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1
Marking Time
The Strange Tale of Calendars
The Strange Tale of Calendars
John C. Stevenson
Emeritus Professor of
Mathematics
C.W. Post
2
![3D"Chesterfield,](3D"slide0025_image002.jpg")
Philip Dormer Stanhope, Earl of Chesterfield. (1694–177=
3)
![](3D"slide0025_image004.gif")
3
The Overall Plan
•<=
/span>Defining Our Terms
•<=
/span>The Earliest Calendars (from bones to the flooding=
=
of the Nile)
•<=
/span>Meton of Athens and the Lunar/Solar Issue
•<=
/span>The Julian Calendar
•<=
/span>The Council of Nicea (when is Easter?)
=
•<=
/span>The Council of Trent (more Easter aggravation)
=
;
•<=
/span>The Gregorian Reform (Easter problem
“solved”)
•<=
/span>Modern Calendar Reform (Chesterfield & beyond)=
•
–
4
Defining Our Terms
–Time (philosophy, hi=
story,
clocks, various kinds of time, the official second)
<=
span
style=3D'position:absolute;top:43.75%;left:16.66%;width:87.26%;height:6.0%=
'>–The Day
(differing measures, mean solar time, the equation of time)
=
–The Year
(various definitions, the mean tropical year)
5
Time & Mind
•Our perceived flow of
time—do we advance in time or does it flow past us?
•How do we measure the flow? Hypertime?
•Does human consciousne=
ss
advance in a time-like direction and how fast?
•Do events achieve
existence as “now” arrives? What meaning has “then̶=
1; or “now”
or “tomorrow”?
6
Philosophy
•Process Philosophers:<=
span
style=3D'mso-spacerun:yes'> the flow of time is a metaphysical
fact and can be grasped only by non-rational intuition.
•Philosophers of the
Manifold: time flow is an
illusion, words like past, now & the future refer to the act of
utterance.
•Emotional
Impact—Regret (joy) for the past, fear (eager
anticipation) of the future.
7
Origin of Ancient Ideas of Time
•Observation of cyclic
phenomena: night/day,
the seasons.
•Observation
of continuing events: turnin=
g of
the stars at night, flow of water, wind.
8
The Greek Critique
•The Pythagorean noti=
on of
extension—units of length or instants of time must b=
e measurable
with integers (1,2,3,….).
•Parmenides & Zen=
o (The
Eleatic School) held that change is logically inconceivable.
9
Zeno’s Paradoxes (ca.450 BC)
![](3D"slide0005_image005.gif")
![](3D"slide0005_image006.gif")
![](3D"slide0005_image011.gif")
![](3D"slide0005_image012.gif")
![](3D"slide0005_image013.gif")
![](3D"slide0005_image014.gif")
10
Cyclic Time in Culture
Plato:
11
The One-Way View
•Jews, Christians &am=
p;
Muslims: creatio ex <=
/span>nihilo
ending in apocalypse
•Evolutionary ideas from Democritus to Lucretius
to Darwin constitute an arrow in time.
12
The Earliest Clocks
•Suspected that clock
making began about 5000 years ago in the fertile crescent. There are no records
extant or implied.
•About 3500 B.C. Egyptians put up obelisks, making
a kind of sundial.
13
Basic Clock Parts
•A constantly occurri=
ng
process that marks equal intervals of time. (Sun across the sky, <=
/span>marked
candles, marked oil reservoir in a lamp, sand glasses,
controlled incense burning.)
<=
span
class=3DBB style=3D'position:absolute;left:-4.36%'>•A means t=
o record
the passing intervals.
14
Kinds of Time
15
DEFINING THE DAY
&#=
8226;The
sidereal day
–Time
elapsed between successive passages of a fixed star across a fixed
meridian
&=
#8211;Earth
spins 360 degrees
&#=
8226;The
solar day
=
211;Time
elapsed between successive passages of the sun across the
meridian
&=
#8211;Earth
spins 361 degrees!
16
![](3D"slide0029_image015.gif")
The solar day is longer than the <=
span
style=3D'position:absolute;top:17.75%;left:8.42%;width:83.14%;height:9.25%=
'>sidereal day
360 degrees around the circle
Sights fixed star
Sights same star 10 sidereal days later when earth has move 10 degrees around the Sun
17
![](3D"slide0017_image016.gif")
3/23 Vernal Equinox
12/22 Winter Solstice
6/22 Summer Solstice
9/23 Autumnal Equinox
![](3D"slide0017_image017.gif")
![](3D"slide0017_image018.gif")
![](3D"slide0017_image019.gif")
![](3D"slide0017_image020.gif")
![](3D"slide0017_image021.gif")
The Seasons
18
Elliptical Orbit Effect
![](3D"slide0031_image023.jpg")
![](3D"slide0031_image024.gif")
Imagined
Circular Orbit
![](3D"slide0031_image025.gif")
Exaggerated
Elliptical Orbit
Sun
![](3D"slide0031_image026.gif")
Earth
19
Deviation of Solar Transit Time From Mean Solar Time
![](3D"slide0032_image028.jpg")
20
![](3D"slide0030_image030.jpg")
Equation of Time
21
![](3D"slide0016_image031.gif")
Earth & the Celestial Sphere
Ecliptic
Apparent motion of
the Sun
Celestial Equator
24o
N
Vernal Eq.
Autumnal Eq.
·
·
![](3D"slide0016_image032.gif")
22
![](3D"slide0026_image034.jpg")
![](3D"slide0026_image036.jpg")
A Pair of Armillaries