Mathematics in the Mythology

You know 60 seconds make 1 minute, 60 minutes make 1 hour and 24 hours make 1 day. Seconds, mintues and hours are modern day units of time. What were the units of time before these terms were introduced? Don’t get any ideas. I am not going to investigate what were the terms used but rather going to focus on what is said in the Hindu Mythology.  We do not have a concept of milliseconds or nano seconds here. The minimum named unit is 1 Kashta which is equivalent to 15 eye-winks.(Again, am taking Vishnu purana as a base for these numbers. Bhagavatha describes more minute units like Anus and Paramanus). Now lets start looking at the numbers and the units.

15 twinklings of an eye    –  1 Kashta
30 Kashta                          –  1 Kala
30 Kalas                            –  1 Muhurta
30 Muhurtas                    –  1 day/night for mortals
30 Days                            –  1 Month
6 Months                         –  1 Ayana
2 Ayanas                          – 1 Year

Now there are two Ayanas – Southern ayana (Dakshinayanam) and Northern ayana (Uttarayanam). Southern ayana is the night and Norther ayana is the day for the gods. So, for Gods 1 day equals 1 human year.

360 divine days              – 1 divine year (360 human years)
12000 divine years         – 4 Yugas (12000 x 360 = 43,20,000 human years )

Now how are these 12000 divine years spread over 4 Yugas?

Krita Yuga          – 4000 divine years (4000 x 360  = 14,40,000 human years)
Treta Yuga         – 3000 divine years (3000 x 360  = 10,80,000 human years)
Dwapara Yuga    – 2000 divine years ( 2000 x 360 = 7,20,000 human years)
Kali Yuga            – 1000 divine years (1000 x 360  = 3,60,000 human years)

That adds up to 10,000 divine years =  36,00,000 human years —> (1)

The period which precedes a Yuga is called Sandhya and the period which follows a Yuga is called Sandhyansa. They are of as many hundred years as there are thousands in the Yuga.  Ideally, the order of these yugas will be like below:

Sandhya of Krita Yuga -> Krita Yuga -> Sandhyansa of Krita Yuga -> Sandhya of Treta Yuga -> Treta Yuga -> Sandhyansa of Treta Yuga -> Sandhya of Dwapara Yuga -> Dwapara Yuga -> Sandyansa of Dwapara Yuga -> Sandhya of Kali yuga -> Kali Yuga -> Sandhyansa of Kali yuga.

Now lets calculate Sandya and Sandhyansa of each Yuga.

Krita Yuga     –  Sandhya + Sandhyansa – 400+400 = 800 divine years ( 800 x 360 = 2,88,000 human years )
Treta Yuga    –  Sandhya + Sandhyansa – 300+300 = 600 divine years (600 x 360  =  2,16,000 human years)
Dwapara Yuga  – Sandhya + Sandhyansa – 200+200 = 400 divine years (400 x 360 = 1,44,000 human years)
Kali Yuga          – Sandhya + Sandhyansa – 100+100 = 200 divine years (200 x 360  = 72,000 human years)

Sandhyas + Sandhyansas for 4 Yugas = 2000 divine years (7,20,000 human years) –> (2)

From (1) & (2), the total of 4 Yugas including the Sandhyas and Sandhyansas = 12,000 divine years ( 43,20,000 human years)

Wait!! Thats not over.

Aggregate of 4 Yugas     –  1 Mahayuga (Great Age)
1000 Great Ages        –  1 day of Brahma  or 1 Brahma (1000 * 12000 divine years =  432,00,00,000 human years)

That’s it ?? No.

1 Brahma is split into 14 time periods named Manwantaras.  1 Manwantara is a life time of divinities like Indra, Manu etc.

1 Manwantara =  71 Mahayuga  + some additional years = 71 x 12000 = 852,000 divine years (852000 x 360  =  30,67,20,000 human years + additional years)

14 Manwantaras = 1 Brahma (Day of Brahma)

At the end of 1 Brahma the dissolution of the universe occurs. Then there is the night of Brahma which is equal in duration as a day of Brahma. At the close of the night of the Brahma, the universe is created again.

1 day of Brahma + 1 night of Brahma = 1 year of Brahma ( I am not sure about this one 😦  )
100 Brahma years = 1 Param which is Brahma’s life time.

Phew! Thats all is mentioned in the Vishnu Purana about Time. This comes in Book 1, chapter 3 of the tranlation work done by  Horace Hayman Wilson, as available in SacredTexts website.

Comments/Corrections/Sugesstions are welcome.

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RAIN !!!

When, do you think, the knowledge about the formation of rain was expiscated? 19th Century? Or may be 18th Century?

When I was browsing through Vishnu Puranam in Sacred Texts, I found the following piece of information about Rain as Narrated by Parashara to his disciple Maitreya. Vishnu Purana is often considered the important purana of the 18 puranas. The following excerpt is from the translation work done by HH Wilson on Vishnu Purana. This comes in chapter IX of Book 2.

” In what manner the world depends upon the sun, be attentive, and you shall hear.

During eight months of the year the sun attracts the waters, which are the essence of all fluids, and then pours them upon earths (during the other four months) as rain; from rain grows corn; and by corn the whole world subsists. The sun with his scorching rays absorbs the moisture of the earth, and with them nourishes the moon. The moon communicates, through tubes of air, its dews to the clouds, which, being composed of smoke, fire, and wind (or vapour), can retain the waters with which they are charged: they are therefore called Abhras, because their contents are not dispersed. When however they are broken to pieces by the wind, then watery stores descend, bland, and freed front every impurity by the sweetening process of time. The sun, Maitreya, exhales watery fluids from four sources, seas, rivers, the earth, and living creatures. The water that the sun has drawn up from the Gangá of the skies he quickly pours down with his rays, and without a cloud; and men who are touched by this pure rain are cleansed from the soil of sin, and never see hell: this is termed celestial ablution. That rain which falls whilst the sun is shining, and without a cloud in the sky, is the water of the heavenly Ganges, shed by the solar rays.

The water which the clouds shed upon earth is in truth the ambrosia of living beings, for it gives fertility to the plants which are the support of their existence. By this all vegetables grow and are matured, and become the means of maintaining life. With them, again, those men who take the law for their light perform daily sacrifices, and through them give nourishment to the gods. And thus sacrifices, the Vedas, the font’ castes, with the Brahmans at their head, all the residences of the gods, all the tribes of animals, the whole world, all are supported by the rains by which food is produced. But the rain is evolved by the sun; the sun is sustained by Dhruva; and Dhruva is supported by the celestial porpoise-shaped sphere, which is one with Náráyan?a. Náráyan?a, the primeval existent, and eternally enduring, seated in the heart of the stellar sphere, is the supporter of all beings”

Vishnu Purana is considered to be composed in First or Second Century AD.  It has more details like the distance of each planets from each other, diameter of the Sun, number of years in each Yuga etc. More information about RAIN are explained in Matsya Purana, Linga Purana and Vayu Purana.