Investigating the Ancient Meroitic Language Using Statistical Natural Language Techniques: Zipf

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Investigating the Ancient Meroitic Language Using
Statistical Natural Language Techniques Zipfs
Law and Word Co-Occurrences

• Reginald Smith
• August 10, 2006
• Sudan Studies Association Conference
• Rhode Island College

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Meroitic is the language of the ancient kingdom
of Kush

• Used for almost six hundred years from 2nd
  century BCE to 4th century CE
• Phonetic language written right to left (like
  Arabic)
• Transliteration made possible by work of British
  archaeologist FL Griffith around 1910

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Meroitic remains largely undeciphered and an
enigma

• No complete vocabulary is available
• Some words such as place names, loan words, or
  simple concepts are known
• For example or qore means
  king
• Perhaps or qes is Kush
• Many attempts have been made to understand
  Meroitic using phonology or comparative
  linguistics
• Scholars have tried in vain to find a known
  language that is a relative (see sources in
  paper)
• We wish we had a bilingual text like the Rosetta
  stone to guide us

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A new method could use mathematics and linguistics

• Statistical natural language processing analyzes
  the properties of language using a mix of
  statistics and linguistics
• There are several properties of languages that
  are the same in all human languages
• Certain techniques can also help us possibly
  infer meanings of words (by relating them to
  other known words)

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Zipfs Law Frequencies of Words

• If you rank order words in a text by how frequent
  ( of times a word appears) they are (1 being
  most frequent) and then relate this to the
  frequency of the word, you get Zipfs Law
• Zipfs Law where F is the frequency of a word,
  C is a constant, R is the rank, and a is known as
  the power law exponent
• For all languages a 1

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Zipf Law Graphs

• When you graph the frequency vs. the rank on a
  log-log graph (graphing the logarithm of
  frequency vs. the logarithm of rank) you get a
  straight line whose slope is a

Zipf line fit on data. The red line is the fitted
slope on the data points
Picture Source University of Helsinki CS
department
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Does Meroitic follow Zipfs Law?

• The two graphs below show log-log plots of
  frequency vs. rank for the Meroitic words in 69
  texts. The slopes are shown for each
• The normal plot counts the words as is. The
  morpheme out plot split out suffixes like lowi
  as the separate words lo and wi
• Since it has a slope of nearly -1 the morpheme
  out model of Meroitic seems to follow Zipfs Law

Normal plot Slope -0.81
Morpheme out plot Slope -1.03
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So what does this show us (besides graphs)

• Despite the apparently low amount of texts
  available, our sample of Meroitic is structured
  just like all other human languages (English,
  Chinese, etc.)
• Therefore, even though we dont know the meaning
  of the words, we know that the language we have
  is representative
• Even though most of our samples are redundant
  funeral stelae
• We can then proceed to use other statistical
  techniques on Meroitic and also compare its
  statistical features to other languages

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Step Two Word Co-occurrence

• When words occur together in a text, they are
  said to co-occur
• I am here has co-occurrence between I-am and
  am-here
• Co-occurrences can tell us about the words if we
  have enough of them
• Words that co-occur with the same words often
  have similar parts of speech or even meanings
• Can we use word co-occurrence in Meroitic to
  analyze classes of words?

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What I did with Meroitic

• I analyzed Meroitic by matching together words
  that co-occurred with the same types of words
• For example if you have two sentences I eat
  horses and We eat lizards
• I match I and We because they both co-occur
  with eat
• I also match horses and lizards because they
  also co-occur with eat (in the opposite
  direction)
• I then graph connected words together and analyze
  them with software
• What happens?

Technical note I actually used undirected edges
for co-occurring words in the graph shown on the
next page
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Meroitic Words Graph
Group 3

• Four main groups of words form that correspond
  well to Meroitic categories including positions
  and titles, verbs, places, and miscellaneous nouns

Group 4
Group 1
Group 2
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Results

• Techniques like the word co-occurrence matching
  can help us categorize Meroitic words that we
  previously guessed on by mapping them against
  words we already know the part of speech for
• Similar statistical techniques may allow us to
  match words with a similar meaning to infer the
  meanings of some words
• This is still speculative though

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Conclusion

• Statistical natural language processing is a new
  approach to Meroitic that could supplement other
  current efforts in the language
• Much more work remains to be done, but this new
  avenue may help us move closer to the goal of
  understanding this beautiful and mysterious
  language
• Acknowledgements I give my boundless
  appreciation to Dr. Richard Lobban and Dr.
  Laurance Doyle for the help and advice they gave
  me on this papers topics