Calendars:

Old meets New

by Paul VanRaden

2023

 

Simple calendars are difficult to make because rotation cycles of the moon around the earth and the earth around the sun are not simple ratios of the earth’s rotation around its axis. A year has 365.2422 days as measured against the sun or 366.2422 days as measured against the stars because the earth orbits the sun once per year spinning toward the east. The year would have 367.2422 days if the earth was spinning at the same speed but toward the west or was spinning as now but orbiting the sun in the opposite direction. The moon circles the earth every 27.32 days as measured against the stars, but the full moon cycle is 29.53 days because the earth also makes a solar orbit every year.

Many countries now use the same calendar that is not simple to learn or to use due to uneven math. Easier calendars were used ages ago and those ideas should be reintroduced for use again. After reviewing the past several thousand years of calendar making, better calendars are presented for use next year (2024) and for the next few thousand years.

Calendars in the News

Mesopotamia, 4,000 BC: A 360-day year and 30-day month was introduced to approximately match the solar and lunar cycles. Today, 6,000 years later, circles still have 360 degrees.

Egypt, 2,600 BC: A 365-day calendar was introduced with 10-day weeks, 30-day months, and 120-day seasons totaling 360 plus 5 extra days added at year end to better match the solar cycle.

England, 2,500 BC: Stonehenge was arranged to track the annual cycle of 365.24 days more accurately.

Babylon, 2,000 BC: Months were defined with 3 weeks of 7 days and a 4th week of 8 or 9 days to give months of 29 or 30 days that precisely fit the lunar cycle of 29.53 days. The calendar of Myanmar still uses alternating months of 29 and 30 days to better match the phases of the moon.

Sinai desert, 1250 BC: A permanent 7-day week was introduced at the time of the 10 commandments. The 7-day week of Israel was later adopted by Greece in 400 BC, Rome in 100, China in 400, and Japan in 900. Previously Rome used 8-day weeks and China used 10-day weeks. Moses instructed his people and their draft animals to rest every 7th day and to let their land rest every 7th year. His people religiously kept the 7-day week but most have disregarded his 7-year cropping advice from Exodus 23:10-11: “For 6 years you shall sow your land and gather in its yield; but in the seventh year you shall let it rest and lie fallow…”

Mexico, 1,200 BC: A 365-day calendar was introduced with 18 months of 20 days plus 5 days at year end, much like the Egyptian calendar.

Egypt, 238 BC: Ptolemy III decreed in 3 languages to add a leap day every 4th year, but it did not happen in Egypt. Ethiopia and Coptic churches still use the Egyptian calendar with 12 30-day months, and its final week includes a leap day every 4th year as requested by Ptolemy III.

Rome, 153 BC: The beginning of the year was moved from March 15 to January 1. Months 5-10 were named as Latin numerals, and month names September, October, November, and December still describe months 7, 8, 9, and 10 from that previous calendar. Those months are now 9, 10, 11, and 12 in the calendar we used since 153 BC, defeating the purpose of the previous, simple, sensible numeric month names.

Rome, 45 BC: The Senate passed a bill introducing a leap day every 4th year, adding days to the year, and distributing them unevenly across the 12 months. Julius Caesar signed the bill into law, which added 80 days to the year 46 BC to revert January 1 back to its original day in the solar year. Numeric month names Quintilis and Sextilis were renamed as Julius and Augustus a few years later, and each year we still spend 2 months honoring those Roman emperors.

Rome, 321: Constantine the Great on March 7 ordered everyone in the Roman empire, except farmers, to rest each Sunday: “On the venerable day of the sun let the magistrate and people residing in cities rest, and let all workshops be closed. In the country however, persons engaged in agricultural work may freely and lawfully continue their pursuits; because it often happens that another day is not so suitable for grain growing or for vine planting; lest by neglecting the proper moment for such operations the bounty of heaven should be lost.”

Cologne (Köln), 1474: German monk Werner Rolevinck’s history of the world was the first to popularize the BC and AD time periods by estimating birth years and events from Adam to Jesus and from Jesus to present. Previously, most dates referred to beginning or ending years of local kings or emperors instead of a simple, global numeric series for the whole world. Rovelinck and later historians include no year 0 between 1 BC and 1 AD and thus 1 BC converts to 0 and 2 BC converts to -1 when converting BC to negative years.

Rome, 1582: The Cardinals voted and Pope Gregory XIII issued a papal bull to skip leap day every 100th year except every 400th year to more precisely match the cycle of 365.2422 days per year. They also skipped 10 days in October 1582 to revert January 1 back to its original day in the solar year after 1627 years of slightly incorrect math. Most people still use that Gregorian calendar which is identical to Julius Caesar’s calendar from 45 BC in 99% of years.

Paris, 1793: The old Egyptian calendar was reintroduced with 10-day weeks and 12 30-day months plus 5 extra days at year end or 6 in leap years to match the solar cycle as in the Gregorian calendar. France also introduced 10-hour days and 100-minute hours at the same time. That calendar was used for 12 years until 1805.

Geneva, 1923: The League of Nations chose the calendar proposed by Moses Cotsworth in 1902 to potentially replace the Gregorian calendar. The International Fixed Calendar (or the Standard Year) has 13 months each year and 28 days each month for a total of 364 days plus 1 day or 2 days if leap year. Each year, month, and week begins on Sunday by including the extra 1 or 2 days in the last week and month.

Tehran, 1925: The Iranian calendar subtracted 622 years to measure time since Muhammad instead of Jesus, and each year starts at the spring equinox (usually March 21 on the Gregorian calendar) to align the calendar directly to earth’s cycle around the sun, a main purpose of a calendar. Precision is also improved because dates of life events for Jesus are less well known than for Muhammad.

Moscow, 1929: The Soviet Union converted to 5-day weeks with 4 workdays and 1 rest day for most workers, then switched to 6-day weeks in 1931 and back to 7-day weeks in 1940. In most ex-Soviet countries, days of the week have numbers rather than names.

New Delhi, 1957: The Indian national calendar became official again after independence from Great Britain. It starts on the spring equinox (March 22) as in the Iranian calendar but with year 0 set equal to year 78 of the Roman calendar. Similar calendar years starting on the spring equinox had been used in India and southeast Asia for thousands of years.

Washington, 2023: Paul VanRaden reviewed past calendars and recommended future calendars in this document.

 

Replace Your Calendar: Out with the Old; In with the New

1)     Number the days of the year from 1 to 365 or to 366 in leap years. That makes Earth’s annual cycle much more obvious.

2)     Instead of notation such as 12-10-2023 in USA or 10-12-2023 in Europe or December 10, 2023, label day 343 of year 2023 as 2023:343.

3)     Start each new year on the same day of the week. Holidays, meetings, birthdays, and other events can then occur on both the same calendar date and day of the week every year.

4)     Replace the Roman calendar from 45 BC with the Egyptian calendar from 2,600 BC as modified by France in 1793 to make calendar math simpler. Similarly, all math became simpler when the Roman numerals used since 500 BC were gradually replaced with Arabic numerals used after about year 1,000. Math became simpler again when almost all countries on earth adopted the metric system from 1800-2000 except for a few (United States, Liberia, and Myanmar) that still use yards instead of meters, etc.

5)     Name the months of the year 1mo, 2mo, 3mo, etc. up to 12mo, following the early Roman pattern of numeric names that some current months still have. The final week should be named YearEnd. New month names will help to avoid confusing new calendar dates with old calendar dates, which is a major problem with the International Fixed Calendar.

6)     Name the days of the week 1day, 2day, 3day, 4day, 5day, 6day, and 7day because those names translate easily to any language. Already Portugal and several countries in eastern Europe give the weekdays numbers instead of names. The English word “today” could be replaced with new word “thisday” for clarity.

7)     Return to the 30-day months used for thousands of years or adopt other constant-length weeks or months to make calendar math much simpler. A 6-day week fits nicely into the 30-day month and is recommended.

8)     With the Egyptian calendar, people may prefer to continue using month-day notation, denoting the 30th day of month 12 as 12mo30, for example, or more simply as perpetual day 360.

9)     Include leap day at year’s end as in the French and International Fixed calendars instead of at the end of February (which was month 12 in the pre-153 BC Roman calendar).

10)  Use 1 longer week at the end of a year to fit the annual solar cycle of 365 or 366 days just like 1 longer week at the end of a month fit the lunar cycle of 29 or 30 days. The Babylonian 7-day week plus a final 8- or 9-day week as developed about 2,000 BC happens to fit both the annual and lunar cycles.

11)  Easily convert calendar dates numbered within year as 1 to 365 or 366 to computer dates stored as perpetual days since January 1, 1900 (or some programs use 1960). Just add the date within year to the beginning perpetual date for the year. For example, January 1, 2024 is 45,290 days after January 1, 1900. The computer would number the 366 days of 2024 as dates 45,291 to 45,656 and store day N as 45,290 + N.

 

Advantages of the new calendar are:

1)     The 365 (or 366) days of the year are numbered consecutively, allowing easier division of time into any desired lengths and simpler calculation of the days between any 2 events. Perpetual days have been used in computing for decades or centuries.

2)     The calendar is constant across all years, and the leap day is added at the end.

3)     The months are the same length, allowing easier multiplication and division of time. Only the last week is variable to include leap day.

4)     Understanding leap year, leap day, and a leap week with 1 or 2 extra days at the end is much easier than remembering 30 days hath September, April, June, November, 31 days in other months, and 28 or 29 in the second month.

5)     The days of the week are always on the same calendar date with no more need to guess where days of the week will fall. If the new year always starts on Monday, Christmas will always be on Tuesday. The last week will begin at Christmas and the next week will start the New Year.

6)     The extra week and the extra leap day holiday at the end come right between 2 other holidays when many people take vacation anyway.

7)     The 7 days of the week are named in most countries for the sun, the moon, and the planets Mars, Mercury, Jupiter, Venus, and Saturn in that order, which were also names of Greek or Roman gods. Many English-speaking countries have sun and moon days but not planet days except for Saturn day. Instead, the other 4 weekdays were named for the ancient German or Norse gods as Tiw’s, Woden’s, Thor’s, and Frig’s days that evolved into Tuesday, Wednesday, Thursday, and Friday. Very strange for English-speaking Christians to repeat the names of ancient, pagan gods every week, and new names are needed. In German, Woden’s day was already renamed to Mittwoch (midweek).

8)     The 6-day week makes tasks done every other day or every third day easier to schedule. For thousands of years, the 7-day week was divided into 6 days of work and 1 day of rest. That was gradually replaced by a 5-day work week and 2-day weekend. Some people now have a 4-day work week and 3-day weekend either every week or every other week by working 9- instead of 8-hour days. A better compromise to reach a similar goal could be a 6-day week with 4 days of work and 2-day weekend.

9)     The 28-day month may be preferred by some women as being closer to menstrual cycles that average 30 days for 20-year-olds and gradually decline to average 27 days for 35-year-olds. Those have a 3- or 4-day standard deviation and even more variation at younger or older ages. A calendar cycle trying to match a biological cycle could be helpful but could also perpetuate a misunderstanding of normal biological variation. Men chose our calendars for the past few thousand years. Women could choose what calendar to use for the next few thousand years.

10)  The Egyptian calendar reminds us of where 360 degrees of a circle came from.

 

Disadvantages are:

1)     The cost of changing and the temporary confusion while introducing the simpler calendar.

2)     The need to remember and convert birth dates, etc. from the old to the new calendar. Smart phones can easily do that.

3)     Some people might like their birthday to gradually rotate across days of the week instead of always on week day or week end.

4)     Holidays known by their Roman calendar dates such as 4th of July or Cinco de Mayo might need renaming.

5)     Some cultures will object to even the tiny revision of 7-day weeks. The current weekdays and weekends will drift by 1 day per year (or 2 days in leap years) compared to the revised, fixed calendar. Israel already had 1 longer day that lasted 2 days in its early history (Joshua 10:12-14) and thus could accept 1 longer week and longer weekend at each year’s end.

6)     The 7-day week was used for as many as 160,000 consecutive weeks (3,000 consecutive years) in some cultures. The 52 weeks of each year multiply to 364 days. Cultures who prefer the 7-day week could use it for 51 weeks of the year and then one 8-day week as described by the Beatles in their #1 song from 1964 (or a 9-day final week in leap years). The 7-day week is tied to the creation story from the Bible, but few people still interpret the 7 days literally. Few believe that the universe began a few thousand years ago and that humans began on day 6 with 1 male. Later that day 1 female was created from 1 of the male’s ribs. According to Genesis, God only worked 6 days in 1 week. He did not work 6 days the next week and did not work the previous week or the previous forever of weeks. The 7-day week is too closely tied to an old story that makes no sense.

7)     What day of the week to start each year is not clear. The 7-day week begins on Saturday in the Middle East and North Africa, on Sunday in North America, and on Monday in Europe and China. Where I grew up, our 7-day week started on Sunday and ended on Saturday, but we worked on Saturday and rested on Sunday which seemed sinful according to the Bible I read. Using the term weekend for Saturday and Sunday implies that the week should end on Sunday and start on Monday.

8)     Transition to any new calendar is not likely to be uniform across the world. Previous mathematical transitions such as from Roman to Arabic numerals or from English to metric units were not uniform and are still not complete. A new calendar can easily present both dates for convenience, just like all food packages at U.S. grocery stores display both English and metric units. Converting from one measurement system to another may not be convenient but can be simple with calculators, computers, or smart phones widely available. Converting old calendar dates to new calendar dates can also be simple, and examples can help people understand the process better.

 

Examples of 2024 whole-year calendars:

Current calendar but with sequentially numbered days

Egyptian calendar with conversion to current

Egyptian calendar

International Fixed Calendar with conversion to current

 

See all 4 examples above in Calendar_Annual.pdf

 

See monthly calendar example with 6-day weeks below.

See wobbly path of the moon around the sun further below.


 

Calendar with 6-day weeks, 30-day months

1mo

1day

2day

3day

4day

5day

6day

January 1

2

3

4

5

6

1

2

3

4

5

6

NewYear Mon

Tue

Wed

Thu

Fri

Sat

7

8

9

10

11

12

7

8

9

10

11

12

Sun

Mon

Tue

Wed

Thu

Fri

13

14

15

16

17

18

13

14

15

16

17

18

Sat

Sun

Mon

Tue

Wed

Thu

19

20

21

22

23

24

19

20

21

22

23

24

Fri

Sat

Sun

Mon

Tue

Wed

25

26

27

28

29

January 30

25

26

27

28

29

30

Thu

Fri

Sat

Sun

Mon

Tue

 

2mo

1day

2day

3day

4day

5day

6day

January 31

February 1

2

3

4

5

31

32

33

34

35

36

Mon

Tue

Wed

Thu

Fri

Sat

6

7

8

9

10

11

37

38

39

40

41

42

Sun

Mon

Tue

Wed

Thu

Fri

12

13

14

15

16

17

43

44

45

46

47

48

Sat

Sun

Mon

Tue

Wed

Thu

18

19

20

21

22

23

49

50

51

52

53

54

Fri

Sat

Sun

Mon

Tue

Wed

24

25

26

27

February 28

March 1

55

56

57

58

59

60

Thu

Fri

Sat

Sun

Mon

Tue

 

etc. for 3mo-11mo and then:

 


12mo

1day

2day

3day

4day

5day

6day

November 27

28

29

November 30

December 1

2

331

332

333

334

335

336

Tue

Wed

Thu

Fri

Sat

Sun

3

4

5

6

7

8

337

338

339

340

341

342

Mon

Tue

Wed

Thu

Fri

Sat

9

10

11

12

13

14

343

344

345

346

347

348

Sun

Mon

Tue

Wed

Thu

Fri

15

16

17

18

19

20

349

350

351

352

353

354

Sat

Sun

Mon

Tue

Wed

Thu

21

22

23

24

25

December 26

355

356

357

358

359

360

Fri

Sat

Sun

Mon

Christmas    Tue

Wed

 

YearEnd

1day

2day

3day

4day

5day

LeapDay

December 27

28

29

30

December 31

 

361

362

363

364

365

366

Thu

Fri

Sat

Sun

LastDay

LeapDay

 

 

 

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Solutions to World Problems

by Paul VanRaden