Wednesday, April 04, 2018

Sources of error in inferring time stamps from celestial coordinates

As indicated in the earlier post - there are errors in every measurement and when absolute accuracy is inaccessible - one has to use measurement precision as a substitute reliability metric.

There is a lot of people making claims about the "age of the Vedas" from random bits and pieces of information regarding positions of certain constellations ("nakshatras") in the celestial sphere.

There is a major problem with reading anything written in the Vedas. Firstly the Vedas are in an extinct language. Secondly the "Vedic information" we come across today is the by product of a complex compression ("Veda Sutra","Veda Sanhita"), translation/transliteration ("Upanishad", "Commentary on the Upanishad")  and transmission (oral/written) and re-expansion process ("Commentary on the Commentary on the Upanishad of the ....") .

At each step in that packaging process, errors will occur. This is a consequence of information entropy. It is next to impossible to estimate the error bounds on the "measurement" (or reading/sampling of this ancient and encoded information) .

This is the first source of error in the inference of time stamps from celestial coordinates. When comparing records of celestial coordinates - one has to decrypt ancient documents - a "measurement" which has no known error bounds on it.

After the record has been decrypted we can tabulate the position of a celestial object versus time. The table will look something like this (I have put in the numbers for Pleiades)

Time stamp(yrs)
Right Ascension
Declination (degrees)
03h 47m 24s
+24° 07′ 00″

This kind of table charts something called the "proper motion" of a celestial object. This appearance is somewhat deceptive as column on the right is actually a measure of the time the earth takes to go around the Sun. This is not a constant quantity - so the "time-stamp" itself has an error bar on it. The Right Ascension and Declination numbers are measured relative to the position of the Sun on the March Equinox. Over long enough timescales these equinoxes move relative to ground positions and the ground position of the observatory will change due to geophysical shifts - one can know these errors and determine bounds but only IF the system of error handling doesn't change over the period of observations

Any graph made with the above table (for example Time Stamp v/s RA & Declination) will have error bars along the X and Y axis. Using this knowledge, if we have enough data, we can fit star positions up to the earliest known observation*. The fit will have errors propagated from the basic measurements and you will be able to use that construct detailed images of what the sky would have looked like**. 

These pictures however will be approximations and the fits will only be reliable over the time period of observation. For predictions outside the range of known reliable observations, we will have to put in a confidence interval around the estimate of the time stamp. Typically the size of the error bars in the data will grow as we go further back in time, and so the estimate of the back-propagated time stamp will also have an extremely large confidence interval associated with it. 

A large confidence interval makes the prediction worthless. 

This is basically what happens when you say "but Rahu was in the Rohini Nakshatram so Vedas must atleasts 10,000 years old". There is no map (i.e. proper motion trajectory) of either Rahu or the Rohini constellation with known error bars, so fitting this data is tricky at best - and backpropagating that over >1kya produces absurdly large confidence intervals. 

It may be possible to parse the Vedic documents for a detailed record of various nakshatras and coincidence events (corrected for nomenclature shifts, observation point shifts and known sources observer error) and see how they line up with existing predictions (w sensible confidence intervals)  from the Hipparchus data, but that is a non-trivial exercise that will take up decades***. 

* The thing to note here is that we have very few reliable recorded observations of specific objects over long timescales. The only one currently estimated to be reliable is the ancient Greek astronomer Hipparchus which is estimated to be about 2.2kya.

** While you may not have enough data points for a single object, you may have enough total objects tracked and a PCA type approach will yield fit parameters with acceptable error-bars. 

*** Why the Hindus-uber-allez types don't want to fund such research is obvious. They are too afraid that the conclusion of such a study will run contrary to their narrative of about the Vedas being way older. 


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