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\title{\textcolor{yellow}{Algorithms in Ancient India}}
\author{Amba Kulkarni}
\institute{ Department of Sanskrit Studies, \\University of Hyderabad}
\date{6th February 2018}

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\frametitle{Ancient India}
Vedas: Around 3000 BC (or even more ancient)\\
Vid: j\~n{\=a}ne (to know), Vedas: Knowledge\\
Oral Tradition\\
4 Vedas: \d{R}gveda, Yujurveda, S{\=a}maveda and Atharvaveda\\
\'{S}ruti (what is heard) Versus Sm\d{r}ti (what is remembered).\\
Each veda is further subclassified into 4 major text types
\begin{itemize}
\item Samhit{\=a} (mantras and benedictions)
\item {\=A}ra\d{n}yaka (Rituals, ceremonies, sacrifices)
\item Brahma\d{n}as (Commentaries on rituals etc.)
\item Upani\d{s}adas (Philosophy, spiritual knowledge)
\end{itemize}
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The oral tradition of Vedic chanting has been declared an intangible heritage of humanity by UNESCO. In a meeting of jury members on November 7, 2003, at Paris, Mr. Koichiro Matsuura, Director-General of UNESCO, declared the chanting of Vedas in India an outstanding example of heritage and form of cultural expressions. The proclamation says that in the age of globalization and modernization when cultural diversity is under pressure, the preservation of oral tradition of Vedic chanting, a unique cultural heritage, has great significance.
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The Jury members included 
\begin{itemize}
\item Dr. Richard Kurin, Director of the Center for Folklore and Cultural Heritage of the Smithsonian Institution (United Nations), 
\item Mr. Juan Goytisolo, Writer (Spain), 
\item Mr. Yoshikazu Hasegawa (Japan), 
\item Ms. Olive W.M. Lewin. Pianist, ethnomusicologist, Director of the Jamaica Orchestra for Youth (Jamaica). 
\end{itemize}
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\frametitle{Tradition of Vedic chanting}

Inscribed in 2008 (3.COM) on the Representative List of the Intangible Cultural Heritage of Humanity (originally proclaimed in 2003)\\
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The Vedas comprise a vast corpus of Sanskrit poetry, philosophical dialogue, myth, and ritual incantations developed and composed by Aryans over 3,500 years ago. Regarded by Hindus as the primary source of knowledge and the sacred foundation of their religion, the Vedas embody one of the world’s oldest surviving cultural traditions. The Vedic heritage embraces a multitude of texts and interpretations collected in four Vedas, commonly referred to as ``books of knowledge'' even though they have been transmitted orally. The Rig Veda is an anthology of sacred hymns; the Sama Veda features musical arrangements of hymns from the Rig Veda and other sources; the Yajur Veda abounds in prayers and sacrificial formulae used by priests; and the Atharva Veda includes incantations and spells. 
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\frametitle{Tradition of Vedic chanting}
Inscribed in 2008 (3.COM) on the Representative List of the Intangible Cultural Heritage of Humanity (originally proclaimed in 2003) ...\\
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The Vedas also offer insight into the history of Hinduism and the early development of several artistic, scientific and philosophical concepts, such as the concept of zero. Expressed in the Vedic language, which is derived from classical Sanskrit, the verses of the Vedas were traditionally chanted during sacred rituals and recited daily in Vedic communities. 
The value of this tradition lies not only in the rich content of its oral literature but also in the ingenious techniques employed by the Brahmin priests in preserving the texts intact over thousands of years. To ensure that the sound of each word remains unaltered, practitioners are taught from childhood complex recitation techniques that are based on tonal accents, a unique manner of pronouncing each letter and specific speech combinations. 
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Although the Vedas continue to play an important role in contemporary Indian life, only thirteen of the over one thousand Vedic recitation branches have survived. Moreover, four noted schools – in Maharashtra (central India), Kerala and Karnataka (southern India) and Orissa (eastern India) – are considered under imminent threat. 
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\frametitle{Preservation of Vedas: Oral Tradition}
According to the Taittiriya Upaniṣad — śikṣā-valli there are 6 main factors that need to be taken into consideration.
\begin{itemize}
\item Var\d{n}a\d{h} (Pronunciation)
\item Svara\d{h} (Accent)
\item M{\=a}tr{\=a} (Duration)
\item Balam (Emphasis)
\item s{\=a}ma (continuity / flow in chanting)
\item Sant{\=a}na\d{h} (Punctuation/ Pause)
\end{itemize}
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\frametitle{Preservation of Vedas: Oral Tradition}
Oral tradition With Mudras and face position\\
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\includegraphics{Vedas-Fritz_Staal.jpeg}
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\frametitle{Preservation of Vedas: Oral Tradition}
Various recitation styles to allow complete and perfect memorization
\begin{itemize}
\item Prak\d{r}ti p{\=a}\d{t}ha
\item vik\d{r}ti p{\=a}\d{t}ha
\end{itemize}
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\frametitle{Preservation of Vedas: Oral Tradition}
Prak\d{r}ti p{\=a}\d{t}ha
\begin{itemize}
\item Sa\.mhit{\=a}: Continuous recitation
\item Pada: Pause after every word
\item Krama: consecutive words are paired and recited\\
1 2; 2 3; 3 4; 4 5; ..
\end{itemize}
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\frametitle{Preservation of Vedas: Oral Tradition}
Vik\d{r}ti
\begin{itemize}
\item Jat{\=a} (matted hair)\\
1 2 2 1 1 2; 2 3 3 2 2 3; 3 4 4 3 3 4; 4 5 5 4 4 5; ...
\item m{\=a}l{\=a} (Garland) \\
1 2; 2 1; 1 2; 2 3; 3 2; 2 3; 3 4; 4 3; 3 4, ...
\item \'{S}ikh{\=a} (hair tied in a knot)\\
1 2 2 1 1 2 3; 2 3 3 2 2 3 4; 3 4 4 3 3 4 5; ...
\item Rekh{\=a} (line)\\
1 2; 2 1; 1 2; \\
2 3 4; 4 3 2; 2 3; 3 4;\\
4 5 6 7; 7 6 5 4; 4 5; 5 6; 6 7;\\
\end{itemize}
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\frametitle{Preservation of Vedas: Oral Tradition}
Vik\d{r}ti ...
\begin{itemize}
\item[5] Dhwaja (Flag)\\
1 2; 99 100; 2 3; 98 99; 3 4; 97 98; 4 5; 96 97; 5 6; 95 96; ......; 96 97; 4 5; 97 98; 3 4; 98 99; 2 3; 99 100; 1 2
\item[6] Da\d{n}\d{d}a (rod) \\
1 2; 2 1; 1 2; 2 3; 3 2 1; 1 2; 2 3; 3 4; 4 3 2 1; 1 2; 2 3; 3 4; 4 5; 5 4 3 2 1; ...
\item[7] Ratha (Chariot)\\
1 2; 5 6; 2 1; 6 5; 1 2; 5 6; 2 3; 6 7; 3 2 1; 7 6 5; 1 2; 5 6; 2 3; 6 7; 3 4; 7 8; 4 3 2 1; 8 7 6 5; ...
\item[8] Ghana (hard)\\
1 2 2 1 1 2 3 3 2 1 1 2 3; 2 3 3 2 2 3 4 4 3 2 2 3 4; 3 4 4 3 3 4 5 5 4 3 3 4 5; ...
\end{itemize}
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\frametitle{G{\=a}yatri mantra}
{\dv ॐ भूर्भुव: स्व: तत्सवितुर्वरेण्यं । भर्गो देवस्य धीमहि, धीयो यो न: प्रचोदयात् ।।   } \\
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We meditate on the effulgent glory of the divine Light; may he inspire our understanding (S Radhakrishnan)
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\frametitle{G{\=a}yatri mantra Ghanap{\=a}\d{t}ha}

{\dv ॐ तत् सवितुस् सवितुस् तत् तत् सवितुर् वरेण्यं वरेण्यं सवितुस् तत् तत् सवितुर् वरेण्यम्।
सवितुर् वरेण्यं वरेण्यं सवितुस् सवितुर् वरेण्यं भर्गो भर्गो वरेण्यं सवितुस् सवितुर् वरेण्यं भर्गः।
वरेण्यं भर्गो भर्गो वरेण्यं वरेण्यं भर्गो देवस्य देवस्य भर्गो वरेण्यं वरेण्यं भर्गो देवस्य।
भर्गो देवस्य देवस्य भर्गो भर्गो देवस्य धीमहि धीमहि देवस्य भर्गो भर्गो देवस्य धीमहि।
देवस्य धीमहि धीमहि देवस्य देवस्य धीमहि धीमहि इति धीमहि।
धियो यो यो धियो धियो यो नो नो यो धियो धियो यो नः।
यो नो नो यो यो नः प्रचोदयात् प्रचोदयात् नो यो यो नः प्रचोदयात्।
नः प्रचोदयात् प्रचोदयात् नो नः प्रचोदयात् प्रचोदयात् इति प्रचोदयात्॥

ॐ भू ॐ भुवः ॐ स्वः ॐ महः ॐ जनः ॐ तपः ॐ सत्यम्।
ॐ तत् सवितुर्वरेण्यं भर्गो देवस्य धीमहि धियो यो नः प्रचोदयात्
ॐ आपोज्योतीरसोऽमृतं ब्रह्म भूर्भुवःस्वरोम्‌॥ }


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%\frametitle{G{\=a}yatri mantra Ghanap{\=a}\d{t}ha}
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\frametitle{Error Correction Error Detection Code}
Error Correction and Error Detection\\
for Reliable delivery of Digital Data\\
over unreliable communication channels\\
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\frametitle{Error Correction Error Detection Code}
\begin{itemize}
\item Error Detection: Detection of errors due to noise
\item Error Correction: Construction of the original error-free data
\end{itemize}
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\frametitle{Error Correction Error Detection Code}
Various Error Detecting Methods in Information Coding
\begin{itemize}
\item Repetition Code\\
Duplicate / Triplicate the data\\
1010 $\rightarrow$ 1010 1010 1010
\item Add Parity bits\\
Even Parity: 1010 $\rightarrow$ 10100\\
1011 $\rightarrow$ 10111\\
\item CheckSum
\item Cyclic Redundancy Check
\item Hash Function
\end{itemize}
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\frametitle{Error Correction Error Detection Code}
Various Error Correcting Methods in Information Coding
\begin{itemize}
\item Parity bit: Single Error correction
\item .
\item .
\item .
\end{itemize}
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\frametitle{Understanding Vedas}
Six Veda\.ngas (Auxiliary disciplines) to understand Vedas\\
\begin{itemize}
\item \'{S}ik\d{s}{\=a}: (phonetics, phonology, pronunciation)\\
The place and articulation of various sounds, possible sounds in Sanskrit,
accent, stress, and rules of euphonic combination of words
\item Chandas: (prosody, Meter)\\
Poetic meters
\begin{itemize}
\item Ak\d{s}ara v\d{r}tta: based on fixed number of syllables per verse
\item M{\=a}tr{\=a} v\d{r}tta: based on fixed number of morae per verse
\item Ga\d{n}a v\d{r}tta: based on fixed pattern of morae per verse
\end{itemize}
\item Vy{\=a}kara\d{n}a: grammatical and linguistic analysis
\item Nirukta: etymology, explanation of words, particularly those that are archaic and have ancient uses with unclear meaning.
\item Kalpa: ritual instructions, Geometry
\item Jyoti\d{s}a: Astronomy, Astrology
\end{itemize}
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