Fall 2021
T7T8T9 (15:30-18:30)
room 旺宏 245
前近代科學史
Introduction to the History
of Pre-Modern Science
11010GEC 150400
Course description:
The main goal of this course is to provide the students with
the basic knowledge of the history of science in premodern era, that is, in the period preceding the
Scientific Revolution that took place in Western Europe
in the 17th century.
Scientific Revolution, a series of events that took place in
European science in the 16th-18th century and radically
changed not only science and technology, but all the
spheres of human life.
Instructor: Alexei Volkov (琅元)
E-mail: lang.yuan.tw@gmail.com
Office: Education Hall 201
The course will include the following topics:
Usually the Scientific Revolution is identified as
appearance of new physical and astronomical theories
of Copernicus, Galileo and Newton. Yet more detailed
investigation shows that the processes were extremely
complex.
- the beginnings of science in ancient Babylon (divination,
medicine, mathematics), Egypt (astronomy and
mathematics), Greece (philosophical foundations, logic,
mathenmatics, astronomy);
We will
W
ill not discuss
di
these
h
processes in
i this
hi course; there
h is
i
another course titled « Scientific Revolution » (offered
in the Center for General Education in Chinese)
especially devoted to this topic.
- Medieval science in East and West:
(a) Medieval European Science;
(b) Islamic science;
(c) Ancient and Medieval Chinese science (mainly, work
on mathematics and astronomy);
- the meeting between the Western and Chinese scientific
traditions that happened in the 17th century.
Why do we study « pre-modern » and not « modern »
science?
Teaching
The reason is: this course is offered to a very wide
audience. The topics, discussed by the scientists before the
Scientific Revolution, are not too technical, and can be
easily understood by all students.
Each session (class) will consist of three parts:
Our study
O
t d off pre-modern
d
science
i
will
ill give
i the
th students
t d t the
th
opportunity to see where the modern science came from,
and what were the most general laws of its evolution.
- A quiz (multiple choice,
choice one question,
question open book)
combined with a break (10-15 min);
Also, the pre-modern science was not as international and
global as the modern science is; therefore, we will have to
learn about several old and rich cultural traditions (Egypt,
Babylon, Greece, Medieval Europe, China…).
- A lecture presented by the instructor (a powerpoint
show), approximately 1h to 1h20;
- A group presentation (20-30 min for each group)
evaluated by the instructor and by students;
- A movie (30-60 min) (only 1 time ).
1
[A typical quiz]
Your name: _____ Your Student ID number: ________
Quiz 3. Choose the correct statement(s):
(A) Thales studied mathematics in Egypt;
(B) Pythagoras was the teacher of Thales;
(C) The Society of Pythagoras was located in Italy;
Instruction, quizzes and exams: all in English .
(D) None of the above.
There will be two exams:
-a mid-term test (2 hours, in class, open book, multiple
choice)
and
- a final exam (3 hours, in class, multiple choice).
Important: The exams questions will be related only to the
instructor’s lectures, not to the your classmates’
presentations.
Course evaluation:
Team presentation:
Quizzes:
Midterm:
Final exam:
15% of the final grade;
20%;
30 %
35%
VERY Important: students who missed the
midterm or the final exam without a serious
reason will not be allowed to take it later.
Materials: No textbook will be available.
Therefore, the students are strongly encouraged to attend
all lectures and to take notes.
The power-point shows will be posted on the e-learning
website of the University http://moodle.nthu.edu.tw/ (all
)
students enrolled in this course automaticallyy have access to it);
each time the powerpoint show will be posted after the class.
2
Students organize teams; each team consists of no less than
four and no more than six students; in exceptional cases teams
can have seven students. Each team chooses a leader. The
leaders send me by email the names, the student IDs of the
team members, and the topics chosen by their teams. They
should send me their emails no later than Monday, October 4.
The list of topics will be presented today in this powerpoint
show;; it will be p
posted on the Universityy e-learning
g website
http://moodle.nthu.edu.tw/.
Topics for presentations:
1. Ancient megalithic astronomical observatories in Europe (esp.
Stonehendge).
2. Great civilizations of Pre-Colombian Central and Southern
America (Olmecs, Incas, Maya), their religion and science (esp.
astronomy and calendar).
3. Ancient
i andd medieval
di l Indian
di science
i
( h
(mathematics,
i astronomy,
astrology,… excluding medicine).
The students who do not join any group will be placed in some
groups by the instructor. On Tuesday, October 5, in class, I will
present to you the teams, and their topics.
4. Islamic science (mathematics, astronomy, astrology,… excluding
medicine).
The timetable of the presentations will be given to you today
and will be also posted on the e-learning website.
5. Cartography in Asia (India, China, Japan, Korea…) before the
18th century.
6. Cartography in the West (Western Europe, Byzantine Empire) and
in Islamic world before the 18th century.
Time
Week 1
09/14
7. History of alchemy in East and West.
8. Traditional medicine in Asia (India, China, Japan, Korea…) before
the 18th century.
9. Traditional medicine in the West (Western Europe, Byzantine
Empire)
i ) and
d iin Islamic
l i world
ld before
b f
the
h 18thh century.
10. Astrology in Asia (including China).
11. Astrology in the West before the 18th century.
12. The early history of counting: pebbles, fingers, sticks… and so on.
13. Science and religion: enemies or partners?
Time Class activities
Week 6 Early Greek science (1):
10/19 Thales and Pythagoras;
mathematical theory of
music; Sophists (Zeno of
Elea), paradoxes; three
construction problems
Week 7 Early Greek science (2):
10/26 Plato and his Academia
Week 2
09/21
Week 3
09/28
Week 4
10/05
Week 5
10/12
Class activities
Presentation topic
n/a
Introduction; explanation
of the grading system;
short overview of the
course
Mid-Autumn Festival
n/a
(no class)
Teacher’s Day
n/a
((no class))
Egyptian science and
T1. Ancient megalithic
technology: astronomy, astronomical observatories in
mathematics,
Europe (esp. Stonehendge).
engineering.
Babylonian mathematics, T2. Great civilizations of Preastronomy, divination, Colombian Central and Southern
and astrology
America (Olmecs, Incas, Maya),
their religion and science (esp.
astronomy and calendar).
Presentation topic
T3. Ancient and medieval
Indian science
(mathematics, astronomy,
astrology,… excluding
medicine).
Time
Class activities
Presentation topic
Week 9 Early Greek science (4): the T6. Cartography in the
11/09
Elements of Euclid
West (Western Europe,
Byzantine Empire) and in
Islamic world before the
18th century.
T4. Islamic science
(
(mathematics,
, astronomy,
y,
astrology,… excluding
medicine).
Week 8 Early Greek science (3):
T5. Cartography in Asia
11/02 Aristotle and his Lyceum; (India, China, Japan,
syllogistics
Korea…) before the 18th
century.
Week 10 Early Greek science (5):
T7. History of alchemy in
11/16
School of Stoics and their East and West.
logic
Week 11
Midterm exam
n/a
11/23
Week 12 Greek, Hellenistic, and
T8. Traditional medicine
11/30
Roman cosmologies:
in Asia (India, China,
Anaximander, Aristarchus, Japan, Korea…) before
Ptolemy, Martianus Capella the 18th century.
3
Time
Class activities
Week 13 Science and Christianity: St.
12/07
Augustine, Isidore of
Seville; Byzantine and
Islamic science
Presentation topic
T9. Traditional medicine in
the West (Western Europe,
Byzantine Empire) and in
Islamic world before the
18th century.
T10. Astrology in Asia
(including China) before
y
the 18th century.
Week 14 Science in European
12/14
universities in the early
second millennium AD;; N.
Copernicus and T. Brahe, J.
Kepler and Galileo
Week 15 Beginnings of science in
T11. Astrology in the West
12/21
China: counting instruments; before the 18th century.
earliest mathematical
treatises; geometry and
geometrical algebra;
mathematics education
Time
Class activities
Presentation topic
Week 16 Earliest Chinese astronomical T12. The early history of
counting: fingers, pebbles,
12/28
records; star maps;
sticks, suan-pan,
computation of calendar
soroban, … and so on.
Week 17 Jesuit order and its scientific T13. Science and religion:
01/04
activities; transmission of
enemies or partners?
Western scientific expertise
p
to
China in the 17th century, part
Activities of M. Ricci, Johann
Adam Schall von Bell and
Ferdinand Verbiest
n/a
Week 18
Final exam
01/11
General history and
history of culture
History of science
Anyy questions?
A
q
???
History of scientific
ideas
History of individuals
and institutions
World map of 1574
China and the Western Science: the
great encounter of the 17th century
Greece
History of Western science
Babylon
History of Chinese science
Egypt
4
Egyptian Science
No later than 3,000 BC ancient Egyptian scribes devised a system
of writing the Greeks later called hieroglyphics (« sacred carvings »).
Egyptian scribes
Babylonian Science
Nut (also spelled Nuit, Newet, and Neuth), the goddess of the sky
Astronomy and astrology: high
quality observations of the Sun,
the Moon, five naked-eye
plants; astronomical tables;
prediction of eclipses.
Mul Apin is a collection of
texts that deals with
Babylonian astrology and
astronomy. The
h text lists
li the
h
names of 66 stars and
constellations and gives rising,
setting and culmination dates.
It was found that the
observations reported in these
tablets were made ca. year
1370 BC.
5
Attica
"Greater Greece,"
(Megalê Hellas Μεγάλη Ελλάς
Colonized in the 8th c. BC)
Ancient Greece
Pythagoras
(b. 580/572 - d. 500/490)
Thales of Miletus
(632/624-546/547 BC)
Socrates
(469-399)
Egyptian priests
(mathematics,
theology, astronomy,
for 13 years)
?
Pythagoras
Plato (429 - 347 BC)
Socrates
(469-399 BC)
Archytas of Taras (428-347)
Egyptian astronomy
Plato (429 - 347 BC)
Created the Academy (open in 387 BC).
« Let no man ignorant of geometry enter! »
Theaetetus
(ca. 417-369 BC)
Aristotle
(384-322 BC)
Eudoxus
(ca. 400-347 BC)
Portrait of Plato. Marble, Roman copy
from the 2nd century CE after a Greek
original of the late 4th century BC
Roman copy, 2nd c. AD, of an earlier
Greek portrait statue (c. 399 BC)
6
Socrates?
Aristotle
(384-322 BC)
Pythagoras
Euclid or Archimedes?
Ptolemy?
Retrograde and direct motion
Buch der Natur (Book of
Nature), by Konrad of
Megenberg (or Konrad von
Megenberg, 1309-1374), written
ca. 1350, 3rd print of 1481
(Library of Congress). In this
picture the planets occupy
positions in the Heavens
according to the traditional
views. Two « stars » between
the Moon (at the bottom) and
the Sun are Venus and Mercury.
Mercury
Euclid
(from a MS
of the 6th c. AD)
7
The Elements, Book 1
23 Definitions;
5 Postulates
5 Common Notions;
48 Propositions
Propositions.
Definition 1:
A point is that which has no part.
Definition 2:
A line is breadthless length.
Definition 3:
The extremities of a line are points.
Definition 15:
A circle is a plane figure contained by one line such that all the
straight lines falling upon it from one point among those lying
within the figure are equal to one another.
Definition 16:
And the point is called the centre of the circle.
Definition 20:
Of trilateral figures,
g
, an equilateral
q
triangle
g is that which has its
three sides equal, (...).
Postulates
Let the following be postulated:
1. To draw a straight line from any point to any point.
2. To produce a finite straight line continuously in a straight line.
3. To describe a circle with any centre and distance.
Common notions
1. Things which are equal to the same thing are also equal to
one another.
2. If equals be added to equals, the wholes are equal.
3. If equals be subtracted from equals, the remainders are equal.
Proposition 1
On a given straight line to construct an equilateral triangle.
Pellegrino Tibaldi (1527–1596), Escola de Atenas, mostrando um debate entre os
académicos (da Academia Platônica) e os Estóicos, afresco de Pellegrino Tibaldi,
Mosteiro El Escorial, Madrid
The Paradoxes
Mathematical practices and traditions
Programme of Aristotle
Crocodile:
A crocodile took a baby of a woman and said: “I will give
the child back if you answer correctly my question. The
question is: will I give the child back to you?” The
woman said: “No”.
No .
If the crocodile does not give the child back, the woman’s
answer was correct, and therefore the crocodile must
return the baby.
Megaro-Stoic
Logic
The Elements
But if the crocodile returns the baby, the woman’s answer
was wrong, and therefore the crocodile can keep the child.
8
Claudius Ptolemy
Claudius Ptolemaeus (Greek: Κλαύδιος
Πτολεμαίος Klaúdios Ptolemaîos; some
authors suggest 90 – 168 for his
lifetime).
His family name
suggests that he
was not a recent
immigrant, but was
descended from a
line of Alexandrian
citizens, and most
likely had access to
Greek astronomical
heritage.
Worship included reading the Bible
and devotional literature. Each
monastery had a school, library and
scriptorium.
(France, Mont St Michel, Benedectine
monastery of Mt St Michel, 8th century AD)
Combination of the three
solutions, epicycle on
deferent, eccentricity of the
Earth, and equant model.
The title of the work of Ptolemy was Mathematical Syntaxis
μαθηματικἠ σύνταξις (or “Mathematical Treatise”), later renamed
Almagest, « The Great [Book] » after it Arabic translation); it seems
that he was not so much concernied with the physical explanation of
the movement of the planets.
Yet he believed in centrality of the Earth which for him was not a
mere mathematical hypothesis.
The Monk
Eadwine.
Romanesque
illuminated
manuscript
p from
Canterbury, ca.
1150.
Scriptorium
9
The rise of
Universities
in Western
Europe
Curriculum: the
Liberal Arts,
Medicine,
Theology, Law.
Note: The
earliest
European
Universities
were not
« founded »,
but emerged
gradually out
of preexisting
schools.
From 711 to 756, the Muslims swept over the Iberian Peninsula,
conquering nearly all of it and establishing a foothold north of the Pyrenees
in Narbonne. In the present-day Spain, they put down local rebellions and
established the Emirate of Córdoba.
Nicole Oresme
Nicole Oresme, also
known as Nicolas
Oresme, Nicholas
Oresme, or Nicolas
d'Oresme (c. 1323 - July
11, 1382)
Oxford, Merton College (founded in 1260s)
An economist,
mathematician,
physicist, astronomer,
philosopher,
psychologist,
musicologist, theologian
and Bishop of Lisieux, a
competent translator,
counselor of King
Charles V of France, one
of the principal founders
of modern sciences, and
probably one of the
most original thinkers of
the 14th century.
Tycho Brahe (1546 – 1601)
10
The Jesuits
Ignatius of Loyola
(1491 – 1556)
C. Clavius
(1538 – 1612)
Perspective rendering,
color picture and plan of the
Stjerneborg (Stellaburg)
observatory on the island of
Hven
History of
mathematics and
astronomy in
traditional China
Counting rods made of bone found in a tomb of the first century
BCE in Shaanxi (or Shǎnxī ) 陝西 province (China). From LI,
Yan, and DU, Shiran. Chinese mathematics: A concise history.
Oxford: Clarendon Press. 1987, p. 9.
朱世傑，四元玉鑑 (1303)
c
b
Set x = b, y = a + c
x³ +2x²y + 2xy - xy² - 2y² = 0
(Equation A)
2y² - xy² + 2xy + x³ = 0
a
(Equation B)
b² - (c - (b-a)) = ab
a² + (c + (b-a)) = ac
b-?
x³ - 2x² -8x = 0
x=4
(Try to solve it!)
11
The abacus
Astronomy and society
in traditional China
Matteo Ricci, 利瑪竇
(1552 –1610)
Francis Xavier
(left), and Ignatius
of Loyola.
Matteo Ricci (right)
and Adam Schall
von Bell
Matteo Ricci (left) and Xu Guangqi (徐光啟)
12
Ricci & Xu 1607
Beijing observatory
Clavius (1574)
Team leaders, send me lists of your teams and
selected topics
by email before 10 pm, September 25 at:
lang.yuan.tw@gmail.com
(You can send me several (no more than 4!) options,
for example, « our first choice is topic 2, second
choice is topic 4, and third choice is topic 8. »)
13