OE1-2.3 Linguistic Wealth: Sanskrit, Literature & Vedic Mathematics

What this is and why it exists

One part of this topic has the strongest hold on an engineer's attention, and it is the grammatical tradition rather than anything else here.

A formal rule system describing a language completely is a remarkable object. This one was written more than two thousand years before anyone used the words formal grammar. It is also the reason this material keeps appearing in computational linguistics.

The vocabulary

• Morphology — how words are built from smaller meaningful parts.
• Generative grammar — a finite set of rules producing the valid forms of a language.
• Paleography — the study of old writing, and the skill of reading it.
• Semantics — the study of meaning.
• Lexicography — the making of dictionaries and word lists.
• Darshana — one of the classical schools of thought.
• Compound — a word formed by joining others, used heavily in Sanskrit.

The mental model

The scale of the material comes first. Many languages, several scripts, and a written record spanning millennia. That range is the raw material of the topic. The first thing to take in is that it is a range rather than a single tradition.

Sanskrit receives particular attention for two properties, and both are structural rather than a matter of prestige.

The first is regularity. Its morphology is unusually systematic. Words are built from roots by adding elements in patterned ways. A large vocabulary is generated by rules from a much smaller set of parts. That is what allowed a grammarian to describe the whole language in a few thousand short rules. Specific rules override general ones, and each rule assumes the ones before it.

That arrangement is what makes the comparison to formal grammar more than a flattering analogy. Rules, an ordering that resolves conflicts, and a mechanism generating valid forms are exactly the components of a generative grammar.

The second property is brevity. The tradition prized compactness, and compound formation lets long descriptions be packed into single words. That makes texts short and makes them hard, because unpacking a compound requires knowing which of several possible relationships was intended.

The proposed connection to computational language processing should be read carefully, and separating two statements is the whole skill.

The first statement is that the grammatical tradition is formally sophisticated and worth studying by anyone working on language computationally. That is well supported and widely accepted.

The second statement is stronger: that this makes the language especially suitable as a computer language, or uniquely fitted to machine processing. That one is contested, and the arguments against it are technical rather than cultural. Programming languages are designed for unambiguous parsing and are already far more regular than any natural language. A rich morphology is a difficulty for a parser, not an advantage.

Hold the two apart. The structural observation is real and interesting. The practical conclusion drawn from it is disputed, and a course that presents the second as settled has overstated the first.

Paleography is the skill that makes any of this accessible, and it is often overlooked. Scripts change over centuries, writing surfaces decay, and scribes make errors that later copies inherit. Reading an old manuscript is a technical field with its own methods, and every text discussed anywhere in this course reached us through it.

The mathematical techniques in this topic are presented as calculation shortcuts. The honest way to study them is to test them. Take several, try them on your own numbers, and sort them into general methods and special cases that work for particular shapes of number. Both kinds are useful, and knowing which you are holding matters when you use one.

Meaning and vocabulary received systematic treatment early, which connects directly to the logic topic at the end of this course. Analysing how a word gets its reference, and how a compound's parts relate, is formal semantics under another name.

The classical schools are the intellectual framework much of this material sits inside, and they differ from one another substantially. Treating them as a single outlook is the error to avoid; they disagree, and the disagreements are the interesting part.

Interpretation of older texts for the present is a question of reading rather than of fact. Different readings exist, they are held by serious people, and a course should present them as several readings rather than one.

What you should now be able to explain or do

Say what makes the morphology regular and how that supports a rule-based description. Explain why the comparison to a generative grammar is structural rather than flattering. Separate the well-supported structural statement from the contested practical one. Say what paleography is and why every text depends on it. Sort calculation techniques into general methods and special cases.

Check yourself