Varga Chart Mathematics

A planet at 29°59′ Aries and one at 0°00′ Taurus are one arc-minute apart, yet their navamsha signs are Sagittarius and Capricorn. The jump is not a calculation error. Varga mathematics turns continuous longitude into discrete symbolic bins; the bins are exact, while their meaning remains disputed.

The ninefold map

Let λ be sidereal longitude measured from 0° Aries. For the D9 navamsha:

r = floor(λ / 30)                 parent sign, 0–11
a = λ − 30r                       degrees inside that sign
j = floor(a / (10/3))             ninth, 0–8
v = (9r + j) mod 12               navamsha sign, 0–11

Each ninth spans 10/3° = 3°20′ = 12,000 arcseconds. Integer arcseconds avoid floating-point accidents at boundaries such as 6°40′ or 23°20′.

The compact formula reproduces the classical rule: movable signs begin from themselves, fixed signs from the ninth, and dual signs from the fifth.

Chart	Parts per sign	Width of one part	Zodiac bins
D1	1	30°	12
D9	9	3°20′	108
D10	10	3°	120
D60	60	0°30′	720

The arithmetic generalizes; the assignment rule does not. D2, D3, D9, D10, and D60 use different classical starting sequences.

Where precision breaks

The function is deterministic only after its inputs are fixed. Ayanamsha choice changes sidereal longitude. Birth-time error moves the ascendant, while uncertain boundary conventions can change the result at an exact cusp. D60 makes the problem visible: a single bin is only 30 arcminutes wide.

Correct code therefore proves reproducibility, not prediction. A calculator should retain the original longitude, ayanamsha, time standard, and boundary rule alongside every derived chart.

What the traditions claim

Parashari and Jaimini practice share the D9 arithmetic but ask different questions of its output.

Tradition	Primary D9 use	Interpretive unit
Parashari	spouse indications and planetary strength	planet qualified across D1 and D9
Jaimini	karakamsha and results from chara karakas	navamsha sign occupied by the atmakaraka

The Brihat Parashara Hora Shastra places navamsha among 16 vargas and assigns it a topic inside a weighted system. The Jaimini Sutras use the atmakaraka’s navamsha position to construct a new reference point. Later practice often combines both, but that combination is an interpretive choice, not a consequence of the equation. overview parashari system supplies the wider rule stack; concept vimshottari dasha supplies its timing layer.

What's contested

The first dispute is textual: should every varga be read as an autonomous 12-house chart, or chiefly as a qualifier of the natal chart and its significators? Parashari and Jaimini lineages do not give identical answers.

The second dispute is empirical. Varga-specific prediction lacks a widely cited blinded test. Carlson’s 1985 experiment tested natal astrology more broadly, not navamsha or competing varga rules. A fair D9 test would need preregistered ayanamsha, birth-time tolerance, boundary handling, interpretive rules, and outcomes.

Why this has to do with other realms

A varga is a quantizer. It discards position inside each bin and preserves a category, the same bargain made by digital audio and image compression. Assumption: all 108 D9 bins are equally likely. A D1-sign and D9-sign pair then carries no more than log₂(108) ≈ 6.75 bits about longitude.

That makes concept information theory a sharper bridge than mysticism. The further move from category to prediction belongs to concept bayesian updating: what evidence should change confidence in one interpretive rule over another?

An open question

Could Parashari and Jaimini rules be encoded as two executable specifications, then tested only on cases where they make different predictions from the D9?

Key Sources

Brihat Parashara Hora Shastra, attributed to Parashara, translated by R. Santhanam (1984), chapters 6–7. Online scan
Jaimini Sutras, translated by B. Suryanarain Rao (1933), Book 1. Digital reader
The Brihat Jataka by Varahamihira, translated by N. Chidambaram Aiyar (1905), chapter 1. Internet Archive
Shawn Carlson, “A Double-Blind Test of Astrology,” Nature 318 (1985), 419–425. DOI: 10.1038/318419a0

Abhishek's take

What grips me is the false confidence that precision can create. A function can place every longitude into the correct one of 108 bins while saying nothing about whether the interpretation attached to that bin predicts anything. I want the arithmetic encoded exactly because exact code makes the disputed claim easier to isolate and test.

Tags: #jyotisha #varga-charts #navamsha #astrology-mathematics #symbolic-systems

Abhishek