vedic texts relate 4 aspects of Puruṣa with 4 types of Kāla (Time).
Puruṣa (as in Puruṣa Sūkta) means any object within a Pura (structure within a boundary surface). It can mean Man (including woman) and any structure or complete universe. Man is a conscious being which can think and act accordingly. The whole Universe or its Creator also is a conscious being called Puruṣa. Here, consciousness is called Chetanā. Chit = point space. Citi (City) = arrangement or design of point spaces. Chetanā = Agent which can do Chiti-चितिरूपेण या कृस्नं एतद् व्याप्य स्थिता जगत्, नमस्तस्यै, नमस्तस्यै, नमस्तस्यै, नमो नमः। (दुर्गा सप्तशती ५/८०) In Universe, Puruṣa is whole or visible parts of Universe or its creator. Uniform homogeneous source is called ‘Rasa’ out of which only ¼ is used in creation of world, remaining ¾ is always in original undisturbed form-पादोऽस्य विश्वा भूतानि, त्रिपादस्यामृतं दिवि (पुरुष सूक्त, ३
Puruṣa has 4 aspects out of which one is beyond description as there is no distinction (Bheda) in its parts. Other 3 are defined as Kṣara, Akṣara, Avyaya-
गीता, अध्याय १५-द्वाविमौ पुरुषौ लोके क्षरश्चाक्षर एव च। क्षरः सर्वाणि भूतानि कूटस्थोऽक्षर उच्यते॥१६॥
उत्तमः पुरुषस्त्वन्यः परमात्मेत्युदाहृतः। यो लोकत्रयमाविश्य बिभर्त्यव्यय ईश्वरः॥१७॥
(1) Kṣara Puruṣa-All objects within a boundary are Kṣara = decaying). This is physical form of objects which always decays.
(2) Akṣara Puruṣa-Though all objects decay, there unseen (Kūṭastha) name or identity and functions remains the same throughout its life. This aspect is Akṣara.
(3) Avyaya Puruṣa-As part of a system, nothing changes. The complete system or world structure is called Avyaya. Its controller is called Īśvara.
(4) Parātpara Puruṣa-Overall Universe or ultimate reality has no distinction in time or space, so it is beyond description, called Parātpara.
Same object has all 4 aspects, first of which has form and decaying. Other 3 are formless and successively more permanent. Our aim is to move from Mṛtyu (transient) to Amṛta (मृत्योर्मा अमृतं गमय), so we first observe real universe forms then move to 3 stages of unseen reality. Unity is later realization- एकत्वं अनु-पश्यतः (ईशावास्य उपनिषद् २)
Kāla (Time) is perception of change. Here also, perception of the smallest or the largest is beyond our imagination, so that aspect is Parātpara Kāla. All types of Kāla explained in Bhāgavaat Purāṇa part 3 chapter 11. Here also length units are defined as per velocity of light which can be units of time if length unit is taken as standard. Definitions of Gītā are given below-
कालोऽस्मि लोक क्षयकृत्प्रवृद्धो । (गीता ११/३२)
कालः कलयतामहम् । (गीता १०/३०)
अहमेवाक्षयः कालो धाताहं विश्वतोमुखः (गीता १०/३३)
Sūrya siddhānta (1/10) defines 2 types-Nitya Kāla (eternal time) which decays world, so it is called Mṛtyu (death) also. Other is called janya (creative-in cycles of yajña which creates) which has 2 types-Mūrta (perceived), Amūrta (beyond perception). ).
सूर्य सिद्धान्त (१/१०)-लोकानामन्तकृत् कालः कालोऽनयः कलनात्मकः।
स द्विधा स्थूल सूक्ष्मत्वात् मूर्तश्चामूर्त उच्यते॥
(1) Nitya Kāla (Eternal time)-Thermodynamic arrow of time-unidirectional change.
(2) Janya Kāla (measure of creative cycles)-Natural cycles of production or Yajña are day, month, year and time units are defined in terms of them. This is calculated in physics (Kalanātmaka). Since we have not resolved mechanical and electromagnetic time, Bhagavān calls him as Kāla which is most difficult in all calculations (Gītā 10/30).
(3) Akṣaya Kāla-Time of a complete system. Measure of running time by calendars.
(4) Parātpara Kāla-Beyond perception and description.
These correspond to 4 Puruṣa-
Niitya Kāla-Kṣara Puruṣa
Janya Kāla-Kṣara Puruṣa
Akṣaya Kāla-Avyaya Puruṣa
Parātpara Kāla- Parātpara Puruṣa
Universe as a whole has 10 dimensions. First 5 dimensions describe mechanical universe. So, there are 5 basic units of measurement corresponding to 5 Mā-Chhandas-Mā, Pramā, Pratimā, Anumā, Asrīvi. Remaining 5 dimensions are different stages of Chiti and describe Chetana (conscious) world. So there are parallel words-Daśa (10), Daśā (state, condition), Diśā (direction). Knowledge of 10 dimensions is 10 mahā-vidyā. 10 dimensions are-
0-Point
1-Line (Rekhā)
2. Surface (Pṛṣṭha)
3, Volume (Stoma, Āyatana, Āyu)
4. Matter-This is not a dimension in GTR which terms matter as curvature of space-time.
5. Time- Nitya Kāla-eternal time
6. Puruṣa-Within structures, creator of order or design.
7. Ṛṣi (String)-Links between any 2 points or objects. Of 7 types-4 fundamental forces of nature (body of symbolic bird-Suparṇa), 2 symmetry (wings), one anti-symmetry (tail).
8. Nāga or Vṛtra (limiting bodies within curved boundary)-similar to concept of limited dimensions in Calabi geometry).
9. Randhta (Defect)-Changes in levels of density, energy which cause creation-janya Kāla.
10. Ananda or Rasa-Same as point dimensions.
Complete description of World can be in 6 ways-from 5 to 10 dimensions-giving rise to 6 Darśana (visions) loosely translated as philosophy. Its representation in word will also need 6 types of Darśa-Vāk (visible word = script). Script is on a surface of 2 dimensions, so its components (letters) are square of dimension numbers-equal to elements of Darśana-
1. Sānkhya- 5x5 elements-Roman script of 25 letters
2. Śaiva-6x6 elements-Hebrew, Latin, Russian, Gurumukhi (with Om).
3. Marut (7x7)-Devanāgarī
4. Kalā (8x8)-Brāhmī
5. Vijñāna (8+9) square-36x3 Vowels, 36x5 consonants, 1 om used in Veda.
6 Sahasra- Many thousand letters beyond Vyoma (Tibbet) in China.
Surya Siddhānta describes 9 types of time units parallel to 9 stages of creation from abstract source. Formative stages are mixed called Varāha (boar or cloud). That is meaning of 9th cloud. All 9 units are defined differently. They can be converted to each other, but it has experimental errors.
सूर्य सिद्धान्त (१४/१)-ब्राह्मं दिव्यं तथा पित्र्यं प्राजापत्यं च गौरवम्।
सौरञ्च सावनं चान्द्रमार्क्षं मानानि वै नव॥ Nine Indian Time-units-
(1) Brahma-Time period of creation from formless (avyakta) to forms is called a day of Brahma or Kalpa. In same period of time, creation dissolves into avyakta (Gītā 8/17,18). Day of Brahma has been defined as of 1000 yugas in Gītā, purāṇas, Sūrya-siddhānta etc. Each yuga is of 12,000 divya-years, 1 divya-year = 360 solar years. Thus, 1 day of Brahmā = 432 crore years.
(2) Prājāptya-Prajāpati started yajña (Gītā 3/10), so prājāpatya period is period of galaxy from where creation started. Rotation period of galaxy is called Manvantara of about 31.68 crore years. Present stage is 7th manvantara. This has been called 7th day in Bible. After 4, 5th days sun, moon, earth were created. So, day cannot mean here rotation of earth or even of sun. This is rotation of first creation galaxy. Modern estimate of period of sun revolution around center of galaxy is 20-25 crore years.
(3) Divya year is of 360 solar years, arrived in 3 ways. This is approximate period of revolution of imaginary planet at 60 AU (or average rotation of about 60,000 Balakhilyas at same distance), called Aloka (dark) boundary of 100 crore yojana diameter, This has been called parivarta yuga in Vāyu, Matsya purāṇas, which is cycle of historic changes. Third view is that north-south motion of sun is like day-night cycle. This cycle of 1 year is 1day (divya).Taking round number 360 for days in a year, divya year is of 360 years.
(4) Guru scale-In period of 60 years Saturn and Jupiter complete integral revolutions-2 and 5. Alternatively, Angirā-effect (upward convection due to radiation pressure takes 60 years to complete (Aitareya Brāhmaṇa 18/3/17,Taittirīya Br, 2/2/3/5-6)
(5) Pitar māna- Synodic revolution of moon in 29.5 days is called 1day of pitars. Varāha is 15 ahargaṇa or 4,096 times earth size-that is parjanya. Intermediate level is pitar, 64 times earth size called pitar. Moon orbit is 61 times earth size. So pitars of human beings also reside on outer region of moon. Our bright half of month is night of pitars and dark half is their day.
(6) Sāvana māna-Sunrise to next sunrise is sāvana or civil (practical) day. 1 month = 30 days, 1 year = 12 months.
(7) Solar-Apparent revolution of sun around earth is yea (sidereal). 1/12th part is 1 month (1 rāśi = 30 deg. Movement).1 day is 1 deg. movement.
(8) Lunar-Synodic revolution of moon around earth is a lunar month.5 angas of pañchānga are defined from moon and sun—Tithi = (M-S)/12deg., 1tithi = 2 karaṇa, yoga = (M+S)/13.3.Nakshatra is average daily motion of moon. Vara (day) is cyclic naming of days.
(9) Nakshtra (sidereal)-Axial rotation of earth with respect to fixed stars is sidereal day of 23 hours 56 minutes. Month, year have 30 and 360 days.
Micro units of time-Śatapatha Brāhmaṇa (12/3/2/1,5) divides mean day length of 12 hours successively by 15 parts into units named as muhūrtta (48 minutes), kṣipra, etarhi, idānī, prāṇa, aktana (or, ana), nimeṣa, lomagartta, svedāyana. It is stated that stars (nakṣatra) in galaxy (Brahmāṇḍa) are like its loma-gartta (roots of skin hairs). Number of lomagartta in a year (Samvatsara) is equal to the number of stars in a galaxy, so this unit of time is called lomagartta which is equal to muhūrtta x 15 (-7) = about 80.000 parts of a second. Similarly its 15th part is svedāyana equal to about 11,20,000 parts of a second. In this time light travels about 270 meters. Rain drops (sveda) move (ayana) about same distance without breaking or joining, so this time unit is called svedāyana. Estimate of number of stars in galaxy was done after 1985 which is correctly estimated in Śatapatha-Brāhmaṇa to be 10 (11). Logic of division by 15 is given that ratio of earth orbit to earth size is same as ratio of Tapah-loka (visible universe) and galaxy, both equal to 2 (15).
Seven Yugas-By joining two cycles of time, a yuga is formed. Munīśvara in his astronomy text Siddhānta Sārvabhauma has stated 5 yugas.
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