Vāstu - Āyādi: The Arithmetic Behind the Six-Fold Test

Every operator in the āyādi has the identical shape. Multiply the dimension by a small constant, divide by a modulus, keep the remainder. In modern notation, (k × d) mod m. There is nothing else in it.

What makes it more than an exercise is the choice of moduli. They are the counts of real cycles — seven weekdays, twenty-seven asterisms, thirty lunar days, along with twelve, ten and eight. The system is projecting a single linear dimension onto a set of calendrical and categorical rings at once, and reading off where it lands on each.

That is a genuinely elegant construction, and it is worth being clear that it is not numerology in the modern dismissive sense. It is a deterministic function from a measurement to a set of categories. Whether those categories mean what the tradition says they mean is a separate question, and the arithmetic has no opinion on it.

This matters more than it sounds, because two practitioners running "the six-fold test" on the same house can be running different functions.

Mānasāra applies the operators to length, breadth and circumference separately:

Mayamata applies every operator to the single quantity (length + width). Bhavan Bhāskar runs a six-fold reckoning on the product, calling it the pada. Vāsturatnākara runs a nine-fold reckoning on the piṇḍa.

Four texts, four different inputs. The operators are recognisably the same family; what they are applied to is not. Any calculator, and any reading, should declare which recension it follows. Two results that disagree may not be a disagreement about the house at all.

This is the one implementation trap, and it is easy to fall into.

Both Bhavan Bhāskar's worked example and the Vāsturatnākara's read a remainder of zero as the divisor itself. Dhana of 0 is read as 12; Aṃśa of 0 is read as 9. A naive modulo returns 0 and silently drops the case.

The correct form is ((k × d − 1) mod m) + 1. Any implementation that uses (k × d) mod m is wrong for exactly one input in every m, and will look right the rest of the time — which is the worst kind of wrong.

Once the numbers are out, the rule is a comparison, and the recensions agree on it even where they disagree on everything else: āya must exceed vyaya. Gain over loss. Mānasāra and Mayamata compute the two quantities differently and then do the same thing with them.

Bhavan Bhāskar's own example: breadth 15 hāth, length 25 hāth, so the pada is 375.

All six reproduce exactly. The book's verdict — everything auspicious except the weekday — follows from its own arithmetic.

The Vāsturatnākara's nine-fold reckoning is a different matter. Running its printed operators against its own printed answers, for a piṇḍa of 687:

Seven of nine reproduce. Two do not — and the Aṃśa operator as printed is not merely wrong, it is degenerate: ×6 mod 6 is identically zero for every possible input, which cannot be anybody's rule.

Two single-digit changes repair both

• Vāra: multiplier 6 → 9. Then 687 × 9 mod 7 = 2, the book's own answer.
• Aṃśa: divisor 6 → 9. Then 687 × 6 mod 9 = 0, read as 9, the book's own answer.

With those two changes all nine reproduce exactly. And the corrections are independently corroborated: Bhavan Bhāskar's six-fold list, from a different text and a different lineage, gives Vāra as ×9 mod 7 and Aṃśa as ×6 mod 9 — precisely the corrected forms.

This is a proposed correction, not a ratified one. It should be checked against the printed Sanskrit before anyone enters it anywhere as fact. The evidence that it is a transmission error rather than a genuine variant is strong — the corrected operators reproduce the source's own answers, and the uncorrected one is mathematically impossible — but strong evidence is not the same as a manuscript.

The same source lists a set of regularities so the practitioner can internalise the table rather than consult it. One of them states that for the four auspicious āyas 1, 3, 5, 7, the ṛṇa runs 2, 1, 7, 5.

Computed across the full range, with the operators as corrected above, it runs 3, 1, 7, 5. The last three agree. The first does not: an āya of 1 forces a ṛṇa of 3, and no input produces 2.

Also recorded as a proposed correction, and also unratified. Three suspect digits in one neighbourhood of one text is a pattern worth someone's attention at the manuscript rather than a reason to lose confidence in the system — the rest of it reproduces to the digit.

Every figure in this article was recomputed with exact integer arithmetic, using the zero-as-modulus convention throughout, and is reported with the operation that produced it.

Measure and Number in Vāstu is a five-part series in the OccultSanctum library. Our daily tools — live panchang, muhurat and chart work — are in Vedic Samay, free on the App Store and on Google Play.