Reflections on Science 80-120

Revolution and Change

Current News:

Bring your paper drafts next Tuesday. We will spend class discussing the current state of your research projects. There is no reading assignment.

You can now pick up your paper prospectuses in my mailbox at 135 K BH. They are in a manilla envelope marked with the class number.

Basic Information:

Room: PH A21

Time: TR 10:30-11:50

Instructor: Kevin T. Kelly.

Assistant: Orlin Vakarelov

Texts (status: in bookstore):


Science classes teach principles and techniques. But this gives a somewhat misleading impression. Real scientists have to deal with surprises that don't fit the textbook rules. At such a time, a momentous decision point is reached: should one tinker a little longer to explain the surprise using standard techniques, or should one break with the past and try something totally new? Textbook science is a single snapshot of an ongoing, dynamic process of change driven by surprise.

This class will focus on scientific change rather than on specific scientific principles and techniques. There is a major debate concerning the nature of scientific change. One one side of the debate, it is maintained that scientific change is orderly and governed by something called "scientific method". On the other side of the debate, it is claimed that scientific change is governed by no method because methods change as science changes. According to this view, scientific change is more like a political revolution, in which new social standards arise spontaneously from the ashes of the old. There is no general consensus today about which side is right.

We will begin with I. B. Cohen's The Birth of a New Physics, which describes in a straightforward way the process by which Newtonian physics (the kind you meet in introductory Physics textbooks) replaced the ancient Greek physics of Aristotle. With this example in hand, we will read Thomas Kuhn's celebrated book The Structure of Scientific Revolutions, which attempts to make the case that scientific change is revolutionary rather than methodologically guided. We will then apply Kuhn's thesis to another major example of scientific change; the emergence of Darwin's theory of evolution in biology. For a more recent example, we will move on to Chaos, in which Gleick argues that the development of chaos theory in the 1960's and 1970's constituted a scientific revolution in Kuhn's sense. Finally, we move on to a contemporary case of scientific change, Stuart Kaufmann's application of chaos theory to the emergence of life, structure, and ontogenesis in At Home in the Universe. Nobody really knows if Kaufmann's program will replace standard Darwinian theory, so you will know what it feels like to be a scientist who has to decide whether or not to take the leap, without benefit of hindsight.

Level of the Course:

The class carries a 100 level number. As such, it must be offered at a level suitable for Freshmen and Sophomores. More advanced students can pursue their interests in the rather open midterm and final essay assignments. I will also be happy to discuss further issues and details in office hours.

Aims of the Course:

The most important aim of the course is to provide a sense of science as a dynamic, surprising process, rather than as the static, cumulative record of smart people's achievements. The focus will be on history and theory comparisons rather than on doing exercises and computations within a particular theory.

As a by-product of our primary aim, we will examine some exciting ideas that you may wish to pursue further.

The course is not a substitute for standard science classes, in which problem-solving skills are developed.

It is also not an aim of the course to give a complete overview of the various philosophies of science. That is done more thoroughly in 80-220, Philosophy of Science.



Given the wide range of the audience, I will expect more of the work of upperclassmen.

Class participation:

I expect enthusiastic and well-informed class discussion. If you don't have anything to say, you will have to listen to me lecture!


A 10% per day late penalty applies to all written assignments. Days are measured from the end of class.

Reading Assignments:

In order to cover all the texts, we must average around 35-40 pages of reading per class (70-80 per week). We have more material than we can cover at that rate. Every topic we will examine could fill an entire course, so it is not imperative that we finish the proposed Syllabus.

For a useful discussion in class, it is imperative that you read the texts carefully. Even though they are not written in mathematical notation, they explain important ideas that will often require drawing in a notebook and repeated readings to understand.

Reading Exercises (33% of the grade)

Due as indicated.

Answers must be typed

Answers must be turned in at the end of class.

Your two lowest scores will be dropped from the average to account for broken computers, illness, etc.

Midterm Paper Assignment (33% of the grade)

Due Oct 14. Get started by Sept 21.

Essay must be typed, double spaced, 10 pt. Times Roman, with proper references.

Essay must be turned in at the end of class on the due date. See paper writing guide.

Option 1 (fun): five pages plus references and footnotes: write a short story about a scientific revolution. The episode should illustrate the older scientific paradigm, the onset of crisis, and the ensuing revolution. It should also involve nontrivial disagreement about method that makes each party prefer its own paradigm (making this work out in a plausible way is not easy). You can set the story in the future or on another planet. Or you can write a quasi-historical story in which the "wrong" side wins due to a slight change in the sequence of events. Try to illustrate as many of the points Kuhn makes as possible.Footnote the story with references to Kuhn indicating which features of scientific revolutions you are trying to illustrate at each stage.

Option 2 (expository): in four pages plus references and footnotes, criticize some feature of Kuhn's argument in The Structure of Scientific Revolutions. Outline one of his arguments and try to poke holes in it, using reasons and examples from the history of science.

Final Paper Proposal (counts as one reading exercise)

Due Nov 11. Get started by Nov 2.

One page outline of your final paper, with a list of plausible references included.

Final Paper Assignment (34% of the grade)

Due Dec. 2. Get started as soon as your prospectus is approved.

Essay must be typed, double spaced, 10 pt. Times Roman, with proper references. See paper writing guide.

seven pages + footnotes and bibliography.

Choose an episode of scientific change.

On the basis of independent library research, describe the episode, including (1) prior paradigm, (2) anomalies, (3) revolutionary response, and (4) process by which the new theory won.

Then argue for or against the thesis that the episode was driven by an underlying, rational "scientific method".

You will be graded first on competent description, second on cogent argumentation, and third on originality.

General Hints


I. The 17th c. Scientific Revolution

II. Revolution vs. Scientific Method

III. The Darwinian Revolution

IV. The New Science of Chaos

V. Order for Free: A New Biological Revolution?

I. The 17th c. Scientific Revolution

Some links:

Internet Modern History Sourcebook: The Scientific Revolution

Online Encyclopedia Britannica: The Scientific Revolution. Use the search engine to obtain reliable outline information on any figure or event in the course.

Biographical search engine for the scientific revolution

Aug 26: Aristotle's physics. Cohen: , Chapters 1,2.


Reading Questions (turn in at the end of class):

  1. What happens when you drop a large and a small ball from the same height at the same time?
  2. What motions did Aristotle take to be natural for terrestrial objects? For celestial objects?
  3. What is a violent motion?
  4. Why must Aristotle's law of motion be restricted to cases in which force exceeds resistance?
  5. Prove that the Earth cannot move on the basis of Aristotelian principles.

Questions to think about:

  1. Aristotle was primarily a biologist. For example, he was the first to see that whales and dolphins should be classed with people and horses rather than with fish. Why might a biologist find Aristotle's theory of motion to be plausible?
  2. For Aristotle, the "final cause" of a change is the culmination of that change. How does this view connect with his theory of natural terrestrial motion?
  3. How might an Aristotelian try to account for acceleration without giving up the theory of natural motion?

Some links:

  1. Aristotle's works (See for yourself, especially, the Physics. Did this guy say something about everything, or what?)
  2. Zeno's paradoxes (See Zeno prove the mystical thesis that motion is impossible. That makes short work of physics).

Aug 31: Copernican Astronomy. Cohen: Chapter 3.


Reading Questions:

  1. What is "retrograde" planetary motion? Draw a picture.
  2. How did Ptolemy account for retrograde motion? Draw a picture.
  3. How does the Ptolemaic system fit with Aristotelian theory of natural motion?
  4. What causes the appearance of retrograde motion in Copernicus' system? Draw a picture.
  5. List two scientific difficulties with Copernicus' theory.

Questions to think about:

  1. Was Ptolemy's theory "refuted" by the evidence?
  2. How, exactly, was Copernicus' theory better?
  3. Wherein did the extra "simplicity" of Copernicus' theory consist?
  4. Is this kind of "simplicity" a reason to think that Copernicus' theory is closer to the truth than Ptolemy's?
  5. What does this say about "scientific method"? Is there a "method" here?

Some links:

  1. Copernicus' Preface to De Revolutionibus (Online! )
  2. Nikolaus Copernicus () On the Revolutions of Heavenly Spheres. Charles G. Wallis (Translator).
  3. Photographs of De Revolutionibus

Sept 2: Galileo and the Telescope. Cohen: Chapter 4.


Reading Questions:

  1. Why was the nova of 1604 a blow to Aristotelian physics?
  2. Why were mountains on the moon a blow to Aristotelian physics?
  3. Why was it good for Copernicus that the fixed stars do not increase in size when viewed through a telescope?
  4. Why were the moons of Jupiter good news for Copernican theory?
  5. Why were the phases of Venus good news for Copernican theory?

Discussion questions:

  1. What does this episode say about the relationship between technology and fundamental science?
  2. Which of the observations, if any, refuted the Ptolemaic theory?
  3. Try to design an Earth-centered universe consistent with all of Galileo's telescope observations.

Some links:

  1. Galileo's Siderius Nuncius (Online!) This is where Galileo announces his telescopic discoveries. Great reading.
  2. Galileo Galilei (1967) Dialogue Concerning the Two Chief World Systems. Stillman Drake, ed. Berkeley: University of California Press.
  3. Rice University Galileo Project (not so great).
  4. Virtual tour of the Galileo room in the Museum of the History of Science, Firenze See Galileo give you the finger! Also see his telescope and inclined plane experiment.

Sept 7: Inertia. Cohen: Chapter 5.


  1. Whose advice would Simplicio follow if he could do it all over again? What is the advice?
  2. How could one object to the inclined plane experiment?
  3. By what method did Galileo arrive at his free-fall law?
  4. How did medieval scholars apply the mean-speed law? How does this illustrate Aristotele's approach to physics?
  5. What was Simplicio's objection to horizontal inertia in projectile motion?

Questions to think about:

  1. If you know some calculus: Solve Simplicio's differential equation to see how position would depend on time. Would it be safe to play baseball in such a world? Name two familiar systems for which this law is correct (hint: one of them is something you should start early).
  2. What was wrong with Galileo's computation of the time of free fall from the moon?
  3. How, physically, does inclined plane motion differ from free-fall? Is the inclined-plane law the same?

Some sources:

  1. Galileo Gallilei (1974) Two NewSciences. Milwaukee: University of Wisconsin Press.
  2. David C. Lindberg (1978) Science in the Middle Ages. Chicago: University of Chicago Press.
  3. Stillman Drake and I.E. Drabkin (1969) Mechanics in Sixteenth Century Italy: Selections from Tartaglia, Benedetti, Guido Ubaldo, and Galileo. Milwaukee: University of Wisconsin Press.
  4. William Wallace (1977) Galileo's Early Notebooks: The Physical Questions. Notre Dame: Notre Dame University Press.

Sept 9: Kepler. Cohen: Chapter 6.


  1. What was the maximum error of Kepler's epicycle theory of Mars' motion?
  2. State Kepler's three laws. Illustrate the first two with a diagram.
  3. Why did the third law suggest that the planets are moved by a force from the sun?
  4. Which came first, the first law or the second law?
  5. What stopped Kepler from proposing an inverse square law for the driving force of the sun?
  6. Why did Galileo dismiss Kepler?

Questions to think about:

  1. How was Copernicus' theory a prerequisite for Kepler's Platonic solid theory?
  2. How do we explain what Kepler tried to explain with the Platonic solids. What if his theory had agreed with the facts?
  3. How could one "deduce" the orbital path of a planet? To illustrate the point, show that heavenly motions are compatible with square orbits so long as the speed law is varied to compensate.
  4. What, if anything, does simplicity have to do with the truth?


  1. Arthur Koestler (1959) The Sleep Walkers. New York: Grosset & Dunlap. This book describes the intimate details of Kepler's discovery in a novelistic format. Highly recommended.
  2. Johannes Kepler (?) Epitome of Copernican Astronomy & Harmonies of the World. Charles Glenn Wallis trans. Great Minds Series.

Sept 14: Newton. Cohen: Chapter 7.


  1. Why did Hooke, Halley and Wren guess that the sun emanates an inverse square attractive force? What couldn't they do?
  2. Using a diagram, explain Newton's proof that a centripetal force of any kind gives rise to Kepler's second law. Using the area law for triangles (1/2 base X altitutde) why is triangle SBC equal to triangle to SBc?
  3. How does Newton explain that all bodies fall from the same height in equal times, regardless of their weight? Can you explain what is going on in simple, nontechnical terms?
  4. Using the answer to the preceding question, show that the same force attracts a stone at the Earth's surface and the Moon. Is it necessary to know G in order to do this test?
  5. What are some phenomena that Newton's theory of universal gravitation unified?

Questions to think about:

  1. How would Newton's argument have been weakened if Galileo had not discovered the moons of Jupiter?
  2. If there were only the Earth and the sun, how could one argue for universal gravitation?
  3. How does Newton's theory of the tides undercut Galileo's argument for Copernicanism?

Class discussion questions:

  1. Summarize Newton's argument for universal gravitation.
  2. Contrast Newton's physics with Galileo's.
  3. Compare Newton's argument with that of Copernicus.
  4. In light of the scientific revolution, what do you think the scientific method is?


  1. Newton's Principia Mathematica online!
  2. Richard S. Westfall (1980) Never at Rest: A Biography of Isaac Newton. Cambridge: Cambridge University Press. This used to be a textbook for the course. That was a crazy idea, but I recommend the book very highly to anyone doing a project on the Newtonian revolution.

II. Revolution vs. Scientific Method

Links (quality not guaranteed).

Sept 21: Normal Science and Paradigms. Kuhn: Chapters I-IV.


  1. How does Kuhn's new-style history of science differ from bad old history of science?
  2. Why is it hard for a new paradigm to emerge from the pre-paradigm stage?
  3. What are the three kinds of problems that arise in normal science?
  4. How to do the problems of normal science resemble puzzles?

To think about:

  1. Do you think any methodologist would say that method uniquely determines scientific beliefs? What room would there be for scientific genius in such a view?
  2. Does the world change in a revolution or does our belief about the world change? Can the two be distinguished?
  3. Do you think the distinction between "is" and "ought" should be judged entirely in terms of its ability to explain historical events? Does "ought" imply "is" or "mostly is"?
  4. What does Kuhn's account of pre-paradigmatic science say about Stephen Hawking's "A Short History of Time" and other such books?
  5. Are paradigms a good thing or a bad thing? Or rather, under what assumptions would they be good or bad?
  6. In artificial intelligence, one can search a tree structure by plunging down a branch and backtracking or by expanding each possible branch at a level in parallel. The former is called "depth-first search". The latter is called "breadth-first" search. Use this distinction to give a procedural model of the distinction between preparadigm and postparadigm science.
  7. Do you agree that unique dominance of a field is a necessary feature of a paradigm?
  8. Was Ptolemaic astronomy pre-paradigm science? Was Galileo's early buoyancy theory of free-fall?
  9. What were some central commitments of the Ptolemaic paradigm?

Sept 23: Crisis. Kuhn: Chapters V-VII. Start doing research for midterm paper.


  1. What does Wittgenstein's theory of family resemblance have to do with the concept of "scientific method"?
  2. What is a discovery?
  3. What does Bruner's experiment illustrate?
  4. Why does avoiding novelty tend to produce it?

To think about:

  1. Do you agree that scientific method would have to explain the constitution of a paradigm?
  2. What else might they explain?
  3. How might you explain that it is hard to capture a paradigm exactly with such rules?
  4. Can you explain why science is taught by examples of solved problems without assuming that there is nothing to science but solved problems?
  5. Can you explain why in periods of crisis the methodological principles formulated by the two sides are not the same without assuming that the two sides really believe in these methods?

Sept 28: Revolution. Kuhn: Chapters VIII-IX.


  1. What are the possible outcomes of a paradigm crisis?
  2. How are scientific revolutions similar to political revolutions?
  3. Why can't science proceed by accumulating novel facts?
  4. How does Kuhn object to the view that Newtonian theory is a limiting case of relativity theory?
  5. What is Kuhn's argument against the proposal that the nonsubstantial aspects of paradigm change are cumulative?

To think about:

  1. Is "cumulativity" vs. "anarchy" a valid dichotomy?
  2. Think of a conception of scientific knowledge in which knowledge does not accumulate.

Discussion questions:

  1. Why is the paradigm prior to scientific method?
  2. What is the anatomy of a scientific discovery? Illustrate with some examlples.
  3. How do crises arise, and what are the possible outcomes of a crisis? Illustrate with examples.
  4. What are scientific revolutions? Pay special attention to the myth of cumulativity in science.

Sept. 30: More on Revolutions. Kuhn: Chapters X-XI.


Due Oct. 5.

  1. In what sense does the world change during a scientific revolution?
  2. How do gestalt phenomena logically differ from scientific revolutions?
  3. Why did Aristotle and Galileo see two different things when they looked at a pendulum?
  4. How does Kuhn respond to philosophers who say that the new paradigm "interprets" the same data differently?

To think about:

  1. Can scientific observation "flip" like Gestalt experiments?
  2. Do you agree believe that scientific revolutions change the world? How could you defend your position?
  3. Is it the data that change, or which data are gathered that changes? Check Kuhn's argument to see if he is clear on this point.
  4. Are meterstick readings more theoretical than pendula or less so?
  5. Does the Dalton example convince you that chemical operations did not provide a stable data pool through the Dalton revolution?

Oct 5: Method and Progress Kuhn: Chapters XII-XIII


Notes on Bayesian methodology (some tips for those who want to criticize Kuhn).

  1. What is wrong with probabilistic theories of scientific verification?
  2. What is Popper's methodology and what is wrong with it?
  3. What "aesthetic" and "subjective" factors enter into paradigm evaluation?
  4. How does science grow? In what popularly conceived sense does it not grow?

To think about:

  1. Is "simplicity" a "logical" or an "aesthetic" virtue?
  2. Is this preference paradigm-specific? What does the winning theory always look like?
  3. Is "faith" in future progress mere faith? Isn't all induction based on "faith"?
  4. Can empirical justification be holistic?
  5. Does the existence of an objective logic of science require that everyone agree at the same time?
  6. In other words, could an objective logic allow for subjective inputs?
  7. Could probabilistic methods apply across different "worlds"?

Oct 8: Summary Kuhn: Postscript


  1. Distinguish paradigms from scientific communities.
  2. How does Kuhn interpret the "different worlds" thesis in the postscript?
  3. How are good reasons related to conversion?
  4. How is Kuhn a convinced believer in scientific progress?

III. The Darwinian Revolution

Some links:

  1. See for yourself: Darwin's major works online!
  2. Creation Science Not everyone converted!
  3. Debating Creation Scientists

Oct 12: Social Context. Ruse: Chapters 1-2.


  1. What does Plato have to do with evolution?
  2. What were Cuvier's arguments against evolution?
  3. What are some criteria for determining whether science had yet become a profession?
  4. How can Darwin's success be accounted for in light of his mediocre university record?

Oct 14: Intellectual Context. Ruse: Chapter 3. Midterm paper due.


  1. Contrast uniformitarianism with catastrophism.
  2. How did Whewell alter Herschell's account of "true causes"?
  3. Why did Herschell's philosophy make him sympathetic to Lyell?
  4. How did Sedgewick and Lyell interpret the idea of "design" differently?

To think about:

  1. Illustrate Kuhn's point about methods being subordinate to paradigms in terms of Whewellian vs. Herschellian philosophy of science in the Uniformitarian/Catastrophist debate.
  2. Does Darwin's reception by the Catastrophists square with Kuhn's account of crisis and revolution?
  3. Did Lyell and Cuvier "talk past one another" concerning directedness?
  4. What kind of phenomena emerge from the "background" to the "foreground" in Lyellian geology?
  5. Can you give a unified, Bayesian account of the difference between Whewell and Herschell?

Oct 19: Mystery of Mysteries. Ruse: Chapter 4.


  1. What was Lyell's view about the orgin of species?
  2. How did Babbage apply his knowledge of computing machines to assist Lyell's position?
  3. Why did Herschell like Lyell's position?
  4. How did Whewell's position differ from Cuvier's?
  5. How did the views of Lyell and Sedgwick on origins fit with religious liberalism and conservatism, respectively?

To think about

  1. Was the origins problem an anomaly? To what paradigm?
  2. Was the science of origins in the pre-paradigm state during this period?
  3. Why did the origins problem become prominent at this time, according to Ruse?
  4. Do you think the industrial revolution played as large a role as Ruse argues?

Oct 26: Archetypes. Ruse: Chapter 5.


  1. How did von Baer's embryology differ from the Transcendentalist embryology reflected in the Meckel-Serres law?
  2. What was Chambers' account of the mechanism of evolution?
  3. What were Hugh Miller's arguments against Chambers' interpretation of the fosil record?
  4. What were Owens' homologies and homotypes?
  5. Why were homologies troublesome for natural theology?

Discussion questions:

  1. Describe the various positiosn on origins prior to Chambers.
  2. Describe Chambers' evolutionary theory.
  3. What were the responses to Chambers' theory?
  4. Describe Owen's archetype theory.

Oct 28: Pre-Origin. Ruse: Chapter 6.


  1. How did Owen's theory transform the progressionist position?
  2. How did Huxley criticize Owen's theory?
  3. How did Huxley's public behavior help to shape the evolutionary debate?
  4. How did Whewell's dispute over extraterrestrial life help the evolutionist cause?
  5. Why did Wallace think that Uniformitarianism implies transutation?

To think about

  1. Why do species variations on small islands support evolution over special creation? Is there a Bayesian reconstruction of the reasoning?
  2. How did the shift to morphological design arguments in natural theology play into the hands of the evolutionists?
  3. How does Wallace's background fit into Kuhn's ideas about the onset of scientific revolutions?
  4. Do you think the Owen-Huxley phenonenon helps or hinders the overall progress of science?
  5. Did evolution cause the downfall of religion or did the downfall of religion help evolution?


  1. Recount the Owen/Lyell debate over origins. (Is there a Bayesian account of the significance of the Stonesfield mammals to progressionism?)
  2. Recount Hooker's and Huxley's pre-evolutionary Lyellian positions.
  3. Describe the relevant religious developments during the 1850s.
  4. Recount the evolutionary theories of Spenser and Wallace.

Nov 2: Origin.of Species. Ruse: Chapter 7.


  1. What were the three choices on origins that were open to Darwin as a Lyellian?
  2. What two ideas did Darwin put together from September to November of 1838?
  3. What philosophical principle led Darwin to emphasize the analogy between natural and artificial selection?
  4. What was Huxley's reason for Darwin's delay in publishing his theory?
  5. How did Darwin explain the similarity among embryos?

To think about:

  1. How did Darwin strive to satisfy both Herschell's and Whewell's conceptions of vera causa?
  2. Try try to work out a quasi-Bayesian model of the Darwinian revolution. What possible theories were taken seriously prior to natural selection?

Discussion questions:

  1. Contrast Huxley's account of Darwin's discovery of natural selection with the account in Darwin's own notebooks.
  2. How did Darwin strive to satisfy the methodological recommendations of Whewell and Herschell?
  3. What was the significance of Darwin's work on barnacles?
  4. Outline the Origin of Species.

Nov 4: Scientific outcome. Ruse: Chapter 8.


Sketch of a Kuhnian Analysis of Darwin's Revolution

  1. How did Wallace and Darwin differ on sexual dimorphism?
  2. What was Jenkin's objection based on the logic of heredity and how did Darwin handle it?
  3. Describe Darwin's pangenesis theory.
  4. What made Darwin doubt his conclusion that infertility is not selected for?
  5. What was Kelvin's argument against natural selection and when was it finally resolved?

IV. The "New Science" of Chaos


Very simplistic online introduction to chaos. There are lots of similar pages that all say about the same thing.

There are tons of archives of animated tours of fractals. Search on your own.

Nov 9: Prologue, Butterfly effect. Gleick.


  1. What planted the seed of a "new science"?
  2. What was Lorenz's response to Von Neumann's program for controlling the weather?
  3. What is the "butterfly effect" and what is its technical name?
  4. Describe Lorenz's waterwheel model of convection and illustrate it with a diagram.
  5. What did physicists expect the waterwheel to do?

To think about:

Discussion Questions:

  1. What possibility was not on the table for physicists?
  2. Why not? Do science textbooks teach more than they intend? What does this say about Kuhn's concept of the tacit knowledge of a paradigm?
  3. Was there a crisis here? What was Lorenz's role in the "revolution"?
  4. How well does Lorenz fit Kuhn's profile of an extraordinary scientist?
  5. Was was discovered? Did it contradict anything in classical physics? How then was it new?
  6. Is Gleick pushing the Kuhn wagon too hard?
  7. Why would anybody want to?

Revolution. Gleick.


No reading questions this time. Final paper prospectus is due.

Life's Ups and Downs. Gleick.


  1. How did ecologists avoid the conclusion that population equations geneate chaos?
  2. How did physics textbooks mislead physicists about chaos?
  3. What was the "electric shock" James Yorke discovered?
  4. When did work on chaos begin in the Soviet Union?
  5. What did May think would make the world a better place?

A Geometry of Nature. Gleick.


  1. What was Bourbaki and how did it influence the relationship between mathematics and natural science?
  2. Intuitively, what does fractional dimension measure? What is the fractional dimension of the Koch curve?
  3. What theme unified Benoit Mandelbrot's work?
  4. What problems of presentation did Scholz encounter?
  5. How does the fractal approach to anatomy differ from the classical approach?

Note: Cohen's list of scientists who declared their own work to be revolutionary!

Strange Attractors. Gleick.


  1. Describe the pre-chaos paradigm in the study of turbulence. What major anomaly did it encounter?
  2. What is a phase space?
  3. What are strange attractors?
  4. What is a Poincare map?
  5. What happened to Poincare maps of the orbits in the Henon galaxy model when the energy level was increased?

No reading assignment for Tuesday. Have your paper in a presentable shape for preliminary presentation to your peers.


Do draw pictures illustrating concepts and examples as you read.

Examples and illustrations are vivid. But our real goal is to see the general pattern of scientific change lying behind them. Try not to lose your focus on the general issues.

Don't get hung up on calculational technique and problem solving. That's what regular science classes are for. Use the "friend" test. Aim to be able to explain the course material to a friend in a simple, entertaining, informal manner with pictures if necessary.

Do try to write down what you don't understand. Often this will lead to understanding. If it doesn't, you can ask about it in class or in office hours.

Do make use of office hours.

Don't get too anxious when you aren't understanding something. The class is episodic and involves results from different sciences, so you will be able to get back aboard later. Or if you find the first book to be too elementary, you probably won't think that the later books are.

Don't assume that everyone else understands what you don't. I can assure you that your classmates are expert actors in this regard! Also, philosophy puts a higher value on genuine puzzlement than on unearned smugness.

Have fun!!! If science weren't fun, nobody would do it!

Some example episodes for the final paper

(star indicates extra mathematical sophistication)

  1. phlogiston theory of combustion ---> oxygen theory (Lavoisier)
  2. catastrophism in geology ---> uniformitarianism (Lyell)
  3. theory of circulation of the blood (Harvey)
  4. atomic theory (Dalton, Perrin)
  5. punctuated equilibrium theory in evolution
  6. particle optics ---> wave optics (Young, Fresnel)
  7. fluid electicity (Franklin)
  8. electrons (Thompson)
  9. plate techtonics in geology
  10. atmospheric pressure (Torricelli)
  11. energy concept and ideal heat engines (Carnot)
  12. DNA and molecular genetics (Watson, Crick, Rosalyn Franklin: interesting feminist angle)
  13. psychoanalysis (Freud)
  14. Bayesian statistics (Ramsey, DeFinetti)
  15. Cartesian physics (Descartes)
  16. elliptical orbits (Kepler)
  17. tidal theory (Galileo, Kepler, Newton)
  18. the clonal selection theory of the immune system
  19. behaviorism ---> cognitive psycyhology
  20. theory of polymers
  21. population genetics (Fisher*)
  22. quantum theory (Planck, Bohr, etc.*)
  23. relativity theory (Einstein*)
  24. black holes (Hawking, Penrose*)
  25. Electromagnetism (Oersted, Faraday, Maxwell*)
  26. statistical mechanics (Einstein*)

Paper Writing Guide


You should choose a thesis pertinent to the topic of the course and argue cogently for it. An argument consists of several premises or reasons followed by a conclusion. The conclusion is marked by such words as "therefore", "thus", or "hence". Reasons are marked by such words as "because" or "since". The conclusion should follow from or at least be supported by the reasons provided. Hint: write out the arguments in outline form like this

Then rewrite the argument as a paragraph, marking the conclusion with "hence", "therefore", etc.


Papers should be based on outside library research. As a rule of thumb, at least five extra sources should be consulted. Your grade will be based, in part, on the relevance of these sources and on your proper understanding of them. You are welcome to consult me at office hours for clarification.


All quotations and ideas borrowed from other sources must be annotated with proper textual references. The bibliography should be at the very end of the paper. Bibliographical references look like this:

The number in parentheses is the most recent publication date for the book (located in books on the publication information page prior to the table of contents). In journal citations, the number before the colon is the journal volume number (usually on the spine of the jounral, as well as on the first page). The numbers after the colon are page numbers on which the article occurs. Page numbers are considered mandatory by publishers.

When a source is used in the text, refer to it right in the text as follows. Note that the reference occurs before the period that ends the relevant sentence.

I will be happy to give specific advice about papers during office hours prior to the due date. Try to formulate focused questions ahead of time (you may find that you know the answer once you formulate the question clearly).