Wednesday, January 5, 2011

Days of Time

Before I get started on the next section I am going to take two more blog posts on how we got to where we are at today.

Mayan Calendar and Moon Cycles
I don't know how many times I have heard the Mayan Calendar is much more accurate than the Gregorian Calendar and that it ends in the year 2012. Please define the meaning of "more accurate" to me.  If by more accurate you mean that it does a better job of keeping in sync with how many actual days there are per year then the two Mayan Calendars are woefully inadequate compared to the Gregorian Calendar.  Two?  Yes, there are two of them.  Actually one could argue that the "Long Count" means they actually have three calendars. Here they are:

The shorter calendar is the Tzolk'in.  It consists of 13 equal periods of 20 days.  Other than it perhaps being used for crop planting or for the theories it is rather misunderstood why they picked the cycles of 20 days.  In the old world, the numbering system of science was the sexagesimal (base 60) system. It does appear likely that the Mayans were using a modified base 20 system though. Note that 13 * 20 gives us only 260 days per cycle.  The main thing of interest here is that it is not aligned with the cycles of the moon.  This is of particular note because both the Jewish and the Islamic and many other calendar systems are tied to the cycles of the moon.  It wasn't until the Julian calendar was created that the days per year were being used, albeit wrongly.  Here is a short program I wrote that shows how the Tzolkin and the Haab calendars finally align again after 73 Tzolkin years and 52 Haab years:

Tzolkin & Haab Year Synchronization

Do not panic.  Mostly what you are seeing is the output of the program itself which I merged into the comment header.  The tiny little program is down at the bottom.

The other calendar is an eye opener.  It is called the Haab which consists of eighteen periods of 20 days each with an extra non year time of five days called the Wayeb.  The fact that it also uses 20 day cycles strengthens the idea that they may have used a base 20 number system.  But note that means these years always have 365 days, not the 365.25 days of the Julian Calendar nor the 365.2425 days per year of the Gregorian Calendar.  And thus my statement that it is not the most accurate calendar system if you intend to synchronize as closely as possible to the sun from one vernal equinox to the next vernal equinox.

So what is the significance of the year 2012?  You will note that these two calendars are almost always staggered from each other. By using haab years as a baseline, they synchronize every 52 years.  For longer periods of time they use what is called the long count.  What the date in the Gregorian calendar of December 21, 2012 corresponds to is just the first day of the fourteenth b'ak'tun.  I have studied this system extensively and the first thing I can say is that this day is nothing more than that.  Their calendars don't end then and can in fact go on into perpetuity not only forwards but backwards as well. Not only that, but if there would be any adjustments made it would be handled much the same as the Gregorian.  The problem with the Gregorian is coming up with how many days there really are in a year.  If the actual measurement is only 365.24219 days per year as I have read some place, then the Gregorian length of 365.2425 days per year is is too big.  In that case we would be adding an extra day every 3225.8 years and would need to drop a day.  But if it is like this Wikipedia page on leap years indicates:

we are supposedly not having too much added each year but too little. Come back in 3226 years and see if a day needs to be added or dropped.  In the mean time please realize the "Leap Year" article is probably correct because all of the leap seconds so far are being added, not subtracted.  The Gregorian calendar is about as accurate as you can get in terms of how many days (360 degree rotation of the earth) there are in a year (a complete 360 degree revolution of the earth around the sun to come back to the same position from one vernal equinox to the next vernal equinox).

Okay, what does this have to do with our DST problem?  It shows that time measurement has always had anomalies. It has always been limited by the ability to measure it, and first getting away from lunar cycles and instead using the length of a solar year as expressed in days per year.  But we had to get how many days there were per year with the Julian as the first attempt at getting it right followed by the Gregorian.  Next, we will be showing how we got hours, minutes and seconds done. This isn't as easy as you think.  Galileo Galilei didn't come up with the idea of the squared rule for falling bodies very easily until he put the balls on an inclined plane and used distances covered as a way for showing that acceleration was proportional to the square of the time and a constant.  That is because he had no accurate time-piece to measure things.  But you can actually use distance traveled to measure time. So, next, hours minutes and seconds.  We didn't even have accurate hours for everybody until the end of the 19th century and accurate clocks for everybody until the 20th century.  Only sea-farers had accurate chronographs from the time John Harrsion invented them up into the 19th century.

Marine Chronometers

Railroads also needed accurate chronometers.  Oh yes, I forgot to mention that all of my operating systems have had two more time zone updates due to DST.  If DST is so simple then why do we keep having these changes?