4. Orientation to the analysis

ஆய்வுக்கொரு முன்னோடி

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"They are useless however learned who cannot impress the wise"
(Kural 728)

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    I have already dealt in great detail in Chapter 1. PREFACE as to why I undertook this research and in Chapter 2. REVIEW what these claims of mathematical miracles in scriptures are about. I had also set out reason for selecting 7 as the common denominator, in the previous Chapter 3. WHY number seven for the Kural?

    The objective of this chapter is to provide an orientation to the readers on the kind of investigations I carried out in Thirukkural to ‘uncover’ the ‘hidden’ mathematical ‘miracles’. I have explained what kind of reference materials were used for this investigation, how Tamil alphabet have been categorized based on the idea of Body and Soul, the philosophical basis of arriving at Conjugant letters from Vowels and Consonants, how Numerical Values (NV) have been assigned to 247 letters in Tamil alphabet, how couplets have to be exploded to find out the number of individual words used to compose it, the different thematic subjects chosen for the analysis and the different computations employed for 'discovering' or arriving at a mathematical pattern.

4.1. Materials for the study
4.2. Life and Body letters
4.3. Numerical values for Tamil letters
4.4. Exploded and unexploded couplets
4.5. Possibilities of mathematical patterns
4.6. Topics of interest for analysis: Leads from the Kural
4.7. You can verify my findings 

4.1. Materials for the study

    The Thirukkural used in this research is the standard version followed throughout the world which is based on Parimelazhagar's work, a commentary of the Kural written during the 13th century AD. Thirukkural being the most popular book in Tamil, there was no dearth of study materials for conducting this investigation. A combination of several study materials on Tirukkural like ‘Search Engines' (both online and offline), concordances, electronic texts, books and research papers formed the basis of this study.

4.1.1. Search engines and softwares
    In the beginning, I relied heavily on various search engines and Kural softwares. Unofortunately, most of these sites are no longer active. The major ones employed were:

1. Siddhart's search engine at Thirukkural Browser
2. Kural Amudhu CD from Chennai Kavigal which also has a search option
3. Maa. Angaih's Display TirukkuRaL which has an extensive search option in Tamil
4. Recently newer online search engines have come, but I have not used them for this study. These are of two types: The first one developed by IIT "Acharya's Tirukkural: Online Search" is worth mentioning. There is no need for any font here as the results displayed as scanned images. The second one employing Kural in Unicode format is also equally impressive. (Muthu.org and Tirukkural.net).

The CD on Kural Amudhu had two major disadvantages as far as the Search option was concerned. The couplets were not completely split into individual words and as a result, a search for the word "ezuththu" (எழுத்து) yielded no hits as it occurred as "எழுத்தெல்லாம்" and "எழுத்தென்ப" in the source text. The best of all search engines is perhaps Siddhart's Thirukkural Browser. This site containing the Kural in Roman transliteration had a distinct advantage over other search engines employing Tamil scripts. For instance, a search for the word "மாற்றல்", which occurs only once in Kural, will prove futile when searched in a text in Tamil script for the simple reason that the word may occur as "மாற்றலரிது". Same is the case with "அரிது". On the contrary, a search for "arithu" or "maaRRal" will give the desired result in a transliterated text even it is written "maaRRalarithu". However, even a transliterated soft copy is not foolproof as it cannot search for words like "ezuththu" from words like "ezuththellaam" or "ezuththenba" because these words are not usually split, for example, as "ezuththu" and "ellaam". This is where concordances come to play. 

4.1.2. Concordances
    Kural being a popular work, there are a few publications available on its concordance. More concordances are being produced, the latest one coming from the Institute of Asian Studies, Chennai. The following six concordances were consulted for this study:

1. G.U. Pope's Lexicon and Concordance of the Kural. [1]
2. Velayutham Pillai [2]
3. N.C. Kanthaiah Pillai's திருக்குறள் அகராதி. [3]
4. P. Markka Sagaya Chettiyar's திருக்குறள் சொற்பொருள் அகரவரிசை. [4]
5. N. Subrahmanian and R. Rajalakshmi. The Concordance of Tirukkural. [5]
6. Chellamuthu, K.C. and Baskaran, S. Computer analysis of Tirukkural. [6]

    No two concordances are similar for the simple reason that they differ in their extent of splitting the words. Some of them were organized based on the root words, while others split every word into meaningful words. Some did not take into account of `sound words' (அசைச்சொல்), while others did. As a result, a word like "உலகம்" (world) occurred as "உலகம், உலகத்தார், உலகில், உலகு" in one concordance, while the other listed four or five more variations (உலகத்தார்க்கு, உலகத்து, உலகத்துள், உலகத்தோடு, உலகத்தும்). Very often, a word that has already appeared as single word was repeated again, this time in conjunction with another. For these reasons, no two concordances agreed with the total number of words in the Kural. The other reason for this difference is that concordances were sometimes wrong. Sometimes words were missing from the list and some times couplet numbers were missing for a word.

1.      Few examples of words missing in concordances: The word anichcham (அனிச்சம்: Couplet 90), aayitai (ஆயிடை: Couplet 1179) was missing from the concordance in "Computer Analysis of Tirukkural" by Chellamuthu and Bhaskaran. The word aLavinaal (அளவினால்: Couplet 574) and karumaththaal (கருமத்தால்) were missing in Chettiyar's திருக்குறள் சொற்பொருள் அகரவரிசை. Words koormai "கூர்மை" (Couplet 997) and pullaavital (புல்லாவிடல்) were missing from திருக்குறள் அகராதி by Kanthaiah Pillai. There are also other types of mistakes. For instance in G.U. Pope's Lexicon and Concordance, couplets which does not contain the intended word were included by mistake. For instance, couplet 45 has been listed under the word theyvam "தெய்வம்" (Divinity) which is not true.

2. Examples of missing couplet numbers: (i) Couplet 998 was not listed for word "ஆதல்" in the Concordance of Tirukkural by Subramanian. Couplet 252 was not listed under "ஊண்".  Couplet 298 was missing from the word kaanappatum (காணப்படும்) in Chellamuthu’s Computer Analysis of Tirukkural. So also couplet 28 under "மொழி".  The word "அது" missed out couplets 764 and 765. These couplets had this word as "அதுவே". If not under "அது", the word should have been at least listed separately as "அதுவே" (as done by Chellamuthu and Baskaran in their work "Computer Analysis of Tirukkural").  

    For these reasons I developed my own text file consisting of completely split couplets typed in TSII and subsequently converted it into Unicode (read further below). The results of an analysis were always confirmed using the electronic texts and hard copies, even though all investigations began with the use of concordances and/or search engines.

4.1.3. Electronic texts of Thirukkural
    Thanks to Kalyana Sundaram, I was able to obtain the electronic text of Thirukkural. The text contained couplets that were partially split for easy reading (see section 4.4. of this chapter to know more on this). I scrutinized this source file for errors and then modified every couplet into two forms: One file containing unsplit couplets following the junction rule and the other file with couplets that have been completely split into individual meaningful words. These files formed the ultimate basis for verification of frequency of occurrence of a letter, word or phrase. The correctness of the split and unsplit couplets were verified with all the available concordances along with the hard copies of Thirukkural texts mentioned above.

4.1.4. Thirukkural Books
    I was basically looking forward to two different kinds of texts: One that contains couplets written following the junction rule (சந்தி விதி) and the other one containing couplets that have been split into individual meaningful words (see section 4.4 of this chapter). While the former helped me in identifying couplets with vowels in them (Vowels appear either in the beginning of the couplet or in the midst as "sound vowels": அளபெடை), the latter form was essential to know the number words employed to compose a couplet.

    Thirukkural books with couplets written as per the junction rule:
    a) Pope, G.U. 1887. The Sacred Kurral of Tiruvalluva Nayanar. Asian Educational Services.
    b) Poornalingam Pillai, M.S. 1999. Thirukkural: With translation in English. International Institute of Tamil Studies.
    Thirukkural books with couplets split into individual words:
    a) Dias, S.M. 2000. Tirukkural - Vol 1 & 2. Ramanandha Adigalar Foundation
    c) S.V. Subramanian, 2001. III Edition. திருக்குறள். கங்கை புத்தக நிலையம். Chennai.
    The couplets in these books, in both forms, were also not without mistakes. Apart from printing and topographical mistakes, there were also discrepancies while following the junction rule (eg. metrical feet in couplet 392 “விவ்விரண்டுங்” has been wrongly printed/written as “யிவ்விரண்டுங்”). In the other form, words were not sometimes split completely (சீர்தூக்கும் in 813 and கண்ணேபோல in 1285).

4.2. Life Letters and Body Letters (உயிர் & மெய் எழுத்துக்கள்) 

    Tamils apparently used the so called Tamil Brahmi (or Dhamili) script during the Cankam (Academy) period of 250 B.C. to 250 A.D. (Siromoney, et al, 1980). Click here to see how couplet 1323 would have looked in Brahmi script. It is the script which has undergone changes though the syntax of Tamil language has changed very little over the centuries (Varadarajan, 1988). Tamil alphabets have evolved towards the present form sometime during the 6th century AD (Siromoney, et al, 1980).

      In Tamil, the word uyir (உயிர்) stands for life, soul or breath and the word mey (மெய்) for body. The 12 Soul letters are the VOWELS (from a[அ] to au[ஔ]) and the 18 Body letters are the CONSONANTS (from k[க்] to n[ன்]).  There is also one unique letter ah (ஃ), which is called Ayutha ezuththu (ஆயுத எழுத்து) or Tool Letter. The rest of Tamil letters are CONJUGANTS of "Life" and "Body" letters and are thus appropriately called "Life/Body" Letters (உயிர்மெய் எழுத்துக்கள்). For instance s+a produces sa, m+i produces mi, L+u produces Lu and so on. The "Life Letters or Vowels" (அ, ஆ, இ, ஈ, உ etc.) are therefore the most important as they only give life to the body letters (க், ந், ம், வ் etc.).  The following table shows all these letters (Life Letters (VOWELS) in red, Body Letters (CONSONANTS) in blue, and Life/Body Letters (CONJUGANTS) in violet.

 Table: Life, Body and Life/Body letters (Vowels, Consonants and Conjugants)  

(a) அ

(aa) ஆ

(i) எ

(ee) ஏ

(u) உ

(oo) ஊ

(e) எ

(E) ஏ

(ai) ஐ

(o) ஒ

(O) ஓ

(au) ஔ

(ah) ஃ

(ka) க

கா

கி

கீ

கு

கூ

கெ

கே

கை

கொ

கோ

கௌ

க் (k)

(nga)  ங

ஙா

ஙி

ஙீ

ஙு

ஙூ

ஙெ

ஙே

ஙை

ஙொ

ஙோ

ஙௌ

ங் (ng)

(sa) ச

சா

சி

சீ

சு

சூ

செ

சே

சை

சொ

சோ

சௌ

ச் (s)

(nja) ஞ

ஞா

ஞி

ஞீ

ஞு

ஞூ

ஞெ

ஞே

ஞை

ஞொ

ஞோ

ஞௌ

ஞ் (nj)

(ta) ட

டா

டி

டீ

டு

டூ

டெ

டே

டை

டொ

டோ

டௌ

ட் (t)

(Na) ண

ணா

ணி

ணீ

ணு

ணூ

ணெ

ணே

ணை

ணொ

ணோ

ணௌ

ண் (N)

(tha)  த

தா

தி

தீ

து

தூ

தெ

தே

தை

தொ

தோ

தௌ

த் (th)

(Na) ந

நா

நி

நீ

நு

நூ

நெ

நே

நை

நொ

நோ

நௌ

ந் (N)

(pa) ப

பா

பி

பீ

பு

பூ

பெ

பே

பை

பொ

போ

பௌ

ப் (p)

(ma)  ம

மா

மி

மீ

மு

மூ

மெ

மே

மை

மொ

மோ

மௌ

ம் (m)

(ya)  ய

யா

யி

யீ

யு

யூ

யெ

யே

யை

யொ

யோ

யௌ

ய் (y)

(ra) ர

ரா

ரி

ரீ

ரு

ரூ

ரெ

ரே

ரை

ரொ

ரோ

ரௌ

ர் (r)

(la) ல

லா

லி

லீ

லு

லூ

லெ

லே

லை

லொ

லோ

லௌ

ல் (l)

(va) வ

வா

வி

வீ

வு

வூ

வெ

லே

லை

லொ

லோ

லௌ

ல் (v)

(za) ழ

ழா

ழி

ழீ

ழு

ழூ

ழெ

ழே

ழை

ழொ

ழோ

ழௌ

ழ் (z)

(La) ள

ளா

ளி

ளீ

ளு

ளூ

ளெ

ளே

ளை

ளொ

ளோ

ளௌ

ள் (L)

(Ra) ற

றா

றி

றீ

று

றூ

றெ

றே

றை

றொ

றோ

றௌ

ற் (R)

(na) ன

னா

னி

னீ

னு

னூ

னெ

னே

னை

னொ

னோ

னௌ

ன் (n)

      As we see from this alphabetical matrix, the first Tamil letter is a or அ (top left) and the last Tamil alphabet is n or ன் (bottom right). Remember, in Tamil and most other Indian languages, the `extras’ that appear as prefixes, suffixes and prefo-suffixes before consonants (e.g. for the letter ka - க: கெ, கா, கொ, கோ, கௌ) are not taken into account as `letters' while counting Tamil letters in a word. For instance, the number of letters in the word poyyaamai (பொய்யாமை) is 4 and not 8 (counted as பொ, ய், யா, மை: po=1,  y=2, yaa=3, mai=4).

4.3. Numerical Values for Tamil Letters
 
    The Numerical Values (NV) formed an important part of the analysis.  Jews, Arabs and Greeks used letters instead of numerals (now called Arabic numerals) in the past. Muslims and Christians apologists who described mathematical miracles from the Qur'an and Bible, have employed these Gematrical Values to assign values for different key Quranic and Biblical letters, phrases and words.

    There is no evidence in the history of Tamil literature to show that Tamils assigned numerical values to the 247 letters in their alphabet. They did use 9 different Tamil letters to designate the numbers from 1 to 9. 

Tamil letters used for different numbers
1	2	3	4	5	6	7	8	9	10
க	உ	ங	ச	ரு	சு	எ	அ	கூ	க0
ka	u	nga	sa	ru	su	e	a	koo	ka0

     Some of the letters in the above table, like those representing 3,4,6,9, are not `exactly' the same as those actually used to represent these numbers. Their forms have undergone slight variation since historical times. Since these letters only represent 9 letters of the total 12 Vowels and 216 Conjugants, they cannot be taken as the basis for deriving the NV of Tamil words. Therefore a separate system of assigning a place value was created to designate a numerical values for these letters.

    This simple system of numbering them was based on the philosophy of categorizing Tamil alphabet as Life and Body letters. The basis of dividing the Tamil alphabets into Life or Soul and Body letters could be easily understood from the dichotomization of Body and Soul in Vedic heritage. Vedanta declares that the Body is only a flesh or carrier, and it is the Soul (or Life) that gives life to the body. It is the Body that perishes and not the Soul which is eternal. 

As the tools of carpenter are his instruments,
so this subtle Body is an instrument of all activities of the Soul,
which is Knowledge Absolute.
(Vivekachoodamani, 100)

In fact Valluvar himself refers to this Body-Soul relationship in many places in his work. He asks in couplet 340......

Is there no permanent refuge for the Soul,
Which makes a temporary shelter in the Body?
(Translated by S. Maharajan)

    The fact that the 12 Vowels are called "Life" or "Soul" indicate that they alone energize a Tamil alphabet. The 18 dotted Consonants are also called "mute consonants" (க், ப், ச், ட், ன், ய், ர் etc) and they get energized only when they interact with Life letters to produce the Conjugants (Life-Body uyirmey letters). The uyirmey letters are also called "syllabic consonants" as consonants, being mere Bodies, have been ensheathed by the Soul (Naicker, 1985).  I have used this simple logic while assigning the numerical values for Tamil letters.

    Citing verse 18 in the Phonology of Tolkappiyam "மெய்யின் வழியது உயிர்தோன்றும் நிலையே", Naicker (1985) says in his work "The Tamil alphabet and its Mystic Aspect" that there is nothing to distinguish (letters) except by their envelop, the body which asserts itself over and above the soul. Thus when ப் (p) merges with இ (i), the resultant பி (pi) is only the body revealed though it is the Soul (in this case இ) which has energized it to lose its dot. 

    I have assigned a numerical values only to those letters which have a Life in them or Vowels in them. Of the 247 alphabets in Tamil, 228 (12 Vowels & 216 Conjugants) have 'life' in them. In other words, the 18 "mute consonants" being mere bodies do not have NV, but only when they interact with the Vowels to become Conjugants or Syllabic consonants (uyirmey letters) that they get NV.

                    Examples of Consonants metamorphing into Conjugants,
                    following the interaction with "Soul" letters (Vowels).
                                k+a gives birth to ka (க)
                                m+aa gives birth to maa (மா)
                                t+i gives birth to ti (டி)
                                v+U gives birth to vU (வூ)
                                l+o gives birth to lo (லொ)
                                k+O gives birth to kO (கோ)
    Thus.....

• The 12 Life Letters or Vowels have been assigned numbers from 1 to 12 based on their placement.
• All the 18 Body Letters or Consonants were not assigned assigned any NV.  [They, however, are counted as letters in a word. For instance, the letters "ப் & ல்" in the word "கப்பல்" have no NV, but are counted as letters. Thus the word kappal ("கப்பல்") is composed of 4 letters, but only க & ப contributes to its NV]
• The "Tool Letter" ah (ஃ) is also not a Life letter (Vowel) and is thus counted only as a letter
• The 216 `Life/Body' Letters or Conjugants were assigned values based on the place value of the Vowels (from a[அ]to au[ஔ]) they have in them. For instance, while ka has a value of 13, kaa is 14, ki is 15, kee is 16, ku is 17 and so on (see table below).

Matrix: Numerical values assigned to Tamil alphabets
	a	aa	i	ee	u	oo	e	E	ai	o	O	au	ah (·)
	1	2	3	4	5	6	7	8	9	10	11	12	0
ka	13	14	15	16	17	18	19	20	21	22	23	24	0 (k)
nga	14	15	16	17	18	19	20	21	22	23	24	25	0 (nk)
sa	15	16	17	18	19	20	21	22	23	24	25	26	0 (s)
nja	16	17	18	19	20	21	22	23	24	25	26	27	0 (nj)
ta	17	18	19	20	21	22	23	24	25	26	27	28	0 (t)
Na	18	19	20	21	22	23	24	25	26	27	28	29	0 (N)
tha	19	20	21	22	23	24	25	26	27	28	29	30	0 (th)
nha	20	21	22	23	24	25	26	27	28	29	30	31	0 (N)
pa	21	22	23	24	25	26	27	28	29	30	31	32	0 (p)
ma	22	23	24	25	26	27	28	29	30	31	32	33	0 (m)
ya	23	24	25	26	27	28	29	30	31	32	33	34	0 (y)
ra	24	25	26	27	28	29	30	31	32	33	34	35	0 (r)
la	25	26	27	28	29	30	31	32	33	34	35	36	0 (l)
va	26	27	28	29	30	31	32	33	34	35	36	37	0 (v)
za	27	28	29	30	31	32	33	34	35	36	37	38	0 (z)
La	28	29	30	31	32	33	34	35	36	37	38	39	0 (L)
Ra	29	30	31	32	33	34	35	36	37	38	39	40	0 (R)
na	30	31	32	33	34	35	36	37	38	39	40	41	0 (n)

    As we see in the above matrix, many Conjugants have the same NVs. For instance, 30 is the NV of 11 different letters: na, Raa, Li, zee, vu, loo, re, YE, mai, po, nhO and thau (ன, றா, ளி, ழீ, வு, லு, யே, மை, பொ, நோ,  தௌ).

    Using this matrix, we find that the NVs of the Tamil words for Vowel, Consonant and Conjugant (உயிர் எழுத்து, மெய் எழுத்து & உயிர்மெய் எழுத்து) are 91, 89 and 119 respectively. Note that only the NVs of Vowels and Conjugants are divisible by seven (91/7=13 and 119/7=17)!
 

Some examples of NVs of some Tamil words
Words in Tamil	Transliteration	Meaning	Numerical Values	Total NV
தமிழ் திரு எண் நான்கு மூன்று	tha, mi, z thi, ru e, N Naa, n, ku moo, n, Ru	Tamil  Sacred  Number, Think, Eight  Four  Three	19+24+0 21+28 7+0 21+0+17 27+0+33	43 49 7 38 60

4.4. Exploded and Unexploded couplets

    As briefly mentioned in the previous chapter “Why number seven for Kural?”, every couplet in the Kural consists of lines and 7 feet (சீர்=Seer): the first line has 4 feet and the second 3 feet.  All the 1,330 couplets been recognized by 7 feet. Though each foot may comprise 1 to even 3 words, there are occasions when two Seer would be composed one word. In other words, the morpheme will be divided at the expense of the meaning of one of them (usually the latter). This occurs often towards the end of the couplet, for the last two feet. Verse 602 is a good example:

மடியை மடியா ஒழுகல் குடியைக்
குடியாக வேண்டு பவர்
madiyai madiyaa ozugal kutiyaik
kutiyaaka vENdu pavar
Those who would enhance their birth
Should keep sloth at bay

    The word `vENdupavar' (வேண்டு பவர்) has been split into vENdu and pavar for metrical reasons. It is like splitting the English word `establishment' into `establish' and 'ment'. The word pavar alone has no meaning, and has to be, therefore, joined with vENdu when we analyze this couplet for the number of words used in composing it. When a couplet with 7 feet is split into all possible meaningful words, it may sometimes contain only 6 morphemes (like couplet 602). A couplet when split usually contains more than seven words (like couplet 392).
    The other most important point is the Sandhi or Junction Rule (சந்தி விதி) in Tamil. Sanskrit and Tamil are the only two languages known to possess elaborate rules of euphonic combinations (Mahalingam, 1997). The most important point is that the beginning and end letters of many words metamorph depending on the last and first letters of the preceding and following words respectively. It is often difficult to appreciate the constituent words unless we explode or split the couplet into all possible meaningful words (morphemes). While doing so, depending on the complexity of the seer or feet, certain letters may be lost from the phonetic text, some times new letters appear, and at times the letters themselves change for another.
(a) Examples for disappearance of Body Letters: k, s, p, th (க், ச், ப், த்) etc.

• Couplet 22: துணைக்கூறின் when split becomes துணை and கூறின்
• Couplet 74: நாடாச் சிறப்பு when split becomes நாடா and சிறப்பு
• Couplet 1100: வாய்ச்சொல் when split becomes வாய் and சொல்
• Couplet 411: செவிச்செல்வம் when split becomes செவி and செல்வம்
• Couplet 888: போலத்தேயும் when split becomes போல and தேயும்

(b) Examples for appearance of new Body Letters (usually m, ம்)

• Couplet 369: ஈண்டுமவா becomes ஈண்டும் அவா
• Couplet 407: புல மில்லான் becomes புலம் இல்லான்
• Couplet 1114: நிலநோக்கு becomes நிலம் நோக்கு
• Couplet 616: ஆக்கு முயற்று becomes ஆக்கும் முயற்று
• Couplet 1: அகர முதல becomes அகரம் முதல

(c) Examples for substitution of new Body letters for the existing ones

• Couplet 1019: குலஞ்சுடும் becomes குலம் சுடும்
• Couplet 702: ஐயப் படா becomes ஐயம் படா
• Couplet 17: நெடுங்கடலும் becomes நெடும் கடலும்
• Couplet 298: அகந்தூய்மை becomes அகம் தூய்மை
• Couplet 455: மனத்தூய்மை becomes மனம் தூய்மை

(d) Examples for appearance of Life Letters (LL) when combined words are split

• Couplet 1330: அதற்கின்பம் becomes அதற்கு and இன்பம்
• Couplet 1: எழுத்தென்ப becomes எழுத்து and இன்பம்
• Couplet 85: விருந்தோம்பல் becomes விருந்து and ஓம்பல்
• Couplet 589: ஒற்றொற்று becomes ஒற்று and ஒற்று
• Couplet 32: அறத்தினூங்கு becomes அறத்தின் and ஊங்கு

(e) Appearance of Life Letters (LL) when words, combined following the ya, va (ய, வ) rule, are split

• Couplet 1: முதற்றே யுலகு becomes முதற்றே உலகு
• Couplet 392: எண்ணென்ப வேனை becomes எண்ணென்ப ஏனை
• Couplet 444: தமரா வொழுகல் becomes தமரா ஒழுகல்
• Couplet 453: உணர்ச்சி யினத்தான் becomes உணர்ச்சி இனத்தான்
• Couplet 1142: அருமை யறியாத becomes அருமை அறியாத

    A Thirukkual book will usually contain couplets that have been split to varying degrees for easy understanding. At one extreme are the couplets with completely interwoven words following the "Junction Rule" (primarily for academicians) and at the other extreme are couplets partly split (for general readers). The Kural we see in most books and those displayed online belong to the latter type. The only way to know the number of words in a couplet is to explode it to individual morphemes as done below for couplet 392.

Table: Original, Partly split and Fully exploded couplet 392
Original unsplit couplet	எண்ணென்ப வேனை யெழுத்தென்ப விவ்விரண்டுங் கண்ணென்ப வாழு முயிர்க்கு	7 feet are  maintained
Words only  partially split	எண்ணென்ப ஏனை எழுத்தென்ப இவ்விரண்டும் கண்ணென்ப வாழும் உயிர்க்கு	Still the 7 feet  are maintained
Transliteration	yeNNenba Enai ezuththenba ivviraNdum  kaNNenba vaazum uyirkku
Couplet fully exploded	எண் என்ப ஏனை எழுத்து என்ப இ இரண்டும் கண் என்ப வாழும் உயிர்க்கு	Every single word  is shown full
Translation	What we call ‘Number’ and the other one called ‘Letter’, These two are eyes of a living being. (Tr: Kulandai Samy)	(Kural 392)

    Note the letters in pink, red and blue in the 3 words in italics. When "Junction Rule" is employed for metrical and phonetic reasons, E(ஏ) metamorph into vE(வே) , e(எ) becomes ye(யெ) and i(இ) becomes vi(வி). The metamorphosis into derivatives of ya and va depends on last letter of the preceding word. To illustrate this point let us look at the word ezuththenba in the above couplet and ezuththellam in couplet 1, the only other place in Kural where the word ezuththu occurs.

In Couplet 392: ஏனை எழுத்தென்ப becomes ஏனை யெழுத்தென்ப
In Couplet 1: முதல எழுத்தெல்லாம் becomes முதல வெழுத்தெல்லாம்

    Another feature we could notice is the change in the number of words between the unsplit and split couplet. The seven seer or metric feet resulted in 11 words when the couplet was exploded. Rarely do we see couplets retaining the same number of words without changing the ‘feet’ and ‘word’ positions (read further to know what ‘feet/word’ positions are), even after split into individual meaningful words. Couplet 434 is a good example:

Unsplit	Split
குற்றமே காக்கப் பொருளாகக் குற்றமே யற்றந் தரூஉம் பகை.	குற்றமே காக்க பொருளாக குற்றமே அற்றம் தரூஉம் பகை.
Guard against error as you would guard wealth, For error is a foe that kills (Kural 434)

4.5. Possibilities for mathematical patterns

            The Kural we know is a compact work, characterized by many inherent features like the seven metrical feet, three divisions based on Virtue-Wealth-and Love, repetitious words within a couplet, common words employed to begin and end couplets and an important message or phrase (e.g. Not-lying: பொய்யாமை and Reality: மெய்ப்பொருள்) being repeated even outside their respective chapters (i.e. Chapater 30: Truthfulness: வாய்மை  and Chapter 36: Realization மெய் உணர்தல். All these features were taken into consideration while designing the methodology for analysis.

4.5.1. Word frequencies and Numerical values
    Any key word or phrase, occurring seven times or in multiples of seven were considered a `miracle’. Sometimes, their couplet numbers were added and any total divisible by seven, was considered a 'miracle'.  Alternately, the NVs of such important words, phrases or couplets were also taken into consideration. The sum of NVs was then divided by seven.

4.5.2. Placement of Couplets and Chapters
    The Kural contains some important Couplets and Chapters that either are either spiritual in nature, emphasis Valluvar’s major teachings, or have something in common. Though Kural is a very organized work with Divisions and Sections, some chapters across these divisions can be brought under a common thread. Similarly couplets emphasizing a point (say Realization) are not only found within the designated chapter but also outside. The mathematical basis of placement of such couplets and chapters, if any, were also analyzed.

4. 5.3. The First and the Last words (முதற்சொல், கடைச்சொல்)
    The Kural being an organized work with 1330 couplets of two lines each, it is easy to identify the words employed at the beginning and end of all the couplets. Every couplet begins with a word which is often repeatedly used in the beginning of other couplets as well. It is a common practice among Tamil scholars to recognize individual couplets with these START and END words (முதற்சொல், கடைச்சொல்). For instance, 13 couplets begin with the word poruL (பொருள்) and 3 couplets end with the word poruL. Siddhart has a web site Thirukkural Browser which provides the option to search a word at the START, END and ANY place in the Kural. Some of the Kural search engines using Unicode text also have such a facility (at Muthu.org and Tirukkural.net).  I will be frequently referring to these sites in my results so that readers can verify my findings online.

4.5.4. Vowels: The Soul of Tamil letters
    While Rashad Khalifa used a set of 24 Quranic initials to claim a set of alphabetical miracles (see Chapter 2: A Review of miracles in other texts), I had 11 of the 12 Life Letters (LL or உயிர் எழுத்துக்கள்) as equivalents.  I looked at the number of couplets in Kural containing Vowels and the frequency of ‘first and end’ words beginning with Vowels. I also looked at the frequency of occurrence and the placement of these 'vowels' in the midst of unexploded couplets.

4.5.5. Feet placement and Word placement (சீரிடம், சொல்லிடம்)

    As mentioned above, every couplet is composed of 7 feet but may contain 6-10 words or more. Thus Feet placement mean the placement of a word in a couplet according to the metrics or feet (this may be from 1 to 7) and Word placement mean the placement of a word after exploding the verse (this may be from 1 to 11, or more). Let us take couplet 392 itself as an example:

Table: Feet & Word placements in Unsplit and Split verses
Unsplit verse	Split verse
எண்ணென்ப வேனை யெழுத்தென்ப விவ்விரண்டுங் கண்ணென்ப வாழு முயிர்க்கு yeNNenba vEnai yezuthenba vivviraNdum  kaNNenba vaazu muyirkku	எண் என்ப ஏனை எழுத்து என்ப இ இரண்டும் கண் என்ப வாழும் உயிர்க்கு yeN enba Enai ezuththu enba iv iraNdum kaN enba vaazum uyirkku
The word `iraNdu' (two) occurs in the 4th feet according to unsplit couplet The only LL (vowel) at the beginning of a feet is e (எ) in this verse. Feet position is used only for unsplit couplets	The word `iraNdu' is placed 7th in this exploded or split verse. Eight vowels (LL) become evident when exploded Word position is used only for split couplets

4.5.6. Possibilities of arriving at a total divisible by 7
    There are possibly 3 different ways of dividing a Figure or a Total to see if it is divisible by the key number (7 in the case of the Kural). The criterion followed here in this analysis is the same adopted by Khalifa & his Submitters and Panin & his friends.

    This is the most commonly employed method is the direct division of the total (see Procedure 1 below). More than 99% of the results presented in this paper are a result of this direct division. If I am referring to a set of 5 verses, their numbers are added up and the total is either (i) straight away divided by 7 and/or (ii) the individual digits of the total are added up to produce a divisible total (see Procedure 2).

Procedure 1	Procedure 2
63    69    52    40  140	212  300  104  114  209
364 (7x52)	939 (9+3+9 = 21)  ..... and 21 is 7x3

    Sometimes, a figure qualifies by both approaches. For instance, 266 is not only divisible by seven (7x38), but its digits 2, 6 and 6 add up to 14, which is also divisible by seven (7x2). 

4.6. Topics of interest for analysis: Leads from the Kural

    Thanks to the information already available in the works of Ivan Panin and Rashad Khalifa, I had little difficulty in selecting the various subject matters or topics to look for mathematical combinations in Kural. Tirukkural being a text which encompasses topics of varying subjects, it is a storehouse of words and phrases with immense possibilities to look for all sorts of combinations and hidden messages. Some of these possibilities are being explained in detail below: 1)

1) Throughout the Kural: Unlike some of the ancient Tamil texts that have survived only in parts, the Kural is available to us in full. But for the minor differences in some of the readings, the text is the same in any copy you buy in any part of the world. The Kural has been divided into three divisions, namely Virtue, Wealth and Love, each consisting of 38, 70 and 25 chapters respectively. As it has been claimed from some of the sacred texts like the Qur'an, I looked for the mathematical patterns that run through the entire text. The results have been presented in Chapter 6: "General findings: பொதுவான கண்டுபிடிப்புகள்".
2) Numbers and Letters: While Khalifa used a set of 24 Quranic initials to claim a set of alphabetical miracles, I had 11 of the 12 LLs (Vowels or உயிர் எழுத்துக்கள்) as equivalents. I looked at the frequency of occurrence and the placement of these 'vowels' in the midst of unexploded couplets. What about numerals? Like any other compact ancient literary text, Tivuvalluvar has also used several 'figures' or numbers (eg. one, two, three, hundred, thousand etc.) throughout the Kural. These figures as well the different 'measures' (eg. length, breadth, depth, height) occurring in the Kural were also analyzed. The unearthing of such numerical and alphabetical  miracles have been dealt in chapter 7: "Numbers and the other one Letters: எண்ணென்ப ஏனை எழுத்தென்ப".
3) First verse: The very first verses in the Qur'an and Bible, namely the Bismillah verse in Qur'an and the Creation verse in Bible, were shown to have amazing set of mathematical combinations, I looked at the Akaram verse in Kural for 'hidden' mathematical 'miracles'. Interestingly, the first verse in the Bible, Qur'an and Kural have striking similarities as all these statements have the word God in them and all speak about some kind of a beginning:
In the beginning God created the heavens and the earth (Genesis 1:1)
In the name of God, most Gracious, most Merciful (Qur'an 1:1)
All alphabet begin with letter A; So does the world with primordial God (Kural 1)
The amazing series of 'miracles' in the first couplet has been unveiled in Chapter 8: "A-the letter and God-the primordial: அகரமும் ஆதிபகவனும்"
4) God and his attributes: The first chapter in Kural "In praise of God" and few other chapters and couplets here and there contain references to the Absolute as well His attributes. These words and phrases were pooled and categorized for finding overt mathematical phenomenon. This has been dealt in chapter 9: "The One Beyond Compare: தனக்குவமை இல்லாதான்".
5) Body and Soul: The dichotomy of 'Body and Soul' (உடம்பு, உயிர்) is characteristic feature of the Indian philosophical system. The body is only a mere carrier of the 'Real' or the 'Self' or 'Soul'. In fact this is the very foundation on which the Tamil alphabetical system of "Body" and "Life" letters (Consonants and Vowels) have been derived. This dichotomy therefore combines well with the usage of the words "Body and Soul" in Tirukkural. This has been dealt in Chapter 10:."Soul's link to the body: உடம்பொடு உயிரிடை நட்பு"
6) Birth, Death and Rebirth: Since Thirukkural is a work of an Indian author who believed in the concept of rebirth or samsara, I decided to investigate into the frequency of occurrence of these words (பிறப்பு, இறப்பு, எழுமை) and their mathematical implications if any. The findings have been enumerated in Chapter 11: "Birth is an awakening: விழிப்பது போலும் பிறப்பு".
7) Celestials and Celestial worlds: Tirukkural contains numerous references to earth and heaven, here and hereafter, gods of life and death, hell and heaven etc. These key words were also analyzed for the presence of any mathematical pattern. The results have been presented in Chapter 12: "Here and hereafter: இம்மையும் மறுமையும்".
8) Truth and Truthfulness: Valluvar uses different terminologies for Truth and Truthfulness, Reality and Realization. Though he devoted two chapters for these, namely "Truthfulness" and "Realization", the emphasis on truthfulness and realization runs throughout the first two books of Tirukkural. The mathematical basis for these terminologies have been presented in Chapter 13: "Wisdom grasps the Truth: மெய்ப்பொருள் காண்பதறிவு".
9) Major teachings: I looked at the major teachings of Valluvar, namely truthfulness and non-killing (பொய்யாமை, கொல்லாமை), Goodness (சான்றான்மை) and wondered if there will be any mathematical basis for these key words. See Chapter 14: "Major teachings for Valluvar: வள்ளுவரின் முக்கிய கருத்துக்கள்".
10) Virtue, Wealth and Love: Rashad Khalifa highlighted the words Name, Merciful and Magnificent (Ism, Rahman and Rahim) as a set of key words from the Bismillah verses in Qur'an (see Chapter 2. Review). So too in Kural did I find the words Virtue, Wealth and Love (aRam, poruL, inbam) as the 3 components of Muppaal (Trivarga) in Tamil. The significant findings on the relationship between Virtue, Wealth and Love has been dealt in chapter 15: "Virtue, Wealth and Love: அறம், பொருள், இன்பம்".
11) Important chapters: The Kural contains 133 chapters. Even though they have been divided across the three divisions, some of the chapters can be grouped together based on a common subject, say friendship, ministry, charity etc. These interesting combinations and their mathematical basis have been presented in Chapter 16: "Chapters: The Magnificent Seven:  அற்புத அத்தியாயங்கள் ஏழு".

4.7. You can verify my findings

    Readers can verify or cross-check the results of my analysis using the Tirukkural texts, translations and search engines available on the net. But remember that they have their own limitations in searching out every word. Moreover, most of the online search engines that were in vogue during the early years of Y2K are no longer active.  

    (i) Using on-line search engines:  Those who know no Tamil, may think of searching for word frequencies in English translations. But they will not be of much use to verify my results unless the translation is very literal (which is usually not the case). For instance, a translator could translate the words seven days (எழு நாள்) as `a week' and in this case you will get neither seven nor days in your search! Search therefore has to be done in Tamil text.
    There are different types of online search engines available for Tirukkural and they are basically of three types: (a) Searching with TSCII text, (b) Search strings with Roman transliterated text and (c) Search using text in Unicode.

(a) TSCII text search: Ma. Angaiah's Display TirukkuRaL has options to search for Tamil and English words in Kural. It displays the couplets based on occurrence of specific words or phrases. Those who know Tamil can search using Tamil words in Kural. To read the Tamil fonts, you have to download the free MURASU ANJAL, a Tamil software from http://www.murasu.com. However, Display Tirukkural like most other search engines has several limitations, the most important of which is its inability to trap words that are not split (for eg. எழுத்து  in எழுத்தெல்லாம்).
(b) Roman text search: The most important and reliable of all search engines I have seen is Siddhart Ramamurthy's Thirukkural Browser which also has the complete text of the Thirukkural in Tamil, scanned and displayed. The advantage of his search engine is that you don't have to type in Tamil but in appropriate transliteration strings in English.  Another search engine of similar nature is "Acharya's Tirukkural: Online Search" developed by IIT, Chennai. Those who know Tamil, can type the words from a keyboard layout and get the results. There is no need for any font here as the results are displayed as scanned images. Of particular use will be their Word List which lists down the different words, from அ to ன.
(c) Unicode text search: Perhaps the most important search engines, that hold a great future are those employing text in Unicode. Your computer should have Unicode support. There should not be any problem in viewing Tamil text in systems with Windows 2000 and above.  The kural in Unicode with a search option is available at least in two sites (at Muthu.org and Tirukkural.net). You don't require any typing software, just type in English and the word appears in the box in Tamil. I have not tested these search engines and they seem to be ok. However, all the couplets containing a particular word do not get displayed for the same reason explained above.

    (ii) Using hard copies of Thirukkural: Of course the best option for those who know Tamil is to get hold of a copy of Thirukkural and verify my findings. One of the easiest ways is to go through the alphabetic index (அகர வரிசை) given at the end of these books. All standard books provide this list in the end. You can verify SOME of my results using this index, particularly those based on the first word of every couplet. However, I must warn that many of these indices have errors! Alternately, one can use Siddhart's Thirukkural Browser to search for couplets which begin with a particular letter or word. This Browser has option to search for couplets using the START and END words of every couplet! This facility is also available at the two sites that use text in Unicode (at Muthu.org and Tirukkural.net).
    (iii) Using downloadable Kural software: Those who know Tamil, but do not have access to any book, can download the much improved Version 3 Viral Nuniyil Kural which also contains English translation. It can installed in your PC or laptop. It displays the entire Thirukkural in Tamil and you can search the Kural too by typing the couplet number (and thus verify some of my findings)! The program requires installing MylaiTSC font, which is also offered FREE.
    (iv) Using electronic texts of Kural: K. Kalyanasundaram's electronic library contains the complete text of Kural in Tamil font and Unicode. Neethan Namasivayam offers the entire THIRUKKURAL in Tamil using special Tamil fonts (UdayaNet.TTF) that can be downloaded free from the site itself. However all these texts contain many words that have not been broken down further. So much so that when you search for certain words like seyal (செயல்), you will fail to trap some of them as words like 'seyalaaRRum' (செயலாற்றும்) have not been split into செயல் and ஆற்றும்.

References :
 
[1] Pope, G.U. 1886.  Concordance and Lexicon of the Kural and Naladiyar. In: The Sacred Kurral of Tiruvalluva Nayanar. Asian Educational Services. Annexure pp: 1-75.
[2] Velayutham Pillai, 1954.
[3] Kanthaiah Pillai, N.C. 1961. திருக்குறள் அகராதி. ஆசிரியர் நூற்பதிப்புக் கழகம். 270 pages
[4] Chettiyar, P.M.S. 1969. திருக்குறள் சொல்லகரவரிசை. The South India Saiva Siddhanta Works Publishing Society, Tirunelveli.
[5] Subramanian, N. and Rajalakshmi, R. 1984. The Concordance of Tirukkural. Ennes Publications, Madurai. 250 pages
[6] Chellamuthu, K.C. and Baskaran, S. 1986. Computer Analysis of Tirukkural. Tamil University, Tanjavur. 336 pages
[7] Siromoney, G., Govindaraju, S. and, Chandrasekaran, M. 1980. Tirukkural in ancient scripts. Department of statistics. Madras Christian College, Madras.
[8] Varadarajan, Mu. 1988. A history of Tamil literature. Sahitya Academy, New Delhi. 375 pages.
[9] Naicker, P.V.M. 1985. The Tamil Alphabet and Its Mystic Aspect. Asian Educational Services, New Delhi. pages 91.
[10] Mahalingam, N. 1997. Rg Vedic Studies: Addendum. International Society for the Investigation of Ancient Civilization. Chennai. 71 pages.