What's Metric Time?

Thetechguy2000 is a pretty smart kid who has a new video up talking about metric time.  He has obviously read Lyle Zapatopi's A Guide to Metric Time, since he mentions Lyle's proposed quinto prefix for 10^-5, so 1 quintoday is equal to 0.864 second. He also talks about Swatch .beats Internet Time.

MJD56161.908 and 33 quintodays

Stardates again

I recently was reading Star Trek Chronology by Michael and Denise Okuda, which has some information about stardates.  They worked on all the Star Trek TV series, except the original one.  On page 95 they state:

Editor's Note: The year 2323 works out as the zero point for the system of stardates developed for Star Trek: The Next Generation, assuming that the beginning of year 2364 (the first season of Star Trek: The Next Generation) was stardate 41000, and that stardates progress at 1000 units per year. In other words, under the Next Generation system of stardates, January 1, 2323 would seem to correspond to stardate 0. This probably shouldn't be taken too seriously, because Star Trek's stardates have never been too internally consistent, but we're mentioning it here because it's kinda fun. (No, we don't know how these stardates relate to the stardates used in the original Star Trek series or the movies, nor do we know what stardates would have been for years between the movies and this point. See the Appendix I [Regarding stardates] for more information on stardates.)

As they said, "stardates have never been too internally consistent", which is why some speculate that stardate 41000 was in May or that there were less than 1000 units per year.  For instance, on the next page they say:

Editors' confession: In "Dark Page" (TNG), an entry in Lwaxana's journal dated stardate 30620.1 is established to be during the year in which she got married, 2328. Unfortunately, under the  Star Trek: The Next Generation system of stardates (which allocates 1,000 stardate units per year, and puts the beginning of the year 2364 at stardate 41000) the beginning of the year 2328 should be around stardate 5000.  Star Trek technical consultant (and Chronology co-author) Mike Okuda decided that a four-digit stardate would be confusing since this sounds like an Original Series number, so he arbitrarily picked 30620, even though it is not consistent with stardates used elsewhere in the show.

In "Appendix I: Regarding Stardates" they give more information, such as the fact that "As with the original series, an increase of a single unit within an episode corresponds to about 24 hours, even though this is inconsistent with a 365-day year."  They also relate a theory that stardates in The Original Series represented months and days from the beginning of a mission, so 1312 indicated thirteen months and twelve days, and 5928 was about five years, although there were plenty of stardates which would have more than 31 days, as in "Errand of Mercy", which took place between stardates 3198.4 and 3201.7.  Assuming 100-day months, that would be more than twelve years spread over 46 months.

In Star Trek 30 Years Special Collector's Edition, it states that Gene Roddenberry "borrowed the notion from the Julian date currently used by astronomers...Roddenberry borrowed the five-digit [Modified] Julian date, shortening it to four digits and renaming it 'stardate.'" I've long suspected that this was the case, due to the strong similarity, such as the subtle use of decimal time: "For Star Trek, Roddenberry added a single digit after the decimal point (50335.2, for example) to represent one of 10 time increments in a 24-hour period."

There was an earlier work, Star Trek Spaceflight Chronology by Stanley and Fred Goldstein, published the same month as Star Trek: The Motion Picture in 1979.  Based upon references in The Original Series, the show was set in the early 23rd century, 2207-2210.  In the 1980s FASA made a game called Star Trek: The Role Playing Game which used this Chronology.  They created "reference stardates" in the form C/YYMM.DD, where C is the century (actually the second digit of the year), YY is the last two digits of the year, MM is the month and DD the day, so January 1, 2000, was 0/0001.01, and the episode "Where No Man Has Gone Before" was 2/0705, or May 2207.  Stardates in the 1900s are negative, so this episode aired on -1/6609.22, which was also the day my sister was born.  Of course, this early Chronology was ignored when TNG was made, and TOS was then set to about 300 years after it was produced.

I posted last month about stardates in Star Trek Online.  With a bunch of math and experimentation, and with a little help from the webmaster of STO Academy, I figured out exactly how they work.

There are several stardate calculators online which do not all agree with each other. I recognized right off that STO's are almost the same as the TNG stardates on TrekGuide.com. This page was changed last year, but the archived page says:

there are exactly 1,000 Stardates per year...Stardate 00000.0 began on May 25, 2322, at 00:00 hours.

Subtract 400 years and you get the following STO stardates:

Stardate: 87000.00 Earthdate: 5/25/2009 12:00:00am UTC

Stardate: 88000.00 Earthdate: 5/25/2010 12:00:00am UTC

Stardate: 89000.00 Earthdate: 5/25/2011 12:00:00am UTC

Stardate: 90000.00 Earthdate: 5/24/2012 9:28:06am UTC

Wait, what? This threw me at first. This year is different from previous years. That is because it's a leap year, so instead of 365 days there are 366, but there are still exactly 1000.00 stardates from January 1 through December 31. That means that the stardates run a little slower than previous years, so instead of 2.74 per day there are 2.73, or about one second slower per 0.01 stardate.

The one thing that does stay constant is that every year starts on xx605.48:

Stardate: 87605.48 Earthdate: 1/1/2010 12:00:17am UTC

Stardate: 88605.48 Earthdate: 1/1/2011 12:00:17am UTC

Stardate: 89605.48 Earthdate: 1/1/2012 12:00:17am UTC

Stardate: 90605.48 Earthdate: 1/1/2013 12:00:17am UTC

That is because there are 221 days from May 25 to January 1, and 221/365 = 0.60548, even though it's a leap year. So with this information, you should be able to use stardates anywhere, not just in the game.

MJD 56154.199

STO 90226.24

FASA 0/1208.14

Update (56158.121): I should include an actual formula for Star Trek Online stardates:

1000×(day-of-year/length-of-year + year - 1923 + 221/365)

Where day-of-year is the number of days from January 1, including the time as a fractional day, found by dividing the hour by 24, e.g. January 2 at 12:00 UTC is 2.5.  Length-of-year is 365 in common years, 366 in leap years.  221 is the number of days from May 25 to the end of the year.  So for August 19, 2012 at 02:50:54 UTC: 1000×(232.11868/366 + 2012 - 1923 + 0.60548) = 90239.68.

Truncated Julian Day

For years I have seen two different definitions of Truncated Julian Day (TJD).  One said that it was the Julian Day with the first three digits truncated, so that it was never more than four digits.  The other said that it was a count of days midnight of JD 2,440,000, or May 24, 1968 (MJD 40000.0).  These two definitions resulted in the same number, until JD 2,450,000, or October 10, 1995 (MJD 50000.0).  By the first definition, TJD changed from 9999 to 0, and by the second to 10000.  I never knew the whole story, which definition is correct, and how it came to be, until now.

I just discovered the original proposal for TJD, NASA Technical Memorandum 80606, "A Grouped Binary Time Code for Telemetry and Space Applications" by A. R. Chi, published December 1979 by Goddard Space Flight Center.  It was defined as part of NASA time code PB-5:

The Day Count System - The four decimal digit day count system is derived from the truncation of the three most significant numbers of the present seven decimal digits of Julian Day Number (JDN), thus the name the Truncated Julian Day (TJD). TJD is arbitrar:ly chosen to begin from 0 at midnight May 24, 1969, (sic) and ends 9999 at midnight October 9, 1995 after which it recycles to zero. The repetition period is 27.4 years. A conversion table from TJD to calendar data in year, month, and day is given in Table II. The four decimal digits of a TJD number are represented by a 14-bit binary number.

By this definition, TJD is always a truncation of the Julian Day, and is never more than four digits, or 9999.  Since it is a binary field represented by 14 bits, it could not physically exceed 16383. Furthermore, this is an integer value.  The time of day is not represented as a decimal fraction, but by a count of seconds of the day from midnight, as well as optional milliseconds, microseconds and nanoseconds.

But that's not the whole story.  A modified time code called PB-5J was later defined with 16 bits for TJD, which allows for integers up to 65535, corresponding to dates up to October 28, 2147.  TJD values greater than 9999 can be found for the year 1995 and after, and a NASA web site converts to and from TJD for any positive value.

So there actually are two different definitions of Truncated Julian Day, one in PB-5 and the other in PB-5J, and it appears to me that the latter superseded the former.

TJD 56153/76300

Mars Time

At August 6, 2012, 05:14:39 UTC SCET (MJD 56145.21850) the Curiosity rover landed in Gale Crater on Mars.  (SCET stands for Spacecraft Event Time, since it took until about 14 minutes later for the data transmission to reach earth.)  In Mars time that was 05:50:16 AMT (MSD 49269.24), about 15:00 local time.  AMT is Airy Mean Time, also known as Coordinated Mars Time (MTC), because it is the Local Mean Solar Time at Airy Crater, which marks zero longitude on Mars.  MSD is Mars Sol Date, and like Modified Julian Dates it is a count of Martian days, which are called "sols", but from December 29, 1873 (MJD 5521.5).

Another sol count is started whenever a craft lands on Mars, so that was on Sol 0 for Curiosity.  There is currently one other craft active on Mars, Opportunity, which was on Sol 3034.  Opportunity is near the Martian Prime Meridian, one hour behind AMT, but Curiosity is on the other side of the planet, 9 hours, 9 minutes and 40 seconds ahead of AMT.

Note that sols are longer than earth days by nearly 40 earth minutes but are divided into 24 Martian hours, so each hour, minute and second is 2.7% longer than those on earth.  Thus, the mission operators start their shifts 40 minutes later each day.  To keep track, they use a Java program call Mars24, which you can download from NASA.  By default it displays AMT and LMST for Curiosity and Opportunity, as well as MJD and MSD with two digits of decimal time.  You can also find more information at Wikipedia.

MJD 56148.377
MSD 49272.317

Stupid people: another reason we need metric time

From here, via Images | These images are pretty sweet.  The video is funny, too.  And just under 2 minutes, too.

MJD 56135.076

Wither Wikipedia?

There has been some buzz for the past few days that Wikipedia is running out of editors.  Actually, the original article was more about the shortage of admins, but whatever.  It's old news to me.  Whenever I make a change on Wikipedia, I always prepare to have to defend it.  It used to be that any change would get immediately challenged and/or reverted, and you would have to spend a lot of time and effort defending it, citing sources and negotiating with other editors over the wording until a consensus was reached.  Each article had its dedicated editors, ready to protect it from spurious changes, while others seemed to scan every change on Wikipedia and swoop in. Now, that rarely happens.  After I make a change, I wait, and wait, expecting a battle, and nothing happens.

I think that a big reason is that Wikipedia is finished.  Obviously it will never actually be finished, but in its early days, there were still lots of major subjects that lacked articles, and lots of articles which lacked much information.  That is not nearly so much the case today, with over four million articles on the English version of Wikipedia, covering the most obscure of subjects.  In fact, I think that many articles have too much information, being cluttered with a lot of insignificant details that can make the more important ones difficult to pick out.  With so much information already there, there is little incentive to add anything.

Another reason that people don't want to edit Wikipedia is what I described above, that it has a reputation of being just too damned difficult.  Anything you edit is likely to get reverted, and you have to be prepared to spend a lot of effort defending it.  There have been plenty of stories about people trying to correct facts about themselves, and not being allowed to.  Amateur editors have a reputation of being actually hostile towards experts trying to set facts straight.  There also has been a slew of rules made that the casual users do not know about, and run afoul of anytime they try to make a correction.  Nowadays, the dedicated editor's role is more that of curator, maintaining the fiercely fought consensus against the hoard of vandals and spammers.  Aside from those with a stake in their personal fiefdoms, there is not much incentive in joining their ranks.

To be honest, sometimes it can be fun to do battle.  I feel disappointed when nobody challenges my edits.  Am I really that good that they cannot dispute me, or is there nobody left minding the store?  I actually depend on other editors to keep me honest, by reviewing my edits and polishing off the rough edges.  But even when they don't, that anticipation forces me to be more thorough, to post my sources and to refine my wording.

And if any n00b tries to change my edits, I put the hammer down on them!

MJD 56128.316

Star Trek Online

I recently began playing the massively multiplayer online role-playing game (MMORPG) Star Trek Online (STO), which is now free to play.  Since I am interested in stardates, I checked out how they were used in the game.  You can access them through your logs by hitting "J".  Your milestones in the game are all stamped with the real-life calendar date and a stardate.  This allowed me to determine the basis for their stardate calculations.  There is an STO stardate calculator already, but it's a little off, and does not make the basis clear.

The game is set in the year 2409, about 45 years after the beginning of Star Trek: The Next Generation (TNG), and about 30 years after the last TNG movie, Star Trek: Nemesis.  The game was released in February 2, 2010 (55229), but the in-game year has remained 2409 two years later, and presumably was also 2409 during the beta testing in 2009, so it may be that the year was intended to be exactly 400 years in the future.

The current stardate in STO is about 90132.  From archived discussions online, I have determined that the stardates were around 87700 when it was released.  Coincidentally, according to the stardate calculator at TrekGuide.com, these are the stardates exactly 400 years in the future.  At least, according to my recollection of TrekGuide's formula, which counted exactly 1000 stardates per year, starting from May 25, 2322 (169296).

However, when I went to check on TrekGuide.com, the dates did not work out.  Instead of 90131 for this date in 2412, I get 86330.  What's going on, I wondered?  On examining TrekGuide's web page, I found that there are actually 918.23186 stardates per year, counting from July 5, 2318.  Could I have misremembered so badly?  Thanks to the Wayback Machine, I was able to determine that my recollection was, in fact, correct.  Sometime between July 2010 (55399.860509) and July 2011 (55759.40857) the page was changed.  (Update: It looks like it actually happened around April 7, 2011 (55658).)  IMHO, I believe that they're over-thinking it, and should have stuck with the original formula.  I doubt that Star Trek's creators were that accurate.

STO is, in fact, using the original TrekGuide stardate formula, as it was when the game was released, but shifted 400 years.  That means that I can calculate STO stardates for the present era as exactly 1000 per year, beginning from May 25, 1922.  This gives an alternative to the "contemporary" stardates that TrekGuide gives, which are based on air dates from 1987-2001.  Using TrekGuide's (original) TNG stardate calculator with dates exactly 400 years from now gives stardates at most a few hours off, so it just needs a little tweaking.

MJD 56119.713
Stardate 90132.02

New metric units

I received the following from James Strom, with my comments added:

Hi! I like to dabble in things like you have at your decimal time site. Decimal time is definitely an idea who's time has come.

Whose time has come?  I'd say it already came and went two centuries ago! 

But for it to be practical it must be compatible with any metric system in use. If the second were changed by anything other than by a power of ten then the cost of conversion would be enormous. The definitions of a joule, newton, ampere, volt, etc. would all have to be changed as well. Can you imagine having to multiply your wattage by 0.864 cubed to arrive at the new watts? A simple way around that is to simply keep the second either the same or 10 or times smaller. I would recommend the latter so as to allow a second to be equal to 1/864th of a milliday and for other reasons.

I agree that the metric system (SI) is a serious impediment to introducing new time units.  Redefining the second would be a practically impossible undertaking, regardless of whether it's by a power of ten.  In fact, with today's technology it's just about as easy to convert decimally as otherwise.  And you cannot simply change unit values while keeping the same names, or nobody would ever know if you were talking about the old or new units.  Remember that everything in the world for hundreds of years has been recorded using essentially the same second.  Likewise for other units, although not for as long.  Creating all new units with the same names, even if they're a factor of 10 different, would create chaos.

I have noticed that if Greenwich is used as the prime meridian then 10 time zones can be created which fit very neatly with the continents. So forget Swatch's idea.

You apparently mean Swatch eliminating time zones.  You do not say why we should favor 10 time zones over one, or 24.  We may as well reform everything at once.  Business today is international.  So is my family.  It seems to me that time zones one-tenth day (2.4 hours) wide lack the advantages of smaller one-hour zones, while being only halfway to a single one for the world.

Any modification of our current system should have as a high priority ease of convertibility. The system described below has that in mind. In fact, it could be used by anyone right now without any trouble.

There is nothing that is as easy to convert as no change at all.  You need to have major advantages to outweigh the disadvantage of any conversion, no matter how easy it might be. And I don't really think that your proposal would be as easy as you claim for those who are currently using these units.

It won't be necessary for any international organization to get everyone else to agree to the change for it to work.

Who would use it, then? 

It also assumes that lower case letters will someday be eliminated.

Why?  That would eliminate half the available symbols for units and prefixes.  It would also require everyone on the Internet to SHOUT all the time. 

I've devised a modification of the current metric system that I think would be simpler, more intuitive, and easy to convert to. It would be similar to the change from the old cgs system (centimeter-gram-second) to the mks system (meter-kilogram-second).

These two systems used different names for nonequivalent units.  It was also a big pain in the ass to change, and not everyone has, yet.

As it is now the basic unit of mass requires a prefix (kilo) and doesn't correspond with weight.

The kilogramme was originally defined as a unit of weight.  The definitions of mass and weight were separated after it was realized that an object's mass is relatively constant, but it's weight is not.  My sisters in Colorado gain weight every time they come to visit me on the coast, but their masses remain the same.  (Unless my Mom is cooking.)  Scales do not actually measure mass, but the force of gravity acting on a particular mass.  However, for everyday use we can use our weight to approximate our mass.  To those relatively few professionals who have to use units of force to measure weights, it is advantageous that mass and weight have different values, lest they get confused.

The unit of density is, unlike almost all other measurement systems, is not even close to that of water but, in fact, less than that of air. This makes it difficult to visualize them.

The SI unit of density is kg/m³.  Water is 1000 kg/m³, or 1 t/m³ = 1 g/cm³ = g/ml.  I have no problem visualizing a cubic meter of water, or of a milliliter (cc).

On the other hand, if a system were devised that made the unit of acceleration close to the force of gravity on earth then it would be easy to picture it. Also, weight would become almost synonymous with mass. This would make it easy to imagine force in terms of these units. And if the unit of density were the same as that of water then there would be the obvious benefits.

I don't have a problem "picturing" these things, nor do I see how that is necessary.  I already weigh myself in pounds or kg, not 780 newtons.  I imagine newtons only when measuring small things in a lab.  (Which I have not done in decades.)  The benefits are not obvious to me.

This is what I propose:

1) The new unit of mass would be called a ton but would have the same mass as a kilogram.

We already have several different ton units causing confusion, and you want to add one that is not even close? 

2) The "new" meter would be equal to one tenth of an "old" meter or a decimeter.

Again, I don't see the benefit of changing the value by an order of magnitude. 

3) The day would be divided into 1,000 minutes. Each minute, in turn, would be divided into 864 seconds. Thus the "new" second would be equivalent to one tenth of an "old" second.

A compromise that has all the problems of both, and the benefits of neither! 

I won't go through the rest, since I am not interested in changing the metric system.  That ship sailed a long time ago.  It took a lot of time and trouble to get the entire world to accept the current metric system, and now that it's done, there is no advantage to massively change it now, even if it's not perfect.  We have discussed these issues ad nauseum on this site in the past.

4) The ampere would remain the same and would be defined as the amount of current that would produce a force of 2X10^-8 Newtons between two wires, etc., in terms of the new units. In other words; the ampere would be 1/10,000th of the value that it have if it were defined by the basic three units alone. That's an improvement over the current system that requires division by the square root of ten million.

5) The unit of angle would be 1/1,000th of a circumference. This would align it with the units of time. The earth, in relation to the sun, would rotate one degree per minute.

6) The unit of temperature would be defined as 1/1,000th of the triple point of water. A celsius-like system could be used as well so that water would freeze at 0 and absolute zero would be -1000.

7) The unit for amount of substance would not change except for its name. It shall be called a quant instead of a mole and be represented by a Q instead of mol.

8) The unit of luminosity would be equal to one joule per second per steradian in terms of the new units and be renamed the young (after the scientist, of course).

Each of the units shall be represented by one letter only without regard to upper or lower case status.

The prefixes shall follow this rule as well.

Thus there will be 26 common units and a like number of prefixes.

Ratio refers to the ratio of the size of the "new" units to that of the "old" ones in the mks system.

Unit       Symbol     Quantity          Formula      Ratio  

Ton                T       Mass                     T            1            
Meter             M      Length                  M          0.1
Are                R       Area                 M^2        0.01
Liter               L       Volume             M^3       0.001
Second           S       Time                    S          0.1      
Hertz              Z       Frequency          1/S           10
Einstein          E       Velocity              M/S            1
Gal                 G       Acceleration   M/S^2          10
Bole                B       Momentum     T*M/S           1
Newton           N       Force         T*M/S^2         10
Planck            P        Action         T*M^2/S        0.1
Joule              J        Energy    T*M^2/S^2           1      
Ampere          A       Current                  A            1
Coulomb         C       Charge              A*S         0.1
Weber            W      Flux                    J/A           1
Volt                V       Potential              J/C         10
Henry             H       Inductance          W/A          1
Farad             F       Capacitance         C/V      0.01
Siemens         S       Conductance        A/V        0.1
Ohm               O      Resistance           V/A         10
Gauss             U       Strength             A/M         10
Maxwell          X       Intensity             V/M        100
Degree           D       Angle                     D       0.36
Kelvin             K       Temperature           K  0.27316
Quant             Q      Amount                   Q           1
Young             Y      Luminosity               Y     6,830  


Symbol  Prefix  Multiple    

V                      10^33      
W                     10^30
X                      10^27
Y          Yotta     10^24
Z          Zetta     10^21
E            Exa     10^18
P           Peta     10^15
T          Tera      10^12
G          Giga       10^9
M         Mega      10^6
K            Kilo       10^3
H         Hecto       10^2
D          Deka       10^1
S           Deci      10^-1
C          Centi      10^-2
L           Milli       10^-3
U         Micro      10^-6
N          Nano      10^-9
B           Pico     10^-12
F        Femto     10^-15    
A           Atto     10^-18
O         Zepto     10^-21
J          Yocto     10^-24
Q                      10^-27
I                       10^-30
R                      10^-33

This system is meant to work with decimal time, a reformed calendar, and the eventual elimination of lower case letters.

But that is the subject of another email.

(Don't worry about copyright or anything. I don't care who gets credit for what. I only bring this up because while googling your name I found some idiot who was trying to take credit for coming up with an obvious idea that dated back to the French Revolution. There's all sorts out there.)

MJD 56115.995

Leap second

On June 30, 2012 (56108.9999884), a leap second was added to Coordinated Universal Time (UTC) at the end of the day, to keep clocks within one second of Greenwich Mean Time (GMT).  23:59:59 was followed by 23:59:60.  This caused some computers to crash.  Since the software should have been able to handle this, the fault is clearly a bug in the software, similar to the Y2K bug.  However, it wouldn't matter if leap seconds did not exist.

I do not think that leap seconds are necessary.  They only are if you want to keep UTC within one second of GMT (UT1).  However, few use GMT today.  In the first place, it is the true solar time only for those exactly on the meridian of Greenwich.  Everywhere else has a mean solar time that differs as you go east or west of Greenwich, so before railroads every town had its own time.  But today we use unified time zones, which are (mostly) one-hour offsets from UTC.  The time in these zones in theory may be a half-hour more or less than actual local mean solar time, and in practice it is in many places much more than that.  Plus, many places practice daylight saving time for part of the year, adding another hour.  Even Great Britain is not always on GMT, and is considering advancing their clocks another hour to be in sync with the Continent.  Nobody actually follows solar time anymore.  So why should we care about GMT?

What would happen if we simply abandoned leap seconds is that UTC would start to drift away from Greenwich.  Every few years the difference would grow by one second.  Eventually, hundreds of years from now, the difference would add up to a whole hour.  But so what?  Local times today are already arbitrary and decided by governments.  If a particular region felt that the change had progressed too much, they could simply adjust their time zone when they chose.  This already happens all the time.

UT is not the only existing time scale.  Various other scales have been defined based up on the same atomic second.  The atomic second is based upon the ephemeris second of 1820.  Since the mean solar day is gradually getting longer, and varies from year to year, the day is slightly longer now than 86,400 atomic seconds, which is why leap years are added.  International Atomic Time (TAI) was synchronized with UTC in 1958 and is now 35 seconds ahead of UTC.  Terrestrial [Dynamical] Time (TT) is 32.184 seconds behind TAI and was introduced in 1984 to replace and be continuous with Ephemeris Time (ET) back to 1900, so it is currently 67.184 seconds ahead of UTC.  GPS time is 19 seconds ahead of TAI, and therefore currently 16 seconds ahead of UTC.  These time scales do not use leap seconds, so the difference between them is constant, but the difference between each with UTC is variable.  Simply eliminating leap seconds would fix UTC in relation to these time scales.

There has been discussion for the past few years about eliminating leap seconds, and this incident will likely increase pressure to do so.

MJD 56112.435

The Higgs boson has been found

I have been watching the live video from CERN in Switzerland and there is a 4.9 sigma signal around 125-126 GeV.  It's being couched in conditional qualifiers, and still needs to be followed up, but they really think that this is it.  You can read more at BBC News.

MJD 56112.382