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.