Graha Maitri: two scoring conventions, one silent choice

Two scoring conventions are in circulation for this koota, and almost nothing tells you which one you got. Graha Maitri is worth 5 points of the thirty-six, and one influential source calls it the most important of the eight. It compares the planetary lords of the two moon signs and asks how those two planets are held to regard one another. Across all 11,664 possible pairings of birth star and pada, 38.9% score full marks.

The two conventions agree at the top of the scale and they agree at the bottom. In between they part company, and the gap between them is not decorative: it covers a third of the possible planet pairings. A calculator that prints a Graha Maitri line without naming its scale has given you a number whose provenance you cannot recover.

Two planets, arrived at by way of two moon signs

Each of the twelve signs has a ruling planet. There are seven planets for twelve signs, so five of them rule two signs each and two — the Sun and the Moon — rule one apiece. Take the sign each person’s Moon occupied at birth, take its lord, and from that point on the koota has stopped being about two people and become a question about two planets.

That substitution is doing a lot of quiet work. Twelve signs collapse into seven lords, which means a great many different pairs of birth charts arrive at the identical Graha Maitri cell. A Taurus moon and a Libra moon are the same input to this koota, because Venus rules both. The rashi calculator will tell you which sign a birth moment lands in, and the lord follows from the sign without any further judgement.

It also fixes the outer limit of what this koota can know. Two moon signs, two planets, one cell in a table. There is no access to temperament, to circumstance, to family finances, or to any of the things the empirical literature on Indian marriage identifies as actually shaping outcomes, and Rao’s work on the economics of the marriage market is a fair sample of how different that material looks from a table of planetary friendships. We describe what named traditions conclude and how common each conclusion is across the whole population. We do not forecast, and nothing on this page is a statement about a person.

Where the two lords turn out to be the same planet, the koota awards its maximum outright. That alone accounts for a substantial share of the full-marks rate, and it is why two people born under quite unrelated stars can clear this component completely: Aries and Scorpio are both ruled by Mars, so the pairing scores five before any friendship question is asked.

Full marks are also awarded when the two lords are mutual friends. There are six such pairs in the classical lists: the Sun with the Moon, the Sun with Mars, the Sun with Jupiter, Mars with Jupiter, Mercury with Venus, and Venus with Saturn. Same-lord pairings plus those six are the whole of the full-marks region, and together they are what produce the measured rate.

Why is the friendship table not symmetric?

Because the classical lists say it is not, and that asymmetry is the engine of the whole koota. Natural friendship between planets is a directional relation. The Moon counts Mercury a friend. Mercury counts the Moon an enemy. That is not a transcription slip and it is not a scribal accident; the sources that record these lists are unanimous on it, which is rare enough in this subject to deserve a pause.

The koota then scores the pair and not the direction, by reading both relations at once and combining them. Both friendly is the top. Both hostile is the bottom. Friend one way and neutral the other, neutral in both directions, friend one way and enemy the other, neutral one way and enemy the other — those are the intermediate cases, and every one of them exists only because the underlying relation runs in one direction at a time.

A symmetric friendship table would collapse this koota to three possible scores.

Which is a real risk, incidentally, not a hypothetical one. A programmer tidying an untidy-looking table into a symmetric one would destroy the middle of the scale while leaving every top and bottom cell intact, and the resulting totals would still look entirely plausible. Our friendship table asserts the Moon-and-Mercury asymmetry by name at load time for exactly that reason: so the tidy-up fails loudly instead of quietly.

One more feature of the lists deserves stating, because people rediscover it and assume something is missing. The Moon has no enemies at all. It counts the Sun and Mercury as friends and the other four as neutral, and the empty enemy list is the data instead of a gap in it. Other planets remain free to count the Moon an enemy, and Mercury, Venus and Saturn all do.

Where do the two scoring conventions part company?

On the two mixed cases that involve an enemy, and nowhere else. Both scales award the maximum for mutual friendship, the same value for friend-and-neutral, the same value for neutral-in-both-directions, and nothing at all for mutual enmity. Four of the six relation types are agreed.

They differ on the remaining two. Where one party counts the other a friend and is counted an enemy in return, the standard scale awards a single point and the alternative awards two. Where the relation is neutral one way and hostile the other, the standard scale awards half a point and the alternative awards a full one. The alternative descends from a different classical lineage — it can be read in the Saravali scan — and it is not a rounding of the first.

The friend-and-enemy case is narrower than it sounds. Across the whole seven-planet table there is exactly one such pair: the Moon and Mercury. Everything else that involves an enemy involves a neutral on the other side. So the two-versus-one disagreement fires only when one moon sign is Cancer and the other is Gemini or Virgo, and the half-point-versus-one-point disagreement carries the rest of the load.

Six pairs sit in that second cell: the Moon with Venus, the Moon with Saturn, Mars with Mercury, Mars with Saturn, Mercury with Jupiter, and Jupiter with Venus. Seven disputed pairs in total, out of twenty-one distinct planet pairings. Exactly a third of the table is scored differently depending on a choice nobody was told about.

How many possible pairings does that choice touch?

Close to one in three under equal weighting, and the direction of the change is always upward. Because five of the seven planets rule two signs apiece, a third of the planet pairings does not translate into a third of the sign pairings by any obvious arithmetic, so we ran it out instead of reasoning about it. Scored across the complete set of ordered star-and-pada pairings, the alternative scale changes the Graha Maitri result for close to thirty in every hundred.

Every one of those changes raises the score. The alternative scale never awards less than the standard one; it awards more in two cells and the same everywhere else. A calculator quietly running the alternative will therefore produce totals that trend high, and a couple comparing two reports will see a discrepancy that looks like one of the two being generous rather than one of the two following Saravali.

The zero, by contrast, is barely reachable. Mutual enmity exists for two planet pairs only, the Sun with Venus and the Sun with Saturn, and the Sun rules a single sign. So the entire bottom of this koota is a Leo phenomenon: unless one of the two moons is in Leo, no scale in circulation can score this component at nothing. That is why the measured zero rate comes out at only 5.6%.

The mean score across the whole population is 3 of five, which is a comfortable middle. This is not a koota that fails people often. It is a koota that shifts them by a point in a region where a point can matter.

Neutral one way, hostile the other

Priya’s birth star is Ashwini, which puts her Moon in Mesha, ruled by Mars. Arjun’s is Purva Bhadrapada, which puts his in Kumbha, ruled by Saturn. Mars regards Saturn as neutral. Saturn regards Mars as an enemy. They have landed squarely in the second of the two cells the conventions disagree about.

Under the standard scale that pairing takes half a point of 5, and their North Indian total comes out at seventeen. Under the alternative it takes a full point and the total is seventeen and a half. Neither reaches the conventional accept line, so in this instance the choice changes the number without changing the verdict.

That is the honest version of the example, and it stays in for that reason. Half a point is often nothing. What makes it matter is that it is not always nothing, and the couples for whom it is decisive cannot tell they are those couples until somebody names the scale. Everything else about their reading — the totals from thirteen and a half to seventeen across five traditions, with the two lowest scores being the two that accept — is on the guna milan tool, variant by variant.

Both of those lords, though, rest on a birth time. The Moon crosses a sign boundary roughly every two and a half days and the lord changes with the sign, so a birth recorded from memory can hand this koota an entirely different planet and produce a defensible-looking score for a pair of charts nobody actually has. Our positions come from JPL’s DE440 ephemerides, which removes one source of error and leaves the important one untouched: what time it actually was.

Notice also what did not happen. Nobody made a mistake. Two competent practitioners working from two published lineages would produce two different numbers here and both could defend theirs from a printed page. This is the situation the page on software and verdicts describes across the whole engine, and Graha Maitri is its quietest example, because it produces no headline, only a total a point or so away from someone else’s.

Why does half a point matter more than it sounds?

Because of where the threshold sits relative to the pile. Eighteen of thirty-six is the conventional accept line; 66.7% of pairings clear it and the mean total is 20.1. The line therefore cuts through the densest part of the distribution instead of through its tail, and a component that moves a chart by a point is operating in the crowded region by construction.

Push the line up and the picture gets starker. Only 49.5% of pairings reach twenty-one, and 33.8% reach twenty-four. A family that has been told to hold out for a high score is holding out for something the distribution makes uncommon, which is a separate problem but not an unrelated one. The page on where the eighteen came from takes that up properly.

Half a point is also easy to lose track of because it is the only fractional value in the entire system. Seven kootas award whole numbers. Graha Maitri, on the standard scale, awards a half.

So a total ending in “point five” is coming from this koota and nowhere else, which is a small piece of forensics to keep in your pocket when two reports are open on the table in front of you. It also feeds the wider measurement: counting every axis on which the five traditions we compare can disagree, 56.4% of enumerated pairings trigger a tested difference or veto. That aggregate does not isolate Graha Maitri, and the alternative scale compared here is not a default of the five presets.

How do you know the friendship table itself is right?

Because it is stated twice in the sources, and the two statements are checked against each other. The reference document behind our tables prints the friend, neutral and enemy lists for all seven planets, and separately prints the fully expanded planet-by-planet point matrix those lists are supposed to generate. Those are two independent statements of the same fact.

We encode both. At load time the engine derives every one of the forty-nine cells from the friendship lists and compares each against the transcribed matrix; a single disagreement stops the code instead of producing a slightly wrong score for one couple in a few dozen, forever. A mistyped cell in a forty-nine-cell grid is invisible to review, and there is no way to catch it by reading harder.

This is not a claim that the classical lists are correct in some deeper sense. It is a much narrower claim, and the only one available: that what we compute is what the named sources say, and that a transcription error cannot survive between the source and the report. Whether the Moon should count Mercury a friend is not a question a checksum can answer.

Historically, planetary friendship doctrine arrived in India entangled with a great deal of imported Hellenistic material, and Pingree’s account of that transmission is the standard treatment. The lists themselves are set out in the Brihat Parashara Hora Shastra, which is where most practitioners would point if asked. Neither text explains why Mercury dislikes the Moon.

The table is agreed; the scale over it is a choice

That split is unusual, and there is no neutral option inside it. On most of the eight kootas the disagreement is about the underlying data: which sign carries which label, which animal pairs badly with which. Here the data is unanimous across the major sources and the argument is entirely about arithmetic.

Which is, if anything, harder to resolve. A disagreement about a table can sometimes be settled by finding an older printing. A disagreement about how many points a friend-and-enemy relation deserves has no evidence that could settle it, because both scales are asserted and neither is derived, and neither text offers a reason.

So choosing the standard scale is a choice, choosing the alternative is a choice, and running software that silently picks one is also a choice — just one the reader was never shown. The defensible position is not to have no position. It is to name the position and say what the other one would have produced.

There is a case for arguing with all of it. The two scales differ only in the direction of generosity, which means the choice is not really a doctrinal one for most software authors; it is a default nobody examined. And the koota it governs is one column of eight, carrying five of the thirty-six points while the other seven carry thirty-one, so treating it as the important one because a printed source called it important is an argument from authority and not from arithmetic. The koota-by-koota breakdown shows how many other components carry the same kind of unexamined default.

If the Graha Maitri score is doing real work in your reading — if it is the koota that carried the total under the line — there is one question to put to whoever produced it, and the graha maitri tool will let you check the answer. Ask which planets rule the two moon signs, and what each is held to be to the other. If one counts the other a friend or a neutral while being counted an enemy in return, you are standing in the cell where the two conventions disagree, and the number you were handed rests on a decision that was never stated out loud.