[javascript clock]

A proposal for CTE, Common Equiform Time

Communicating when is tricky in our global age. The time of day differs across time zones, as may the date. Conventions exist for this situation, such as "your time", "local time", and so on. In a space age, people may be in no time zone at all.

The current primary global standard is UTC (Coordinated Universal Time), an offshoot of GMT (Greenwich Mean Time), which privileges a particular time zone, roughly that of England. UTC approximates the real local date and time there (not counting daylight saving, or summer, time) with a cluster of atomic clocks.

However, UTC has drawbacks:

• Specifying a date requires use of our rather messy traditional calendar, which UTC inherits. Computing the number of days between two dates is not trivial, due to not only the jumbled sequence of month lengths but the leap year rules which have changed over the years and historically differed from one country to the next.¹
• It does not flow at a steady rate. As the Earth's rotation is not constant but slows slightly over time, increasing the length of the day, UTC is kept aligned with "sundial" time by adding leap seconds. An extra second is added at the end of June or December of certain years, as decided by international consensus after observation. It is not predictable, so future times cannot accurately be notated, in the far future not even vaguely. For past times one must maintain a table of leap seconds. Elementary computations such as the difference between two times may be difficult or impossible.
• It is not defined at all for moments before 1961 or (in its present form) 1972.

There are various strategies to address these issues:

• Astronomers often use the Julian day for the date of an event, rather than year, month, day. This is a numeric count of days since a fixed date remote in the past (January 1, 4713 BC), and is thus much easier to work with mathematically. Furthermore, when astronomers measure in years, they usually mean a Julian year, defined as exactly 365.25 days, regardless of the era or calendar in use. However, the Julian day is a cumbersome and unintuitive way to communicate (it's around 2.5 million today), and it uses the SI day of 86400 seconds, as TAI does, and thus also drifts from the solar day.
• TAI (International Atomic Time) is an atomic time scale without leap seconds. Thus, it slowly drifts away from UTC, a second at a time. This makes it predictable, but it no longer corresponds to the solar day or any other astronomical cycle. More generally, Terrestrial (Dynamical) Time (TT or TDT or TD) is used by astronomers for dating events based on a theoretical constant clock, infinitely far back or forward in time. TAI is used to approximate TT, subject to refinement.
• Most international organizations cite past dates using the Gregorian calendar from October 15, 1582 on, and the proleptic² Julian before that, even though only a few jurisdictions made the switch right at that time.

My conclusions:

• It is not possible to both track the solar day and have a uniform flow of time. Compromise on this point is unavoidable and may as well be embraced.
• For many purposes, regularity and predictability of the time scale is more important than correspondence to natural cycles; for those where keeping to natural cycles is vital, a non-uniform and unpredictable scale must be employed.
• We can think of any tolerated inaccuracy in the day as the universal meridian slowly moving, a perhaps more palatable way to think of it, with the benefit that there is now no fixed privileged meridian such as Greenwich. I suggest that even a day that is off by several minutes from the real day, can be thought of having a tolerably drifting meridian.
• The year is a more natural unit to measure arbitrary durations with than the day. This may seem unintuitive, as the day is in many ways the basis of our existence, and the year a more subtle effect. But we describe long durations in number of years, almost never number of days, and short durations never in fractions of days, but usually parts of a second. Neither "one million days" nor "one millionth of a day" mean anything to most of us; it's only in a small intermediate range that use of the day is intuitive.
• Once we part with the notion that a common clock day must correspond in a fixed way with our local civil date and time, or that the number of days must match up, we are freer to alter the calendar units such as months as we please to simplify the system.
• Basing a time scale on a fixed year duration will suffer drift, as the year is not constant either. However, the error is smaller and accumulates much more slowly, and is less noticeable than a change of (say) hours in the day.

Thus, I propose (Common) Equiform³ Time, or CTE⁴ or TE⁵. We fix a year length (say in terms of atomic time), and a certain moment as the calendar's start. Then we divide up the year into twelve equal months of thirty equal "days". A date and time can then be given as a successive series of units—year, month, day, hour, minute, second—each defined simply and exactly in terms of the others, and all always of equal duration.⁶

A year then has exactly 360 days. 360 is a very nice number to work with, much better than 365, or 365.2425. Due to its large number of factors, it was chosen as the number of degrees in a circle and was heavily used in ancient times. Today, mathematicians call it a collossally abundant⁷ as well as a superior highly composite⁸ number. We can easily divide the year, exactly, with no refuge in approximation, into halves, thirds, quarters, fifths, sixths, eighths, tenths, twelfths, fifteenths, eighteenths, twentieths, and so on. The number of months, 12, is a similarly gifted number, divisible into two, three, four, and six. Many of our current rough units of time (e.g., three months, fifteen days, etc.) are based on ignoring the inaccuracy in the correspondence to actual calendar time, but in CTE all these will be exact in all cases.

The advantages:

• As noted, time units are all exactly defined in terms of each other, with convenient ratios, and are always the same.
• It does not fix any one meridian.
• Its year, our basis of long durations, will correspond well to the real year, throughout a long time period. See below.
• The inaccuracy in the day is within the tolerance of the human Circadian rhythm, so hypothetical space travellers could live by this schedule if they chose.⁹
• The CTE day is close enough to the solar day that for imprecise durations they are interchangeable. E.g., about three days CTE is about three solar days, five months CTE is close to the many possible lengths of the underdefined five Gregorian months.
• The CTE date approximates the standard date, so to the casual reader it may look like a timestamp in an unrecognized time zone, and not be jarring or bizarre.

The disadvantages:

• The day is off by a noticeable amount, about twenty minutes. This corresponds to a shift in the meridian of a couple hundred miles a day (depending on latitude).
• The "second" is a specific, rigorously-defined SI unit, while the CTE "second" will be something else, longer.
• With UTC there is a fixed relationship between universal and local time, at least allowing ready recovery of the local time, but with CTE every day is offset differently.
• For now of course no one uses it.

Partly due to the second point, and also because the second is a fairly long time even in human terms¹⁰, I am resurrecting the old subdivision of the second into 60 parts, called a third or tierce, the latter adopted for CTE to avoid ambiguity with the fraction. Tierce (as I am decreeing is the plural¹¹) may be used after the seconds in a timestamp for additional precision and can be considered a basic unit of CTE.

There are relevant and interesting time-related matters I consider beyond the scope of this particular proposal, and independent of it:

• Many have suggested renumbering the years and abandoning the AD/BC system. Reasons given: it is Christian-centric, and poorly calculated at that; it is inconveniently recent, requiring a confusing switch to BC (or negative years) well within human history; there are better choices of epochs; and so on. Astronomers use zero and negative numbers for BC, which simplifies year arithmetic. Some use CE/BCE as "secular" replacements for AD/BC, without renumbering.¹²
• Relativistic effects due to the orbit of the Earth around the Sun affect the flow of time relative to the rest of the universe. Others have worked out the repercussions of this in more detail than I care to. My intent is best met by using T_eph or the all but identical Barycentric Dynamical Time (TDB), which uses the time frame of the center of the solar system without the gravity of the sun, except scaled so that it in the long run matches the time frame of a clock on the Earth's surface.¹³ The periodic variations are at most about 1.6 milliseconds.¹⁴
• It is perhaps inconsistent that months and days start at one, while hours, minutes, and seconds start at zero. Some systems (e.g., Java) do start months at zero. I have halfway dodged this issue by using three-letter names for months—I feel that names "speak" more than numbers—but this has the disadvantage of being English-centered. Some authors use upper-case Roman numerals for months.
• There is no attempt to even approximate the lunar cycle. Tying the months to the moon was abandoned long ago in the Roman calendar. The lunar cycle, while quite stable in the long run, is less so than the year, making it a poorer choice for CTE.
• There are many proposals for calendar reform. CTE, however, is not a calendar in the usual sense of providing names for days; rather, it names moments. One could turn it into a system for days in a manner analogous to how the ISO names weeks based on the Gregorian calendar, but I'm not particularly recommending it.

Details

To define this system, we must (1) pick a year length, and (2) specify its alignment by fixing to a known moment. In doing this, we shall not discard the existing science of time measurement, but build upon it with our own definitions.

There are of course an infinite number of choices for the year length; the tropical year is slowly shrinking, so any one in a range would be as good as any other. My first instinct was to use the astronomers' convention, a Julian year of 365.25 days of 86400 SI seconds. But this year is significantly off.

The number of SI seconds in a year is to the nearest integer 31,556,925. This, adopted for CTE, is a nice number to work with; it has three factors of three, and two factors of five, which only one out of 675 numbers do. Dividing by 360 to get the number of SI seconds in a day gives a nonrepeating decimal with the tolerable figure of 86758 1/8 = 86758.125 SI seconds to a day. This makes the CTE year equal to exactly 365 31/128 SI days, a somewhat tame denominator, being a power of two. The tropical year length crosses this value in approximately 2035, which is as good as any other date; by contrast, the Gregorian year GMT was exact around 3000 BC, the Gregorian year TT around 250 BC, and the Julian year—who knows?

Choosing an "epoch"—fixing a calendar point or base—is a tricky affair. Calendar epochs are invariably saddled with political, religious, or even personal meaning, and equally invariably seem arbitrary and a matter of taste. Basing on historical or even astronomical events introduces unavoidable imprecision and the risk of embarrassing new information. The best achievable way to note a moment is to tie it to the most accurate standard available today, atomic time scales, which is what professionals in the field actually do.

The use of the year 2000 as a baseline is widespread and fairly natural. Astronomers use J2000.0, a moment in 2000, as their calculation epoch¹⁵; much post-Y2k software uses a 2000 epoch; its significance as a millennium milepost is obvious; its passage has/had a large cultural impact; and it is a major marker in the Gregorian calendar. Thus, my proposal is to simply equate the beginning of 2000 CTE with the beginning of 2000 Gregorian.¹⁶

There is finally the issue of which time scale to use for the Gregorian moment—UTC, TAI, TT (adjusted to TDB or T_eph), or even GPS. These differ by some tens of seconds, and each has advantages¹⁷, but I went with TT as it is the most stable, and most closely matches CTE in intent.¹⁸ Of course, all these scales are trivially interconvertible anyway.

Thus CTE is aligned with this equation:

2000 Jan 01 00:00:00 CTE = 2000 Jan 01 00:00:00 TDB exactly¹⁹

This moment is 1999 Dec 31 23:58:55.816 UTC, discounting relativistic effects.

This completes the definition.

Stability

To measure how well CTE matches the tropical year, we sample the dates of the seasonal points across many years. However, just tracking, say, the vernal (spring) equinox, gives poor results, because (a) the exact moments of the seasonal points wobble erratically due to the complex motion of the Earth and Moon, and (b) the lengths of the seasons oscillate over long periods of time due to precession. Instead I look at the average of the four seasonal points of a year, what I shall call the midsummer average, in order to diminish these effects.

To provide a sense of the stability of the midsummer average, here is a sampling of seasonal points in CTE through the first half of the 21st century:²⁰

CTE	Vernal	Summer	Midsummer	Autumnal	Winter
2000	Mar 19 04:17:01	Jun 20 14:32:21	Aug 06 00:58:55	Sep 22 21:56:38	Dec 21 11:09:41
2010	Mar 19 04:06:39	Jun 20 14:05:58	Aug 06 00:41:44	Sep 22 21:30:59	Dec 21 11:03:20
2020	Mar 19 04:16:27	Jun 20 14:13:40	Aug 06 00:53:39	Sep 22 21:44:56	Dec 21 11:19:31
2030	Mar 19 04:11:30	Jun 20 13:54:05	Aug 06 00:44:41	Sep 22 21:33:50	Dec 21 11:19:18
2040	Mar 19 04:23:27	Jun 20 14:01:34	Aug 06 00:56:01	Sep 22 21:44:14	Dec 21 11:34:49
2050	Mar 19 04:23:57	Jun 20 13:41:07	Aug 06 00:44:48	Sep 22 21:20:48	Dec 21 11:33:20

The midsummer value shows variation on the order of 15 minutes.²¹

Increasing the scale, here are seasonal points in CTE at 1000-year intervals:

CTE	Vernal	Summer	Midsummer	Autumnal	Winter
BC 5001	Mar 20 06:25:56	Jun 21 18:42:24	Aug 04 16:33:42	Sep 19 03:03:08	Dec 17 14:03:21
4001	Mar 19 22:58:40	Jun 22 03:43:09	Aug 05 00:12:57	Sep 20 01:28:04	Dec 17 20:41:54
3001	Mar 19 15:15:52	Jun 22 07:49:48	Aug 05 07:15:02	Sep 20 22:49:06	Dec 18 07:05:20
2001	Mar 19 08:25:22	Jun 22 06:49:10	Aug 05 13:29:29	Sep 21 17:51:37	Dec 18 20:51:47
1001	Mar 19 03:22:42	Jun 22 00:55:15	Aug 05 18:13:37	Sep 22 08:28:08	Dec 19 12:08:23
0001	Mar 19 00:35:29	Jun 21 15:20:57	Aug 05 21:39:03	Sep 22 18:17:31	Dec 20 04:22:15
AD 1000	Mar 19 00:52:04	Jun 21 03:27:00	Aug 05 23:57:09	Sep 22 22:55:26	Dec 20 20:34:08
2000	Mar 19 04:17:01	Jun 20 14:32:21	Aug 06 00:58:55	Sep 22 21:56:38	Dec 21 11:09:41
3000	Mar 19 09:34:15	Jun 20 01:19:23	Aug 05 23:59:01	Sep 22 14:53:29	Dec 21 22:08:55
4000	Mar 19 16:42:55	Jun 19 13:35:16	Aug 05 21:55:58	Sep 22 03:38:21	Dec 22 05:47:22
5000	Mar 20 00:52:48	Jun 19 04:05:31	Aug 05 18:31:40	Sep 21 12:35:47	Dec 22 08:32:33
6000	Mar 20 08:29:18	Jun 18 21:23:42	Aug 05 13:51:12	Sep 20 19:21:04	Dec 22 06:10:43
7000	Mar 20 14:23:53	Jun 18 17:00:13	Aug 05 07:37:46	Sep 20 00:43:31	Dec 21 22:23:27

The results are what we would expect: a cusp around the year 2000, when our figure for the year is most exact, and a quadratic error accumulating in both directions. One can see that the error accumulates to about a day over six thousand years. At this rate, 38,000 years out it would be off by a year.

However, this is not the whole story. The year is shrinking primarily due not to changes in the Earth's orbit but to changes in the rate of precession.²² These changes, and thus the year length, oscillate with a period of about 41,000 years; we happen to be on a "downward" part of the cycle. The total discrepancy thus oscillates as well, and in the long run is considerably smaller than the variation above suggests.

Lacking precise figures for trends at this time scale, I developed a rough model²³ of this oscillation. This table shows this approximation for several cycles, by giving the values at the alternating apex and nadir over each ~41,000-year cycle, and the average of successive extrema:

	Extremum	Midsummer	Average	Midsummer	Extremum
BC	123313	Aug 19 01:23	Aug 18 01:03
			Aug 14 14:10	Aug 10 02:56	97417	BC
	81501	Aug 12 19:59	Aug 11 11:27
			Aug 08 22:20	Aug 05 00:42	57177
	39723	Aug 08 11:48	Aug 06 18:15
			Aug 05 02:55	Aug 01 18:01	16915
AD	2036	Aug 06 00:50	Aug 03 21:26
			Aug 03 03:35	Jul 30 06:56	23360	AD
	43786	Aug 05 11:04	Aug 02 21:00
			Aug 03 01:15	Jul 30 15:27	63637
	85538	Aug 06 18:29	Aug 03 16:58
			Aug 04 19:01	Aug 02 19:33	103908
	127303	Aug 09 23:06	Aug 06 09:19
			Aug 08 09:10	Aug 06 19:14	144162
			Aug 10 22:05

For comparison, the Gregorian date for the last entry on the right is June 23 TT, and will likely be several years earlier GMT or UT.

While the precession cycle remains stable over millions of years, in the table above the dominant effect becomes the extrapolated change in the sidereal year, right now slightly less than one second per 10,000 years,²⁴ which pushes the midsummer average later into August, with quadratic growth. However, while the long-term behavior of this change is not known very precisely, it, too, is almost certainly at least roughly periodic. One estimate²² is a cycle of 70,000 years with a variation of ±1.2 seconds, in which case the net effect is merely an oscillation of about four hours in each direction. The long-term stability is thus greater than the above model suggests, and it is the disparity from the long-term average rate of precession that predominates, which is a linear effect. Over a million years the total shift seems to be about a month.

On a geologic time scale, the year remains remarkably stable even over hundreds of millions of years. Research on ancient corals and other lifeforms^25,26,27 have confirmed that the number of days in a year was once much larger, with some estimates ranging up to 1800 soon after the formation of the Earth, and projected to about 150 at its destruction,²² but this is almost entirely due to the changing length of the day.²⁸

From the formation of Earth to now, the number of years that have elapsed CTE, about 4.5 billion, differs from the number of actual tropical cycles by probably less than 1%. Similar remarks apply to the time to the presumed future immolation of Earth by a dying Sun in about 5 billion years, although speculation about such distant events, which may be disrupted by the influence of man, involves much uncertainty.

The tropical year before the existence of the Earth or after is of course meaningless.

Examples

Here is a sampling of CTE moments, as best as I can reconstruct them. Many moments are listed where the time of day is not known very precisely; more precision than actually exists may be given anyway.

Moment	Conventional	CTE abridged list · full list
BC
Last simultaneous transit of Mercury and Venus ends29	373173 Sep 22 16:57 TT	373181 Sep 26 17:50
Julian Day 0.0 TT	4713 Jan 01 12:00:00 TT	4714 Nov 22 14:54:45
Ussher's date for creation30,31,32	4004 Oct 22 18:00 Qurna	4004 Sep 19 21:51
Hebrew calendar epoch (AM 1 Tishri 1)	3761 Oct 06 18:00 Jerusalem	3761 Sep 06 05:38
Solar eclipse supposedly recorded in Ireland33,34	3340 Nov 30 16:02:56 UT 3340 Dec 01 21:06:26 TT	3340 Nov 03 12:19:21
Mayan calendar epoch35 (0.0.0.0.0)	3114 Sep 05 sunset	3114 Aug 10 00:
Yellow Emperor epoch, New Moon36	2697 Feb 10 17:34:42 TT	2697 Jan 17 19:12:25
Possible Hittite solar eclipse37	1312 Jun 24 19:10:53 TT 1312 Jun 24 10:30:50 UT	1312 Jun 11 08:19:51
Ramses II becomes Pharaoh	1279 May 31 12: Egypt	1279 May 15 16:
Inferred return of Odysseus to Ithaca38	1178 Apr 11 05: Ithaca	1178 Mar 28 15:
Traditional date of 1st Olympics39	0776 Jul 21	0776 Jul 11
Supposed battle eclipse predicted by Thales40,41	0585 May 28 19:28:50 TT	0585 May 20 14:11:46
Death of Alexander the Great42,43	0323 Jun 11 16:30 Babylon	0323 Jun 05 20:02
Mt. Vesuvius eruption44	0079 Aug 24 13: Pompeii	0079 Aug 21 12:
Julius Caesar killed (Ides of March)45	0044 Mar 15 12: Roman 0044 Mar 14 12: Rome	0044 Mar 10 09:
Common Era epoch	AD 1 Jan 01 00:00:00 UT	0001 Dec 29 06:42:44
AD
Inferred crucifixion of Jesus46,47	0033 Apr 03 15:00 Judea	0033 Mar 30 17:19
Indian national calendar epoch (1 Chaitra 0 SE)	0078 Mar 22 00:00:00 IST	0078 Mar 20 05:38:43
Vernal equinox in year of Nicene Council	0325 Mar 20 12:01:21 TT	0325 Mar 19 00:41:27
Crete earthquake	0365 Jul 21 04: GMT	0365 Jul 20 08:
Islamic calendar epoch (AH 1 Muharram 1)	0622 Jul 15 18:00 Mecca	0622 Jul 16 13:52
Death of Charlemagne48	0814 Jan 28 09:00 Aachen	0814 Feb 02 04:07
Crab Nebula supernova observed in China	1054 Jul 04 evening	1054 Jul 08 09:
Fall of Constantinople49	1453 May 29 06: local	1453 Jun 06 11:
Columbus sights Americas50	1492 Oct 12 02: ET	1492 Oct 21 02:
Gregorian calendar switch in Rome	1582 Oct 04 24:00:00 Rome 1582 Oct 15 00:00:00 Rome 1582 Oct 04 23:12:07 TT	1582 Oct 14 01:53:48
Gunpowder Plot discovered	1605 Nov 05 00:00 OS London	1605 Nov 15 02:12
Closest point of comet observed by Halley51	1682 Sep 15 07:10:15 TT	1682 Sep 15 14:33:59
Gregorian calendar switch in England	1752 Sep 02 24:00:00 London 1752 Sep 14 00:00:00 London 1752 Sep 14 00:00:44 TT	1752 Sep 14 08:57:48
Lisbon earthquake52	1755 Nov 01 09:40 Lisbon	1755 Nov 01 09:22
Shot heard round the world (America)	1775 Apr 19 05:00 Concord	1775 Apr 18 08:04
Bastille stormed	1789 Jul 14 17:30 Paris	1789 Jul 14 00:20
French Revolution calendar epoch (1 Vendémiaire An I)	1792 Sep 22 00:00:00 Paris 1792 Sep 21 23:50:39 UT	1792 Sep 22 13:26:17
Premiere of Beethoven's 5th and 6th53	1808 Dec 22 18:30 Vienna	1808 Dec 22 02:43
Fort Sumter attacked54	1861 Apr 12 04:30 local	1861 Apr 11 14:36
Abraham Lincoln dies55	1865 Apr 15 07:22:10 D.C.	1864 Apr 15 16:56:04
Republic of China epoch (ROC 1)	1912 Jan 01 00:00:00 GMT+8	1911 Dec 29 23:51:19
Titanic hits iceberg	1912 Apr 14 23:40 local 1912 Apr 15 03:00 GMT	1912 Apr 13 22:31
Archduke Ferdinand killed	1914 Jun 28 10:45 Sarajevo 1914 Jun 28 09:32 GMT	1914 Jun 26 16:01
Massacre of the Romanovs56	1918 Jul 17 03:00 YEKST 1918 Jul 16 21:00 GMT	1918 Jul 14 21:51
Sacco and Vanzetti executed57	1927 Aug 23 00:26:55 EST	1927 Aug 21 13:11:44
Hindenburg ignites	1937 May 06 19:25 EST	1937 May 05 11:07
Germany invades Poland	1939 Sep 01 04:45 CET	1939 Aug 30 10:38
D-Day, H-Hour	1944 Jun 06 06:30:00 BDST 1944 Jun 06 04:30:00 GMT	1944 Jun 05 12:00:46
Hiroshima atom-bombed58,59	1945 Aug 06 08:15:36 JST	1945 Aug 05 04:06:24
Shot heard round the world (baseball)	1951 Oct 03 15:58 EST	1951 Oct 02 18:48
Rosenbergs executed60	1953 Jun 19 20:16 EDT	1953 Jun 18 22:46
JFK killed	1963 Nov 22 12:30 CST	1963 Nov 22 01:22
Armstrong steps on moon61	1969 Jul 21 02:56:15 UTC	1969 Jul 19 17:40:44
Nixon disembarks in China62	1972 Feb 22 03:30 UTC	1972 Feb 22 04:22
Challenger explodes63	1986 Jan 28 11:39:13 EST	1986 Jan 28 16:22:11
Chernobyl explodes64	1986 Apr 26 01:23:45 MSK	1986 Apr 24 16:03:40
Berlin Wall opened65	1989 Nov 10 00:00 CET	1989 Nov 09 19:02
Yitzhak Rabin shot66	1995 Nov 04 21:30 IST	1995 Nov 04 14:28
Hong Kong handover	1997 Jul 01 00:00:00 HKT	1997 Jun 29 20:56:33
J2000.0	2000 Jan 01 12:00:00 TT 2000 Jan 01 11:58:56 UTC	2000 Jan 01 11:49:40
9/11, first collision	2001 Sep 11 08:46:40 EDT 2001 Sep 11 12:46:40 UTC	2001 Sep 11 15:23:21
Iraq invaded67	2003 Mar 19 21:34 EST 2003 Mar 20 05:34 Bagdad	2003 Mar 18 06:08
Earthquake causing deadly tsunami68	2004 Dec 26 00:58:53 UTC	2004 Dec 25 21:43:02
Mayanism doomsday69,70	2012 Dec 21 11:12:43 TT 2012 Dec 21 11:11:36 UTC	2012 Dec 21 10:59:04
Now71	[javascript]	[javascript]
UNIX year 2038 problem72	2038 Jan 19 03:14:08 UTC 2038 Jan 19 03:15:31 TT	2038 Jan 19 15:51:43
Total solar eclipse of 2186, longest for thousands of years73	2186 Jul 16 15:14:54 TT 2186 Jul 16 15:08:05 UT	2186 Jul 15 18:03:40
Halberstadt performance of ASLSP to end74	2640 Sep 05 00:00:00 CET	2640 Sep 05 11:09:22
Westinghouse time capsule to be opened75	6939 Sep 19 00:29:32 TT	6939 Sep 20 02:00:38
Crypt of Civilization to be opened76,77	8113 May 28 local	8113 May 29
Next simultaneous transit of Mercury and Venus begins29,78,79	69163 Jul 26 22:58 TT	69163 Aug 15 15:35

Fun facts

• The CTE day, hour, minute, and second are 46751/46080 of their SI counterparts, which is equal to 1.0145616319444444....
• The CTE day is 24 hours, 20 minutes, and 58 1/8 seconds SI. The SI day is 23 hours, 39 minutes, and 19 43591/46751 (19.9324...) seconds CTE.
• 68.674 CTE seconds is approximately 69.674 SI seconds, so that CTE gains one second relative to SI in about that time. The decimal part where they are equal is exactly 452/671.
• The CTE year is 27 SI seconds shorter than the Gregorian year TT, and 11 minutes, 15 seconds (SI) shorter than the Julian year TT.
• Although obviously the TT and CTE date-time values are occasionally the same, as they cross each other repeatedly, they only meet at a time with a whole number of a seconds at the start of a year (in fact, it is possible only every 128 years from the epoch).^80,81 Exactly 25 years start at the same moment in TT and CTE in the proleptic Gregorian calendar: 305 BC, 0080, 0464, 0592, 0848, 0976, 1232, 1360, 1488, 1616, 1744, 1872, 2000, 2128, 2256, 2384, 2512, 2640, 2768, 3024, 3152, 3408, 3536, 3920, 4304. If we use a cutoff for the Julian calendar, all years before the cutoff (say 1582) are eliminated, but we pick up the lone year AD 336.
• 18,700,416 CTE years is equal to 18,700,400 Gregorian years TT. After one of these cycles, the CTE and Gregorian calendars repeat in tandem, though offset by sixteen years per cycle. Thus, "on average" 1,168,776 CTE years equals 1,168,775 Gregorian years, and in this time they fall one year apart.
• We can create a Julian Day for CTE. If we fix JDE 0 as BC 4713 Jan 1 (BC 4713 Feb 09 10:30:00 TT), then 2000 Jan 1 CTE is 6712×360 = 2416320 JDE (compared to 2451545 JD). I would also set JDE whole dates at midnight rather than JD's noon, introducing a 0.5 difference.
• Days of the week do not seem to port well to CTE, but, to match many colloquial uses, a useful definition of the week as a duration would be 1/4 of a month, or 7 1/2 days. Then two weeks is always half a month, six weeks a month and a half, and so on.

Notes

2. Proleptic means extending calendar rules infinitely far into the past, before the rules were implemented. The Julian calendar was fully adopted around 4 AD, but historians and astronomers routinely give exact dates long before then, with the understanding that the Julian rules are being retroactively applied. Exceptionally (and confusingly), early Roman dates are often given in the actual calendar used in Rome at that time.
3. I avoided the less obscure word "equal" since it has a large number of meanings, many undesirably loaded, and indeed "equal time" itself has a meaning in American law.
4. This abbreviation follows the precedent of "UTC" (and "ISO") in compromising between the English and French word orders, as well as avoiding CET, Central European Time.
5. I intended that TE refer to the various time units in this scheme, and CTE to a canonical alignment of them, much as how CE refers to an alignment of years, but I am not consistent on this minor point.
6. CTE is not merely a time scale in the sense that the other examples are, as it alters calendar dates as well as the day length.
10. Of course, a second is not a very long time, but much human perception happens at the subsecond level, and if I'm waiting for a particular moment, I feel it's not quite enough to know it only down to the second.
11. The traditional plural is of course tierces, which is annoyingly disyllabic; the use of one form is on analogy with, e.g, stone as a weight.
12. There have also been those who shun the "pagan" month names—e.g., March is named after the Roman god Mars—but few care anymore.
15. I considered using J2000.0 as an epoch too, except (a) it's not clear how to place it within 2000 CTE, and (b) it will be superseded in about twenty years and soon forgotten.
16. I considered many possible epochs, including fairly complicated means of maximizing agreement with Gregorian dates. In the end, I rejected them all as too arcane to be accepted as non-arbitrary.
17. E.g., UTC is used as civil time, and TAI is emerging as the standard leap-free atomic scale.
18. TAI is a real-world scale, defined by the actual value of clocks, which may be inaccurate (and known to be inaccurate), whereas TT is a theoretical ideal, though in practice realized by atomic clocks. UTC and TAI are only defined hitherto for a few decades, whereas TT is used by astronomers for moments in the remote past and remote future. The civil time standards may even be subject to further tweaks, such as the proposed "TI" (international time), a leap-free replacement for UTC slated for 2022, but TT trucks on. Scales such as TDB are correlated to TT, and astronomical values such as ΔT are defined in terms of it.
19. As this proposal is young, minor alterations on the subsecond level to make it a better scale would still be acceptable. I mostly have in mind relativistic correction. I have found little information on galactic center time frames or even local group ones, but they exist in theory, although the difference is likely very tiny.
20. Most of the computations are done with the obsolete Astrolabe package or its successor Astronomia.
21. By sampling a longer sequence of seasonal points, the variation could be further smoothed out.
23. The year length in CTE days is computed by 359.999963 - 0.0004 sin(2π(y-640)/41000) + 1.1×10^-9·y, where y is the number of years from the epoch. This is minimally designed to accommodate the known cycle and the current rate of change of the sidereal year while giving a fairly good fit for the known values over several millennia. Tweaking the parameters does not substantially change the shape of the trend.
28. Many articles on this subject take a constant length for the year as a given, even over billions of years, and use this assumption to infer the day length, month length, and so on.
31. Ussher did not specify a meridian. Some suggest his intent was Jerusalem, whereas others would place it at a candidate Garden of Eden, as I have.
32. ΔT (the difference between TT and solar time) this far back is very approximate.
34. The author provides a much higher value for ΔT than most other sources in order to make this identification.
35. This is the most widely accepted date, although a few scholars argue for two days later.
36. There are three dates commonly given for this epoch. This is the middle one.
39. This estimate is based on the tradition that the Olympics start on a midsummer full moon.
47. The date of 0030 Apr 07 runs a close second
69. This is the most recent 0.0.0.0.0 date in the Mayan calendar, 1,872,000 days after the previous epoch, also on the winter solstice. Popular mysticism authors predicted cataclysms at that moment. To my knowledge, none were observed.
71. This time is taken from your computer's clock, not any external source.
72. I can only estimate the number of leap seconds there will be at this point, if indeed leap seconds are still used.
75. While I cannot find an exact date, a point was made of lowering it right at the autumnal equinox, so it is likely that is when it is intended to be extracted.
77. No time of day is specified and, unlike the Westinghouse capsule, there is not attempt to refer to astronomical events to help future generations get the time right. Given this, and anyway the great uncertainty of ΔT, I provide only a date.
79. Because I dislike the large number of abandoned and dated websites on the Internet, I will note here that this page will have to be updated in 69163, to reflect that the next transit will be in 224508.
80. The proof takes a few steps but is not hard. Fix a moment, and let s_x be the number of seconds of type x from the epoch. Then since a CTE second is 46751/46080 SI seconds, we have 46080s_si = 46751s_te. Since both must translate to the same date and time, a fortiori they have the same time of day, so s_si ≡ s_te (mod 86400). Since the earlier ratio is in lowest terms, we get that 46080 | s_te, so that by the congruence gcd(86400,46080) = 5760 | s_si. Writing s_si = 46080k, we get 46751s_te = 46080×5760×k, so that as before 46080×5760 | s_te. But that product is a multiple of 86400, so 86400 | s_te, so by the congruence 86400 | s_si, and by the same argument we get 46080×86400 | s_te. But that many CTE seconds is exactly 128 CTE years, thus the original moment must be at the start of a year.
81. In fact, as the above proof shows, we have the stronger result that the two scales can only read the same time of day at a whole number of seconds if the time is at midnight, at the start of a year CTE, every 128 years CTE from the epoch.