THE CONSTANT AND INTERNATIONAL
CALENDAR FOR ETERNITY
Fakas Institute
78, Laranakos Ave. 1046 Nicosia, Cyprus
E-mail: fakas@zenon.logos.cy.net
With my
present work I wish to present a calendar that will be Constant, International
and Eternal. For its compilation I took into consideration the mathematical
measurements as far as the duration of the tropical year which were reported
since the era of the Greek mathematicians and astronomers Aristarchos of Samos
and Iparchos up until the more accurate ones that are recorded in the
“Astronomical Almanac 2000 AD ”. I call it eternal due to the change I
introduced as far as the leap milleniums are concerned which are kept
sychronized with the tropical year. I call it constant because by using blank
days a calendar of 4 equal trimesters, of exactly 13 weeks each, is created,
where each date has the same name day. I call it International because it has
great potentiality of becoming accepted internationally through the UN.
1. INTRODUCTION
For the last 3 – 4 years, as the second
millenium was approaching to its end, I have been working on the issue of a
calendar. As a mathematician it has always given me food for thought but,
especially, now that we are approaching the end of the 2nd
millenium. I do believe that mathematicians hold the key to a lot of social
problems, especially those concerning mathematical calculations, as it is the
case with the Calendar for which I am about to elaborate.
Since the ancient times humanity without
taking into consideration exact measurements was sinchoning with moon months,
which is the time between two consecutive full moons (synodius month). This
month was directed into 4 weeks according to the moon´s phases: new moon, 1st
quarter, full moon, and last quarter.
As far as the year is concerned the
humanity had a very early alignment with the 4 seasons: Winter, Spring, Summer
and Autumn. By watching the Sun and very correctly, indeed, the four seasons
with its palindromic movement along the western horizon. It noticed that in the
winter it set on the far south point of the horizon (December Solstice) and in
the summer on the far northern point of the horizon (June Solstice). The
duration of the year was equal two consecutive reinstalments of the sun on the
December Solstice. They are created also suitable buildings [6] in which the
rays of the Sun penetrated once a year so as to notify the phenomenon with
great accuracy and everything was going on smoothly! ! !
Problems were created when, we, the
scientists told the people: Not to worry! Stop watching the moon and the Sun we
will create for you a calendar with days, weeks and months. In this way
calendars were created since the dawn civilization. The more recent ones are
those of the Roman Emperor Unman (700 BC), the calendar of the Roman Emperor
Julius Caesar (44 BC) and even more recent one of Pope Gregorius the 13th
(1582 AD).
All calendars presented error, because
they were not exactly in alignment with the tropical year. The most recent one
of those approached the duration of the tropical year.
The calendar which I have the
honor to present to you today I believe that it will not have an error because
I have synchronized it with the tropical year which duration has been
calculated at times as follows:
(a)
from the
mathematician and astronomer Aristarchos of Samos (3rd century
BC):365d 5h 45m 50s = 365,240162 days [2].
(b) from the mathematician and astronomer Iparchos (2nd
century BC)
: 365d 5h 55m 12s = 365,2466666 days [2]
(b)
According to the astronomer Stavros Plakides
: 365d 5h 48m 48s = 365,242217d [2].
and (d) according to the Astronomical
Almanac for the year 2000 AD
: 365d 5h 48m 45,2s =
365,242190 [4].
2. WHICH
CALENDARS HAVE I USED AS A BASIS
The international, constant
calendar for eternity is an evolution of the following 3 calendars:
a) The Julian Calendar
The Julian Calendar is the creation of
the Greek – Alexander astronomer Sosigenis who was called to Rome by the
Emperor Julius Caesar [2], [7].
The Julian Calendar was in use in all
countries from 44 BC up until 1582 AD. In that year became no longer valid for
countries which were Roman – Catholic. It remained in use in Great Britain up
until 1752, in Greece up until 1923 [2] and in Turkey up until 1927 [1].
This calendar is in use, even today, by
most Christian – Orthodox Churches but only as an ecclesiastical name-day
calendar. It has 365,25 days (average) instead of 364,242190 of that of the
tropical year. It is divided into 12 months which have names and as many days
as those which are found in the Gregorian Calendar which is used worldwide at
present.
Every normal year of the Julian Calendar
has 365 days whereas the leap year, 366 days. The extra day is added at the end
of February as the 29th day. Leap years are those, which can be
divided by 4 such as : 1996, 2000, 2004, 2100 etc. [2] . [ 7].
The error of the Julian Calendar
according to Plakides amounts to 11,208 minutes per year and it is estimated as
follows:
(365,25days – 365,242217days) x 24hours
x 60minutes = 11,208 m [2].
If we take into consideration the more
recent measurements Almanac 2000AD [4] the error amounts to 11,246 minutes per
year and it calculated as follows:
(365,25d – 365,242190d) x 24h x 60m =
11,246m
b) The Gregorian Calendar
The Gregorian Calendar was created by
the Calavries astronomer Lilio under order by Pope of Rome Gregory the 13th.
Pope Gregory the 13th in 1582 AD noticed that the spring equinox by
which Easter is determined was no longer the 21st of March as the A´ Ecumenical
Synodos in 325 AD had declared but it had moved and so the date of Easter was
calculated in the wrong way. Lilio suggested to Pope Gregory two corrective
measurements: to sent a declaration to all catholic states determining the
following day of the 4th of October 1582 to be called the 15th
of October 1582, as well as, leap century years will be only those divided by
400.
According to this calendar leap
centuries are 2000, 2400, 2800… etc. With this new arrangement every 400 years
the leap years will be only 97 instead of the 100 the Julian Calendar has. For
example in 400 years from 2000 – 2399 AD amounts the Julian´s leap centuries
2000,2100,2200 and 2300 only 2000 is a leap year, according to the Gregorian
Calendar. With this arrangement the Gregorian Calendar has 365,2425 days
(average).
Pope Gregarious with its new
calendar had brought no other improvement on the Julian Calendar.
The Error
of the Gregorian Calendar
The Gregorian Calendar exits the
tropical year by 24,4512 second per year; this time is estimated as follows:
(365,2425d – 365,242217d) x 24 hours x 60m
x 60 s = 24,451s per year
And according the newest measurements
(Almanac 2000 AD) the Gregorian Calendar is bigger than the tropical year by
26,784sec
Calculation: (365,2425d-365,242190d)
x24hx60mx60s=26,784sec
This error amounts to a whole day in 3533,56
years according to Plakides and 3225,8064 years according to Almanac 2000AD.
Calculation (24hx60mx60s):
24,45123s=3533,56 years
Calculation: (24h x 60m x 60s):
26,784s=3225,8064 years.
and
c) The Universal Calendar
In 1887 Mastrofini created a calendar
and named it “The new Universal Calendar”. Mastrofini had no intention of
correcting astronomically the Gregorian Calendar but only some imperfections it
had, such as the inequality in the number of days of every month and of every
quarter of the year and the continually change of the 1st day of
year resulting to a generalized change of all days in the year. The Gregorian
Calendar has to proceed by using 14 different calendars 7of normal years and 7
of leap years. Each of the above mentioned calendars has the 1st day
of its year as a different day.
The Universal Calendar solved this
problem by introducing one blank day for each of the normal years and two blank
days for each of the leap years. Blank days belong to no month and have no
name. This way we have a single calendar, which is divided into 4 equal
quarters of 91 days each.
Mastrofini´s calendar has never been
applied despite the two unsuccessful attempts to do so. (1st January
1939.by the Society of Nation and 1st January 1950 by the U.N: both days
been Sundays) [2] ,[ 7].
The error of the Universal Calendar
amounts to 26,784sec per year as in the Gregorian Calendar.
3. THE
CONSTANT AND INTERNATIONAL CALENDAR FOR ETERNITY (C.I.C.E.)
Having taken into consideration the
advantages and disadvantages of the above mentioned calendars I suggest a
calendar which can be called eternal because in the future it will need no
adjustments because it will always be synchronized with the tropical year. This
can be achieved by a) preserving the leap years of the normal years as
determined by the Julian Calendar b) Preserving the leap century years as
determined by the Gregorian Calendar and c) Introducing a new rule for the
millenium years. This will be leap years when they are divided by 4000. By this
arrangement the calendar approaching even more the tropical year. (e.g. leap
milleniums will only be 4000,8000,12000,16000,20000 etc)
According to this arrangement
every 20,000 years we will have 4845 leap years instead of 4850 that the
Gregorian Calendar has and 5000 that the Julian Calendar. The Calendar will
have a duration 365,242250 and will be bigger than the tropical year only by
0,00006 days or 5,184 sec. every year.
Calculation: (365,24225days – 365,2419
days) x 60minutes x 60 seconds = 5,184sec.
This error amounts to 24 hours every
…16667 years.
Calculation: (24h x 60m x 60s): 5,184s =
16666,666 years.
The difference of 5,184 seconds that
still exists with the tropical year is corrected introducing a second rule:
Those leap milleniums that come before
the year during which the error of 5,184 seconds amounts to a whole day (24
hours) those leap milleniums loose their extra day as leap years.. This
decision will be taken from a universal authority which can be called
International Earth Revolving Service as the International Earth Rotation
Service, which already exists, and it is mentioned below.
In this way our calendar will not
differs the tropical year more or less than a day.
A similar process is enforced by
the International Earth Rotation Service which decides every 1 – 2 years and
adds 1 second on the current time of the International Atomic Time (I.A.T.) to
synchronies it with the time of the daily revolving of our planet. In this
case, also a constant period of time has not been determined in which this
adjustment will take place. The error is corrected as soon as it reaches 0,9
second so that the difference will not exceed the second.
Apart from calling it eternal we
can also call it constant as I use Mastrofini´s blank days but with a vital
difference. Mastrofini gave these days no name or date. I, on the other hand,
call them also “blank days” but they do have a date: the 31st of
December for all years and also the 31st of June for the leap years. In a
different approach the blank day proceeds the first of January and has number
00 January for all the year and for leap years as 00 July.
The existence of date doesn´t
create any problems to the calendar being constant but on the contrary it is a
very useful arrangement
One third arrangement I have done
has to do with the day with which the year it commences whereas for the
Universal Calendar the first day is always a Sunday here we can have the first
day as Saturday or for that matter any other day chosen. Sundays and Saturdays
are preferred because they are days off.
Personally, I prefer Saturday as
we can have both the celebrations of the 1st day of the year and on
Sunday it´s religious day. It should be taken under consideration that
Mastrrofini suggested Sunday because then it used to be the only day off.
Another suggestion is that the 1st
of the year is blank day and instead of blank to be called the 1st of the year.
The error
of the Constant and International
Calendar for eternity
By being constantly sychronized
with the tropical year it is expected to have no future errors.
This calendar contains all the
advantages of the 3 previously mentioned calendars and avoids all their
disadvantages.
As a result we have:
a)
It
consists of 4 equal quarters of 91 days each and each one has exactly 13 weeks.
(13 weeksx7days=91days)
b)
All the
days have their own date even the blank days.
c)
All months
have the same number of days either 30 or 31.
d)
It is easy
to memorize it , as it is repeated every year, even every quarter
e)
It is
eternal because it will equal the tropical year and need no future adjustment.
All these are great advantages for
the Commerce, the Industry, Transportation and generally the Society as a
whole.
Having in view all of the above I
introduce to you the three Plans of the Calendar
(C.I.C.E.) and the table No.1 which
describes the leap years.
The leap year of the
normal years is that which is divided by 4.
The leap year of the centuries is that
which is divided by 400.
Leap year of the millenium years is that
which is divided by 4000 except if it is the millenium divided by 4000 and is
proceeding the year for which the 5,184sec. error completes a whole day (24
hours).
The three plans are as follows:
THE
CONSTANT AND INTERNATIONAL CALENDAR FOR ETERNITY
(normal
years)
|
JANUARY FEBRUARY MARCH APRIL MAY JUNE JULY AUGUST SEPTEMBER |
|
S. S.
M. T. W.
T. F. S.
S. M. T.
W. T. F. S. S. M.
T. W. T. F. 01 02
03 04 05
06 07 01 02
03 04
01 02 08 09
10 11 12
13 14 05
06 07 08
09 10 11 03 04 05
06 07 08
09 15 16
17 18 19
20 21 12
13 14 15
16 17 18 10 11 12
13 14 15
16 22 23
24 25 26
27 28 19
20 21 22
23 24 25 17 18 19
20 21 22 23 29 30
31
26 27 28
29 30 24 25
26 27 28
29 30 |
|
OCTOBER NOVEMBER DECEMBER |
|
S. S.
M. T. W.
T. F. S.
S. M. T.
W. T. F. S. S. M.
T. W. T.
F. B. ,,, 01 02
03 04 05
06 07 01 02
03 04 01 02 08 09
10 11 12
13 14 05
06 07 08
09 10 11 03 04 05
06 07 08
09 15 16
17 18 19
20 21 12
13 14 15
16 17 18 10 11 12
13 14 15
16 22 23
24 25 26
27 28 19
20 21 22
23 24 25 17 18 19
20 21 22
23 29 30
31
26 27 28
29 30 24 25
26 27 28
29 30 31 |
(leap yeas)
|
JANUARY
FEBRUARY MARCH JULY AUGUST
SEPTEMBER |
|
S. S.
M. T. W.
T. F. S.
S. M. T.
W. T. F. S. S. M.
T. W. T. F.
01 02
03 04 05
06 07 01 02
03 04 01 02 08 09
10 11 12
13 14 05
06 07 08
09 10 11 03 04 05
06 07 08
09 15 16
17 18 19
20 21 12
13 14 15
16 17 18 10 11 12
13 14 15
16 22 23
24 25 26
27 28 19
20 21 22
23 24 25 17 18 19
20 21 22
23 29 30
31
26 27 28
29 30 24 25
26 27 28
29 30 |
|
APRIL MAY
JUNE OCTOBER
NOVEMBER DECEMBER |
|
S. S.
M. T. W.
T. F. S. S. M.
T. W. T.
F. S. S.
M. T. W.
T. F. B. 01 02
03 04 05
06 07 01 02
03 04
01 02 08 09
10 11 12 13 14 05
06 07 08
09 10 11 03 04 05
06 07 08
09 15 16
17 18 19
20 21 12
13 14 15
16 17 18 10 11 12
13 14 15
16 22 23
24 25 26
27 28 19 20 21
22 23 24
25 17 18
19 20 21
22 23 29 30
31
26 27 28
29 30 24 25
26 27 28
29 30 31 |
Plan
2: 1st of the year Sunday
THE CONSTANT AND INTERNATION, CALENDAR FOR ETERNITY
(normal years)
|
JANUARY
FEBRUARY MARCH APRIL
MAY JUNE JULY
AUGUST SEPTEMBER |
|
S. M.
T. W. T.
F. S. S.
M. T. W.
T. F. S. S. M. T.
W. T. F. S. 01 02
03 04 05
06 07 01 02
03 04
01 02 08 09
10 11 12
13 14 05
06 07 08
09 10 11 03 04 05
06 07 08
09 15 16
17 18 19
20 21 12
13 14 15
16 17 18 10 11 12
13 14 15
16 22 23
24 25 26
27 28 19
20 21 22
23 24 25 17 18 19
20 21 22
23 29 30
31
26 27 28
29 30 24 25
26 28 29
30 |
|
OCTOBER
NOVEMBER DECEMBER |
|
S. M.
T. W. T.
F. S. S.
M. T. W.
T. F. S. S. M. T.
W. T. F. S.
B. 01 02
03 04 05
06 07 01 02
03 04
01 02 08 09
10 11 12
13 14 05
06 07 08
09 10 11 03 04 05
06 07 08
09 15 16
17 18 19
20 21 12
13 14 15
16 17 18 10 11 12
13 14 15
16 22 23 24 25 26
27 28 19
20 21 22
23 24 25 17 18 19
20 21 22
23 29 30
31
26 27 28
29 30 24 25
26 27 28
29 30 31 |
(leap years)
|
JANUARY
FEBRUARY MARCH JULY
AUGUST SEPTEMBER |
|
S. M.
T. W. T. F. S. S.
M. T. W.
T. F. S. S. M. T.
W. T. F. S. 01 02
03 04 05
06 07 01 02
03 04
01 02 08 09
10 11 12
13 14 05
06 07 08
09 10 11
03 04 05
06 07 08
09 15 16
17 18 19
20 21 12
13 14 15
16 17 18 10 11 12
13 14 15
16 22 23
24 25 26
27 28 19
20 21 22
23 24 25 17 18 19
20 21 22
23 29 30
31
26 27 28
29 30 24 25
26 27 28
29 30 |
|
APRIL MAY JUNE OCTOBER NOVEMBER
DECEMBER |
|
S. M.
T. W. T.
F. S. S.
M. T. W.
T. F. S. S. M. T. W.
T. F. S.
B. 01 02
03 04 05
06 07 01 02
03 04
01 02 08 09
10 11 12
13 14 05
06 07 08
09 10 11 03 04 05
06 07 08
09 15 16
17 18 19
20 21 12
13 14 15
16 17 18 10 11 12
13 14 15
16 22 23
24 25 26
27 28 19
20 21 22
23 24 25 17 18 19
20 21 22
23 29 30
31
26 27 28
29 30 24 25
26 27 28
29 30 31 |
Plan 3: 1st of the year Blank Day
THE CONSTANT AND INTERNATIONAL CALENDAR FOR ETERNITY
(normal years)
|
JANUARY
FEBRUARY MARCH |
|
B.D. S.
M. T. W.
T. F. S. S. M. T.
W. T. F.
S. S. M.
T. W. T.
F. S. 00 01
02 03 04
05 06 07 01
02 03 04
05 01 02
03 08 09 10
11 12 13
14 06 07
08 09 10
11 12 04 05 06 07
08 09 10 15 16 17
18 19 20
21 13 14
15 16 17
18 19 11 12 13 14
15 16 17 22 23 24
25 26 27
28 20 21
22 23 24
25 26 18 19 20 21
22 23 24 29 30
27 28 29
30
25 26 27
28 29 30
31 |
|
APRIL MAY
JUNE JULY AUGUST SEPTEMBER OCTOBER NOVEMBER
DECEMBER |
|
S. M. T.
W. T. F.
S. S. M.
T. W. T.
F. S. S. M. T. W.
T. F. S. 01 02 03
04 05 06
07 01 02
03 04 05 01 02
03 08 09 10
11 12 13 14 06
07 08 09
10 11 12 04 05 06
07 08 09
10 15 16 17
18 19 20
21 13 14
15 16 17
18 19 11 12 13 14
15 16 17 22 23 24
25 26 27 28 20 21 22
23 24 25
26 18 19
20 21 22
23 24 29 30
27 28 29
30
25 26 27
28 29 30
31 |
(Leap years)
|
JANUARY
FEBRUARY MARCH JULY AUGUST SEPTEMBER |
|
B.D. S.
M. T. W.
T. F. S.
S. M. T. W.
T. F. S. S. M. T.
W. T. F. S. 00 01
02 03 04
05 06 07 01
02 03 04
05 01 02
03 08 09 10 11 12 13
14 06 07
08 09 10
11 12 04 05 06 07
08 09 10 15 16 17
18 19 20
21 13 14
15 16 17
18 19 11 12 13 14
15 16 17 22 23 24
25 26 27
28 20 21
22 23 24
25 26 18 19 20 21
22 23 24 29 30
27 28 29
30
25 26 27
28 29 30
31 |
|
APRIL MAY
JUNE OCTOBER NOVEMBER DECEMBER |
|
S. M. T. W. T.
F. S. S. M. T.
W. T. F.
S. S. M.
T. W. T.
F. S. 01 02 03 04
05 06 07 01
02 03 04
05 01 02
03 08 09 10 11
12 13 14
06 07 08
09 10 11
12 04 05
06 07 08
09 10 15 16 17 18
19 20 21 13 14 15
16 17 18
19 11 12
13 14 15
16 17 22 23 24
25 26 27
28 20 21
22 23 24
25 26 18 19 20 21
22 23 24 29 30 27 28
29 30 25 26
27 28 29
30 31 |
5.
ACKNOWLEGDEMENT
I would like to thank the priest
f. Constantinos Koukos, the Archbishop of Greece Christodoulos, the astronomer
and academic professor Mr. Georgios Kontopoulos who encouraged me to
compilation this Calendar.
I would also, like to thank Mr. Lakis Hatzinikolaou, astrodynamic reader, with whom I discussed many details of the Calendar, Mr. Petros Papageorgi, teacher of literature who corrected the Greek text. and Mr. G Papadopoulos and Miss Christiana Papaeleftheriou who correct the English text.
Finally, by looking at the Astronomical
Tables drawn by Jean Meeus [5] we see the reconstitution of the Sun per year at
point γ from 1 AD up until 3000 AD which takes
place at the same time with a mistake of only 3 to 4 minutes every year. We
conclude that: our planet bearing our houses, our belongings and all of us
rotating around its axis in a very great speed completes its revolving around
the sun at the same time every year. By looking at all these we can not but
accompany the Profit and King David and pray with him to the Creator and Lord
of Heavens, of the Earth, of the Moon and of the Sun: [9]:
“ O LORD, how manifold are thy works! In
wisdom hast thou made them all: the earth is full of thy riches”. “ The heavens
declare the glory of God; and the firmament sheweth his handy-work. Day unto
day uttereth speech and night unto night sheweth knowledge…”.
6.
REFERENCES
[1] Peter Duffet – Smith: Easy P.C.
Astronomy – Cambridge University Press
{2} Stavrou Plakide
Introduction to Mathematical Astronomy
Volume A (Athens 1959)
[3] Laurence G. Taff Celestial Mechanics
A computational guide for the
practitioner
[4] The Astronomical Almanac for the year
2000 - Washington: U.S. Government Printing Office London: The stationery
office
[5] Jean Meeus
Astronomical Tables of the Sun, Moon,
and Planets (Willmann – Bell, Inc.)
[6] Nicolaou D. Nicolaou
The Great Cosmography – Publishing House
Afon D. JAKA – Athens (1963)
[7] D. Cotsaki – K. Chasapi Cosmography
- Athens (1970)
[8] P. Kenneth Seidelmann Explanatory
Supplement to the Astronomical Almanac – University Science Books Mill Valley,
California
[9] Old Testament, Brotherhood Theologon
“ZOI” (1950)