E - Comparative Calendars & Design Context

Different Answers to Different Calendar Problems

E.1 Purpose

Solarian did not emerge into an empty field.

Humans have been designing and reforming calendars for thousands of years. Modern organisations already use week-based operating calendars alongside conventional civil dates. Mars alone has inspired dozens of published calendar proposals, while previous work has extended planetary calendar design to the moons of Jupiter and Saturn.

This appendix places Solarian within that broader design landscape.

It is not intended to identify a winning calendar.

That would miss the more useful point.

Different calendar systems optimise different things.

A design that prioritises seasonal fidelity may reasonably look different from one that prioritises continuous weeks. A calendar designed specifically for Mars may make different choices from a protocol intended to remain recognisable on Ceres, Titan, Neptune and an artificial habitat.

The useful comparison is therefore:

What problem is each calendar trying to solve?

rather than:

Which calendar is best?

E.2 Calendars are bundles of design choices

A civil calendar has to make several decisions that are easy to confuse with one another.

It must decide, explicitly or historically:

• what counts as a civil day;

• whether the week is continuous;

• how many intermediate periods divide the year;

• whether those periods are equal in duration;

• whether they correspond to astronomical phase;

• how astronomical remainder is intercalated;

• where New Year begins;

• whether dates recur on fixed weekdays;

• how much inherited cultural vocabulary is preserved;

• and whether the calendar is intended for one world or several.

There is no astronomical theorem that selects one correct combination.

The same physical world can support several coherent calendars because the requirements differ.

Mars demonstrates this particularly well.

A major review by Thomas Gangale and Marilyn Dudley-Rowley reported more than seventy authors publishing Martian timekeeping proposals over the preceding 125 years.

The astronomy was the same.

The design briefs were not.

E.3 Gregorian — inherited civil infrastructure

The Gregorian calendar solves a very specific terrestrial problem remarkably successfully.

It keeps the civil year closely aligned with Earth's seasonal year using:

• twelve inherited months;

• years of 365 or 366 days;

• leap-day intercalation;

• and a continuous seven-day week.

Its months vary between 28 and 31 days.

Month boundaries and year boundaries move through the weekday sequence.

Those properties are inconvenient for some operating purposes, but they are outweighed on Earth by an enormous advantage:

almost everyone already uses it

Gregorian is embedded in law, commerce, culture, religion, software, archives and everyday life.

That makes it extraordinarily powerful infrastructure.

It does not make its architecture universal.

Gregorian answers:

How should terrestrial civil society organise the terrestrial year while preserving a long inherited calendar tradition?

Solarian asks a different question.

E.4 The 4-4-5 family — operations before astronomy

Modern business provides a useful counterexample to the assumption that civil months are always the most practical operating units.

Week-based fiscal calendars commonly organise a 52-week year into periods of:

4 weeks · 4 weeks · 5 weeks

repeated across thirteen-week quarters.

Variants such as:

4-5-4

and:

5-4-4

use the same basic logic.

Formal accounting practice also permits 52–53-week tax years whose year-end remains tied to a consistent weekday. The United States Internal Revenue Service, for example, explicitly recognises 52–53-week fiscal years.

The important idea is not the specific accounting convention.

It is the design objective.

Gregorian optimises continuity with civil history.

A 4-4-5 calendar optimises comparability between operating periods.

A four-week period always contains four complete weeks.

A thirteen-week quarter always contains thirteen complete weeks.

Monday-to-Sunday trading patterns do not change merely because February happened to be involved.

The frozen Solarian manuscript uses this as an important terrestrial analogy: Earth already layers operating calendars over Gregorian when organisations need cleaner week-based cadence.

Solarian's Earth R1 calendar consequently resembles the 4-4-5 family closely.

But the direction of reasoning is different.

4-4-5 starts from an Earth business problem.

Solarian arrives at a similar form after applying a multi-world architecture back to Earth.

E.5 Mars — where the choices become visible

Mars is an unusually productive calendar laboratory because some terrestrial relationships survive while others do not.

Its natural solar day remains close to twenty-four Earth hours. Its seasons remain recognisable. Its year, however, lasts roughly twice as long as Earth's.

That creates several legitimate design choices.

Should Mars retain twelve months? Should it use twenty-four, keeping each month closer to familiar terrestrial duration? Should every month begin on the same weekday? Should the seven-sol week remain absolutely continuous? Should a month represent elapsed time or orbital angle? Should familiar Earth month names survive?

There is no uniquely astronomical answer.

Several historically important proposals illustrate the trade-offs.

E.6 Levitt — keep twelve months

I. M. Levitt's Martian calendar retained a twelve-month annual structure.

In the form described in later comparative work, most months contain 56 sols, while four contain 55. That produces months of approximately eight Martian weeks and preserves a familiar twelve-part annual hierarchy. In short months, maintaining fixed month-start weekday positions requires interruption of the ordinary seven-sol sequence.

The architectural choice is clear.

Levitt preserves: twelve months per year and relatively regular month structure.

The consequence is that a Martian month becomes almost twice as long as the familiar terrestrial one.

That is a coherent choice if continuity of annual structure matters more than continuity of familiar month duration.

E.7 Darian — keep the month human-scaled

Thomas Gangale's Darian Calendar makes a different choice.

It divides the Martian year into: 24 months

mostly containing: 28 sols with shorter 27-sol months used to reconcile the year.

This keeps most months close to four seven-sol weeks and therefore close to the familiar human scale of a terrestrial month.

Darian also makes the calendar perennial. Each month begins on the same weekday position. A particular numerical date therefore always falls on the same weekday. That regularity has a cost.

At the end of a 27-sol month, the normal seven-position weekday sequence is shortened so that the following month can begin again on its designated first weekday.

This is not an error. It is a design trade.

Darian gives priority to: stable date–weekday relationships

And: human-scale months

Over: an inviolable continuous seven-position week

Solarian makes the opposite choice on the week.

E.8 Šurán — preserve whole weeks

Josef Šurán's 1997 proposal is particularly relevant to Solarian because it takes the week seriously as an indivisible unit.

His common Martian year contains: 672 sols

arranged into: 24 × 28-sol months

Or: 96 complete seven-sol weeks

In shorter years, one complete week is omitted rather than breaking the weekday sequence.

That produces: 672-sol years

And: 665-sol years while preserving complete weeks.

This is an important precedent.

Solarian does not claim to have invented the idea of correcting a planetary calendar in whole weeks.

Šurán had already demonstrated that principle on Mars.

What Solarian does is generalise whole-week correction into a wider architecture in which:

• minths;

• mears;

• orbital months;

• years;

• expansion joints;

• and multiple worlds

all sit on the same structural logic.

E.9 Zubrin — make the month astronomical

Robert Zubrin approaches the Martian month from almost the opposite direction.

Instead of dividing the year into broadly equal periods of elapsed time, his proposal treats a month as approximately: 30° of Martian orbital travel

Because Mars moves at different speeds around its eccentric orbit, those months contain substantially different numbers of sols.

This gives the month a strong astronomical meaning. A month describes a consistent angular section of Mars's path around the Sun.

The price is irregular elapsed duration. This is precisely the trade-off explored later in Solarian's Pluto analysis.

Equal-angle divisions maximise orbital-phase fidelity. Equal-time divisions maximise temporal regularity.

On moderately eccentric worlds the two can remain close enough to coexist. On highly eccentric ones they eventually pull apart.

Zubrin therefore represents a different answer to the question: What is a planetary month for?

E.10 Exodus — maximise familiarity

Dennis Silin's more recent Exodus Calendar returns to a twelve-month structure and deliberately emphasises familiarity.

The published proposal uses the familiar terrestrial month and weekday names. Eleven months contain 56 sols, while December absorbs the year-form difference and varies in length. The calendar uses a repeating 22-year intercalation cycle containing 668-, 669- and 670-sol years.

The objective is unusually explicit: reduce the amount a future Martian resident has to relearn.

That produces a very different design from Darian despite both calendars representing exactly the same planet.

Darian preserves something closer to familiar month duration.

Exodus preserves familiar month count, names and weekday vocabulary.

Again, neither choice is dictated by Mars. They reflect different assumptions about cognitive migration from Earth.

EJ.11 Marian — separate the human and astronomical jobs

The Marian Calendar developed by the present author is the immediate intellectual precursor to Solarian.

Its key architectural move is to stop insisting that one intermediate unit perform both of the jobs historically bundled inside Earth's month.

It separates: a roughly four-week human operating interval

From: a one-twelfth-of-year astronomical month

The main text describes Marian explicitly in those terms. That separation matters.

Once month-as-human-cadence and month-as-orbital-division are recognised as different functions, there is no longer any reason they must remain identical in duration.

On Mars, both still fit together reasonably comfortably.

Solarian takes the next step and asks whether the same distinction survives on worlds where the orbital year lasts:

• five Earth years;

• twelve years;

• thirty years;

• eighty-four years;

• or 165 years.

The answer is the mear/month separation developed throughout this book.

E.12 A useful comparison of the Mars designs

The major Martian approaches can be compared by what they preserve.

The table is not a scorecard.

Each column represents an objective that a designer may value differently.

That is exactly the point.

E.13 Beyond Mars — Darian extensions

Planetary calendar work has not stopped at Mars.

Gangale extended Darian-style time architecture to the four Galilean moons and later to Titan.

Those designs are particularly relevant because they confront a problem Earth and Mars largely hide:

the local astronomical cycles cease to sit comfortably at human social scale

The Galilean work explored locally useful circads and week structures rather than simply imposing Earth's day unchanged. For some Galilean calendars, whole weeks rather than individual days were also used for intercalation. Gangale's Titan work likewise treats local physical cycles as design inputs rather than assuming terrestrial time units must simply be copied outward.

This is important prior work.

It establishes that planetary calendrics need not mean: Gregorian, but on another planet.

It also demonstrates that calendar design can be treated as a general problem of time architecture rather than merely date naming. Gangale and Dudley-Rowley explicitly used that broader framing in their work on extended space missions.

Solarian shares that systems perspective.

It differs principally in what it tries to standardise across destinations.

E.14 Synthetic years versus orbital years

The outer Solar System introduces a fundamental choice.

Consider Saturn.

One Saturnian orbit lasts almost thirty Earth years. A civil designer can reasonably respond in two ways.

Option A — create a shorter synthetic civil year

The word year remains human-scaled. The physical Saturnian orbit is represented separately.

Option B — retain the real Saturnian year

The astronomical year remains physically meaningful. Human recurrence moves into another unit.

Solarian adopts Option B.

The human-scale recurrence unit is: the mear

The astronomical unit remains: the year

This is not inherently superior to a synthetic-year architecture.

It reflects Solarian's design objective: preserve local astronomical meaning without making human operations live at astronomical scale.

That distinction is one of the central departures from many destination-specific designs.

E.15 Earth operating calendars and Mars calendars solve related problems

At first glance, a retail 4-4-5 calendar and a Martian calendar have almost nothing in common.

In fact they expose the same underlying issue.

The inherited astronomical or civil period is not always the period humans want for operations.

Earth businesses respond by layering: clean week-based operating periods

Over: Gregorian civil months

Marian responds by separating: human-scale planning intervals

From: astronomical Martian months

Solarian generalises the same separation:

minth / mear for people

month / year for orbit

This is why the business-calendar analogy matters. It demonstrates that functional layering is not exotic.

Humans already do it whenever one calendar hierarchy is asked to perform incompatible jobs.

E.16 What Solarian borrows

Very little in Solarian needs to be historically unprecedented in isolation.

Its ingredients have precedents.

From ordinary terrestrial calendrics come:

• twelve-part years;

• leap correction;

• eras;

• continuous weeks;

• local naming traditions.

From week-based business calendars come:

• whole-week operating periods;

• thirteen-week quarters;

• 52/53-week years;

• the idea that operating cadence can differ from ordinary civil-month structure.

From Martian calendar design come:

• local astronomical years;

• non-Earth civil days;

• 24-period human-scale structures;

• whole-week correction;

• perennial calendar logic;

• alternative month counts;

• explicit seasonal and orbital orientation;

• and recognition that calendar design is partly a social-design problem.

From outer-world calendar work comes:

• the need to reconsider human-scale time when planetary cycles become extremely long;

• calendars spanning moon systems rather than simple planetary surfaces;

• and the idea that the same design philosophy can be extended beyond one planet.

Solarian should acknowledge all of that. There is no value in claiming invention of ingredients that already exist.

E.17 What Solarian changes

The distinctive move is primarily architectural.

Solarian asks: What is the minimum common grammar required for many locally different calendars to remain mutually intelligible?

That produces several linked design choices.

1. Two explicit calendar layers

Human: week → minth → mear

Astronomical: orbital month → orbital year

Neither layer is required to impersonate the other.

2. The same twelve-position structure on both sides

Twelve minths form one mear.

Twelve orbital months form one year.

That symmetry creates the Repeat Factor.

3. Integer Repeat Factor

Where synchronization is useful: R = minths per orbital month = mears per orbital year

The same integer connects both layers.

4. An explicit independent regime

Where the scales do not nest sensibly, as on Venus and Mercury, Solarian does not force synchronization.

The two calendars simply run independently.

5. Whole-week quantisation throughout

The week is not merely a subdivision.

It is the smallest structural adjustment unit.

Major boundaries remain on week boundaries.

6. Distributed expansion joints

Astronomical mismatch is absorbed at declared locations rather than through ad hoc broken weekdays.

7. Common heliocentric orientation

Standard astronomical calendars share one λ₀ reference direction.

Their Month 1 positions therefore carry broadly corresponding heliocentric meaning.

8. A common week coordinate

SWI allows standard-day worlds to share one underlying week sequence while non-standard-day worlds map to it.

9. Machine-readable profile architecture

Local cultural names sit above stable structural identities and deterministic conversion.

10. Explicit graceful failure

A world can retain: day; week; minth; mear; SWI; and orbital year even where the default twelve-month astronomical layer ceases to represent orbital phase satisfactorily.

The architecture is intended to degrade locally rather than collapse globally.

E.18 The distinction is the combination

It is tempting in a new system to search for one feature and declare: This is the invention.

Solarian does not reduce very well to that kind of claim.

Whole-week intercalation has precedent. Four-week operating periods have precedent. Twelve-month astronomical calendars have precedent.

Planet-specific calendars have precedent. Outer-world calendar design has precedent.

Shared absolute chronology has precedent.

The stronger claim is about the combination and relationship of those elements.

Solarian combines: a portable human cadence

With: locally meaningful heliocentric calendars

Through: integer structural relationships where useful

while retaining: whole-week continuity

and adding: cross-world weekly and machine interoperability.

The system should therefore be judged primarily as an architecture.

Not as the invention of the week, leap week, month or planetary year.

E.19 No priority claim beyond the evidence

This appendix is not an exhaustive history of calendar design.

The literature on Earth calendars is enormous.

The literature on speculative planetary calendars extends through astronomy, science fiction, engineering studies, individual proposals and material that has never entered conventional academic indexing.

The Mars literature alone is unusually large.

Accordingly, Solarian Protocol v1.0 does not make a blanket claim that no previous author has ever proposed any individual element contained here.

Nor does this appendix attempt to prove absolute historical priority for the complete architecture.

A stronger scholarly priority claim would require a dedicated systematic literature review.

The more defensible statement is narrower:

Solarian deliberately integrates these elements into one protocol intended to remain structurally recognisable across many different heliocentric worlds, while separating human cadence from local orbital scale.

That is the contribution being documented.

E.20 What earlier systems reveal about requirements

The comparative history also reinforces a broader point from the main book.

Calendar arguments often appear to be arguments about arithmetic.

Usually they are arguments about requirements.

Darian asks whether fixed date-weekday relationships and human-scale months are worth periodically shortening the week.

Šurán gives the continuous week greater priority.

Zubrin gives stronger meaning to orbital phase.

Exodus gives familiarity unusually high priority.

4-4-5 gives comparability between operating periods priority over conventional civil-month boundaries.

Gregorian gives enormous weight to inherited continuity because centuries of society are already built on it.

Solarian gives priority to:

• continuous weeks;

• portable human cadence;

• local astronomical meaning;

• multi-world interoperability;

• and bounded, visible irregularity.

Change those priorities and another calendar may be preferable.

That is not a weakness in calendar design.

It is what design means.

E.21 Comparison by design objective

The broader landscape can therefore be reduced to a matrix.

This table deliberately avoids an overall score.

The systems have different objective functions.

E.22 The most important precursor is the problem, not a calendar

The deeper lineage of Solarian may not be any individual prior calendar.

It is the repeated discovery that one temporal hierarchy cannot conveniently perform every job.

Businesses discover it when Gregorian months frustrate operational comparison.

Mars calendar designers discover it when terrestrial month duration and one-twelfth of the Martian year diverge.

Outer-world designs discover it when a physical year becomes longer than a meaningful human recurrence cycle.

Pluto reveals another version when equal elapsed time and equal orbital angle diverge too far.

Each case exposes the same systems problem:

different temporal functions want different units

Solarian's answer is to separate those functions first and reconnect them only where the relationship remains useful.

That is the conceptual lineage that matters most.

E.23 Context, not replacement

None of this makes Solarian a replacement for the earlier work.

Gregorian will remain useful on Earth whether or not anybody ever adopts Solarian.

4-4-5 calendars will remain useful to businesses because they solve a specific operating problem.

A future Martian civilisation could rationally choose Darian, Exodus, Marian, another existing proposal or something not yet invented.

A Titanian society may eventually care about things no terrestrial designer anticipated.

Solarian makes a narrower proposal.

If many such local calendars eventually exist, giving them a small amount of common structural grammar may be more useful than either: forcing one Earth calendar everywhere

Or: allowing every world's civil time to become structurally unrelated to every other.

The prior calendar literature demonstrates the richness of the local design problem.

Solarian addresses the connective one.

E.24 Reference works

The comparative discussion in this appendix draws particularly on:

Gangale, Thomas & Dudley-Rowley, Marilyn.
Issues and Options for a Martian Calendar. Planetary and Space Science, 53, 1483–1495, 2005. The paper surveys the unusually large history of Martian calendar proposals and frames the design problem in terms of competing choices and standardisation.

Gangale, Thomas.
The Darian System / Darian Calendar for Mars. The reference material describes the 24-month, 27/28-sol structure and its perennial weekday arrangement.

Gangale, Thomas.
The Darian Calendar for Titan and associated Galilean calendar work. These extend planetary time architecture beyond Mars and include consideration of locally appropriate circads, week structures and leap-week intercalation.

Šurán, Josef.
A Calendar for Mars, 1997. The proposal uses 24 four-week months in the full year and complete-week omission in shortened years.

Zubrin, Robert.
A Calendar for the Planet Mars. The proposal defines Martian months through equal angular sections of orbital travel rather than equal elapsed-time divisions.

Silin, Dennis V.
The Exodus Calendar: A Simple Timekeeping System for Martian Colonists. Journal of the British Interplanetary Society, 78(9), 305–307, 2025. The calendar uses a familiar twelve-month architecture and a 22-year intercalation cycle.

United States Internal Revenue Service.
Guidance on 52–53-week tax years, illustrating established terrestrial use of whole-week annual accounting structures.

The final bibliography of this book should carry the formal citation record.

E.25 The design-context conclusion

The history of calendar design does not point towards one inevitable calendar.

It points towards something more useful.

Humans repeatedly redesign time when the job changes.

Earth inherited one answer. Businesses quietly layer another on top. Mars has generated dozens more. The outer Solar System forces still more radical choices.

Solarian belongs in that tradition.

Its particular proposition is that a multi-world civilisation does not need one universal local calendar.

It needs enough shared architecture that different local calendars remain recognisable to one another.

That is a different design problem from the one Gregorian, Darian, Šurán, Exodus or any other single-world calendar set out to solve.

And that is the context in which Solarian should be judged.

Not as the last calendar.

As a grammar for having many of them.