Bully Timestamps

The Bully Timestamp System is an original research project designed with the following objectives in mind:

1. 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.
2. A timekeeping system which is fundamentally binary and compatible with computer architecture.
3. 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.
4. A timekeeping system with a built-in mnemonic device, to promote education and understanding.

What is the Bully Timestamp System?

Figure 1: Modern Time Keeping

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

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

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

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)

Figure 2: Rubber Seconds

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 10¹⁰ (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 10¹⁰ (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 10¹⁰.

The UTC rate of −150 parts per 10¹⁰ 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 10¹⁰ (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