Holdun Consistent Calendar
H O W
Abbreviations used in text:
TC - Traditional Calendar (Sunday first day of week version)
HCC - Holdun Consistent Calendar
The bottom line at the top
In the HCC the length of a second is adjusted to allow for the consistent number of days (336)in a calendar year.
Length of a second
In the TC the length of a second is adjusted to allow for the consistent number of days in a calendar year.
A second is defined as the time that elapses during 9,192,631,770 cycles of the radiation produced by the transition between two levels of the cesium-133 atom.
Consider the length of a HCC second similarly as the time that elapses during 8,456,647,011 cycles of the radiation produced by the transition between the same two levels of the same cesium-133 atom.
There is nothing in nature that demands that a tic of a clock is as long as it is. The only important thing for yearly calendar time keeping though is that at the end of a year, the earth has made a (as close as can be managed) 360 degree rotation around the sun. That is - one solar year (or sidereal year).
To achieve the aim of a much simpler and much more practical yearly calendar, the HCC surrenders the mission of a practical daily calendar time keeping (tracking the rotation of the earth on it's axis) to focus on the aim of simplicity and practicality within the constraint that, above all else, that at the end of a year the earth has made an exactly 360 degree rotation about its axis. Once again the 'no free lunch' rule comes into play.
While there are 86,400 seconds in a TC day, there are 79,482 (and change) seconds in an HCC day. So an HCC day is roughly 92% the length of a TC day. This saving of approximately 8% goes toward accounting for the elimination of 29 non-leap year days (30 leap year days) in the yearly calendar in order to achieve the aim of a 12 month by 28 days per month calendar.
Length of a Tic
In programming on a PC the shortest amount of time that can be added or subtracted is the millisecond. It would be nice to program in micro, nano, or better yet picoseconds, but that is beyond what is available on a PC. A supercomputer with access to an atomic clock is on my Christmas List. But for the day to day application of the HCC, the millisecond is sufficient.
Consider the millisecond as a 'tic'. In the TC, there are, as the name would imply, 1000 tics to a second, then 60 seconds to a minute, sixty minutes to an hour, 24 hours to a day. But in the HCC, while there are 1000 HCC tics to a HCC second, those HCC tics are about 92% shorter than a TC tic. (that is to say an HCC tic is slower than a TC tic), so an HCC second (1000 HCC tics) is about 92% less than a TC second of 1000 TC tics, an HCC minute of 60 HCC seconds is about 92% less than a TC minute, an HCC hour of 60 HCC minutes is about 92% less than a TC hour, an HCC day of 24 HCC hours is about 92% less than a TC day.
So.... How many 'tics' to an HCC second? This question is the heart of the HCC calendar.
There are probably many approaches to answering this question, but this was the one I used.
First off, how many seconds are there in TC year? Because of leap years, it depends. So how many seconds in an 'average' year?
To account for leap years, first consider the Gregorian Calendar rules of when a leap year is added.
1. if the year is evenly divisible by 4, it will be a leap year...
2. unless the year is evenly divisible by 100, then it won't be a leap year...
3. unless the year is evenly divisible by 400, then it will be a leap year.
For example:
1995 - not evenly divisible by 4, so not a leap year.
1996 - evenly divisible by 4, not by 100, so a leap year.
2000 - evenly divisible by 4, 400, so a leap year.
2100 - evenly divisible by 4, 100, but not by 400 so not a leap year.
So in every 400 year period there are:
400 years of 365 days each.
In addition there are:
100 years divisible by 4 for another 100 days.
So there would be:
(400 x 365) + (100 x 1) days in 400 years.
But 3 of those years (divisible by 100 but not 400) are not leap years.
So in 400 years there will be:
(400 x 365) + (97 x 1) days in 400 years.
Which equals:
146000 + 97 = 146097 days in 400 years.
Division by 400 (to give average number of days every year) will come later to keep fractions at bay awhile. If you are curious and since the calculator is at hand, there are 365.2425 days in a TC year on average. So in non-leap years the TC calendar is shorter than an average year, while in a leap year it is longer than an average year.
Note that a solar year is 365.2422 days. This is the aim of the TC calendar which it will one day achieve when a new TC calendar rule proposal is adopted to eliminate the leap year if the year is divisible by 4000. As you might appreciate, there is no great rush.
Then to find the number of seconds in a year in the TC:
# of hours = 146097 days/400 yrs x 24 hrs/day = 3,506,328 hrs/400 yrs.
times 60 min/hr = 210,397,680 min/400 yrs.
times 60 sec/min = 12,622,780,800 sec/400 yrs.
divided by 400 yrs = 31,556,952 sec/yr.
Now we turn our attention to the HCC.
Find the number of seconds in an HCC year:
12 months/year x 4 weeks/month x 7 days/week = 336 days/year.
times 24 hrs/day = 8064 hrs/year.
times 60 min/hr = 483,840 min/yr.
times 60 sec = 29,030,400 sec/yr.
So now the question becomes: since there are more seconds in a TC than an HCC, How much bigger does an HCC tic need to be to compensate for this difference?
Find relative size of HCC to to TC tic:
# of sec/yr in TC (31,556,952).
divided by # of sec/yr in HCC (29,030,400).
equals 1.08703125 TC units to HCC units.
Therefore, in the TC one tic = 1 microsecond, 1000 tics equals one TC clock second.
In the HCC then one tic = 1.08703125 microsecond, 1000 tics equals one HCC clock second.
So to add 1 HCC second in the HCC clock to match the TC clock year to year, add 1000 tics or 1,087.031.25 microseconds.
Or; note to self; 1,087,031,250 nanoseconds when I get my supercomputer.
But by executive decision of the HCC Board of Directors (me), it was decided not just to match what the current TC calendar offers but what the goal of any yearly calendar should be - to match the solar year. So, using similar calculations as with the TC calendar ...
Find relative size of HCC to to solar year tic:
# of sec/yr in a solar year (31,556,925.22).
divided by # of sec/yr in HCC (29,030,400).
equals 1.08703032752 solar year units to HCC units.
Therefore, in a solar year one tic = 1 microsecond, 1000 tics equals one solar year clock second.
In the HCC then one tic = 1.08703032752 microsecond, 1000 tics equals one HCC clock second.
So to add 1 HCC second in the HCC clock to match the solar year clock year to year, add 1000 tics or 1087.03032752 milliseconds.
Or; note to self; 1,087,030,327,520 picoseconds when I get my supercomputer 2.0.
This will keep the HCC calendar accurate relative to the earth's rotation about the sun for millions of years. (Not really calculated, but way longer than needed even for the optimists out there!)
Where do the microseconds come from?
Since I am unable to keep track of the number of vibrations of the cesium atom with picometer precision on my desktop computer, I rely on the javascript date function to provide the number of microseconds that have elapsed since the the beginning of the Unix Epoch which began on January, 1, 1970. I access that value on a TC second by second basis and calculate the HCC date and time from that.
And that's all there is to it.