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Marking Time
(Lecture 3)
(Lecture 3)
John C. Stevenson
Emeritus Professor of
Mathematics
C.W. Post
Cleopatra and Caesar
![](3D"slide0002_image002.gif")
![](3D"slide0002_image004.gif")
![](3D"slide0002_image006.jpg")
The Roman Calendar Before Cleopatra
•Begins in 753 BC (4th year of 6th Olympiad, the first being in
776 BC)
•By
tradition Romulus introduced a 304 day calendar consisting of 10
months
•About
675 BC Numa added two months to make 355 days and a 22 day
month Mercedonius every second year
Month Names
•<=
/span>January:
for Janus the doorkeeper
•<=
/span>February:
for Februalia =3D sacrifice time
•<=
/span>March (Martius):
for Mars =3D war time
•<=
/span>April: <=
/span>Aprilis
=3D “to open” =3D Spring
•<=
/span>May: Maia
=3D goddess of growth
•<=
/span>June: Juvenis
=3D “youth”
•July (formerly Quintilis)<=
span
style=3D'font-size:75%'> : Julius
Caesar
•August (formerly Sextilis) : Caesar
Augustus
•<=
/span>September to December =3D months 7 to 10, begin=
ning
with March before N=
uma
added the two initial months above
![](3D"slide0004_image007.gif")
Added
by Numa
What Were the Big Issues?
•The Pontifex Maximus or the Pontifical College changed intercalary days based on politics or =
whimsy
•Even done correctly the cycle over 4 years =
=
averaged 366.25 days
•Preoccupation with Hannibal meant no corrections <=
/span>and by 190 BC the calendar was ahead of the =
seasons by 119 days
What Did Caesar Do?
=
226;While
dallying in Alexandria he met Sosigenes and talked of
calendar reform
=
226;Acting
on Sosigenes recommendations he:
&=
#8211;Added
10 days to the existing 355
&=
#8211;Established
the leap year rule
=
211;Added
90 days to 46 BC making it 445 days and pulling the vernal equ=
inox
back to late March from late June
Lengths Of The Months
Month=
Pre-Julian Post-Julian
Januarius 29 31
Februarius 28 28/29**
(Intercalaris* 22
or 23)
Marius 31 31
Aprilis 29 30
Maius=
31 31
Junius 29 30
Quintilis 31 31
Sextilis 29 30
September 29 30
October 31 31
November 29 30
December 29 31
Total=
355
(*+ 22 or +23) 365/366=
**
![](3D"slide0015_image008.gif")
In a leap year
![](3D"slide0007_image009.gif")
The Astrological Saturday
[4]
21
14
7
Moon
[3]
20
13
6
Mercury
[2]
19
12
5
Venus
[1]
18
11
4
Sun
24
17
10
3
Mars
23
16
9
2
Jupiter
22
15
8
1
Saturn
Next Day
![](3D"slide0008_image010.gif")
The Planetary Week
Saturn/Saturday
![](3D"slide0008_image011.gif")
Jupiter/Thursday
![](3D"slide0008_image012.gif")
Mars/Tuesday
![](3D"slide0008_image013.gif")
Sun/Sunday
Venus/Friday
![](3D"slide0008_image014.gif")
Mercury/Wednesday
![](3D"slide0008_image015.gif")
Moon/Monday
![](3D"slide0008_image016.gif")
Days of the Week
<=
span
class=3DBB style=3D'position:absolute;left:-4.21%'>•Tuesday:<=
span
style=3D'mso-spacerun:yes'> For Tiu, Anglo Saxon for
Mars
<=
span
class=3DBB style=3D'position:absolute;left:-4.62%'>•Wednesday=
: For Woden (=3D Mercury)
Constantine the Great
•In 312 he “saw” a crucifix in <=
/span> the Sun
•Edict of Milan 313: Tolerate =
Christians
•In 321 established a 7-day week beginning on Sunday
=
•Forbade work on Sundays in 323
•<=
span
style=3D'font-size:86%'>Summoned the Council of Nicaea in 325
<=
span
style=3D'font-size:86%;visibility:hidden'>•
![](3D"slide0010_image018.jpg")
![](3D"slide0011_image020.jpg")
The Council of Nicaea
The town of IZNIK (Nicaea) lies <=
span
style=3D'position:absolute;top:25.5%;left:4.3%;width:37.45%;height:4.0%'><=
span
style=3D'font-family:Arial;font-size:75%;color:black'>on the eastern shore=
s of
the lake of the same name. The town is in the city limits of the =
<=
span
style=3D'font-family:Arial;font-size:75%;color:black'>'green' Bursa and it=
is 79
km far from the city center. Its population is 34000.
IZNIK is remarkable for the <=
span
style=3D'font-family:Arial;font-size:75%;color:black'>monuments belonging =
to the
R=
oman,
Byzantine and Ottoman Age. Most of the historical buildings are well
preserved. Thus the region looks like an <=
span
style=3D'font-family:Arial;font-size:75%;color:black'>open-air museum. Tha=
t's
why IZNIK is proclaimed as an historical urban place to be <=
span
style=3D'font-family:Arial;font-size:75%;color:black'>protected.
See: <=
u>http://www.turizm.net/cities/iznik/
Turkey
The Problem of Easter by 325
•Christianity decriminalized
•Faith is rooted in
historical events and thus needs a universally agreed calendar&=
#13;
•Last Supper seems to be 1st=
day of Passover
•Easter linked to Judai=
sm
since the Jews must determine the time of 15 Nisan
<=
/div>
•Solution at Nicaea lin=
ks
Easter to the Vernal equinox and legislates it be a Sund=
ay.
The Solution
=
226;Make
Easter the first Sunday after the first full moon following the
vernal equinox.
&=
#8211;Seemingly
separated Easter from Passover
=
211;Eliminated
dependence on Jewish elders to determine the correct
date
=
226;New
Problem: There was no adequa=
te method
at hand for determining the date of the vernal equinox closer
than a few days.
Solution to the New Problem
=
226;Fix
the date of the Vernal Equinox at March 21 no matter what happens=
in
the sky
=
226;Ignore
the fact that every year the Julian calendar lags by a furthe=
r 11
minutes
R=
11;Note
that in 325 the equinox had slipped back from March 25 to about Ma=
rch
21
Other Easter Calculations
•Under the =
Julian
calendar the days of the week for January 1 repeat every 28 (4 x 7) years
=
•Toss in the
Metonic cycle of 19 years to get a great cycle of 532 (28 x 19) years
–P=
roblem:
luna 16-22 (Rome) vs. luna 15-21 (Alexandria) unresolved
•D=
enis
the Small in ca. 530
–A=
dopts
the Roman 21 March date for the equinox
–A=
dopts
the luna 15-21 rule
–C=
rafts
a 95 (5 x 19) year table for the date of Easter
![](3D"slide0020_image022.jpg")
18
![](3D"slide0021_image024.jpg")