Namkha Calculator

Python library for calculating Namkha thread-cross color schemes in the tradition of Chögyal Namkhai Norbu Rinpoche, with all the methods covered in the source text.¹ Classical Tibetan astrology calculations were added for cases where the source refers to them for complete instructions.²

This library is the engine behind the Namkha Webapp, which provides a user-friendly interface and renders the results as a PDF.

Table of contents

• Development status
• Usage
  • API reference
    • Functions
    • Input
    • Timezone resolution
    • Errors
    • Result
  • Namkha types
    • Month Namkha
  • Calculation notes
    • Latitude "trimming"
• Contributing
• License
• Acknowledgments
• References

Development status

TODO

• Year Namkha calculation (CNNR and Classic)
• Birth-time edge-case warnings
• [WIP] Automatic historical timezone detection from coordinates
• Month Namkha calculation
• Day Namkha calculation
• Hour Namkha calculation
• More pre-calculated test cases
• Further investigation into the high-latitude regions problem

Acknowledgments

Whatever wisdom this contains belongs to the Tibetan astrological traditions and their holders; whatever faults it contains are our own.

We thank everyone who supported the Namkha Calculator project financially, on GoFundMe and through direct donations. Your help means a great deal to us, and it carried us through many obstacles!

We would also like to express our gratitude to:

• Migmar Tsering
• Maria Rita Leti
• Adriano Clemente
• Svante Janson
• Edward Henning
• Giovanni Totino, the director of Shang Shung Publications Italy
• Alexander Khosmo and Tatiana Ulyanova, for their guidance on Tibetan astrology
• the Gakyil of Merigar East – Oana Marcu and Krisztina Balla, for providing indispensable educational materials
• Karma Teleg Dondrup (tibastro.be)
• Sven Vandermeeren, Olli Hartikainen and everyone who supported us in the most challenging moments.

Usage

from datetime import datetime

import namkha_calculator as nc
from namkha_calculator.zone_derivation import resolve_timezone

birth_datetime = datetime(1985, 3, 15, 14, 30)  # naive local time
birth_location = nc.Location(latitude=52.52, longitude=13.40, name="Berlin")

# Work out the timezone once, before calculating.
resolved_timezone = resolve_timezone(birth_location, birth_datetime)

# Notes that follow from the birth details alone, known before any calculation.
for note in nc.input_notes(resolved_timezone, birth_location, birth_datetime):
    print(f"[{note.note_type.name}] {note.message}")

subject = nc.Subject(
    name="John Doe",
    gender=nc.Gender.MALE,
    birth_datetime=birth_datetime,
    birth_location=birth_location,
    resolved_timezone=resolved_timezone,
)

result = nc.calculate_namkha(
    namkha_type=nc.NamkhaType.YEAR,  # or NamkhaType.MONTH
    subject=subject,
    method=nc.CalculationMethod.CLASSIC,  # or CalculationMethod.CNNR
)

for aspect in result.harmonized_aspects:
    threads = ", ".join(e.value for e in aspect.harmonization_seq)
    conflict = " (conflicted)" if aspect.is_conflicted else ""
    print(f"{aspect.name.name}: center={aspect.center.value}, threads=[{threads}]{conflict}")

for note in result.calculation_notes:
    print(f"[{note.note_type.name}] {note.message}")

API reference

Everything here is available as nc.<name> after import namkha_calculator as nc. The one exception is resolve_timezone, which comes from namkha_calculator.zone_derivation.

Functions

Input

Location – latitude and longitude in decimal degrees, plus an optional name.

Gender – MALE or FEMALE.

NamkhaType – YEAR, MONTH, DAY or HOUR. See Namkha types for which of them the library calculates.

CalculationMethod – CNNR (Chögyal Namkhai Norbu Rinpoche's terma) or CLASSIC (classical Tibetan astrology). Only YEAR accepts CNNR.

Subject – birth data for one person, or for another entity with a known creation time, e.g. a company.

All fields are keyword-only.

Subject does not work a timezone out for itself. Call resolve_timezone first and pass what it returns, as the example above does.

Subject also has four read-only properties, all based on the resolved timezone:

ResolvedTimezone – the timezone a calculation runs on, frozen with the birth details it was worked out for.

Three more fields record the birth details this timezone belongs to: for_latitude, for_longitude and for_birth_date. assert_binds(location, birth_datetime) compares them and raises StaleTimezoneError when they differ. Subject and input_notes both call it, so a timezone worked out for another place or date can never reach a calculation.

modern_zone_key holds the zone covering the coordinates today. For a birth before 1970 that can differ from key. tzinfo rebuilds the timezone itself from key or offset_seconds. Every other field is a plain value, so the whole object stays hashable and picklable.

Timezone resolution

Call resolve_timezone once, before any calculation, and pass its result to Subject and to input_notes. It is the only place the timezone is worked out, and the only place that reads the coordinates.

It sits in its own module, apart from nc, because it does expensive map data calls, which the rest of the calculation never needs:

from namkha_calculator.zone_derivation import resolve_timezone

Timezone data is bundled with the package, so results are the same on every operating system, and every zone keeps its own real history from before 1970.

How the birth timezone is worked out:

• You provide zone_key or offset – that timezone applies, and derivation is CERTAIN. Pass only one of the two. zone_key is an IANA key from the bundled data, and nc.zone_keys() lists every one of them; offset is a timedelta, for a birth time known only as a UTC offset. The library checks either one against the birthplace first, because a wrong timezone can belong nowhere near it.
• You provide neither, birth from 1970 on – the zone covering the coordinates, again CERTAIN. Zone histories are guaranteed that far back, so a zone that later split for political or other reasons still gives the right rules.
• You provide neither, birth between 1880 and 1970 – standard time was still being introduced then, and the borders of modern time zones must not be projected back into that period. The library looks the birthplace up in bundled historical world maps (1880–1960, from historical-basemaps) and takes the zone that belonged to the same country in the birth year. The answer is an estimate and carries the TIMEZONE_ESTIMATED caution, or TIMEZONE_BORDERS_UNCERTAIN when the maps around the birth year disagree (see Calculation notes). If standard time had not reached that region yet, no caution follows: the clock then comes from the longitude, not from the zone. This case is still work in progress.
• You provide neither, birth before 1880 – the oldest map is drawn for 1880 and says nothing about earlier borders, so no country is looked up. The zone covering the coordinates today is kept. What the clock showed at the birth comes from that zone's own history. Almost everywhere that is still the mean solar time of the birth longitude, with the LOCAL_MEAN_TIME notice and no caution, because the zone did not provide a concrete offset. A few places had a civil clock this early, London from 1847 among them. There the zone does decide the clock, so the TIMEZONE_ESTIMATED caution follows.
• You provide neither, open water or a point in no timezone – the nautical Etc/GMT±N zone for the longitude, or, where no timezone matches at all, the longitude's mean solar time. Both are estimates.

Each country introduced standard time on its own date, some as late as the 1950s. Until that date, whatever zone applies, the birth runs on the mean solar time of the birth longitude and gets the LOCAL_MEAN_TIME notice. This overrides a zone_key you provide as well, because no zone was in use yet.

The zone key is then not the name the clock carried, so ask nc.timezone_label(resolved_timezone, birth_datetime) for the name you show a reader. It returns "mean solar time" when the offset came from the longitude, None when you provided a bare offset, which is then the whole answer, and the zone key in every other case.

on_summer_time says which reading of an ambiguous fall-back hour applies. It is kept only when the birth time really falls in a repeated hour; anywhere else it decided nothing and is dropped.

Birth dates are proleptic Gregorian; a Julian-calendar source date must be converted first (see the PRE_GREGORIAN_DATE caution under Calculation notes).

Errors

Bad input raises. Nothing is quietly replaced by a second-best answer.

The three timezone errors share the base class TimezoneError, which is itself a ValueError. The two timezone checks run only on a timezone you provided. A timezone the library derives already matches the location.

Result

NamkhaCalculationResult

Every field is filled on every result.

The three birth_* fields describe the birth period, which is the period the requested NamkhaType names: the birth year for YEAR, the birth month for MONTH. The field names keep the birth_ prefix for every type.

mewa_numbers holds four keys: MEWA_LIFE, MEWA_BODY, MEWA_CAPACITY and MEWA_FORTUNE. Each value is an int that also carries .element, the Element that mewa number stands for.

HarmonizedAspect

CalculationNoteItem

note is the one to branch on. message is written for a developer reading a log; an application showing notes to a reader is expected to supply its own wording per note.

Element and Animal are str enums, so a value is its canonical name in English: Wood, Fire, Earth, Metal, Water, and Mouse, Ox, Tiger, Hare, Dragon, Snake, Horse, Sheep, Monkey, Bird, Dog, Boar.

Namkha types

The library calculates YEAR and MONTH. DAY and HOUR are already in NamkhaType, but calculate_namkha raises NotImplementedError for them.

YEAR accepts both methods, CNNR and CLASSIC. Every other type accepts CLASSIC alone and raises ValueError for CNNR.

Month Namkha

The Tibetan month of birth is resolved from the birth instant, the same way the year is. A Tibetan month begins at the dawn that begins its first day, so a birth before that dawn belongs to the month before. A birth close to that dawn, or to the one that begins the next month, gets the PERIOD_BOUNDARY caution (see Calculation notes).

A birth in a leap month gets the number, element, animal and mewa of the regular month it precedes.

The month element and animal follow the Phugpa formulas Janson gives (see ³, section E.2: Attributes for months, under "Animals" and "Elements"). The library checks them against every month header in Henning's output over the years 1800–2598.

The month mewa steps back by one each month, across the year boundary too. It is pinned by a single anchor: the Tiger month opening a Tiger astrological year has mewa 2.

No Phugpa source prints a month mewa, so these numbers are a reconstruction. They come from two sources: Janson's Tsurphu formula (see ³, section E.2: Attributes for months, under "Numbers"), the reverse order, and the triples the Vaidurya dkar po gives per month animal (see ¹, section 10: THE NAMKHA FOR HARMONIZING THE ELEMENTS OF THE MONTH OF BIRTH).

Calculation notes

result.calculation_notes carries every note. All but PERIOD_BOUNDARY follow from the birth details alone, and input_notes(resolved_timezone, location, birth_datetime) returns those without running a calculation. PERIOD_BOUNDARY needs the calculation itself, so only the result has it.

PERIOD_BOUNDARY (caution) is attached when the birth time falls within 5 minutes of a calculation-period boundary: for YEAR, the Tibetan year start/end; for MONTH, the dawn that begins the month and the dawn that begins the next. That close to a boundary the result can flip to the neighboring period, so the birth time must be precise.

HIGH_LATITUDE (notice) is attached when abs(latitude) >= 60.0. Above this limit the library falls back to a fixed 5:00 AM day-start instead of civil twilight, which affects birth period boundary detection.

AMBIGUOUS_LOCAL_TIME (caution) is attached when the clocks went back and the naive birth time therefore happened twice that day. The library reads it as standard (non-DST) time. Pass on_summer_time to resolve_timezone to choose the other reading; the note then becomes a notice: AMBIGUOUS_LOCAL_TIME_RESOLVED.

The opposite case is an error: a time the clocks skipped going forward, or a whole date dropped by a dateline jump. A birth time that never happened at all is rejected with a ValueError.

TIMEZONE_ESTIMATED (caution) is attached when no timezone was given and it could not be derived from the location and date with certainty (pre-1970 birth, or birth on open water); the best historically recorded regional time was used.

There is one exception. For the dates where time standardization has not reached the birth region, the offset is read from the birth longitude instead of from the zone. The zone then has no effect on the result, so the caution is left out and the birth carries only the LOCAL_MEAN_TIME note.

TIMEZONE_BORDERS_UNCERTAIN (caution) is attached instead of TIMEZONE_ESTIMATED. A birth never gets both.

The historical maps are snapshots at fixed years. When the snapshot before the birth year and the one after it put the birthplace in different countries, the library cannot tell which country held it at the moment of birth. Each country implies its own clocks, so an uncertain country means an uncertain zone.

Borders that changed and changed back between two snapshots are invisible to the maps, and no open dataset we know of can fill that gap. The Soviet occupation of eastern Poland from 1939 to 1941, which imposed Moscow time, is one such case.

To settle it, look up the birthplace's legal time in historical sources and pass it to resolve_timezone as zone_key. The World Historical Gazetteer is a good place to start: it tracks which state a place belonged to over time.

LOCAL_MEAN_TIME (notice) is attached when the birth clock time was read from the longitude, not from civil timezone rules. That happens before standard time reached the region, on open water, and outside every timezone. It also happens where the timezone data holds no clock at all, as in the far north of Canada: the records for Iqaluit begin in 1942 and those for Inuvik in 1953. A birth before the records start keeps the TIMEZONE_ESTIMATED caution: the library guessed that clock.

PRE_GREGORIAN_DATE (caution) is attached to births before the Gregorian calendar was adopted at the birth place (15 October 1582 at the earliest, as late as the 1920s in some regions), as a reminder that a Julian-calendar source date must be converted to Gregorian.

Latitude "trimming"

In the Tibetan calendar a new day begins at dawn, not at midnight. The library defines dawn as the start of civil twilight – the moment the sky first starts to brighten before sunrise (in traditional texts, when one can see the lines on the palm of their hand). This boundary decides which Tibetan hour (and therefore Tibetan day, month, etc.) a given birth time belongs to.

Closer to the poles (i.e. at higher latitudes) this breaks down. For long parts of the year there is no dawn: the midnight sun in summer, when the sky never fully darkens, and the polar night in winter, when it never properly brightens. On those dates civil twilight does not start (or does not end), so there is no dawn to anchor the day to and the astronomical lookup returns nothing.

As far as we know, Tibetan astrologers have not agreed on a solution to this problem. For now the library does the following: it "trims" the usable latitude range at 60° north/south. Below that limit it uses the real civil-twilight dawn. At or above it, it falls back to a fixed 5:00 AM local time (a convention also found in Tibetan tradition) as the day-start and attaches the HIGH_LATITUDE notice. This issue is a subject of further research.

Contributing

Issues, PRs and questions are welcome.

See CONTRIBUTING.md for details.

License

GPL-3.0-or-later. The package bundles:

• historical world border maps from aourednik/historical-basemaps (GPL-3.0) – bundling them is why this project is GPL rather than MIT;
• an IANA tzdb zoneinfo tree compiled with backzone data (public domain);
• a filtered JPL DE440 ephemeris (public domain).

Timezone boundary lookups use timezonefinder (MIT), whose boundary data derives from timezone-boundary-builder (ODbL).

References