## Tuesday, April 1, 2014

### astro picture for the day/ Throught for the day - 3102 B.C!

Image credit ESO/MUSE consortium/R. Bacon

This astronomy picture of the Orion nebula is from the ESO's new 'Muse' 3d spectrograph.  They're pretty excited about it.  I must say it's pretty close and maybe better than the Hubble Space Telescope image.  There may be details that my eye anyways, can't see.

- Thought for the day,

3102 B.C.

I don't want to get into too much large numbers and technicalities, but the Indians divided up time into cycles of various thousands and millions of years. The fundamental return of all planets is called Mahayuga which is 4,320,000 years long. It is divided into 4 quarteryugas of equal duration, and the last quarteryuga is Kaliyuga which starts according to the Indians around Friday, Febuary 18, 3102 B.C!

There was a sunrise and midnight system, they tried to calculate the number of revolutions. Aryabhata, around 510 A.D. The mean(average) motions motions of the sunrise and midnight calculations did not agree. Brahmagupta tried to make corrections of these. He did so by making the general solution to linear Diophantine equations.

Kind of like there's a quadratic equation that allows you to solve all second degree equations just by plugging in, there's were efforts to solve number theory, and make a closed form solution. The linear Diophantine general form equation was arrived at first, as far as I can tell, by Brahmagupta. He used Euclid's algorithm. There's actually two forms of it. One is a subtraction form(real easy, just subtract the smaller of two numbers of a number couple . . . repeatedly till you can't calculate anymore), and a division version; the division form is expressed as a=bx+r, r is the remainder. After the first division of a by b, you divide b by r. This is a slight change from regular division. You can repeat this and solve say G.C.D problems. Most people learn how to calculate G.C.D. by prime factor trees today. That's a later more sophisticated way. Euclid's algorithms turns out to still be interesting and valuable for number theory purposes that most people never see, like the linear Diophantine equation. There's a few more things to arrive at the linear Diophantine equation though. One performs the Euclidean algorithm till you get to 1. Then you rearrage one of the Euclidean algorithms to get 1 on one side. Then you rearrange another to get a remainder term that is analogous to the previous algorithm calculation, and then substitute. Do some simplifiying, and one gets the linear Diophantine equation. I'm just describing it.

Brahmagupta didn't correct Aryabhata empiracly. He did so assuming the date of 3102 B.C.

But, here's the kicker, a Kaliyuga is one tenth a Mahayuga, or 432,000 which equals 2x60^3. 60 is a common number of Babylonian mathematics. This number occurs in some Berossos, a Babylonian astrologer who moved to Greece to found a school of astrology around 300 B.C.

Berossos tells of a conflagration will take place at conjuctions in cancer, and a deluge when they come together in Capricorn. In Persian sources, a deluge is said to take place whenever the planets come together in the space between Pisces and Aries; the last time this happened was on Febuary, 3102 B.C.!(at least according to astrology, not scientific fact; this is a date long enough ago, that they could just say there was a conjunction back then).

We don't know whether Berossos got his 3102 from the Indians or the other way around, but in some quotes mentioned by Van Der Waerden in his "Geometry and Algebra of Ancient Civilizations", he suggests the end of the world predicted by astrological means was a common idea. He mentions one quote from the "Laws of Manu."

----------------- more astronomy for the day

Spitzer infrared space telescope 360 degree panorama of our entire Milky Way galaxy!