Catalog description

Common shapes and patterns emerge repeatedly in the design of living organisms and among the structures of materials from which the Earth is made. We will explore several general principles that underlie such regularities of pattern and proportion. From the symmetry patterns of flowers and crystals, from the shapes of dinosaurs' legs and mountains, and from the branching patterns of veins, arteries and rivers, we will discover important similarities and critical differences between living and non-living things. We will show that understanding nature involves both the recognition of common patterns and the analysis of departures from them.

Rationale

The course will focus on the analysis and explanation of common shapes, patterns, scales and proportions that are characteristic of natural phenomena. We will ask why it is that some patterns are characteristic of a particular system or category of phenomena, whereas others appear in a wide variety of contexts.

The course will include studies of symmetry, shape and proportion, growth patterns in living and non-living systems, modular structures such as crystals, cells and fractals, and the creative role of breaking symmetry. The course will end with a section on perspective, relating our perceptions of the world to the nature of our observations and our attempts to represent (construct) the forms of natural phenomena in the arts.

The course has three objectives that are more important than its specific material: (i) To show how many properties of natural phenomena are based on a few general principles; (ii) to show that a clear grasp of some simple quantitative relationships leads to a first-order understanding of many aspects of the natural world; (iii) to explore the relationship between patterns in nature and our conceptions of beauty.

Approach

Each class session will include a segment in which we will be engaged in a case study, mapping, measuring or analyzing the properties of a system that exemplifies the principles under consideration. These exercises will not be elaborate, but they will involve direct observation (gathering, analyzing and evaluating data) wherever possible. Some exercises will involve the modeling of patterns or quantitative relationships exhibited by natural phenomena.

We will use two main texts. One is a trade book, written for a general audience, that focuses on the dynamics of pattern formation. The second is a classic collection of plates that we will draw on repeatedly as a sort of encyclopedia of patterns that are expressed in the shapes of living things.

               The Self-made Tapestry: Pattern Formation in Nature, by Philip Ball, 1999. Oxford                University Press, 287 p.

               Art Forms in Nature: The Prints of Ernst Haeckel, reprinted with two new essays, 1998.                Munich and New York, Prestel-Verlag, 139 p. 

Requirements

                                                                        Percentage of course grade

          Portfolio (cumulative)                                             65%

          Final poster presentation                                        25%

          Class participation                                                    10%

You have the opportunity to select the material on which you wish your work in this course is to be evaluated. Your portfolio will consist of those class assignments that you choose to include in it. Normally, these will originate as projects undertaken in class that you will write up and annotate with appropriate comments based on reading your text, consultation of reserve readings, or material from other sources (all with appropriate citations). You will receive comments and suggestions for improvement of your work on individual projects during the semester. You may incorporate improvements into the versions of these assignments that you include in your final portfolio. If you do so, you must include the original versions in a separate packet, although these will not affect your final grade. The object of this procedure is for you to create a body of work that is exciting and satisfying to you.

Materials

You will need sharp pencils (not too hard), a ruler and an eraser to work on many of the projects we will undertake together. Some projects will involve simple calculations for which a calculator will be necessary. You will need a loose-leaf binder in which to accumulate your work and ultimately in which to submit it as your portfolio.

Instructor Roger D. K. Thomas

e-mail: r_thomas telephone: 291-4135; home phone, 560-0486

office hours: Monday, 2:30 &emdash; 4:30 pm

Thursday, 2:30 &emdash; 4:30 pm (or 6:00 pm)

also as available or by appointment

Preceptor Erin A. Sipe         e-mail: ea_sipe telephone: 358-6864

Course Web Site http://www.fandm.edu/academics/foundations/NTW114/default2.html

Professor Annalisa Crannell, Jack Stewart '03, and I put some of the material we have developed for this course on a web site. This site is still under construction. You will find a variety of resources there. We will use it directly for some projects. We aim to make additions and improvements to the site, as a result of our work, this semester.

Schedule of class topics

Tuesday Introduction: perceiving, analyzing, and communicating about shape

Jan. 15 Tapestry, p. 1-15.

Thursday On magnitude: the inconstancy of proportions

Jan. 17 Haldane, J. B. 1965. On being the right size, pp. 474-478.

Johnson, G. 2000. Of mice and elephants . . . a matter of scale. In:

 

The Best American Science Writing, 2000, edited by J. Gleick, pp. 23-29.

Thompson, D'Arcy W. 1961. On Growth and Form, abridged by

J. T. Bonner, pp. 15-48. Chapter 2, On magnitude.

 

Tuesday On symmetry: the chimaera of perfection

Jan. 22 Tarsov, L. 1986. This Amazingly Symmetrical World, pp. 15-25, 41-50.

Hargittai, I. 1986. Limits of perfection, in Symmetry: Unifying Human

Understanding, pp. 1-17.

Jablan, S. 1998. Modularity and Art. http://members.tripod.com/~modularity/d3.htm

Thursday Project: Kunstformen der Natur

Jan. 24 Breidbach, 0. 1998. Brief instructions to viewing Haeckel's pictures, in Artforms in Nature, pp. 9-18.

Tuesday Project: Kunstformen der Natur

Jan. 29 Eibl-Eibesfeldt, I. 1998. Ernst Haeckel &emdash; the artist in the scientist, in Artforms in Nature, pp. 19-29.

 

Thursday On Gulliver and the heights of mountains

Jan. 31 Tapestry, p. 161-164.

Hubbert, M. K. 1945. Quarrying the State of Texas, abstracted from

Strength of the Earth, Amer. Assoc. Petrol. Geol., Bull. 29: 1630-1653.

In J. Gilluly et al., (1959) Principles of Geology, 2nd ed., pp. 166-167.

Tuesday On the shapes of volcanoes

Feb. 5 Tapestry, p. 175-178.

Francis, P. 1993. Volcanoes: a Planetary Perspective, pp. 103-113

and 141-145.

 

Thursday On the shape of the Earth and our maps of its surface

Feb. 7 Berthon, S. and Robinson, A. 1991. The Shape of the World, pp. 9-25.

Thompson, M. M. 1987. Maps for America, 3rd Edition, pp. 14-17 and

236-245. For more detail on conventions, see pp. 27-71.

Chamberlin, W. 1950. The Round Earth on Flat Paper, published

separately by the National Geographic Society, pp. 39-122.

 

Tuesday On the shapes of the planets and their moons

Feb. 12 Beatty, J. K. and Chaikin, A. (editors) 1990. The New Solar System, 3rd edition, especially Chapter 20, "Small bodies and their origins", pp. 251-258 and data tables, pp. 289-294.

Thursday Symmetry I. Linear structures: silicates, carbon chains and spirals

Feb. 14 Farmer, D. W. 1996. Groups and Symmetry, pp. 39-42, Strip patterns.

Atkins, P. 1987. Molecules, pp. 1-12 and 34-37.

Tarsov, L. 1986. This Amazingly Symmetrical World, pp. 26-27, 62-67.

Pauling, L. and Hayward, R. 1964. The Architecture of Molecules,

plates 11, 13, 48, and 50.

Tuesday On the spiral growth of shells

Feb. 19 Tapestry, p. 11-13.

Thompson, D'Arcy W. 1961. On Growth and Form, abridged by

J. T. Bonner, pp. 172-193.

Meinhardt, H. 1995. The Algorithmic Beauty of Sea Shells, pp. 1-17.

Thursday On spiral patterns in the growth of plants

Feb. 21 Tapestry, p. 104-109.

Snow, R. 1955. Problems of phyllotaxis and leaf determination.

Endeavour 14: 190-199.

Prusinkiewicz, P. 1990. The Algorithmic Beauty of Plants, pp. 99-118.

Difficult, but beautiful and fascinating!

Tuesday On branching patterns in the growth of trees

Feb. 26 Tapestry, p. 127-130.

McMahon, T. A. 1975. The mechanical design of trees. Scientific

American 233 (1): 92-102.

Thursday On branching networks: river systems, arteries and highways

Feb. 28 Tapestry, p. 110-139.

LaBarbera, M. and Vogel, S. 1982. The design of fluid transport systems

in organisms. American Scientist 70: 54-60.

March 1 SPRING BREAK

March 10

 

Tuesday Symmetry II. Patterns in two dimensions &emdash; the silicates of Flatland

March 12 Tarsov, L. 1986. This Amazingly Symmetrical World, pp. 26-35.

 

Thursday On close packing in physical systems &emdash; patterned ground, Fingal's Cave

March 14 and the Rayleigh-Bénard effect.

Tapestry, p. 165-181.

Gray, N. H. 1986. Symmetry in a natural fracture pattern: the origin

of columnar joint networks, in Symmetry: Unifying Human Understanding, pp. 531-545.

 

Tuesday On close packing in living systems: turtle shells, trilobite eyes, sheet of

March 19 epidermal cells and the honeycomb

Tapestry, p. 30-33.

Thursday Symmetry III: Patterns in three dimensions &emdash; silicates and diamonds

March 21 Tapestry, p. 16-49.

Tarsov, L. 1986. This Amazingly Symmetrical World, pp. 51-61.

Battey, M. H. 1972. Mineralogy for Students, pp. 3-28, Ionic properties,

packing.

 

Tuesday Possible worlds: on Platonic solids and crystal classes

March 26 Tarsov, L. 1986. This Amazingly Symmetrical World, pp. 36-40.

Battey, M. H. 1972. Mineralogy for Students, pp. 29-38 and 63-65.

 

Thursday Breaking symmetry: on the shape of water

March 28 Pauling, L. and Hayward, R. 1964. The Architecture of Molecules,

plates 11, 13, 48, and 50.

Tuesday On the sizes of ions and their solubility: the ties that unbind

April 2

Thursday Breaking symmetry: amino acids, proteins and snails

April 4 Tarsov, L. 1986. This Amazingly Symmetrical World, pp. 67-70.

Tuesday On size and shape: changes in proportion in growth, evolution and

April 9 perception

Thompson, D'Arcy W. 1961. On Growth and Form, abridged by

J. T. Bonner, pp. 15-48. Chapter 2, On magnitude.

Pelli, D. G. 1999. Close encounters &endash; an artist shows that size affects shape. Science 285: 844-846.

Thursday On brain size: fact, fallacy and fiction

April 11 Allman, J. M. 1999. Evolving Brains, pp. 159-207. Chapter 7, The evolution of big brains.

Gould, S. J. 1981. The Mismeasure of Man, pp. 30-72. Chapter 2,

American polygeny and craniometry before Darwin.

Tuesday POSTER PRESENTATIONS

April 16

Thursday On giants and dwarfs

April 18 Moog, F. 1948. Gulliver was a bad biologist. Scientific American

179 (5, Nov.): 52-55.

Alexander, R. McN. 1989. Dynamics of Dinosaurs and other Extinct

Giants. See especially Chapter 11, Giant birds, pp. 150-158.

 

Tuesday On art as the mirror of Nature: rules of perspective

April 23 Walters, N. V. and Bromham, J. 1974. Principles of Perspective,

pp. 12-43.

Willats, J. 1997. Art and Representation, especially Chapters 1 and 2,

Introduction and Projection Systems.

Thursday On art as the prism of Nature: from naturalism to abstraction

April 25 Ritterbush, P. C. 1968. The Art of Organic Forms. Chapter 1, To set form above nature, pp. 1-15.

MacGillavry, C. H. 1986. The symmetry of M. C. Escher's "impossible"

images, in Symmetry: Unifying Human Understanding, pp. 123-138.