This document formally defines the terminology and notations of the 7date calendar system.

The 7date calendar is a method of recording dates, and is considered an alternative to the traditional Gregorian calendar (which has dates written as February 19th, 2014, for example).

The 7date calendar is presented as a means of addressing several weak points of the Gregorian calendar. It can be seen as a suggestion analogous to the metric system of centimeters, meters, and kilometers over the imperial system of inches, feet, and miles. Specifically, Gregorian months have nonstandard lengths, are often named instead of numbered, and do not track well with weeks.

The key concept of the 7date calendar is to represent a date in the standard format

```
<days-elapsed-this-year(7)>.<year(10)>,
```

where (7) indicates that the *days-elapsed* portion is written as a base-7 number; the year is written in standard base-10. For example, January 1st, 2031 is written as 0.2031 since on January 1st, zero days have fully elapsed within that year. January 2nd, 2031 is written 1.2031 and January 8th is written 10.2031 - the "10" portion representing 1 full week having elapsed, keeping in mind that this is base-7 notation.

Futher details of the notation are given in the sections *common notation* and *digital notation* below.

This document introduces two new words:

**7date**: This word is meant to grammatically fit anywhere the term "Gregorian date" would fit. For example, you could ask "What's today's date?" or, similarly, "What's today's 7date?"

**7month**: This word indicates exactly 49 days. There are 7 full 7months in a year covering the first 343 (that's 7 * 7 * 7) days, and a final block of either 22 or 23 days, depending on whether or not the current year is a leap year. Thus, each year is close to 7.5 7months long.

The common notations are those meant to be used for most human-targeted use cases. The other notation discussed below is a *digital notation*, meant for notation stored digitally that will be both read by humans and processed as data.

A full 7date is written in the form

```
<days-elapsed-this-year(7)>.<year(10)>
```

This is analogous to writing a full Gregorian date such as 5/23/2017.

The day-of-year, without a year specified, is written in the form

```
<days-elapsed-this-year(7)>.
```

The trailing period is part of the notation. It is identical to the full form with the year omitted. This form can be used to specify a date more concisely when the year is clear in context, or to denote a repeating annual date; for example: my birthday is 304.

A specific 7month, or the final half-7month, of a year can be written as

```
<7months-elapsed-this-year(7)>--.[<year(10)>]
```

The brackets [] around the year indicate that it's an optional part of the notation; omitting the year indicates that it is implied by context, or that we are talking about a recurring range of dates, analogous to speaking of "every February" in the Gregorian calendar.

As an example, the first 7month of 2026 is written 0--.2026. The last is written 10--.2026.

A specific week is written as

```
<weeks-elapsed-this-year(7)>-.[<year(10)>]
```

The first week of the year is 0-. and the last is 103-.

Notice that these notations are compatible in the sense that the 7month 3--. consists exactly of the 7dates 300. through 366., inclusively. In general every dash - can be thought of as a wildcard character that can be replaced with any base-7 digit (so, 0-6) to arrive at the dates in the denoted range.

Another perspective of this is to realize that every 7date, such as

206.2056

provides multiple pieces of information at once:

- This date is in the 7month 2--.
- This date is in the week 20-. which means 14 weeks have elapsed this year.
- The day of the week on 206. is the same as all other dates that year that end in 6.

More details about day-of-week are provided in the section *referring to days of the week* below.

A concept similar to a leap year is necessary in any calendar system that respects both days and years, as these time units are built into the physical properties of our planet and solar system. The 7date calendar uses the same leap year system as the Gregorian calendar with the exception that the added day is the last day of the year.

When 7dates are recorded digitally as a field that may be sorted, the following format is suggested:

```
<year(10)>-<4-characters, 0-padded, with days-elapsed-this-year(7)>
```

For example, the 7date 23.2020 would be written as 2020-0023 as part of a filename.

This can be considered the 7date version of the ISO 8601 international date format, which is essentially YYYY-MM-DD.

The advantages of this standard are that:

- It is easy for humans to read when they're familiar with the 7date;
- it is easy for software to parse as a 7date; and
- it is easy for software to sort, as any lexicographic string sorting algorithm will also put the dates in chronological order.

Sorting software does not need to know that the 7date calendar even exists; for example, the unix command *ls* sorts filenames by default, so that files starting with a 7date in digital notation will be presented in chronological order.

Unicode technical standard #35, denoted as tr35 (*tr* refers to *technical report*), contains a suggested shorthand notation for strings that express date formats. This 7date specification suggests extending these format patterns with two new substrings:

**7**, a single character, denotes the regular expression [1-6][0-6]*, to be interpreted as the number of days elapsed in a given year in base-7;

**7777**, exactly four characters, denotes a 0-padded, 4-character-long string with regular expression [0-6]{4}, also to be interpreted as the number of days elapsed in a given year in base-7.

The terms *0-day*, *1-day*, up through *6-day* refer to any 7date ending on the given base-7 digit. These are suggested as terms analogous to traditional day names such as Monday or Tuesday.

At the time of this writing, the vast majority of people are unaware of the 7date. They are unlikely to move away from the Gregorian calendar, or even to consider alternatives to it. Because of this, it is suggested that the numbered day terms (0-day, 1-day, etc.) remain unsynchronized with traditional day-of-week names (Monday, Tuesday, etc.). In this way, a small subset of 7date users can speak precisely about dates without confusion of others using the Gregorian calendar.

This section briefly discusses some advantages under the hypothetical situation that numbered week days (0-day, etc.) come to replace named week days (Monday, etc.) as the standard perspective of weeks. It is admitted that this hypothetical situation seems unlikely; however, its consequences are interesting.

The primary difference between numbered and named weeks is that numbered weeks are reset at year boundaries. Specifically, the 7date 1030.{Y} is followed by 0.{Y+1} when Y is a non-leap year, and 1031.{Y} is followed by 0.{Y+1} when Y is a leap year. In other words, once a year, a 0-day or 1-day is followed immediately by a 0-day.

A major advantage is that any 7date automatically includes which day of the week that date falls on. Specifically, the last base-7 digit of the day provides the day of the week. For example, 234.2037 is a 4-day.

Among other things, this eliminates the problem that certain holidays often move within the calendar to accommodate both a day-of-week and a day-of-year expectation. For example, Thanksgiving in the U.S. officially occurs on the fourth Thursday on November. Thanksgiving could have a fixed 7date that is guaranteed to fall on the same day of the week (using numbered days-of-week) each year.

It is suggested that the weekend becomes 0-day and 1-day, so that the common work week is 2-day through 6-day. Then another advantage arises: at the end of each year, a long weekend occurs with 3 consecutive weekend days most years, and 4 weekend days at the end of leap years.

The primary disadvantage of the 7date calendar - as it would be for any new calendar system - is that no one knows about it. This impedes the use case of communicating dates clearly to others. However, this is a necessary disadvantage to any significant improvement on the Gregorian calendar. Even with low adoption, the 7date calendar is useful for dates recorded within a small group - including, possibly, a single person - which is aware of the system.

Another liability is the fact that many people are new to base-7 notation. This can add an intimidation factor the adoption of the 7date calendar. However, in practice, calendar users are already familiar with thinking in terms of weeks, which lends itself directly to thinking in terms of a week-based numbering system. In other words, it is expected that the use of base-7 is more frightening than difficult to those new to it.

Finally, the 7date calendar has no replacement for time units that are approximately 30 days long - traditional months. In many cases, a month-based periodicity can be replaced with a frequency of once every two weeks, or once every four weeks.

It is easy to be aware of a once-every-two-weeks schedule using 7dates since we can easily check if a base-7 number is even or odd. Specifically, a base-7 number is even if and only if the sum of its digits is even. For example, 103. is an even day, while 23. is an odd day. This means that a once-every-two-week schedule starting on 0. would include 1030. and exclude 230.

It is also possible to quickly check if a base-7 number is a multiple of 4. In this case, one can alternately add and subtract the digits; if the result is a multiple of 4, then so is the original base-7 number. For example, 26. is a multiple of 4 since 2-6=-4 is; 50. is not a multiple of 4 since 5-0=5 isn't. Thus, a once-every-four-weeks schedule starting on 0. would include 260. but exclude 500.

It is not expected that every 7date user would employ these arithmetic approaches; the point is instead that it is easier to work with exact week-based schedules in the 7date as opposed to the Gregorian calendar.

One advantage of the 7date calendar is that it coexists relatively well with the Gregorian calendar. In particular, the years of the 7date calendar are the same as Gregorian years; and there is a one-to-one mapping between 7date dates and Gregorian dates. Many other suggested calendar systems do not have both of these mappings.

A human can reasonably learn to convert between 7dates and Gregorian dates by memorizing 7dates associated with the start of each Gregorian month. It may be more practical, however, to simply look at a calendar designed to assist such conversions. An example of such a calendar can be found here.

Another advantage of the 7date is that it helps bring together the two dominant day-based cycles: Gregorian dates and named week days. In traditional time measurement, these cycles are essentially independent. For example, it is difficult to determine which day of the week an arbitrary Gregorian date falls upon. This problem is solved completely if numbered week days replace named days. Even if named week days are used, knowing the named day of the week on any 7date in a year makes it easy to determine the named week day of any 7date throughout that year; for example, 0.2718 is a Tuesday, so we immediately know that 231.2718 is a Wednesday.

Finally, the 7date calendar carries with it the simplification of a unified and precise numerical base-system. Consider how much easier it is to work with cm, m, and km as opposed to inches, feet, and miles. Analogously, the 7date has consistent time-unit lengths - unit lengths that are related by multiples of 7.

Tyler Neylon

100.2014