Ouion Movement, Roun Time (Floating Point Time)

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Roun Time

A Floating Date Explained
By Simon Roberts

Example: http://time.chronolabs.coop/?gmt=3D10.00
GPL3 code: http://bin.chronolabs.coop/time.chronolabs.coop.1.1.zip

It was necessary to build a better date control that allows for more
dynamic bases of trigram plotting as each one has movement of time per
line, per segment, and the deeper in layers you go the more movement
you have over more time.

As there will be natural language you will be able to plot from a
group of trigrams that represent different segments of a text, for
example if ant finds a word that it does not understand then it will
prompt you for information for example if you input for and object
like movement - for example a car. For example you input '30 times a
day for around 100kms' into movement in the plot window under object.
Ant not first knowing what this means will prompt you to break '%n
times a %p for around %n%d'; removing common keywords from the array.
This would come out as:-

'%n times a %p' = '[repetition]'
'%n%d' = '[distance]'

It will be necessary to only use a triangulated calendar for the
initial presentation of the calendar set for roun time, that also
present a hypothesis that what is an ouninoun, a micro small part of
the roun time fractional component. Once we have a list of calendar=E2=80=
and dates of people it will be possible to divination what the date is
at the moment of calendar. This precision variable will flow one
motion a day, with the time being the fractional decimal place.

This will mean you can + - x / ^ log() Mod() or do whatever you want
to the date easier as it is fractional, with whatever component the
Roun time will be a integral component of the motion of measurement
within this application and as it will be component driven in ActiveX
it will be possible to put it in your computer software.

Of course the diagram above does not take into account that there is
365.25 days in a year, this is that it takes every year 365.25 days to
revolve around the sun. Now it is good that existing date theorem take
this into account, but the year for different planets and solar bodies
need to be measured as well, this can be done with Roun time. See the
variable that you times the reciprocal by to get the date components
is not dynamic the amount of hours, minutes and seconds can also
change on other planets, the idea is to have a date system that can be
also used for astrological application.

So the working for something like the current date in Roun time to the
number of years would simply in maths work both in the compiler as
well as for general mathematicians this is to get the number of years
in the date you divide the amount of days plus with the reciprocal
which is the time by 365.25 where you would then round up and report
this as the number of years within the roun time that is here. This
means that there is an opportunity to make error, but you will find
you will have to make the following function as a day doesn=E2=80=99t truly
turn over the date correctly unless you take the .25 into account not
to do this you have to look at the constant and at ability for it to
only click over.

Of course the number of days in a revolution around a star or astral
body is then not stored in a modern date as it has to support accurate
pin-point calculation of other planetary or quantum bodies in the
heavens. Therefore meaning that with the current system of dates the
year in the seed or floating point this time is not stored, more
worked out on the spot with the number of roun_days in a year.

The Roun Date output will be designed to read from right to left like
the Japanese as the date is seen mainly in the right hand corner of
documents and machines. As I have been a big fan of star trek this
could be seen as a method of being able to calculate a80=98star-date=
that is universally compatible with other planetary bodies in the
heavens and for the calculations on our computers and blackboards.

Some Suggested Method of Displaying Roun time:

Method 1: YYYY-MMM-DD.TTTTTT = 2006-Dec-08.090909
Method 2: YYYY.MMM.DD.TTTTTT = 2006.Dec.08.090909
Method 3: YYYY.DDD/Y.TTTTTT = 2006.234.090909
Method 4: YYYY.DDD/L.TTTTTT = 2006.894.090909

I am attempting to not change much with roun time so it is easy to
read and easy to understand, there is many opportunities for expansion
on this text, but I am starting by providing an easy template for your
mind to form image from.

At this stage the number of months in a year is 12, I am thinking
about staying with this and the number of days will change as well;
names of them could be initially presented in Latin origins, this is
the most ideal scenario, which offers a new position, however, there
is the disadvantage to this is that there has to be a new system
introduced to the populus that some will find difficult to follow as
they are set in their ways.

For the moment I will explore the maths of roun time as well as first
the constants in roun time example here on our planetoid80=93 Earth.
These constants are for this planet we are on, time is unique in space
in that like water, can flow at different rates and positions. This
means that a normal calendar is not compatible with space travel as
such, as a year is different on any planet your on80=93 this is varied=
how long it take to orbit the centre of it=E2=80=99s solar system


In this time we will be using the roun time of 24-June-2006
22:15:32.876 which makes the roun time represented by R(t) in its
entirety in this article. The value of this date would be R(t) =
732866.132024733327829747123082 which is equal to 24-June-2006

This example shows the mathematical process of getting the fields seen
in method 1 of the suggested way of displaying roun time. This will
allow you to see the simple working with the floating point variable
to get the time of the day or placement of this information.

Through the next couple of steps and examples, I will explore some
simple methods with you of modulating the data in the roun time to
receive large on the following page is a simple explanation of the
functions and properties of roun that will allow for easy splining of
time from the floating point time seed.

Most calendars are intended to follow some celestial cycle, such as
the phases of the moon or the seasons. These cycles usually don't
consist of a nice, integral number of days or months, so sometimes
complicated rules for varying the length of years and months must be
used to keep them in alignment with the target cycle.

The epoch of a calendar is its adopted starting point: the start of
year 1 (or day 1) of the calendar. This is not necessarily the same as
the day when the calendar was first used. For example, the currently
used epoch for the Julian and Common calendars was invented about 500
years after the time indicated by that epoch.

An era is the period of time after an epoch, and so is connected to a
particular calendar. To fully specify a particular day, one must
specify not just the date corresponding to that day in the chosen
calendar, but also which calendar one uses, for readers who might not
use the same calendar system. This is done by specifying the era. For
example, the period starting with year 1 of the Common calendar is the
Common Era. Year 1432 of the Common calendar is referred to as year
1432 of the Common Era, or 1432 C.E.

Roun_HoursInDay = R(rh) =80=9824=E2=80=99
Roun_MinutesInHour = R(rm) =80=9960=E2=80=99
Roun_SecondsInMinute = R(rs) =80=9960=E2=80=99
Roun_MillisecondsInSeconds = R(rms) =80=991000=E2=80=99
Roun_MicrosecondsInMillisecond = R(rmc) =80=991000=E2=80=99
Roun_DaysInYear = R(rd) =80=99365.25=E2=80=99
Roun_Zeropoint_TimeWeigth = R(ztw) =80=980.0=E2=80=99
Roun_Zeropoint_DayWeight = R(zp) =80=991=E2=80=99

Factoring constants80=93 f(zad):
Roun_ZAD_DaysFromEpoch = R(zdfe) =80=98732691.5=E2=80=99
Roun_ZAD_BCYear = R(zady) =80=982006=E2=80=99
Roun_ZAD_BCMonth = R(zadm) =80=981=E2=80=99
Roun_ZAD_BCDay = R(zadd) =80=981=E2=80=99
Roun_ZAD_BCHour=3D R(zadh) =80=980=E2=80=99
Roun_ZAD_BCMinute=3D R(zadi) =80=980=E2=80=99
Roun_ZAD_BCSeconds = R(zads) =80=980=E2=80=99
Roun_ZAD_BCDayName = R(zaddn) =80=98Sunday=E2=80=99
Roun_ZAD_FollowingLeap = R(zadfl) =80=982008=E2=80=99
Roun_Planet = R(p) =80=98earth=E2=80=99
Roun_Planet_DiameterKM = R(dkm) =80=98127565.3=E2=80=99
Roun_timeseed_mask = R(m) =80=98d.hhmmssmsxmcx=E2=80=99

The best way of seeing a floating point time is how it is store
sitting there floating translucently flamboyant in the device using
the time. A floating point was a new number that came out before the
turn of the century, it was a mathematical magic with the way the
floating point stores thousandths of million of decimal/reciprocal
places in a number in less bits than a larger number, as well as being
globally supported in a lot of UNIX databases.

Currently most if not all computer systems, use a form of UTC Time,
Universal Time. However not all time you want to track is on the same
spinning roundly thing like a solar system containing different bodies
that have each there own r(zad) factorials , or a factory process that
is a more linear system of time that has each its own sequences.

This means that a hypothesis could be draw that a better more portable
system of date keeping should be kept, where the fundamental maths and
system of timing can be derived from a floating point whole and time
from the reciprocal of that precision number allow for absolute
measurement and moment of movement.

For Example there are two primary different sequences that could be
used here on the planet earth there is two different systems of the
way the calendar can move for the leap year we have here on earth with
the measurement of 365.25 days in each year. Let=E2=80=99s explore sequence
one for example with the two different system of calendars that can be
applied on earth in roun time one is deficient the other is not.

Leap year System - Earth: (None Deficient)
F1(seq) = { 31, 30, 31, 30, 30, 30, 31, 30, 31, 30, 31, 30 } = 365
F2(seq) = { 31, 30, 31, 30, 31, 30, 31, 30, 31, 30, 31, 30 } = 366
F3(seq) = { 31, 30, 31, 30, 30, 30, 31, 30, 31, 30, 31, 30 } = 365
F4(seq) = { 31, 30, 31, 30, 30, 30, 31, 30, 31, 30, 31, 30 } = 365

Leap year System - Earth: (Deficient)
F1(seq) = { 31, 30, 31, 30, 30, 30, 31, 30, 31, 30, 31, 30 } = 365
F2(seq) = { 31, 30, 31, 30, 31, 30, 31, 30, 31, 30, 31, 30 } = 366
F3(seq) = { 31, 30, 31, 30, 31, 30, 31, 30, 30, 30, 31, 30 } = 365
F4(seq) = { 30, 30, 31, 30, 31, 30, 31, 30, 31, 30, 31, 30 } = 365
..Through to F32(seq)

As the leap year system that is deficient would provide a closer
system for farming and agriculture as the month and seasonal shifts
will be similar but; the none deficient system as a function would be
a less difficult system to navigate from a sociological perspective
but it does offer closer match to seasonal shifts that are common
place on a planet supporting life like earth.

The great thing about roun time is it portability, you can take it in
whatever direction you need to, there are around 8 major calendars
here on earth and from our test we found roun time was even compatible
with the Mayan calendar which means that we can have a more versatile
and more mathematically computable format of retrieving the date of
the period.

A Floating Point Precision Number Explained:

A floating-point representation requires, first of all, a choice of
base or radix for the significant, and a choice of the number of
digits in the significant. In this article, the base will be denoted
by b, and the number of digits, or precision, by p. The significant is
a number consisting of p digits in radix b, so each digit lies between
0 and b-1. A base of 2 (that is, binary representation) is nearly
always used in computers, though some computers use b=3D16. A base of 10
(that is, decimal representation) is used in the familiar scientific

As an example, the revolution period of Jupiter=E2=80=99s moon Io could be
represented in scientific notation as 1.52853504797 105 seconds. The
string of digits "1528535047" is the significant, and the exponent is
5. Now this could be represented as any of

1528.53504797 102
1528535047.97 10-4
.00000152853504797 1011

The main benefit of scientific notation is that it makes
representations like the last one unnecessary, by allowing the decimal
point to be put in a convenient place. True floating-point notation
uses a precise specification that the point is always just to the
right of the leftmost digit of the significant, so the correct
representation is

1.52853504797 105

This, plus the requirement that the leftmost digit of the significant
be nonzero, is called normalization. By doing this, one no longer
needs to say where the point is; it is deduced from the exponent. In
decimal floating-point notation with precision of 10, the revolution
period of Io is simply

For any fixed precision p, the floating-point numbers can represent
only a subset of the real numbers (This is so even if the possible
exponents are any integer. In actual computer representations, there
is a finite range for the exponent, and the total set of floating-
point numbers is actually finite.) This incompleteness is the same as
what people are used to when they express measurements to a certain
number of decimal places, as in "The atomic weight of Hydrogen is
1.008". Correct analysis of floating-point arithmetic requires a more
precise awareness of what this means. There is a common misconception
that Floating-point numbers are imprecise. They are only
approximations to the real numbers.

It is the floating-point arithmetic operations, not the numbers
themselves, that are imprecise. Every floating-point number is in fact
exact, and exactly represents a real number. For example, the floating-
point representation of80, with binary precision 24.

Function: RounCalendar($unixtime, $gmt,[ $poffset, $pweight,
$deficency, $timeset ])

On the following page is the routine for calculating the true calendar
system in roun time, the roun time calendar is by far the most
accurate calendar to date, the following php code will calculate it.
To calculate other calendar system, you can also use the function of

We are still to name the 12 months in roun time, but they will be
eventually assigned a name and hopefully be given there rightful place
amongst the clocks and timepieces of the world.

// Ounion Movement for Time - doc: http://www.chronolabs.org.au/bin/roun-ti =
//Function Rountime Calendar
function RounCalendar($unix_time, $gmt, $poffset = '2008-05-11 10:05
AM', $pweight = '-20.22222222223', $defiency=3D'deficient', $timeset=3D
function RounCalendar($unix_time, $gmt, $poffset = '2008-05-11
14:45:38', $pweight = '-1.599999991', $defiency=3D'deficient', $timeset=
array("hours" => 24, "minutes" => 60, "seconds" => 60))
    // Code Segment 1A2=E2=82=AC=E2=80=9C Calculate Floating Point
    $tme = $unix_time;

    if ($gmt>0){
    } else {
    $ptime = strtotime($poffset)+(60*60*$gmt);
    $weight = $pweight+(1*$gmt);

    $roun_xa = ($tme)/(24*60*60);
    $roun_ya = $ptime/(24*60*60);
    $roun = (($roun_xa -$roun_ya) - $weight)+(microtime/999999);
    // Code Segment 2A2=E2=82=AC=E2=80=9C Set month day arrays
    $nonedeficient = array("seq1" =>
                           "seq2" =>
                           "seq3" =>
                           "seq4" =>

    $deficient =     array("seq1" =>
                           "seq2" =>
                           "seq3" =>
                           "seq4" =>
                           "seq5" =>
                           "seq6" =>
                           "seq7" =>
                           "seq8" =>
                           "seq9" =>
                           "seq10" =>
                           "seq11" =>
                           "seq12" =>
                           "seq13" =>
                           "seq14" =>
                           "seq15" =>
                           "seq16" =>
                          "seq17" =>
                           "seq18" =>
                           "seq19" =>
                           "seq20" =>
                           "seq21" =>
                           "seq22" =>
                           "seq23" =>
                           "seq24" =>
                           "seq25" =>
                           "seq26" =>
                           "seq27" =>
                           "seq28" =>
                           "seq29" =>
                           "seq30" =>
                           "seq31" =>
                           "seq32" =>

    $monthusage = isset($defiency) ? $ : $deficient;
    // Code Segment 3A2=E2=82=AC=E2=80=9C Calculate month number, day =
number, day
count etc
    foreach($monthusage as $key => $item){
        foreach($item as $numdays){
       // As well as Function MayanTihkalCalendar
    $revolutionsperyear = $ttl_num / $i;
    $numyears = floor((ceil($roun) / $revolutionsperyear));
    $avg_num_month = $ttl_num_months/$i;
    $jtl = abs(abs($roun) - ceil($revolutionsperyear*($numyears+1)));
        foreach($monthusage as $key => $item){
            foreach($item as $numdays){
                    if ($ii=3D=3Dfloor($jtl)){
                        if ($roun<0){
                            $daynum = $tt;
                            $month = $t;
                        } else {
                            $daynum = $numdays-($tt-1);
                            $month = $avg_num_month-($t-1);
                        $sequence = $key;
                if ($nodaycount=3D=3Dfalse)

    $timer = substr($roun, strpos($roun,'.')+1,strlen($roun)-
    $roun_out=3D $numyears.'/'.$month.'/'.$daynum.' '.$day.'.'.
   $roun_obj = array('stardate'=3D>"$numyears.$day", 'rounfloat' =>
$roun, 'year'=3D>$numyears,'month'=3D>$month, 'day'=3D>$daynum, 'jtl'=3D>$j=
$timeset['hours']),'minute'=3D> floor(intval(substr($timer,2,2))/100*
$timeset['minutes']),'seconds'=3D> floor(intval(substr($timer,4,2))/100*

    return $roun_obj;

Systems and Processes80=93 Time Segmenting

Traditionally time movements in mathematics are seen as a homogeneous
movement in the old school algebraic deductions; however with
understand in means of Qoun and other types of times in fields like
quantum physics within this finite system of time. This means in
Ounion movement is more now being isopolymorphic and allows for a free
flowing system and comparative tables. This time dependant linear
system within roun time but this does not always apply with other
system and process which can always have an analytical test or series
of tests that can prove the nature of that special segments or
isopolymorphic movement that can be describe in our current day
algebraic topography.

Here on the planet we have factors of orbital rate, planet size,
spatial factorials that are defined in quantum physical evolution of
these formulae is applied; but these are not always defined in
movement having an orbital calendar system for days of the month and
seasons of the year. These other system in time would be the
substitute for the ZAD environmental constants that could have fare
differences in the environment needing to be track within its
comparable time sequences and segments.

But a time defined in a quantum singularity maybe in theory a Qoun
time segment as it would have none radial properties in most
instances, Quantum singularities have been produced in test
environment often with damage to life and limb. Other such segments
exists, you would be able to use the segmentation method to build the
basis of a time zone system based on the factors in the R(zad)
Constants Grouping. At this stage I will not explore the more complex
motion of time, such as in space itself where there are other factors
in the physics as well as the bountiful supply of possible applicable
formulas that can be used in factor Qoun time Q(zad) factors.

A Qoun time would be similar to the system of time keeping that was
seen in some well known 21st century treknology known as the star
date. This was a none calendar system that could be used to navigate
nautical space, that layer of area in all accomplishment that we have
yet to reach as a people here in the 22nd century as an explorative
deep-space missions.

To complete the segmenting of Roun-time to a universally compatible
system if predetermined month names are not used then a combination of
the dates of the existing calendars, there epochs and figurer heads in
historical and philosophical standpoints as well as royalty and
ancient as well as post modern history must be factored in.

To truly divinise a result you must look at all the deithy
representation in the time dependant linear system a chart of time
must be plotted with any similarities in deithy representation in the
seasons, festivity and spiritual ramification must be factored in.

From this the list of gods and deithy as well as figure heads can be
cross pollinated and then used to form the basis of names of the
month. This as you can see from data collection is a big task and
quiet laborious even for the most dedicated mathematics analyst.

Step 180=93 Time (TTTTTT)

First remove the whole number from the roun time and now let R(r) =
the reciprocal of the floating point. Now we have to work out the
value of the floating point in the planetary bodies by subtracting 1
from R(rh), R(rm), R(rs), R(rms) & R(rmc). So the time in a string
output with the decimal output would look like:

R(w) = (((R(rh)-1)/100) + ((R(rm) -1)/10000) + ((R(rs) -1)/1000000)
        + ((R(rms) -1)/1000000000)+ ((R(rmc) -1)/ 1000000000000))
t(i) =    R(r) .

This will give you t(i) which looking something like this
0.221532876918 where you have removed the days from the roun time and
divided like seen in the process at the beginning of this article.

Lets look at some of the working: Now where R(r) =
0.132024733327829747123082 and R(w) = 0.595959999999 then the working
to get Hours minutes and seconds is seen above in Step 1 now in this
working here with R(r) & R(w) are set then t(i) = 0.221532876918 then
t(i) = 0.HHMMSSMSxxMCxx. that means the time in this example is in
24hour clock80=93 22:15:32.876 otherwise known as quarter past ten and
thirty two seconds.

This is how you deduct time or the motion of a single day with roun
time, with this method you can convert times between astral bodies
like planets and have a similar star-date that is compatible as well
as comparable to another time in another solar system. This floating
point is much like the existing Timestamps done by the bios clock,
however this timestamp does not need conversion or any functions to
add and subtract or divide or multiple the instance of time, as it is
a floating point not a timeseed, more so a floating - timeseed.

If you wanted to for example find the difference between two dates,
normally you would have to use datediff or a similar function within,
the language you are coding in, however with roun time all you have to
do is subtract from one and another and power out the remainder of the
two variable being subtracted from one another.

When you calculate the time you can have massive reciprocals that are
absolutely micro-fine measurements of time, that are possibly very
hard, if not impossible to track with a domestic home computer. It
would take dedicated processors to do such a massive amount of maths

Warning: Although this system is designed to have milliseconds and
microseconds into its computation systems building a timer system to
work with such force that the count is accurate would have to be
achieved in A+ or similar low level compiler.

Step 280=93 Date of year

The month system is going to be broken up into 30 day blocks, there is
a tolerance of 5 days outside a leap year and 6 days during a leap
year the months will have the following sequences that consist of
either 30 or 31 only days in a month. In a leap year the forth motion
of the orbit of earth in this example is what adds the day onto80=98Ma=
this is when 0.25 * 4 = 1 day when R(rd) = 365.25 days in year.

The calendar should move in a motion of either one day to three days
should befound in the calendars motion of days per month. In this
example we will show you how to deduct the day as well as the year
from the roun time R(t).

The calendar starts on R(zdfe) which means by the default ZAD
constants you will be able to determine the day, whether it is a leap
year, if the number is negative then the death of a religious figure
like AD/BC in the Gregorian calendar the all powerful deity known as
Jesus. PO or Point of Origin or the Epoch as it is called in UTC,
Georgian and Julius Calendars, will exist in other species and
sentient life forms, this is a question that is not unique to here and
now on earth and need to be built into the measure.

F1(seq) = { 31, 30, 31, 30, 30, 30, 31, 30, 31, 30, 31, 30 } = 365
F2(seq) = { 31, 30, 31, 30, 31, 30, 31, 30, 31, 30, 31, 30 } = 366

Based in R(t) divide by R(rd) to get the year that the date is based
in so rounded up then if the year is represented by T(y) then the
method below will describe how to get the year, similarly day is seen
as T(d), Month T(m) :

T(y) = R(t) / R(rd)

R(zadfl) is the next leap year that follows the ZAD indicator for what
timeseed represent the beginning of the calendar. Based on a function
to test for leap year then use month sequence correlating to the
correct number of days in a year. Comparing R(t) to R(zad); calculate
from the ZAD Indicators that exist for the conditions of R(zad), you
will be able to find month, day, day name from this function the test
function will be represented by F1(x).

Solve: What is the measurement in this formulae represented by (=E2=80=A6):
T(=E2=80=A6) = F1(y(R(t)y))

Solve: What is the measurement in this formulae represented by (=E2=80=A6):
T(=E2=80=A6) = F1(m(R(t)y))

Solve: What is the measurement in this formulae represented by (=E2=80=A6):
T(=E2=80=A6) = F1(d(R(t)y))

Roun time is portable into the major calendars listed below, these are
a synopsis of each
calendar and the scales of years that are used in it. These will be
support by the roun
time control developed by Cronolabs Australia. Roun-time at this stage
does not have
names for the month itself officially, these will be divinised from
data collected in the
zero-point application to be first released late 2006.

Common Calendar

We refer to the calendar system that is in most widespread
international use around the world today as the Common Calendar. The
Common Calendar consists of two parts: it uses the rules of the Julian
Calendar for dates up to 4 October 1582, and the rules of the
Gregorian Calendar for dates starting with 15 October 1582. In the
Common Calendar, 15 October 1582 was the day immediately following 4
October 1582. The era of this calendar is referred to as the Common
Era (C.E.).

Julian Calendar

The Julian Calendar is a solar calendar that was introduced in the
Roman Empire, in the year now referred to (in the Common Calendar) as
-44, during the reign of Julius Caesar, for whom it and its fifth
month are named. The calendar was slightly reformed by emperor August,
for whom the sixth month is named. After this reform, which was
complete by the year now referred to as year 8 C.E., this calendar was
used continuously in many regions of Europe until 1582 C.E., though
there was variation (over both time and region) in such things as the
used epoch, the used day count within each month, and which day was
the first day of the year. The following description reflects the
modern choices for these things. In this calendar, each year consists
of 12 months with between 28 and 31 days per month, with new days
starting at midnight. Each new day starts at midnight. The English
names of these months and their lengths are listed in the following

In this calendar, years have either 365 or 366 days. The longer years,
called leap years, occur every fourth year, whenever the year count is
evenly divisible by 4. For example, the years 1000 and 1004 were leap
years. The extra day is inserted at the end of the month of February,
as the 29th day of February. January 1 is now the beginning of the new
year, though this was not always the case.

Many different epochs have been used in conjunction with this
calendar, for example, the assumed year of the foundation of the city
of Rome (-753 C.E., referred to as year 1 A.U.C. -- ab urbe condita),
or the beginning of the reign of emperor Diocletian (284 C.E.), or the
approximate birth year of the Messiah of the Christian faith (1 C.E. =
1 A.D. -- anno Domini) For dating historical events, use of the final
rules of the Julian calendar (with the Common Era) is extended into
the past. This anachronistic calendar is referred to as the Julian
Proleptic Calendar, or, if confusion is unlikely, as the Julian

Lunar Calendar

This is a lunar calendar, represented by the (fractional) count of New
Moons since the first New Moon after JD 0 (Julian Day Numbers). The
count is based on the mean motion of the Moon, disregarding short-term
perturbations. In this calendar, an integer date corresponds
(approximately) to New Moon, and a date ending in .5 corresponds to a
Full Moon.

Number Month Name Length
1 January 31
2 February 28 (29 in a leap
3 March 31
4 April 30
5 May 31
6 June 30
7 July 31
8 August 31
9 September 30
10 October 31
11 November 30
12 December 31

Gregorian Calendar

The Gregorian Calendar was introduced in the Catholic parts of Europe
in 1582 C.E. by Pope Gregory XIII (then the religious leader of the
Roman Catholic faith) as an improvement upon the Julian Calendar to
keep the average length of the calendar year better in line with the

The rules, months, and days of the Gregorian calendar are the same as
those of the Julian Calendar, except for the leap year rules. In the
Gregorian calendar, a year is a leap year if the year number is evenly
divisible by 4, but not if the year number is evenly divisible by 100,
and this last exception must not be applied if the year number is
evenly divisible by 400. For example, 1600 and 2000 are leap years,
but 1700, 1800, and 1900 are not.

Islamic Calendar

The Islamic calendar is a strict lunar calendar. The beginning of a
new month is tied to the first sighting of the lunar crescent in the
evening after a New Moon. Because the beginning of the month is
determined by observation, it cannot be accurately predicted. However,
for secular use a tabular calendar is available that is determined by
fixed rules. This tabular calendar is described below. The Islamic
tabular calendar has 12 months per year, that each have 29 or 30 days,
starting at sunset. The month names and lengths in days are listed in
the following table.

There are 11 leap years in a fixed cycle of 30 years. In a leap year,
the extra day is added at the end of the month of Dhu al-Hijjah. The
epoch of the calendar is sunset of 15 July 622 C.E. and "year of the
Era of the Hegira" may be abbreviated to A.H. (=3D Anno Hegirae). The
epoch coincides with the migration of the Prophet Mohammed from Mecca
to Medina. The Roun GetCalendar() Function takes an A.H. date to refer
to the date that is current at noontime. The first noon after the
epoch was the noon of 16 July 622 C.E., so the Roun GetCalendar()
Function equates 1 Muharram 1 A.H. with 16 July 622 C.E.

Egyptian Calendar

Ancient Egyptians used a calendar that had 365 days in a year, without
exceptions. The year was divided into 12 months of 30 days each, plus
5 extra days (referred to by the ancient Greeks as the epagomenai)
after the last month. Because of its great regularity, this calendar
was used by ancient Greek and European astronomers until only a few
centuries ago. The names and lengths of the months of the Egyptian
calendar are listed in the following table.

The Roun GetCalendar() Function regards the epagomenai as a 13th
month. The era used for this calendar by the Roun GetCalendar()
Function is the Era of Nabonassar, used by Ptolemy, with epoch 26
February -746 C.E. Other eras that have been used elsewhere are the
Era of Philippos (which marks the death of Alexander the Great)
starting in year 425 of Nabonassar, the Era of emperor Hadrian of
Rome, starting in year 864 of Nabonassar, and the Era of emperor
Antoninus of Rome, starting in year 885 of Nabonassar.

Number Month Name Length
1 Muharram 30
2 Safar 29
3 Rabi`a I 30
4 Rabi`a II 29
5 Jumada I 30
6 Jumada II 29
7 Rajab 30
8 Sha`ban 29
9 Ramadan 30
10 Shawwal 29
11 Dhu al-Q`adah 30
12 Dhu al-Hijjah 29 (30 in a leap year)

Number Name Length
1 Thoth 30
2 Phaophi 30
3 Athyr 30
4 Choiak 30
5 Tybi 30
6 Mecheir 30
7 Phamenoth 30
8 Pharmuthi 30
9 Pachon 30
10 Payni 30
11 Epiphi 30
12 Mesore 30
epagomenai 5

Latin Calendar

The ancient Romans started the Julian calendar which eventually
evolved into the Common calendar. However, the method of the Romans
for designating dates in their calendar was quite different from ours.
We refer to the Common calendar with the Roman way of designating
dates (in the Latin language) as the "Latin Calendar". The Romans did
not know Arabic numerals. They wrote numbers using letters, according
to the following table.

If a "smaller" letter (i.e., earlier in the table) follows a "bigger"
one (i.e., later in the table), then the values add up, but if a
smaller letter precedes a bigger one, then its value must be
subtracted from the total. For example, DCX stands for 500 + 100 + 10
=3D 610, but CDX stands for 500 - 100 + 10 = 410. The Latin names for
the months are listed in the following table. They are similar to the
English month names, which are derived from them. In the Latin
language, the way to write a word -- and especially the last part of a
word -- depends on the context. The table lists three forms that are
useful in the calendar.

Three days in each month had names: the Kalends (hence calendar), the
Nones, and the Idus (as in "Beware the Ides of March"). The Kalends
was the first name of a month. The Idus was the 13th day in most
months, but the 15th day in March, May, July, and October.

The Nones was 8 days before the Idus, so it was the 5th or 7th day of
the month. These days were referred to using month names from the
second column of the table; for example Kalendae Ianuariis, Nonae
Februariis, Idibus Martiis. The day preceding one of these days was
referred to using month names from the third column of the table,
after the word Pridie; for example, Pridie Kalendas Apriles, Pridie
Nonae Maias, Pridie Idus Iunias.

The Romans indicated other days of the month by counting backwards
from the next later Kalends, Nones, or Idus. This means that days in
the second half of every month (after the Idus) would be referred to
as "so many days before the Kalends of the next month". In addition,
the Romans counted inclusive. In figuring out the difference between
two numbers, they'd count both the first and the last numbers. For
example, to get from today to tomorrow, the Romans would count two
days rather than just one. So, the 30th day of June, which is the day
before the Kalends (first day) of July, would be referred to as Pridie
Kalendas Iulias, and the day before that (the 29th of June) as Ante
Diem III Kalendas Iulias. The "ante diem" means something like "the
earlier day".

The Romans used to count years from the (mythical) year of the
founding of the city of Rome in year -751 of the Common Era. They
referred to a year count in the era as Ab Urbe Condita ("since the
founding of the City"), abbreviated to A.U.C. However, our Latin
calendar uses the same era as the
Common calendar. The year number is introduced by the word
"Anno" (year). As an example of a complete date, the 15th of December
of 1965 is referred to as "Ante Diem XVIII Kalendas Ianuarias Anno
MCMLXVI", which translates loosely as "The 18th inclusive day before
the Kalends of January of the year 1966".

The Romans did not know of the number zero or of negative numbers.
Such year numbers are printed in the Latin calendar using the usual
Arabic numerals. In addition, numbers greater than or equal to 4000
are also printed using Arabic numerals.

Letter Numeric Value
I 1
V 5
X 10
L 50
C 100
D 500
M 1000

Number Latin Month Names English Month Name
1 Ianuarius Ianuariis Ianuarias January
2 Februarius Februariis Februarias February
3 Martius Martiis Martias March
4 Aprilis Aprilibus Apriles April
5 Maius Maiis Maias May
6 Iunius Iuniis Iunias June
7 Iulius Iuliis Iulias July
8 Augustus Augustis Augustas August
9 September Septembribus Septembres September
10 October Octobribus Octobres October
11 November Novembribus Novembres November
12 December Decembribus Decembres December

Hebrew Calendar

The Hebrew calendar is a lunisolar calendar. Its current rules were
pronounced in the 4th century C.E. by Patriarch Hillel II. New days
start at sunset, new months start at a New Moon, and new years start
in the northern hemisphere spring.

A Hebrew calendar year has 12 or 13 months, that each have 29 or 30
days. The month names and lengths in days are listed in the following
table. Biblical tradition lists Nisan as the first month but has the
new year start on the first day of Tishri. The Roun GetCalendar()
Function counts months from the start of the year in Tishri. The month
numbers, names, and lengths (in days) are listed in the following
table There are 7 leap years in a fixed cycle of 19 years. The Roun
GetCalendar() Function treats Adar and Adar II as a single month,
which has 30 days in a non-leap year and 59 days in a leap year. This
way, Nisan and later months always corresponds to the same month
number, regardless of whether the year is a leap year or not.

The epoch of the Hebrew calendar is sunset of 6 October -3760 C.E.,
which was taken to be the date of the creation of the world. The Era
of the Hebrew calendar is referred to as A.M. (=3D Anno Mundi). The
first noon after the epoch was the noon of 7 October -3760 C.E., so
the Roun GetCalendar() Function equates 1 Tishri 1 A.M. with 7 October
- 3760 C.E.

Julian Day Number

Julian Day Numbers were introduced by astronomers in the 19th century
C.E. as a continuous day numbering scheme without years or leap days.
The epoch (the start of day 0) is 1 January -4712 C.E.

at 12:00:00 TT (by recommendation of the International Astronomical
Union). For precise astronomical calculation, fractional Julian day
numbers are used. The Roun GetCalendar() Function returns fractional
Julian day numbers, assuming that the fractional part of the day
specification in the source calendar is measured since the midnight
before the noon corresponding to that date. This means that an integer
date in the source calendar corresponds to a JD (=3D Julian Date) ending
in ".5".

To get the integer count, round to the nearest integer; round JDs
ending in ".5" up to the next greater integer.

For the official definition of the Julian Date by the International
Astronomical Union, see at http://maia.usno.navy.mil/iauc19/iaures.html#B1

Mayan Tikal Calendar
The peoples of Central America used a great number of calendar
systems, but they all followed the same overall pattern. The calendar
described here is the Mayan "Tikal" calendar.

The Tikal calendar used a cycle of 20 days with a name for each day in
the cycle, and a cycle of 13 days with a cardinal number for each day
in the cycle (starting with 1). These two cycles were counted
concurrently, so that after day "6 Ik" followed day "7 Akbal" and then
"8 Kan". A particular combination recurred after 260 days, which
period was called the "tzol kin" in the Yucatecan language.

The names of the days in the 20-day cycle were as follows: Imix, Ik,
Akbal, Kan, Chicchan, Cimi, Manik, Lamat, Muluc, Oc, Chuen, Eb, Ben,
Ix, Men, Cib, Caban, Etz'nab, Cauac, Ahau. There was also a year
count, called haab, with a year of 365 days divided into 18 months of
20 days each and a 19th month with 5 days only. The months had names,
and the days had numbers, and

Number Month Name Length
1 Tishri 30
2 Heshvan 29 or 30
3 Kislev 29 or 30
4 Tevet 29
5 Shevat 30
6 Adar 30
Adar II 29
(only present in leap years)
7 Nisan 30
8 Iyyar 29
9 Sivan 30
10 Tammuz 29
11 Av 30
12 Elul 29
Days Designation
353 deficient ordinary year
354 regular ordinary year
355 complete ordinary year
383 deficient leap year
384 regular leap year
385 complete leap year

these were counted as we are used to today, so after day "1 Pop"
followed day "2 Pop" and so on.
However, the numbers started at 0 instead of 1. The Mayan names of the
months were: Pop, Uo, Zip,
Zot'z, Tzec, Xul, Yaxkin, Mol, Ch'en, Yax, Zac, Ceh, Mac, Kankin,
Muan, Pax, Kayab, Cumku, Uayeb.
There were no leap years in the central American calendars, so the
year count ran out of step with
the seasons by about one day every four years.

A particular date was usually identified by its position in both the
tzol kin and the haab, for instance as
"6 Ik 2 Pop", and for the next day "7 Akbal 3 Pop". After 52 years (of
365 days) the same tzolkin/
year-count designation would return. This period is often referred to
as a "calendar round" or a
"Mayan century".

In many cases, Mayan monuments display dates in only the calendar-
round manner, which means that
these dates return every 52 years (of 365 days). This means that we
can pinpoint those dates in the
modern calendar only up to a multiple of 52 years.

The Spanish conquistadores who conquered Central America in the 16th
century ordered the
destruction of much of the Mayan written records, and the precise
correlation between the Mayan
calendars and modern calendars is therefore not exactly known.

The Roun GetCalendar() Function can return, in text form, the Tikal
designation (tzol kin -- haab) for
any date in the modern calendars, based on the most widely accepted
correlation between the Mayan
and modern calendars.

The Mayan Long Count

The Mayan Long Count is a calendar consisting of 5 cycles that
indicate the number of days since the last beginning of the full
cycle. The name, definition, and length of each cycle is indicated in
the following table.

A particular date in the Long Count is written as a set of five
numbers, one for each subcycle,
separated by periods (.). For example, the date means 1
baktun, 2 katun, 3 tun, 4 uinal, 5 kin
after the beginning of the full cycle. The beginning of the last
cycle, at long count, is thought
to correspond to 6 September -3113 C.E.

The Long Count corresponds to 21 December 2012 C.E., and
the current full cycle will be
complete on 13 October 4772 C.E. The Roun GetCalendar() Function can
return, in text form, the
Long Count corresponding to any date.

Annotation: Time Scales
Various time scales are in use. International Atomic Time (TAI) is a
uniform time scale with a unit of
one SI second. It was implemented around 1960. Each TAI minute is 60
SI seconds, each TAI hour
equals 60 TAI minutes, and each TAI day equals 24 TAI hours.
Coordinated Universal Time (UTC) is
the basis of most administrative times on Earth. Its units are the SI
second, the minute, the hour, and
the day, and it differs from TAI by an integral number of seconds. By
infrequent and irregular insertion
of leap seconds, the UTC day start is tied to the Earth's rotation.
The length of specific UTC minutes,
hours, and days may therefore differ from TAI minutes, hours, and
days. Universal Time (UT, UT1) is
a non-uniform time scale tied to the Earth's rotation. It has no leap
seconds, so the length of its unit
(the UT second) depends on the Earth's rotation. UT differs from UTC
by less than 0.9 seconds
through the judicious insertion of leap seconds in UTC. Terrestrial
Dynamical Time (TDT) -- or
Terrestrial Time (TT) for short -- was implemented in 1984 as the
dynamical time scale for geocetric
phenomena. Barycentric Dynamical Time (TDB) was implemented in 1984 as
the dynamical time scale
for solar-system barycentric phenomena. The difference between TDT and
TDB is always less than
0.002 seconds. The difference between TDT and TAI is fixed at about 32
seconds. Before 1984,
Ephemeris Time (ET) was used as a uniform time scale for ephemerides,
instead of TDT and TDB.
TAI time is bases of measure in UTC (Universal Time) and will be used
as a precursor for Roun time.

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