When Panini Rules Applied Mathematically...

[RamanaMurthy Bathala]

DearSir,

Rule 1: (Savarna Deerga Sandhi) If any simple vowel (short or long) is followed by a similar simple vowel (short or long), the two vowels blend into one long similar vowel (Pāṇ. VI.I, 101);

अ + अ = आ     (1.1)

अ + आ = आ     (1.2)

आ + अ = आ     (1.3)

आ + आ = आ    (1.4)

Rule 2: (Guna Sandhi) If अ a or आ ā, followed by the dissimilar vowels इ i, उ u, ऋ ṛ (short or long), blends with इ i or ई ī into the गुण Guṇa ए e; with उ u or ऊ ū into the गुण Guṇa ओ o^* ; with ऋ ṛ or ॠ r̥̄ into the गुण Guṇa अर् ar (Pāṇ. VI.I, 87);

अ + इ = ए     (2.1)

आ + इ = ए     (2.2)

अ + उ = ओ    (2.3)

आ + उ = ओ    (2.4)

 

Rule 3:  (Vriddhi Sandhi) अ a or आ ā, followed by the diphthongs ए e, ओ o, ऐ ai, or औ au, blends with ए e into the वृद्धि Vṛddhi ऐ ai; with ऐ ai also into ऐ ai; with ओ o into the वृद्धि Vriddhi औ au; with औ au also into औ au  (Pāṇ.VI.1,88); e.g.

अ + ए = ऐ        (3.1)

आ + ए = ऐ        (3.2)

अ + ओ = औ       (3.3)

आ + ओ = औ       (3.4)

 

Let us apply the above rules in reverse direction.

ऐ = अ + ए           Vriddhi resolved  by (3.1)

  = अ + (अ + इ)     Guna resolved by (2.1)

  = (अ + अ) + इ     

  = (आ) + इ         by (1.1)

  = ए                by (2.2)

So ऐ ai = ए e

Let us apply similarly to औ

औ = अ + ओ             Vriddhi resolved  by (3.3)

   = अ + (अ + उ)        Guna resolved  by (2.3)

   = (अ + अ) + उ   

   = (आ) + उ           by (1.1)

   = ओ                  by (2.4)

So औ  au = ओ o

 

ऐ ai = ए e and औ  au = ओ o

The above mathematical equations giving to Vriddhi = Guna.

I think somewhere mistake is done.

Regards

Ramana murthy

[Sivakumari Katuri]

एवं यदि चिन्त्यते तर्हि
ए+इ - अयि
(अ+इ)+इ
अ+(इ+इ)
अ+ई =ए
अयि = ए इति भवेत् ननु!
> Regards
>
> Ramana murthy
>
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[Hnbhat B.R.]

I think he doesn't know Sanskrit, but only English and mathematics! 

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[Sivakumari Katuri]

If that is the case
>> ए+इ = अयि
>> (अ+इ)+इ
>> अ+(इ+इ)
>> अ+ई =ए
>> It should be अयि = ए

>> > Regards
>> >
>> > Ramana murthy
>> >
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[Amba Kulkarni]

Dear Ramanamurthy garu,

You are assuming that associativity hold good.

a+(b+c) = (a+b) + c

This is called law of associativity.

However, in the case of Sandhi, this rule does not hold.

You will notice this especially in the case of verb formation with upasargas.

That is the reason, we need to appeal to 'pUrv-anitya-antaranga-apavaadanaam uttarottara baliiyasi'.

Best regards,

Amba Kulakrni

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[RamanaMurthy Bathala]

Respected Amba Kulkarni ji,

 

Thanks for identifying the mistake done by me.

 

In fact, you have brought back my high school maths to memory.

In the given case, associative law does not hold good.

 

Even the commutative law also does not hold good in case of Sandhis.

As per commutative law: :

(a+b) = (b+a)

अ + इ is not same as  इ + अ

अ + इ = ए

इ+ अ = य

So commutative law also does not hold good.

 

The mistake I have done is applying algebra learnt at high school days. Should have forgotten once left the school.

 

Regards

Ramana murthy

[Amba Kulkarni]

Namaste Ramanmurthy garu,

Well, but the distributivity holds good as in the case of 'anuv.rtti' in Panini.

You may refer to section on Anuv.rtti in my article on Brevity in Panini's Ashtadhyayii at

http://sanskrit.uohyd.ac.in/faculty/amba/PUBLICATIONS/papers/panini_brevity_interwoven_world.pdf

best regards,

Amba

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[G S S Murthy]

Ambaji,

Your article is beautiful. I bow to you,

Thanks and regards,

Murthy

My web site : http://murthygss.tripod.com/index.htm
and also my Sanskrit blog :

http://simplesanskrit.blogspot.com/

http://gssmurthy.blogspot.com

[Taff Rivers]

RamanaMurthy Bathala,

==>:

The above mathematical equations giving to Vriddhi = Guna.

I think somewhere mistake is done.

==>

  Are you are missing something?

1. Those rules only apply to the process of composing Sanskrit.

2. And only to combinations of vowel letters between words.

3. As to the the reverse process of decomposing such compositions.

      There can arise the major problem due to ambiguity.

       For example, when the blended vowel is the long a आ,

       what was the original pair of a's?

अ + अ

अ + आ

आ + अ

आ + आ

In such cases, the matter can only be resolved by the composer him or herself.

If that is not done, endless are the disputes... 

The faculty needed one of mental deduction, not one of logic, mathematical or otherwise.

You may wish to locate such a pair of words, yourself to so decompose. 

Regards,

Taff Rivers

 

  Wearing his analytical hat.

[krishna kaushik]

Dear Ramanamurthy garu,

If you must consider in light of "addition", then you ought to take into account the "vector addition".

Using 'vector addition',

     a + b NOT= b + a

In sandhi, not only the gross sound (uccaraNa) is considered but other factors as implied in the setting of Maheshvara suutra sequencing.

regards

Krishna

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