11
Study of the Indus Valley Scripts through Linguistic and Markov Chain Methods* Niladri Sarkar** * The project was accomplished under the sponsorship of Indian National Commission for History of Science between August 2012 and July 2015. **Assistant Professor, Department of Physics, Birla Institute of Technology & Science, Pilani-333031; Email: [email protected] 1. INTRODUCTION The main aim of this project was to study and apply statistical and linguistic methods in order to understand the nature and the structure of the Indus Valley Scripts. The focus was on the application of the Markov Chain Method on the Indus Scripts. A new method based on Metropolis Algorithm has also been used for deciphering the scripts. Indus Valley Civilization was one of the most technologically advanced civilizations of the ancient world. It existed roughly between 6000 BC-1800 BC and was at its peak between 2550 BC-1900 BC. This civilization was contemporary with the ancient river valley civilizations of Nile, Euphrates and Tigris. It had well established trading relations with its contemporary civilizations. It was an urban civilization with very well planned cities and ports. There were magnificent drainage systems, well built roads, facilities of water storage, great public baths and very well planned houses made of burnt bricks. One feature that is quite unusual from its other contemporary civilizations is the relative even distribution of their wealth. There is no evidence of any extravagant monument building by any king or any influential person of that era to placate any supernatural and superstitious beliefs if at all existed(Kenoyer, 1998). These salient features described above makes it more superior civilization than its contemporaries. However, unlike its counterparts in Egypt, Persia and Mesopotamia, the Indus Civilization did not survive until the historical times. A gap of about 1200 years between the sudden demise of the Indus valley civilization and the golden period of Ashoka remains. Many scholars and archaeologists have shown some similarity between the religion and culture of this civilization and those of later known times. Some of the symbols and motifs discovered during various excavations are still seen in present times. The most common example is the symbol known as the ‘svastika’, incised on hundreds of Harappan tablets, generally single but occasionally double, with no preferred direction. This symbol continues to be depicted on pottery at several early sites, on punch-marked coins, on some of Ashoka’s edicts and other early inscriptions. Another typical symbol is the ‘endless knot’ which appears on several inscriptions of the ninth century AD in Gujarat and can still be seen today in some of the rangolis drawn by Indian woman in front of their houses during auspicious occasions. The motif of ‘intersecting circles’ is a frequent one on Harrapan pottery. This type of design occurs on top of the Boddhi throne at Bodh Gaya, which dates from the third century BC. Apart from these, there are lots of other symbols like the hollow cross, the tree on a raised platform, the fish, the peacock, the antelope, the Pipal leaf and many other symbols which are common to Indus seals or pottery and punch-marked coins or Indian Journal of History of Science, 51.2.1 (2016) 292-302 DOI: 10.16943/ijhs/2016/v51i2/48441 Project Reports

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Study of the Indus Valley Scripts through Linguisticand Markov Chain Methods*

Niladri Sarkar**

* The project was accomplished under the sponsorship of Indian National Commission for History of Science between August2012 and July 2015.

**Assistant Professor, Department of Physics, Birla Institute of Technology & Science, Pilani-333031; Email:[email protected]

1. INTRODUCTION

The main aim of this project was to studyand apply statistical and linguistic methods inorder to understand the nature and the structureof the Indus Valley Scripts. The focus was on theapplication of the Markov Chain Method on theIndus Scripts. A new method based on MetropolisAlgorithm has also been used for deciphering thescripts. Indus Valley Civilization was one of themost technologically advanced civilizations of theancient world. It existed roughly between 6000BC-1800 BC and was at its peak between 2550BC-1900 BC. This civilization was contemporarywith the ancient river valley civilizations of Nile,Euphrates and Tigris. It had well establishedtrading relations with its contemporarycivilizations. It was an urban civilization with verywell planned cities and ports. There weremagnificent drainage systems, well built roads,facilities of water storage, great public baths andvery well planned houses made of burnt bricks.One feature that is quite unusual from its othercontemporary civilizations is the relative evendistribution of their wealth. There is no evidenceof any extravagant monument building by any kingor any influential person of that era to placate anysupernatural and superstitious beliefs if at allexisted(Kenoyer, 1998). These salient featuresdescribed above makes it more superiorcivilization than its contemporaries. However,unlike its counterparts in Egypt, Persia and

Mesopotamia, the Indus Civilization did notsurvive until the historical times. A gap of about1200 years between the sudden demise of theIndus valley civilization and the golden period ofAshoka remains. Many scholars andarchaeologists have shown some similaritybetween the religion and culture of this civilizationand those of later known times. Some of thesymbols and motifs discovered during variousexcavations are still seen in present times. Themost common example is the symbol known asthe ‘svastika’, incised on hundreds of Harappantablets, generally single but occasionally double,with no preferred direction.

This symbol continues to be depicted onpottery at several early sites, on punch-markedcoins, on some of Ashoka’s edicts and other earlyinscriptions. Another typical symbol is the ‘endlessknot’ which appears on several inscriptions of theninth century AD in Gujarat and can still be seentoday in some of the rangolis drawn by Indianwoman in front of their houses during auspiciousoccasions. The motif of ‘intersecting circles’ is afrequent one on Harrapan pottery. This type ofdesign occurs on top of the Boddhi throne at BodhGaya, which dates from the third century BC.Apart from these, there are lots of other symbolslike the hollow cross, the tree on a raised platform,the fish, the peacock, the antelope, the Pipal leafand many other symbols which are common toIndus seals or pottery and punch-marked coins or

Indian Journal of History of Science, 51.2.1 (2016) 292-302 DOI: 10.16943/ijhs/2016/v51i2/48441

Project Reports

PROJECT REPORT: STUDY OF THE INDUS VALLEY SCRIPTS 293

other artifacts of later historical times. Pipal treeis still regarded as one of the most sacred of treesin India today. All the above mentioned facts pointto a very strong link between people and cultureof the Indus Valley civilizations and those ofknown historical times, which roughly begin from500 BC. We can identify ourselves with the peopleand culture of historical times due to the continuityof the communication between the past and presenttimes through various written and engravedrecords of the past, which have been decipheredsuccessfully till date. However, the moment wetry to connect ourselves with the people of IndusValley, a missing link appears. This is because wehaven’t completely understood the Indus Scriptsproperly. This is the greatest obstacle towardsunderstanding this civilization, and a successfuldecipherment of this script may bridge the gapbetween the Indus Valley Civilization andhistorical times. Only written evidences that wesee today are the Indus Scripts which is found onthe thousands of terracotta seals excavated fromvarious archeological sites of Harappan andMohenjodaro(Kenoyer, 1998, Kak, 1987).

This was not a prehistoric settlement wherepeople were hunters and fisherman. The conceptof wheels was known to them. People haddeveloped various skills like pottery and had the

knowledge of metallurgy. There were magnificentdrainage system, well built roads, facilities forwater storage, great baths and planned housesmade of burned bricks of optimized dimensionsto sustain extreme environmental conditions. Theyalso made toys for children. If we try to reconstructa model out of the ruins of Indus ValleyCivilization, it will very well resemble with anyof the ancient urban civilization with planned citiesand ports. One can see such models in theHarrapan gallery of the National Museum in New-Delhi. Hence forth, so many things should havedeveloped during that era along with thedevelopment of a language.

In order to correctly interpret the IndusScripts, following objectives and methodologieswere adopted. These are:

(i) Linguistic analysis of the Indus Script todetermine the grammatical structure of thetexts and its affinity to documented naturallanguages.

(ii) Determination of the Entropic evidences forthe linguistic structure in the Indus script usingMarkov chain model.

(iii) Syntactic connections between the signs ofthe Indus Scripts should be established.

Fig. 1. Typical Indus Valley Seals which are painted for more clarity. The seals depict a one horned bull and an elephantwith inscriptions at the top. There are similar seals of one horned bull with different inscriptions

294 INDIAN JOURNAL OF HISTORY OF SCIENCE

(iv) Application of conditional entropy on IndusScripts and comparing it with other knownscripts and non-scripts will establish a strongevidence for the linguistic structure of theIndus Scripts.

The project was accomplished under thefollowing chapters:

I. Traces of the lost civilization and its scripts.II. Scientific & linguistic approaches towards

understanding of the Indus Scripts.III. Scientific Evidence of a Script and a Language

by Markov Chain Model.IV. Conclusions and future work to be done.

2. TRACES OF THE LOST CIVILIZATION

AND ITS SCRIPTS

This section starts with a concept ofsudden end of an era. The reason for this is due tothe fact there exist a gap of about 1200 years ofmissing information between the Indus Period tothe Indian historical times. If we look into otherancient civilizations, there exists a strong linkbetween the ancient times and modern times. Onecan see an analogous example in the catastrophicend of the Dinosaurs after the Jurassic era.However, many other species which existed duringthat era continue to survive till the present times.Hence, the only things which we find today afterthe sudden extinction are the fossils in the case of

dinosaurs and the traces of the ancient cities andits scripts in the case of Indus Valley Civilizationalthough both the events may have occurred duringvery different eras separated by millions of years.The dawn of the mankind occurred much later afterthe catastrophic end of the Jurassic Age. It evolvedvery slowly with man learned to hunt and toolmaking for various purposes. With time and ages,the humans very slowly learnt the art of speakingwhich created very early languages with a limitedstock of words. Such primitive languages evensurvive today in the present times with the tribesof Andaman Islands and aboriginal people ofAustralia, New-Zealand and other native peoplesmall Pacific Islands. Many of these primitivelanguages are agglutinative where the complexwords are strings formed by joining themorphemes together without changing thespellings and the phonetics of the individual units.With the evolution and enrichment of thelanguage, the ideas were exchanged betweenpersons and from hunting and cave dwellingevolved early settlements which finally resultedinto small villages which finally integrated to formtowns and cities of the early civilizations.

The cities of the ancient times likeMohenjodaro and Harrapa at sometimes housedsome more than 40,000 inhabitants. These werethe important and greatest cities and the centersof trades during that time.

Fig. 2. (a) The Sudden and Catastrophic End of an Era and (b) the only evidence of the life that existed during the Jurassicera can be obtained from the fossil records

PROJECT REPORT: STUDY OF THE INDUS VALLEY SCRIPTS 295

Apart from these, from the evidences ofthe types of the Indus Seals and artifacts whichwere found in many parts of Modern North-Western India and the parts of Western Pakistan,one can infer that there existed a regular networkof towns and cities which had spread over an areaof about 1.25 Million Sq. Kms. There are verystrong evidences that there existed Harrapancontacts with the Western Asia. Similar type ofsigns of the Indus seals have been found in someround seals which were excavated at Ur. Thereforeign countries have been identified asparticipants in the trade from 2400 BC to 1900BC. They were Dilmun, Magan and Meluhha.Dilmun is the Islands of Tarut, Baharin andFailaka. Magan is the Oman peninsula and theIranian Markran across the Gulf. Meluhha is theIndo (undivided India)-Iranian borderlands and theIndus Civilization. A very important picture whichis found as drawing on the pots in far off placesfrom Indus valley is that of peacock. Woods formaking chairs and Ivory were some of the mostimportant products that were imported from theport cities of the Indus Valley. There existevidences of irrigation channels. The pottersmastered the techniques of air reduction to producehigh quality ceramics. The ceramic style whichappeared in the Indus Valley is Kot Dijjian ware.Most of the globular vessels had a wide bandpainted around its neck. The remains of typicalHarrapan large storage jars were discovered at

Wadi Asimah in the Oman Mountains in 1987.The correct interpretation of the Indus ValleyScript is a challenging problem. We are still unsureabout its origin and know very little about it. Wedon’t know whether these signs represent a welldeveloped language. We can guess it by lookinginto the developments that had occurred duringthat period. From the ruins of Indus Valley, onecan infer that it was an advanced civilization whichflourished along with other contemporary rivervalley civilizations of Nile, Euphrates and Tigris.It had trade links with Western Asia. One thing iscertain that there existed very well definedlanguage because without it they wouldn’t haveestablished trade relations.

3. SCIENTIFIC & LINGUISTIC APPROACHES

TOWARDS UNDERSTANDING OF THE INDUS

SCRIPTS

This chapter deals with the Scientific andLinguistic approaches made for understanding thenature of the Indus Scripts (Kak, 1987; Jayaswal,1933; Mahadevan, 1977; Fairservis,1992; Parpola,1994). Over 4000 inscriptions mostly on seals,tablets and pottery have been excavated fromvarious Harrappan sites. About 400 distinct signshave been identified of which only 200 have beenused more than five times. Various methodicalattempts have been made in the past ninety years.Sir John Marshall in 1924 was the first to suggest

Fig. 3. From an Early Settlement to a well established Port Cities which had trade links with Western Asia

296 INDIAN JOURNAL OF HISTORY OF SCIENCE

that the Indus civilization was non-Aryan and thatits language probably close to the Dravidianfamily. Piero Meriggi considered the Dravidianlanguage of Brahui, spoken in Baluchistan as theonly reasonable contender. The Spanish JesuitHenry Heras who spent most of his time in India,had numerous publications on the Indus script thatculminated in 1953 in a book called Studies inProto-Indo-Mediterranean culture. Experts havelong pointed to important structural features of theIndus script that resemble with the features inBrahmi script. The use of composite signs andmodifiers, respectively call to mind the use ofcomposite letters and diacritical marks in Brahmito denote vowels as in later Indian scripts. SubhashKak, Stephen Langdon and G.R. Hunter haveindependently proposed a parallel between theIndus and Brahmi scripts. The mysteriousinscription in the Vikramkhol caves in Odisha hasbeen studied by eminent epigraphist K.P. Jayaswaland has concluded that the inscription provides alink between the letter forms of the Indus Scriptand the Brahmi Script. Soviet scholars, headed byYurij V. Knorozov, who have publishedextensively on the Indus script, have based theirwork on the number of different signs they coulddistinguish. They have come to the conclusion thatthe script is logo-syllabic rather than syllabic oralphabetic. Based on the statistical analysis of thedistribution of various signs, they have concludedthat signs which occur more frequentlyrepresented grammatical markers, while thoseoccurring less so, represented root morphemes.Iravatham Mahadevan has contributed greatlytowards the documentation of the Indus scripts andits technical aspects. He has stressed on thepictorial meaning of the Indus signs and tried towork out its interpretations from the symbolic usesof the depicted objects in later Indian traditions.Since 1976, Walter A. Fairservis, one of theleading archaeologists specializing in theHarrappan culture has elaborated on generalassumptions and principles relevant to thedecipherment of the Indus script. In recent times,

a Finnish team lead by Professor Parpola haspresented a decipherment of a small number ofinterlocking Indus signs and has proposed amethod which may permit further progress indecipherment. In spite of all this, none of theattempts at deciphering the Indus script has gainedwide acceptance, although there have been solidcontributions on various technical aspects of thescript. First and the most important thing in thedecipherment is the collection of the material intoa corpus. Accuracy is vital in such a corpus. It isextremely important to generate various kinds ofstatistical data namely, frequencies of individualsigns and sign combinations, of text with differentlengths, of object types, of iconographic motifsetc, and to tabulate the distributions of signs andother variables in relation to different criteria.

Fig. 4. The Inscriptions of Vikramkhol Caves in Odisha

For the linguistic analysis of the script, onehas to first know the direction of the writing. AskoParpola has proposed the following criteria fordetermining the direction of the writing. Whensigns are incised on pots, the lines drawn firstcould become partially obliterated by those drawnlater. One criterion proposed for the determinationof the direction is based on the idea that theanimals depicted on the Indus seals, and thepictograms in the accompanying inscriptionsshould face in the direction in which the writingwas to be read. More dependable evidence issupplied by the spacing, both in the individual

PROJECT REPORT: STUDY OF THE INDUS VALLEY SCRIPTS 297

signs and in inscriptions. Sometimes theinscription is shorter than the allotted space. Textsstarting from the right edge and leaving an unusedspace to the left may reasonably be expected torun from right to left. Numerous tests haveestablished right to left as the most probabledirection of writing in the Indus inscriptions. Thiswas already clear in the early 1930s to Gadd andSmith, Marshall and Hunter. However, a fewuncertain cases still remain. IravathamMahadevan, who carefully recorded the directionof the original in each of his 3,573 lines,distinguished 2,974 lines running from right to leftand 235 going from left to right, in addition toambiguous sequences, such as 190 single-signlines, 12 symmetrical sequences and 155 cases thatare doubtful on account of damaged or illegiblelines. A top-to-bottom sequence is recorded forseven lines. After the completion of thepreliminary tasks of collecting and establishingthe direction of writing, several attempts have beenmade for a structural analysis of the Indus scriptby Asko Papola, Iravatham Mahadevan and others.There exist evidences of patterns which reflectsan intrinsic structure in the Indus Scripts. Thereare evidences on the direction of the writing. Ithas been established by various methods that thedirection of the writing is from right to left. Also,the scripts show diacritical modification of basic

signs and ligaturing. For example, shows an evidence of this ligaturing. There areevidences of double ligaturing as well. For

example, shows the evidence of double

ligature. The example and showdouble and single ligaturing. There are mirrorimages like . There aresome signs which occur more frequently than theothers. For example, the sign occurs as aterminal in many strings. This sign showsdiacritical modification as well. This modificationoccurs as , , and respectively.

Also, the fish sign shows the same

modification as . There exist mirror images ofsign pairs like and where the axis ofreflection lies horizontally. Sometimes signs occurwith two, three and four fold repetitions. Someexample of such repetitions are , ,

, , and respectively.There are evidences of two different words in a

string. For example, and

have the word

which is common in both strings. One can split astring into three segments as

. There are alsoevidences of inflexion in the strings. Some pair ofstrings like and

show inflexions where theterminals and act as inflexion suffixes.

4. THE INSCRIPTION FROM THE CITY

DHOLAVIRA IN KUTCH, GUJARAT

A very important discovery by Dr R. S.Bisht is an inscription which may have indicatedvery important information about the city, possiblyits name. These are ten signs made from the piecesof crystalline rock. The following figure showsthe inscription and two other inscriptions that beara same pattern of three signs.

298 INDIAN JOURNAL OF HISTORY OF SCIENCE

Here, we identify the sign sequence,

a possible Trigram.

5. SCIENTIFIC EVIDENCE OF A SCRIPT AND A

LANGUAGE BY MARKOV CHAIN MODEL

The problem here is that both the languageas well as the script is unknown to us. Only onething is certain that these are not randomlygenerated string of signs. These were used bypeople of that era for trade purposes as one canguess from the seals as similar type of seals arefound in Western Asia. However the Indus sealswere rectangular in shape, whereas the foreignseals where mostly circular in shape. The figuresand the scripts had similarities. Various tests basedon the concepts of entropy in the communicationtheory have been applied on these scripts. Theresults have shown that there is an intrinsicstatistical structure in these scripts. One canconstruct crosswords out of these strings whichindicate non zero redundancy.

6. CONCEPTS OF ENTROPY IN

COMMUNICATION THEORY

How to analyze these seals is one of themost challenging problems. The first thing whichcomes to our mind is whether these are a part ofsome scripts which lead to a language or just signswhich may convey some ideas like the modernday traffic sign boards. For this, one may take helpfrom the concepts of entropy in communicationtheory. According to Shannon’s informationtheory, there is entropy associated with everyspoken language (Shannon, 1948). One canunderstand it in terms of the existence of 2-D and3-D cross-word puzzles. The ratio of the entropyof a source to the maximum value it can have iscalled the relative entropy. Entropy in a language

is a measure of the number of degrees of freedomto construct meaningful words from a set of limitedunits which may be alphabets in case of Englishlanguage or some set of signs in the case of IndusScripts. There exists in every language whether itis a natural spoken language or a computerlanguage, an intrinsic statistical structure whichinvokes a constraint in the usage of the alphabetsor building blocks. For example, the occurrenceof “u” after “q” in English language is highlyprobable than the occurrence of “q” after “u”.Hence, when we write in any language, a fraction‘F’ of the letters chosen is determined by theinternal structure of the language and the rest ‘1-F’ letters can be chosen freely. This ‘F’ is relatedto the redundancy of a language. If redundancy iszero, then we will not have a language as allcombinations are possible.

7. WHAT IS A MARKOV CHAIN?We will now describe the Markov chain

in terms of a language (Shannon, 1948; Rao &Rajesh, 2009; Rao 2009). Suppose we have astring of symbols of a language which may beknown or unknown. For examples, let’s take astring from an Indus seal,S={ }. Now, we define thestring ‘S’ as a set of states where each symbol isan element of the set. Now this set ‘S’ would be asub-set of the language which may contain a verylarge collection of strings which are sequences ofthe signs. Hence, the language, L={S1,S2,…..,SN,…} will be the set of all the possiblemeaningful sequences of the signs. Now, if wetake a particular string ‘S’ from ‘L’. Now, one canonly move from the first sign of this string to thenext sign and so on with a transition probability,Pij. Now, the transition probability can be obtainedfrom the transition matrix of the particularlanguage ‘L’. One can understand it from thetransition matrix of signs which is shown in fig.5. From a matrix like this, we can construct therelevant strings which may belong to the language

PROJECT REPORT: STUDY OF THE INDUS VALLEY SCRIPTS 299

set L. Here, we find that corresponding to everysign in the outer column there is an associatedstrength assigned for the occurrence of the nextsign. Now, the construction of such a matrix forthe Indus script is a challenging problem. Forexample for a known language like English, it isvery easy to construct such a matrix by writing acomputer code in MATLAB or C. All that isrequired for this is a book or a novel in a digitalform. Now, the signs which will be placed at theother column and the row of the matrix will bethe alphabets and the space. The computerprogram will assign the strengths for the first ordertransition. A simple observation that one sees hereis the strength of the occurrence of the alphabet‘u’ after ‘q’ than the strength of the occurrence ofthe alphabet ‘q’ after ‘u’. It will observed that theformer’s strength will be very large compared tothe latter’s strength. Now with the help of thetransition matrix, one can construct a relevantstring which may belong to the language set. Thealgorithm for generating a first order sequence ofstrings is shown below.

(i) Choose a sign randomly from the outercolumn of the Matrix.

(ii) Now, generate a random number between ‘0’to ‘1’.

(iii) Now, the Next Sign in the sequence wouldbe according to the value of the randomnumber generated and this will correspondto the first order transition strength.

(iv) Once, the sign is assigned, repeat the processtill a terminal sign comes in the string.

In this way, one can generate lot of stringsof which few may belong to the language set ‘L’.

8. SEQUENCES OF STRINGS GENERATED BY

MARKOV CHAIN METHOD

The following figure shows the saturationof the first order transition matrix for three Indussigns. The elements of the matrices will not changeafter 5 iterations.

Fig. 5. A Matrix of Indus Signs for First Order Transition

The probabilities of the threestates, , are 0.4,0.2 and 0.4 after5 iterations and will continue to be that for higheriterations. The states will be independent of thestarting states. This type of chain is called “RegularMarkov Chain”. The following figure shows atransition matrix for an Absorbing Markov Chain.

The states and are the absorbing states. It

300 INDIAN JOURNAL OF HISTORY OF SCIENCE

is impossible to leave that state. However, it ispossible that one can go from all the non-absorbingstates to the final absorbing state.

Chain and Monte Carlo Method using Metropolisalgorithm(Harvey). Under this an intelligent guessabout the language is to be made by narrowingdown the known ancient languages which werespoken during that particular era in Western Asia.Then a statistics of that particular language has tobe recorded by recording the first order transitions,proportion of the consecutive signs. A matrix ofconsecutive signs will have the transitionprobabilities as its elements. Then, we have toreplace properly the unknown signs of the IndusScripts by the known signs of that particularlanguage by comparing the statistics of the Indusscripts with the known signs. Then, we have tocompute the first order transition probability ofthis new assembly. Then, we have to make arandom transposition of the assigned signs. Afterthis, again the first order transition probability isto be calculated. We have to keep on makingrandom transpositions till the program convergesto the first order transition probability of theknown ancient language. This type of techniquewill work, provided we get some texts of knownancient languages of that era.

9. MONTE CARLO METROPOLIS ALGORITHM

Start with a known text of ancientlanguage. Calculate the probability of first ordertransition, i.e, the probability of the occurrence ofthe consecutive symbols. Call it P(f0). Now,choose an unknown Indus String, f=

. Replace the signs of thestring with usual known alphabets, f : {UnknownSigns———> Known Alphabets}. Calculate thefirst order transition probability, P(f) of this string.Now, make a random transposition with thealphabets assigned to two unknown signs. Again,compute the first order transition probability,P(f1). If P(f1)>P(f), then accept the change. IfP(f1)<P(f),generate a random number, Rn,between 0 and 1. If Rn<P(f1). Then, accept thechange. Else, the transposition is rejected. Keepon repeating the above procedure till P(f) saturatesi.e, no more transposition is allowed.

The following figure shows the transitionsfrom transient states to final absorbing states:

The following figure shows some possiblestrings of Indus scripts obtained from the abovetransition matrix.

Having, made such logical observations,one needs a scientific methodology to decipherthese scripts. The technique which can besuccessfully applied here is based on Markov

Possible strings

PROJECT REPORT: STUDY OF THE INDUS VALLEY SCRIPTS 301

Flowchart for the Monte Carlo Metropolis Algorithm

10. CONCLUSIONS AND FUTURE

WORK TO BE DONE

An attempt based on Shannon’sinformation theory has been attempted on IndusScripts. The construction of the crosswords gaveus some weak indication of a language in thescript. This can be said because the strings havebeen chosen random from the corpus. However,it doesn’t give us any clue about the origin of the

language and its connection with the presentclosely related language. This is very importantsince we cannot proceed without knowing thelanguage. So it is important to narrow down ourchoices on ancient languages that were spokenduring that era. Now, by targeting a particularlanguage, the Monte-Carlo method withMetropolis algorithm should be used on theunknown Indus Scripts. The Metropolis algorithm

Choose an unknown Indus String, f

Replace the signs of the stringf : {Unknown Signs———> Known

Alphabets}

Calculate the first order transition probability, P(f) of this string

Make a random transposition with the alphabets assigned to two unknown signs

Compute the first order transition probability, P(f1)

If P(f1)<P(f),generate a randomnumber, Rn, between 0 and 1

Else, accept the change,P(f)=P(f1) and go to step 4

If Rn<P(f1). Then, accept the change,P(f)=P(f1) and go to step 4

Else, reject the change,and go to step 4

302 INDIAN JOURNAL OF HISTORY OF SCIENCE

will insure the convergence of the problem. Themost ambitious work that can be attempted is thetesting of the Markov Chain Monte Carlo Methodusing Metropolis algorithms.

BIBLIOGRAPHY

Fairservis, Walter A, The Harappan Civilization and itsWriting: a Model for the Decipherment of the IndusScript, New Delhi, 1992.

Harvey, Gould; Jan, Tobochnik and Wolfgang, Christian.An Introduction to Computer Simulation Methods:Applications to Physical Systems (3rd Edition).

Jayaswal, K. P., ‘The Vikramkhol Inscription’, The IndianAntiquary, 1933, vol. LXII, p.60.

Kak, Subhash. ‘On the Decipherment of the Indus Script: APreliminary Study of its Connection with Brahmi’,IJHS. 22(1987): 51-62.

Kenoyer, J. M. Ancient Cities of the Indus Valley Civilization,Oxford University Press & American Instituteof Pakistan Studies, Karachi & Islamabad,1998.

Mahadevan, I , The Indus Script: Text, Concordance andTables, Archeological Survey of India, New Delhi,1977.

Parpola, A, Deciphering the Indus Script, CambridgeUniversity Press, 1994.

Rao, P. N., Rajesh et. al., A Markov Model of the IndusScript, PNAS, 5 August, 2009.

Rao, RPN, et. al., Entropic Evidence for LinguisticStructure in the Indus Script, Science 324 (2009):1165.

Shannon, C. E. The Bell System Technical Journal, 27,(1948): 379.