TALAMANA · THE AI LITERACY MAP FOR ARCHITECTURE AND DESIGN · Foundations · AGE 12—15 · FACTUAL · DURABLE
Early algorithms: the Sulba Sutras
A rule that works is knowledge, even when nobody has written why.
The idea
Before the word "algorithm" existed, Indian priests needed altars of set shapes: a square of a given area, a square twice another, a circle close in area to a square. The Sulba Sutras — texts attached to the Vedas, the earliest usually dated to around 800 BCE — give the steps: peg, cord, arc, mark. Some are exact; the circle-and-square ones are good approximations, and the texts do not say which is which. One rule gives the square root of two to five decimal places. A rule that reliably produces a result is knowledge, even when nobody has written why it works.
Why it matters
Knowing how to do something, step by step, is a kind of knowledge. Machines run on exactly this kind. So did builders nearly three thousand years ago.
See it in the studio
On site, a mason sets out a right angle with a 3-4-5 rope triangle. No protractor, no theorem recited, only a procedure that works. The Sulba Sutras carry the same knowledge. The procedure is the knowledge.
Watch for this
Thinking a step-by-step rule is "lower" than an explanation. The texts give no proofs, and they mix exact methods with approximations without saying which is which. That is a fair warning about every rulebook, including the ones inside machines. And do not call these "the oldest" algorithms: Mesopotamian procedures are older. The Sulba Sutras are an early and remarkable example, and that is enough.
Try it
With a cord and two pegs (string and two pencils will do), construct a square using only arcs and straight lines, never the markings on a ruler. Write your steps as a numbered list. Hand the list to a friend and see whether they get a square.
Prove it
Construct a square with string and pegs, explain each step, and say which step would go wrong if you skipped it.
How it works
"Sulba" means cord or rope. The four main texts — Baudhayana, Apastamba, Manava, Katyayana — open with geometric and arithmetic constructions and end with instructions for building altars. The constructions include the rule we now call the theorem of Pythagoras, stated as a procedure rather than a proof, and a value for the diagonal of a unit square: 1 + 1/3 + 1/(3×4) − 1/(3×4×34), which is 577/408, the square root of two to five decimal places. Historians date the texts between roughly 800 and 200 BCE; as with most texts of that age, the dates are uncertain.
What this idea builds on
- A starting idea.
What this idea opens up
Sources
Open this idea on the map · The complete map · Logika · RBDS AI Lab, India · revised every edition.