The zero(s) of Panini and the mathematical zero

EDIT September 2019:

Due to my bad English I wrote "rot" when the correct term should be "root" Now that's corrected.

(Note, there are no diacritical signs for transcriptions of Sanskrit words in this journal)

Panini (long a both i short) lived in the northwestern India about 500 BC and composed the oldest preserved grammar in the history. More about his grammar for the classical language in India, Sanskrit, can be read of in,

Panini
Wikipedia on Panini
Modern computer owes its origin to Panini
Panini's Grammar and Computer Science  


This journal will be restricted to deal with some similarities between the grammatical zero(s) of Panini and the mathematical zero.

A word (pada) in Sanskrit according to Panini is something that either ends on a finite verb ending (producing a finite verb) or a case ending (producing mainly nouns and adjectives). A case ending is always added to a nominal steam (pratipadika). A nominal steam is in most cases constructed by adding a primary suffix to a verbal root (dhatu) or by adding a secondary suffix to an already constructed nominal steam. So is the word deshah 'country' constructed by adding the nominative singular ending -s, which becomes -h last in a world according to the rules of so called sandhi (euphonically rules), to the nominal steam desha- (the lexical form of the word). desha- is then constructed from the verbal root dish- ‘to show’ (i in a verbal root often become e when a primary suffix is added). This can be shown by the scheme:

complete word_____________________________
nominal steam _____________
root_____
DESH ----------------  A ------------------- S
rot ----------------   primary suffix -------- case ending

However from the same root dish- the complete world dik ‘direction’ is constructed (sh becomes k last in a world according to the rules of sandhi). Here there are neither any primary suffix nor any case ending added, or? So how does Panini and his Indian grammatical fellows explain this? In order to see how this world is constructed according to Panini, let's look at the scheme below:

complete word_____________________________
nominal steam _____________
rot_____
DISH ---------------- VI ------------------- S
root ----------------   primary suffix -------- case ending

Then the primary suffix -vi- and the nominative ending -s are replaced with ”absence”. ”Absence” is a kind of grammatical ”zero” (in fact Panini has 4 grammatical zeros to choice among when he wants to make elision of a word element). The primary suffix -vi- (Panini calls it technically for -kvip-) is always elided by him. When he replace it by ”absence” there is a rule saying, that a substitute, wherever it is, has the same significance as the original. This is also the case if the substitute is ”absence”. In the next step also the nominative singular ending -s is replaced by ”absence” according to a rule saying that there can't be more than one consonant at the end of a word in Sanskrit. Thus we can reconstruct the previous scheme into:

complete word_____________________________
nominal steam _____________
root_____
DIK -----------------  0 ------------------- 0
rot ----------------   primary suffix -------- case ending

The word dik 'direction' can in this way be grammatical regarded as dik-0-0 where the first zero lifts the verbal root into a nominal stem, and the second zero lifts the nominal steam to a complete world in the nominative singular. Now compare how in the number 300, the first zero lifts the number 3 to denote tenth and the second zero lifts the number 3 to denote hundreds!

Now someone has suggested that the mathematical zero may be inspired by one of the grammatical zeros of Panini. If this is true would probably never be cleared out. But the interesting thing is that both the grammatical zero (or zeros) and the mathematical zero have similar functions, namely to be significant entities! The mathematical zero and the decimal system were invented in India and was carried to Europe by the Arabs. The Swedish word for number ”siffra” is direct borrowed from the Arabic language, and is in turn a translation from Sanskrit ”shunya” meaning 'empty'. The ancient Indians were not afraid regarding emptiness to be a positive entity in a lot of areas. Both the grammatical zeros and the mathematical zero are examples of that. That’s also the message of this tedious journal.

UPDATE October 2016:

Check out my journal Hyperlinks in Old Indian Sanskrit Grammar