# Bully Metric Timestamps

Bully Metric Main Page
The Bully Timestamp System is an original research project designed with the following objectives in mind:
* A timekeeping system which is sufficiently independent of Earth's motions and orientation, so that "leap" seconds, "leap" years, and other correctional adjustments are not required.
* A timekeeping system which is fundamentally binary and compatible with computer architecture.
* A timekeeping system with enough scope to uniquely and unambiguously identify each point in time, beginning with the Big Bang, and continuing into the foreseeable future.
* A timekeeping system with a built-in mnemonic device, to promote education and understanding.

# What is the Bully Timestamp System?

The Bully Timestamp System is neither a clock nor a calendar. Clocks are tied to the rotation of the Earth and measure Universal Time (UT) in terms of days and fractions of days (for example: hours, minutes, and seconds). Calendars are tied to changes in the seasons, which result from the orbit of the Earth around the Sun (Ephemeris time), and from the precession of the equinoxes. Calendars measure time in terms of days, weeks, months, and years. Clocks and calendars are used for tracking biological processes such as setting a time to wake up in the morning or determining when to plant crops. It is essential for clocks and calendars to remain correlated with the earth's actual orientation for proper management of biological processes.
Since clocks and calendars are tied to the motion of the Earth, and these motions are somewhat irregular, it becomes necessary from time to time to insert leap seconds, or make other corrections, to keep clocks and calendars in sync with the Earth's actual orientation. As shown in figure 1 above, the Earth's rotational motion (UT) can experience variations on the order of 500 milliseconds per year. The Earth's orbital motion (ET) can experience variations on the order of 40 milliseconds per year. During the 110 year period (1930 AD ... 2040 AD) shown in figure 1, the accumulation of Earth's rotational variations resulted in an increase of Delta T (ET-UT) from less than 25 seconds to more than 70 seconds.
The Bully Timestamp System measures elapsed time in terms of Bully timestamps (shown on the far right axis in figure 1). Bully timestamps are not directly tied to the motions of the Earth, and hence, it is never necessary to insert leap seconds or other corrections into Bully timestamps. The Bully Timestamp System can be directly related to International Atomic Time (TAI), which is the passage of elapsed time as measured using atomic clocks.

## Time span covered by Bully timestamps

${16}^{12}\cdot 3055\ seconds=27,249,360,000\ years$
A unique hexadecimal twelve digit Bully timestamp is realized every 3055 seconds TAI. The universe is currently understood to be less than 13.8 billion years old, which means that there are enough unique Bully timestamps to span the entire age of the universe.

## The Bully Mnemonic

$({10330}\cdot {0.40})({\frac {10330}{0.40}})({10330}\cdot {3055})=(4132)\cdot (25825)\cdot (31558150)$
${1\,Sidereal\,Year}={31,558,150\,Seconds}$
${1\,Tropical\,Year}={31,556,926\,Seconds}$
$1\,Great\,Year\approx 25,824\,Sidereal\,Years\approx 25,825\,Tropical\,Years$
${1\,Galactic\,Year}\approx 4132\,Great\,Year\approx 213,417,800\,Tropical\,Years$
The Bully Mnemonic is a technique for remembering the exact number of seconds that occur in Earth's sidereal year and tropical year, a good approximation of the Earth's Great Year, and a rough approximation of the Solar System's galactic year. Click on the following link to learn more about the Bully Mnemonic and the role it plays as the mathematical foundation of Bully timestamps.
The Bully Mnemonic
The Bully Mnemonic Extension
The Bully Metric

## Why do we need Bully timestamps?

The inability of computers to predict long term variations in Earth's motion has resulted in the creation of multiple time standards. Each standard is a reflection of circumstances that existed during the deployment of a particular system. For example, as shown in figure 1 above, The GPS system was deployed January 6, 1980. At that time, there was a Delta T adjustment (TT-UTC) of more than 51 "leap" seconds. The LORAN-C upgrade, on the other hand, occurred in 1972 when the Delta T adjustment (TT-UTC) was closer to 42 "leap" seconds. The resulting timestamps provided by GPS and LORAN-C differ by nine seconds due to the disparate circumstances under which these systems were deployed. Also, LORAN-C timestamps differ by ten seconds from TAI due to the fact that TAI was deployed in 1958.
Click on the below links for a comparison of six time standards (local, UTC, GPS, Loran, and TAI):
LeapSecond.com
ipses.com
csgnetwork.com
The unpredictability of leap second insertions is an ongoing source of confusion and expense. Click on the following link for more information:
The second is broken

# Realized vs. Estimated Bully timestamps

Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one. However, since atomic time standards did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered "realized" when time is measured with an accuracy of ${10}^{-10}$.

## Estimated Bully Time

History of Earth

## Realized Bully Time

Current Bully Timestamp (GitHub)
There have been over 655360 realized Bully timestamps (8209 27F9 0000 ... 8209 2804 0000) during the 66 years of modern atomic time keeping (1958 AD ... 2024 AD). Given the availability of atomic clocks, it is anticipated that Bully timestamps will continue to be realized with great regularity for the foreseeable future. Each Bully timestamp should be considered "realized" after it occurs and is measured using precise clocks.

### Leap Seconds (1972 - Present)

The below table (derived from the Wikipedia "Leap Second" article), lists all leap second insertions that have occurred since the introduction of leap seconds in 1972. For each leap second insertion, the below table lists the preceding Bully timestamp (that had been "realized" immediately prior to the leap second insertion), and the subsequent Bully timestamp (that was "realized" immediately after the leap second insertion).
A few details are worth noting in the table. The TAI and UTC already differed by 10 seconds at the beginning of 1972 due to rubber seconds (see discussion below), so when Bully Timestamp 8209 27FB E7FB was realized, the TAI time was 1972-06-30 23:34:45 TAI, whereas UTC time was 1972-06-30 23:34:35 UTC. An additional 27 leap seconds have been inserted into UTC during the fifty year period between 1972 and 2022, making a total of 37 leap seconds difference, so when Bully Row Timestamp 8209 2802 EBC0 was realized, the TAI time was 2017-01-01 00:32:00 TAI, whereas UTC time was 2017-01-01 00:31:23 UTC. You will also note that Bully Row timestamps are realized during TAI times with a seconds value ending in five or zero. The Bully Row and TAI both measure elapsed time as determined by atomic clocks, so these systems will always have this simple relationship.
Announced leap seconds to date :
| Year | 30 Jun | 31 Dec | Bully Row Timestamp | International Atomic Time (TAI) | Coordinated Universal Time (UTC) |
| 1972 | +1 | +1 | 8209 27FB E7FB 8209 27FB E7FC 8209 27FB FC4F 8209 27FB FC50 | 1972-06-30 23:34:45 TAI 1972-07-01 00:25:40 TAI 1972-12-31 23:45:05 TAI 1973-01-01 00:36:00 TAI | 1972-06-30 23:34:35 UTC 1972-07-01 00:25:29 UTC 1972-12-31 23:44:54 UTC 1973-01-01 00:35:48 UTC |
| 1973 | 0 | +1 | 8209 27FC 24A2 8209 27FC 24A3 | 1973-12-31 23:57:50 TAI 1974-01-01 00:48:45 TAI | 1973-12-31 23:57:38 UTC 1974-01-01 00:48:32 UTC |
| 1974 | 0 | +1 | 8209 27FC 4CF4 8209 27FC 4CF5 | 1974-12-31 23:19:40 TAI 1975-01-01 00:10:35 TAI | 1974-12-31 23:19:27 UTC 1975-01-01 00:10:21 UTC |
| 1975 | 0 | +1 | 8209 27FC 7547 8209 27FC 7548 | 1975-12-31 23:32:25 TAI 1976-01-01 00:23:20 TAI | 1975-12-31 23:32:11 UTC 1976-01-01 00:23:05 UTC |
| 1976 | 0 | +1 | 8209 27FC 9DB6 8209 27FC 9DB7 | 1976-12-31 23:30:50 TAI 1977-01-01 00:21:45 TAI | 1976-12-31 23:30:35 UTC 1977-01-01 00:21:29 UTC |
| 1977 | 0 | +1 | 8209 27FC C609 8209 27FC C60A | 1977-12-31 23:43:35 TAI 1978-01-01 00:34:30 TAI | 1977-12-31 23:43:19 UTC 1978-01-01 00:34:13 UTC |
| 1978 | 0 | +1 | 8209 27FC EE5C 8209 27FC EE5D | 1978-12-31 23:56:20 TAI 1979-01-01 00:47:15 TAI | 1978-12-31 23:56:03 UTC 1979-01-01 00:46:57 UTC |
| 1979 | 0 | +1 | 8209 27FD 16AE 8209 27FD 16AF | 1979-12-31 23:18:10 TAI 1980-01-01 00:09:05 TAI | 1979-12-31 23:17:52 UTC 1980-01-01 00:08:46 UTC |
| 1981 | +1 | 0 | 8209 27FD 531C 8209 27FD 531D | 1981-06-30 23:19:00 TAI 1981-07-01 00:09:55 TAI | 1981-06-30 23:18:41 UTC 1981-07-01 00:09:35 UTC |
| 1982 | +1 | 0 | 8209 27FD 7B6F 8209 27FD 7B70 | 1982-06-30 23:31:45 TAI 1982-07-01 00:22:40 TAI | 1982-06-30 23:31:25 UTC 1982-07-01 00:22:19 UTC |
| 1983 | +1 | 0 | 8209 27FD A3C2 8209 27FD A3C3 | 1983-06-30 23:44:30 TAI 1983-07-01 00:35:25 TAI | 1983-06-30 23:44:09 UTC 1983-07-01 00:35:03 UTC |
| 1985 | +1 | 0 | 8209 27FD F484 8209 27FD F485 | 1985-06-30 23:55:40 TAI 1985-07-01 00:46:35 TAI | 1985-06-30 23:55:18 UTC 1985-07-01 00:46:12 UTC |
| 1987 | 0 | +1 | 8209 27FE 597D 8209 27FE 597E | 1987-12-31 23:40:35 TAI 1988-01-01 00:31:30 TAI | 1987-12-31 23:40:12 UTC 1988-01-01 00:31:06 UTC |
| 1989 | 0 | +1 | 8209 27FE AA3F 8209 27FE AA40 | 1989-12-31 23:51:45 TAI 1990-01-01 00:42:40 TAI | 1989-12-31 23:51:21 UTC 1990-01-01 00:42:15 UTC |
| 1990 | 0 | +1 | 8209 27FE D291 8209 27FE D292 | 1990-12-31 23:13:35 TAI 1991-01-01 00:04:30 TAI | 1990-12-31 23:13:10 UTC 1991-01-01 00:04:04 UTC |
| 1992 | +1 | 0 | 8209 27FF 0EFF 8209 27FF 0F00 | 1992-06-30 23:14:25 TAI 1992-07-01 00:05:20 TAI | 1992-06-30 23:13:59 UTC 1992-07-01 00:04:53 UTC |
| 1993 | +1 | 0 | 8209 27FF 3752 8209 27FF 3753 | 1993-06-30 23:27:10 TAI 1993-07-01 00:18:05 TAI | 1993-06-30 23:26:43 UTC 1993-07-01 00:17:37 UTC |
| 1994 | +1 | 0 | 8209 27FF 5FA5 8209 27FF 5FA6 | 1994-06-30 23:39:55 TAI 1994-07-01 00:30:50 TAI | 1994-06-30 23:39:27 UTC 1994-07-01 00:30:21 UTC |
| 1995 | 0 | +1 | 8209 27FF 9C4B 8209 27FF 9C4C | 1995-12-31 23:12:05 TAI 1996-01-01 00:03:00 TAI | 1995-12-31 23:11:36 UTC 1996-01-01 00:02:30 UTC |
| 1997 | +1 | 0 | 8209 27FF D8B9 8209 27FF D8BA | 1997-06-30 23:12:55 TAI 1997-07-01 00:03:50 TAI | 1997-06-30 23:12:25 UTC 1997-07-01 00:03:19 UTC |
| 1998 | 0 | +1 | 8209 2800 1560 8209 2800 1561 | 1998-12-31 23:36:00 TAI 1999-01-01 00:26:55 TAI | 1998-12-31 23:35:29 UTC 1999-01-01 00:26:23 UTC |
| 2005 | 0 | +1 | 8209 2801 2FDC 8209 2801 2FDD | 2005-12-31 23:45:40 TAI 2006-01-01 00:36:35 TAI | 2005-12-31 23:45:08 UTC 2006-01-01 00:36:02 UTC |
| 2008 | 0 | +1 | 8209 2801 A8F0 8209 2801 A8F1 | 2008-12-31 23:18:40 TAI 2009-01-01 00:09:35 TAI | 2008-12-31 23:18:07 UTC 2009-01-01 00:09:01 UTC |
| 2012 | +1 | 0 | 8209 2802 3604 8209 2802 3605 | 2012-06-30 23:45:00 TAI 2012-07-01 00:35:55 TAI | 2012-06-30 23:44:26 UTC 2012-07-01 00:35:20 UTC |
| 2015 | +1 | 0 | 8209 2802 AEFC 8209 2802 AEFD | 2015-06-30 23:32:20 TAI 2015-07-01 00:23:15 TAI | 2015-06-30 23:31:45 UTC 2015-07-01 00:22:39 UTC |
| 2016 | 0 | +1 | 8209 2802 EBBF 8209 2802 EBC0 | 2016-12-31 23:41:05 TAI 2017-01-01 00:32:00 TAI | 2016-12-31 23:40:29 UTC 2017-01-01 00:31:23 UTC |

### Rubber Seconds (1958 - 1971)

Prior to 1972, the rate of UTC atomic clocks was offset from a pure atomic time scale by the BIH to remain synchronized with UT2, a practice known as the "rubber second" (see figure 2). The rate of UTC was decided at the start of each year. Alongside this shift in rate, an occasional 0.1 s step (0.05 s before 1963) was also implemented as needed.
As shown in figure 2, for 1958-1961, the offset rate was −150 parts per 10$^{10}$ (or 0.47 seconds per year). This stretching of UTC "rubber seconds" meant that fewer of them would occur during a Bully Timestamp. For example, during the 1958-1961 time period, each Bully timestamp was realized after exactly 3055 seconds TAI, which corresponded to 3054.999955264 seconds UTC. For 1962–63 the offset rate was set to −130 parts per 10$^{10}$ (or 0.41 seconds per year, or 3054.999960285 seconds UTC per Bully timestamp), and then for 1964–65 the offset rate was returned to −150 parts per 10$^{10}$.
The UTC rate of −150 parts per 10$^{10}$ turned out to be notably inadequate during the 1964-1965 time period, and multiple 0.1 s steps were needed (see figure 2). Beginning in 1966, the offset rate was set to −300 parts per 10$^{10}$ (or 0.94 seconds per year, or 3054.99990835 seconds UTC per Bully timestamp), and this continued until the inauguration of Leap Seconds in 1972.
At the beginning of 1958, the TAI and UTC clocks were in sync, with 1958-01-01 00:00:00.000 TAI occurring at the same time as 1958-01-01 00:00:00.000 UTC. By the end of 1972, the UTC clock had been adjusted (using rubber seconds and time steps) by ten leap seconds, so that 1972-01-01 00:00:10.003 TAI occurred at the same time as 1972-01-01 00:00:00.003 UTC. The following table illustrates the slow accumulation of leap seconds prior to 1972, resulting in this ten second difference.
Rubber Seconds and Accumulative (TAI - UTC) Time Delta :
| Bully Timestamps International Atomic Time (TAI) Coordinated Universal Time (UTC) | (ΔTAI - ΔUTC) | Accumulative Difference |
| 8209 27F9 9F04 . . . 8209 27F9 EFAA 1958-01-01 00:00:00.009 TAI . . . 1960-01-01 00:00:00.951 TAI 1958-01-01 00:00:00.012 UTC . . . 1960-01-01 00:00:00.008 UTC | 0.946 sec | 0.943 sec |
| 8209 27F9 EFAA . . . 8209 27FA 1819 1960-01-01 00:00:00.951 TAI . . . 1961-01-01 00:00:01.420 TAI 1960-01-01 00:00:00.008 UTC . . . 1961-01-01 00:00:00.002 UTC | 0.474 sec | 1.418 sec |
| 8209 27FA 1819 1961-01-01 00:00:01.420 TAI 1961-01-01 00:00:00.002 UTC . . . 1960-12-31 23:59:59.997 UTC | 0.005 sec | 1.423 sec |
| 8209 27FA 1819 . . . 8209 27FA 2F85 1961-01-01 00:00:01.420 TAI . . . 1961-08-01 00:00:01.651 TAI 1960-12-31 23:59:59.997 UTC . . . 1961-07-31 23:59:59.953 UTC | 0.275 sec | 1.698 sec |
| 8209 27FA 2F85 1961-08-01 00:00:01.651 TAI 1961-07-31 23:59:59.953 UTC . . . 1961-08-01 00:00:00.003 UTC | -0.050 sec | 1.648 sec |
| 8209 27FA 2F85 . . . 8209 27FA 406C 1961-08-01 00:00:01.651 TAI . . . 1962-01-01 00:00:01.845 TAI 1961-08-01 00:00:00.003 UTC . . . 1961-12-31 23:59:59.999 UTC | 0.198 sec | 1.846 sec |
| 8209 27FA 406C . . . 8209 27FA 8A54 1962-01-01 00:00:01.845 TAI . . . 1963-11-01 00:00:02.694 TAI 1961-12-31 23:59:59.999 UTC . . . 1963-11-01 00:00:00.097 UTC | 0.751 sec | 2.597 sec |
| 8209 27FA 8A54 1963-11-01 00:00:02.694 TAI 1963-11-01 00:00:00.097 UTC . . . 1963-10-31 23:59:59.997 UTC | 0.100 sec | 2.697 sec |
| 8209 27FA 8A54 . . . 8209 27FA 9111 1963-11-01 00:00:02.694 TAI . . . 1964-01-01 00:00:02.757 TAI 1963-10-31 23:59:59.997 UTC . . . 1963-12-31 23:59:59.991 UTC | 0.069 sec | 2.766 sec |
| 8209 27FA 9111 . . . 8209 27FA 9B1F 1964-01-01 00:00:02.757 TAI . . . 1964-04-01 00:00:02.997 TAI 1963-12-31 23:59:59.991 UTC . . . 1964-04-01 00:00:00.113 UTC | 0.118 sec | 2.884 sec |
| 8209 27FA 9B1F 1964-04-01 00:00:02.997 TAI 1964-04-01 00:00:00.113 UTC . . . 1964-04-01 00:00:00.013 UTC | 0.100 sec | 2.984 sec |
| 8209 27FA 9B1F . . . 8209 27FA AC06 1964-04-01 00:00:02.997 TAI . . . 1964-09-01 00:00:03.283 TAI 1964-04-01 00:00:00.013 UTC . . . 1964-09-01 00:00:00.101 UTC | 0.198 sec | 3.182 sec |
| 8209 27FA AC06 1964-09-01 00:00:03.283 TAI 1964-09-01 00:00:00.101 UTC . . . 1964-09-01 00:00:00.001 UTC | 0.100 sec | 3.282 sec |
| 8209 27FA AC06 . . . 8209 27FA B980 1964-09-01 00:00:03.283 TAI . . . 1965-01-01 00:00:03.531 TAI 1964-09-01 00:00:00.001 UTC . . . 1965-01-01 00:00:00.091 UTC | 0.158 sec | 3.440 sec |
| 8209 27FA B980 1965-01-01 00:00:03.531 TAI 1965-01-01 00:00:00.091 UTC . . . 1964-12-31 23:59:59.991 UTC | 0.100 sec | 3.540 sec |
| 8209 27FA B980 . . . 8209 27FA C005 1965-01-01 00:00:03.531 TAI . . . 1965-03-01 00:00:03.720 TAI 1964-12-31 23:59:59.991 UTC . . . 1965-03-01 00:00:00.104 UTC | 0.076 sec | 3.617 sec |
| 8209 27FA C005 1965-03-01 00:00:03.720 TAI 1965-03-01 00:00:00.104 UTC . . . 1965-03-01 00:00:00.004 UTC | 0.100 sec | 3.717 sec |
| 8209 27FA C005 . . . 8209 27FA CD7F 1965-03-01 00:00:03.720 TAI . . . 1965-07-01 00:00:03.968 TAI 1965-03-01 00:00:00.004 UTC . . . 1965-07-01 00:00:00.094 UTC | 0.158 sec | 3.875 sec |
| 8209 27FA CD7F 1965-07-01 00:00:03.968 TAI 1965-07-01 00:00:00.094 UTC . . . 1965-06-30 23:59:59.994 UTC | 0.100 sec | 3.975 sec |
| 8209 27FA CD7F . . . 8209 27FA D459 1965-07-01 00:00:03.968 TAI . . . 1965-09-01 00:00:04.166 TAI 1965-06-30 23:59:59.994 UTC . . . 1965-09-01 00:00:00.111 UTC | 0.080 sec | 4.055 sec |
| 8209 27FA D459 1965-09-01 00:00:04.166 TAI 1965-09-01 00:00:00.111 UTC . . . 1965-09-01 00:00:00.011 UTC | 0.100 sec | 4.155 sec |
| 8209 27FA D459 . . . 8209 27FA E1D3 1965-09-01 00:00:04.166 TAI . . . 1966-01-01 00:00:04.323 TAI 1965-09-01 00:00:00.011 UTC . . . 1966-01-01 00:00:00.009 UTC | 0.158 sec | 4.313 sec |
| 8209 27FA E1D3 . . . 8209 27FB 35E5 1966-01-01 00:00:04.323 TAI . . . 1968-02-01 00:00:06.188 TAI 1966-01-01 00:00:00.009 UTC . . . 1968-01-31 23:59:59.903 UTC | 1.973 sec | 6.286 sec |
| 8209 27FB 35E5 1968-02-01 00:00:06.188 TAI 1968-01-31 23:59:59.903 UTC . . . 1968-02-01 00:00:00.003 UTC | -0.100 sec | 6.186 sec |
| 8209 27FB 35E5 . . . 8209 27FB D3E0 1968-02-01 00:00:06.188 TAI . . . 1972-01-01 00:00:10.003 TAI 1968-02-01 00:00:00.003 UTC . . . 1972-01-01 00:00:00.110 UTC | 3.707 sec | 9.892 sec |
| 8209 27FB D3E0 1972-01-01 00:00:10.003 TAI 1972-01-01 00:00:00.110 UTC . . . 1972-01-01 00:00:00.003 UTC | 0.108 sec | 10.000 sec |