Geodesy and geometry of the Decimal Number Zones

 Geodesy and geometry of the Decimal Number Zones

The new Decimal Numbering Zones (DNZ) system is based on the concept of dividing the day into 1000 units called "beats", which are equivalent to 1 minute and 26.4 seconds, and the key is that this time is universal and does not depend on the sexagesimal system of time zones to avoid calculations of time differences.

It consists of dividing the surface of the Earth into 40 zones, so that each of them corresponds to 25 "swatch beats" of the day. We call each of these parts "numbering zones" and not "time zones" because while a time zone assigns the same number to approximately the same position of the sun, the Swatch Internet Time system has the same number worldwide, and what's different is the numbers that are assigned to the 4 key points of the day: Midnight, sunrise, noon, sundown.

Since a day is a complete rotation of the planet and a complete rotation has 400 gradians (i.e. 360°, but this system is decimal and not sexagesimal, therefore, it is convenient to use the system of hundredths of a degree and convert each degree notation into gradians), dividing 400g by 40, results in each time zone having an angular amplitude of 10 gradians (i.e. 9° sexagesimal). Since the meridians are not parallel, a time zone has a variable width. It is maximum at the equator with a width of 1,001.875 km (i.e. a thousand kilometers and a bit) and it narrows towards the poles. Considering the corresponding volume up to the Earth's axis, it can be compared to a slice of orange or tangerine.

Prime meridian and reference time

The time zone system and the geographic longitude system need a prime meridian to be applied on the Earth's surface, since, due to the rotation movement, all points on Earth are equal in terms of longitude and time. For technical, political and historical reasons, the meridian chosen was that of the Royal Observatory of Greenwich, in London.

The Biel Meridian was chosen as the "zero meridian" to measure Internet Time in 1998, but it was not until 2024 that this concept was used for the DNZ system. Meridians are identified by two elements: their measurement in degrees and their position with respect to the zero meridian.

The city of Biel is located at 8.05gE (eight point zero five gradians east) compared to the Greenwich meridian, so in the new DNZ system It was decided that they would be in the same DNZ, the DNZ "between 0 and 10 degrees East" and therefore, in that time zone, @000 would be considered midnight, @250 would be "sunrise", @500 noon, @750 sunset... The DNZ of Biel and Greenwich is called "DNZ of Biel-Greenwich (BG)".

For example, the longitude of the city of Lima is 76°W, or 84.4 degrees West, which means that it is between 80 and 90 degrees West, which is the "DNZ of Lima".

Since this and the Biel-Greenwich numbering zone are separated by 8 DNZ's, add 1 to the 8, which will give you 9 (the "numbering zone difference number (NZDN)"), and multiply it by 25 (the difference number of "beats" on each cosecutive DNZ), and you will get 225. That is the hour that will be considered "midnight" in the Lima DNZ. From there, the other hours are taken: @475 is sunrise, @725 is noon, and @975 is sunset.

That is the formula to find the NZDN of your local DNZ. If it is west of the BGNZ, add it, if it is east, subtract it. If it comes out less than zero, subtract it from 1000, since it is a cyclical system.

In the cycle of the day, in addition to midnight, sunrise, noon and sunset, which are the "4 key points of the day"​, there are 225. They add another 4 that are located in the exact middle of the intervals between each "Key Point". This makes the day divided into 8 exact parts, each with a duration of 125 beats. Their main objective is for all 40 world time zones to have at least 2 of the 8 key points that end in 00, or at least 4 that end in 0. For example, in the Lima DNZ, using the above information, @350 would be "mid-morning", and @600, "mid-afternoon".

This new system is more exact than the current Time Zone system, because it is always the same number throughout the planet, the only thing that changes is the numbering of the 8 key points in different regions. 40 time zones are more exact than 24. And it is better to use a time system that is better adapted to our numbering system.

NOMENCLATURE OF THE 40 NUMBERING ZONES

The numbering zone of Lima is called "Lima DNZ" but it can also be called "90 gradians West of BNZ (Biel Numbering Zone) or BZ (Biel Zone)". The same way, the DNZ of Athens can be refferred to as "20 gradians East of BZ"

The following table contains two number ranges, and one place name. The first number range represents the longitude of the numbering zone. The second number range actually represents the swatch beat time when it's midnight and dawn, respectively in each of these 40 time zones. The names are of the places which are contain within the designated Numbering Zone.

WEST:

200-190 500-750 Wallis and Futuna

190-180 475-725 Palmerston

180-170 450-700 Kiritimati

170-160 425-675 Tahiti

160-150 400-650 Ivvavik

150-140 375-625 Pitcairn

140-130 350-600 San Francisco and Vancouver

130-120 325-575 Sonora and Las Vegas

120-110 300-550 Guadalajara

110-100 275-525 Tabasco and Veracruz

100-90 250-500 Tegucigalpa, Honduras; San Jose, Costa Rica

90-80 225-475 Lima and New York

80-70 200-450 Caracas and Punta Cana

70-60 175-425 Asuncion, Paraguay

60-50 150-400 Curitiba

50-40 125-375 Rio and Salvador

40-30 100-350 Fayal (Western Azores)

30-20 075-325 Reykjavík

20-10 050-300 Canarias Zone

10-00 025-275 Madrid

EAST:

00-10 000-250 Dijon and Amsterdam (also known as Biel-Greenwich)

10-20 975-225 Nuremberg, Prague and Berlin

20-30 950-200 Athens and Belgrade

30-40 925-175 Gerson

40-50 900-150 Medina

50-60 875-125 Qatar

60-70 850-100 Ashgabat

70-80 825-075 Samarkand, Dushanbe and Kabul

80-90 800-050 New Delhi

90-100 775-025 Kathmandu

100-110 750-000 Aceh

110-120 725-975 Kuala Lumpur, Cambodia, Laos and Singapore

120-130 700-950 Hong Kong and Wuhan

130-140 675-925 Taipei, Taiwan

140-150 650-900 Nagasaki

150-160 625-875 Tokyo

160-170 600-850 Melbourne and Canberra

170-180 575-825 Pohnpei

180-190 550-800 Palikir and New Caledonia

190-200 525-775 Auckland