Taught in 1998 by Lawrence Badash at the University of California, Santa Barbara
Course requirements
Reading assignments
Schedule of Lectures
Appendix1: Greek chronology Appendix 2: Babylonian astronomy

Textbooks. Please purchase the following paperbacked books: 

1. Stephen F. Mason, A History of the Sciences.

2. John North, The Norton History of Astronomy and Cosmology.

3. David C. Lindberg, The Beginnings of Western Science. 

4. Henry M. Leicester, Historical Background of Chemistry.

Course Requirements:

Midterm examination (essay type; may be a takehome). 

Final examination (essay type; may be a takehome). 

Research paper: About 12 pages, typed, with footnotes and bibliography, on a topic approved by the professor. Paper is due the seventh week of the quarter. Grade is based on content and writing skills. If your writing skills are poor and you are unwilling to seek help on campus NOW, please do not take this course. 

This course fulfills the General Education Writing Requirement. Attend meeting in Library, room 1414C, on Thursday, 8 October 1998, for discussion of resources for term paper. 

Reading Assignments: Required reading, in books other than those you are asked to buy, can be done in the Library's Reserve Book Room. An asterisk (*) means recommended reading (not on exams).

Introduction (week 1) 
1. Isis (quarterly journal of the History of Science Society). Thumb through some recent issues. 
2. George Sarton, A Guide to the History of Science, browse.

Pre-History (week 1) 1. Stephen F. Mason, ch. 1. 2. John North, ch. 1. 3. David C. Lindberg, ch. 1. 4. *Charles Singer (ed.), History of Technology, vol. 1, browse. 5. *Sarton, History of Science, vol. 1, ch. 1 (this is not his Intro. or Guide to the History of Science). 6. *Edward Chiera, They Wrote on Clay.

Egyptian and Babylonian Antiquity (weeks 1-3) 1. Mason, ch. 2. 2. North, ch. 2-3. 3. Henry M. Leicester, ch. 1-3. 4. Asger Aaboe, Episodes From the Early History of Mathematics, Introduction, ch. 1. 5. Singer, vol. 1, pp. 793-801. 6. *H.J.J. Winter, Eastern Science, ch. 1 (i-ii). 7. *B.L. Van der Waerden, Science Awakening, ch. 1-3. 8. *Sarton, History of Science, vol. 1, ch. 2-3; vol. 2, pp. 335-42.

Greece (weeks 4-6) 1. Mason, ch. 3-5. 2. North, ch. 4. 3. Lindberg, ch. 2-5. 4. Leicester, ch. 4. 5. M.R. Cohen and I.E. Drabkin, A Source Book in Greek Science, section on chemistry plus section on mathematics or physics or astronomy. 6. *Sarton, History of Science, vol. 1, ch. 16-17, 19-20; vol. 2, ch. 2-7. 7. *Aaboe, ch. 2-4. 8. *Van der Waerden, ch. 4-8.

Rome, Islam, China, India (week 7) 1. Mason, ch. 6-9. 2. North, ch. 5-9. 3. Lindberg, ch. 7-8. 4. Leicester, ch. 5-7. 5. *De Lacy O'Leary, How Greek Science Passed to the Arabs. 6. *Winter, ch. 1 (iii-iv), 2-4. 7. *Joseph Needham, Science and Civilization in China.

Middle Ages (weeks 8-9) 1. Mason, ch. 10-11. 2. North, ch. 10. 3. Lindberg, ch. 9-12, 14. 4. Leicester, ch. 8-9. 5. Weisheipl, Development of Physical Theory in the Middle Ages. 6. *A.C. Crombie, Medieval and Early Modern Science, both volumes.

From the Closed World to the Infinite Universe (weeks 9-10) 1. Mason, ch. 12. 2. North, ch. 11-12. 3. *Crombie, vol. 2, ch. 2 (section 2). 4. *Alexandre Koyré, From the Closed World to the Infinite Universe, ch. 1-6. 5. *Harlow Shapley and Helen Howarth, A Source Book in Astronomy. 6. *Angus Armitiage, Copernicus. 7. *J.L.E. Dreyer, Tycho Brahe. 8. *Max Caspar, Kepler. 9. *Arthur Koestler, The Watershed

Schedule of Lectures UCSB History 106A Fall 1998 

1. 29 Sep. Intro. What is science, evidence?

2. 1 Oct Ancient history. Egyptian mathematics. 

3. 6 Babylonian mathematics. Egyptian astronomy.

4. 8 Astronomical concepts. [Library meeting instead. 0930 in room 1414C.]

5. 13 T Film: Rivers of Time. Babylonian astronomy. 

6. 15 Babylonian astronomy. 

7. 20 T Pre-Socratics. 

8. 22 Pre-Socratics. Review exam questions. 

9. 27 T Greek physics. 

10. 29 Greek physics. Greek mathematics. Midterm.

11. 3 Nov T Greek astronomy. 

12. 5 Greek astronomy. Roman science. 

13. 10 Film: Perfection of matter. Latin science. 

14. 12 Byzantium. Transmission. Arabic science. Term papers due.

15. 17 Film: Islam and the Sciences. Arabic science.

16. 19 Middle Ages. 

17. 24 Renaissance. Revival of astronomy.

18. 1 Dec Scientific instruments. Copernicus. 

19. 3 Tycho Brahe. Kepler. Review exam questions.

20. Galileo's astronomy. Course evaluation.

(Final exam, if not a takehome, is Tuesday, 8 Dec., 0800-1100)

Films. Film order for Fall Quarter 1998 To be shown at 0930, in HSSB 1215

Oct. 13 Oct. 15 Rivers of Time U. of Arizona $18.50

Nov. 10 Nov. 12 Perfection of Matter McGraw-Hill $12.15

Nov. 17 Nov. 19 Islam and the Sciences Bowker $18.00

Greek Chronology

ca. 1200 B.C. Trojan War 
1000-600 Aegean-Cretean period. Linear B 
776 First Olympic year 
700 or earlier Homer
ca. 625-545 Thales 
ca. 611-547 Anaximander 
late 6th/early 5th Anaximenes 
ca. 582-500 Pythagoras 
ca. 570-475 Xenophanes 
ca. 550-475 Heraclitus 
ca. 500-430 Empedocles 
488-428 Anaxagoras 
ca. 484-425 Herodotus (historian) 
460-377 Hippocrates (physician) 
ca. 440 flourished Leucippus 
ca. 420 flourished Democritus 
470-399 Socrates
427-347 Plato 
409-356 Eudoxus 
ca. 388-310 Heraclides 
384-322 Aristotle 
323 died Alexander the Great
ca. 310-230 Aristarchus 
ca. 295 flourished Euclid 
287-212 Archimedes 
ca. 280 flourished Strato 
ca. 260 flourished Ctesibius 
ca. 250 flourished Philo 
ca. 262-200 Apollonius 
ca. 190-120 Hipparchus
ca. 50 A.D. flourished Hero 
ca. 85-165 A.D. Ptolemy
ca. 250 flourished Diophantus

Babylonian Astronomy

Was their accuracy astoundingly good or an artifact of "cooked" numbers?

This is a modern exercise in the way Babylonian astronomers approached a problem (it is not taken from a cuneiform tablet). The goal is to show you the way they developed an idea and how their number system led them to conclusions that look remarkably sophisticated and accurate. It is not meant to deprecate their accomplishments, which were significant.

Problem: We wish to develop a solar theory in which the sun moves through the heavens at the rate of 30°/month through ß degrees, and at a somewhat slower rate of 30°-c/month (c is a constant) through the rest of the year, or 360°-ß.

We can express the time it takes for one cycle (in months) as:

ß + 360-ß = 12;22,8 30 30-c

Note that 12;22,8 is a number actually found in Babylonian texts for the length of the year: 12 months + 22/60 months + 8/602 months. Note also that we are mixing sexagesimal numbers and our own in this exercise, but that should not be confusing.

Multiply both sides of the equation by 30 and by 30-c:

30ß(30-c) + 30(30-c)(360-ß) = 30(30-c)(12;22,8) 30 (30-c)

ß(30-c) + 30(360-ß) = 30(30-c)(12;22,8)

30ß - ßc + 30(360) - 30ß = 30(30-c)(12) + 30(30-c)(;22,8)

-ßc + 30(360) = 30(360) - 30(12c) + 30(30-c)(;22,8)

c(360-ß) = (30-c)(11;4)

c(360-ß) + c(11;4) = 5,32.

This is a Diophantine equation: one equation with two unknowns. It is found in Greek math (note the name Diophantus) and is probably a direct descendent of Babylonian math. But it is out of the mainstream of Euclid-Archimedes-Apollonius.

To solve it we must assume a value for one of the unknowns. We expect c to be small, since the sun obviously does not drop to a much slower velocity. We also would like ß to be near 180°, for symmetry. So we play around. c must be 15 times something to remove the 4 in 11;4 and make ß a whole number. Therefore, let c = 15/k:

15(360-ß) + 15(11;4) = 5,32 k k

Convert Babylonian numbers to our numbers:

15(360-ß) + 1(166) = 332 k k

This is beginning to look very pretty (very Babylonian), since we have 166 and 332.

332k = 15(360-ß) + 166

k = 15(360-ß) + 1 332 2

We are not really solving an equation. We are looking for pretty numbers. This being so, we want a factor of 332 that will remove the 360-ß. Factors are 332 x 1, 166 x 2, 83 x 4. Choose 166, since it is closest to half a circle. Therefore, 360-ß = 166, and 

ß = 194°

Putting this number into the equation, we get k = 8. This makes 

c = 15 = 15 = 1 7 k 8 8

Thus, 30°-c/month = 28 1° /month velocity. 8

This gives us a step function for solar velocity, in which it moves at 30°/month for 194° and 28 1/8° /month for 166°. It looks wonderfully precise (what accurate eyeball-astronomers they were!), but it's really due to artful cooking of rough observations.

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