From my scrapbook consisting of bits & pieces of information, notes that I have been noting down on bharatiya scientific heritage. I am assuming the role of a dumb aggregator here, all the details that exist in this article are from various references.
The most efficient way to secure ancient wisdom was to hide it in plan sight, we are now discovering leftovers of this in polymorphic forms. For that same reason, even after many hundred years of destructive invasion and systematic cultural drain, these knowledge packets live in various parts of the world.
The current generation is at a point where they don’t know what they don’t know.
The fact that ancient wisdom is not available in text that can be indexed, searched or easily identified is causing an alternate universe; one that is gradually shrinking. I hated the fact that 90% of what I learnt in my 20+ years is just throwaway information, wished if we retained the ancient way of schooling.
Ancient Indian Mathematics is an amazing subject for research, it’s not easy to decipher the work easily as information is more horizontally spread. An example of this is the way numbers were expressed, mostly as a combination of words, in fact it was more of a metered way of understanding the range, value and multipliers.
To put a western context to this, let’s take a crude example below : The eight handed legionary Arnold used a hundredweight mallet in mid daylight hit a horse head on his pearly birthday.
this could be a verse written on a book about strongman game.
The above sentence could be backed by various metered system that needs to be understood first, for example hundredweight is actually 112lb ,horse head is 7FT , pearl is 30, 8 hands is the length of the man (9inch X8) ;the output of this force lets say is 100 units (Newton). All the more a legionary is from the roman army which depicts the strength of a fully grown man.
Another similar example is the number 2020 could be written as [void-deuce-twice] or [nix twain duple]
Hence the range of knowledge possibly is sprinkled over various texts, manuscripts and books which includes the edits & supplemental work to vedas etc. These work primarily in Sanskrit has mentions of words which are name, noun or adjective could have a numerical angle to it. So a simple verse might convey one thing, on the other hand it would be a mathematical formula beautifully hidden inside it.
Based on this logic, there were two ways of expressing numbers:
1) Bhutasamkhya – using word numerals, mostly with obvious examples from nature example moon is only 1 , eyes are two etc. There are no specific mapping to what is what, so it needs additional references to understand this right. Sometimes its just a clever word-play.
Using this model one can write the year 2020 as akasha-nayana-nabhas-kara where akasha is sky which is considered as 0, nayana is 2 , nabhas(sky) is 0, and kara is 2. This way of expression starts with units places or least significant numbers which allows easy representation of large numbers.
There are many cryptic works using this numbering system with words that are polymorphic which bring a poetry like feel to many phrases, examples of such notation are swaras=7,eye=2, ved=5, gunas=3, bhuta=4, Akash=0
2) Katapayadi – This is an alphabetical notation where digits are expressed by consonants of Sanskrit alphabet. Ka,ta,pa,ya etc, the nine integers are represented by consonant groups as shown in the similar table (as shown in Wikipedia).
The adaptation of this system was primarily in Kerala and it spread to other parts of India. This system was also known as Paralpperu (sea-shell) as this was used in the astromical realm . Sea shells were placed in appropriate places as reference and then relevant mnemonics were chanted to explain numerical computations. This is also is sometimes referred as akshara-sankhya (alphabet numbers)
A very apt example of the Katapayadi number system is in the devotional poem Naraneeyam by Melpathur where it ends with the phrase AyurArogyaSaukhyam which has two meanings to it, one is that the poet is wishing the reader longevity(ayur), health(arogya) and happiness(saukhya) and on the other hand its a timeline for the completion of work.
Applying Katapayadi to this is (aa=0,yu=1,ra=2,ro=2,gya=1,sow=7,khya=1 which 1712210 days since start of the current Yuga) Feb 18, 3102BCE.
Mathematical References of Ka-Ta-Pa-Ya number system
Pi is the ratio of a circle’s circumference to its diameter, this finds mention in 15th century work called Karanapaddhati by Puthumana Somayaji who is an astronomer mathematician.
The verse goes as this
അനൂനനൂന്നാനനനുന്നനിത്യൈ-
സ്സമാഹതാശ്ചക്രകലാവിഭക്താഃ
ചണ്ഡാംശുചന്ദ്രാധമകുംഭിപാലൈര്-
വ്യാസസ്തദര്ദ്ധം ത്രിഭമൗര്വിക സ്യാത്
anūnanūnnānananunnanityai
ssmāhatāścakra kalāvibhaktoḥ
caṇḍāṃśucandrādhamakuṃbhipālair
vyāsastadarddhaṃ tribhamaurvika syāt
anūnanūnnānananunnanityai (10,000,000,000) as caṇḍāṃśucandrādhamakuṃbhipālair (31415926536)
Which was represented by the Greek letter “π” since the mid-18th century, which tells us that people knew Pi before it became Pi.
This work was expanded by Sankara Varman, an astronomer mathematician from Kerala school of mathematics in 1819 who further expanded pi to upto 31 decimal places.
Usage in Music
The musicologist Venkatamakhin classified the ragas in 72 scales in 12 tone division of the octave, this was presented in the court of tanjore. Using the bhustasamkhya system , he named the 12 divisions as
indu (1), netra (2), agni (3), veda (4), bana (5), rtu (6), rsi (7), vasu (8), brahma(9), dik (10), rudra (11) and aditya (12).
For the individual names of the raga, he used the Katapayadi notation : the first two letters of each name indicate the serial number of raga, the rest of the letters have remaining description of raga.
So KanakAngi is 01, Rasikapriya is 72, the below Melakarta chart is also an encoding for someone to remember the notes in the ragas.
