FSEM 040 - The Shapes and Patterns of Life (Fall 2001)

Instructor: Warren Weckesser
314 McGregory, (315) 228-7228
Email: WWeckesser@mail.colgate.edu
Office Hours: Tuesday, 7:00-9:00 PM
 Wednesday, 12:30-2:30 PM
Lecture: MWF 9:20-10:10, 312 McGregory
Text: On Growth and Form, by D'Arcy Thompson.
Additional reading, including book excerpts, journal articles, and web pages, will be assigned throughout the course.
Web Page: https://math.colgate.edu/~wweckesser/fsem040/

Course Content

The shapes and patterns of life are incredibly diverse and beautiful. When we see the stunning beauty of a butterfly's wings, the spiraling pattern of seeds in a sunflower, or the precise hexagonal grid of the honeybee's comb, we are led to ask "How does that form?", and perhaps more importantly, "Why does that form?" These are difficult questions to answer! One might hope that one could follow the example of classical physics, and use a mathematical formulation of a set of fundamental principles. Unfortunately, it seems that biological systems are far too complicated--there is little hope for, say, an "equation of a cell". In 1917, D'Arcy Thompson wrote "the zoologist or morphologist has been slow [...] to invoke the aid of the physical or mathematical sciences... Even now the zoologist has scarce begun to dream of defining in mathematical language even the simplest of forms." Thompson was an early proponent of the application of mathematics to the study of biological forms, despite their apparent complexity. In this seminar, we will read more of what Thompson had to say in his classic On Growth and Form. We will also study more recent research, in which the scarce dreams of early zoologists are becoming reality. Despite the complexity of biological systems, there have been remarkable successes in understanding the formation of biological shapes and patterns.

To begin to answer the questions of "why" and "how", we will have to understand the fundamental ideas of evolution and natural selection. We will also have to understand the constraints put on natural selection by the laws of physics. The tools that we will use in our study are mathematics, computer simulation, and critical thinking.

Here is another quote (slightly condensed) from D'Arcy Thompson that summarizes the intent of this course: "The terms Growth and Form are to be understood in their relation to the study of organisms. We want to see how, in some cases at least, the forms of living things, and of the parts of living things, can be explained by physical considerations, and to realise that in general no organic forms exist save such as are in conformity with physical and mathematical laws."

General Information

Project

There will be a significant project required for this course. A "project" will be a written report (in the form of a research paper) on a subject related to the content of the course. It may also include components such as computer simulations, a web page that you designed, class demonstrations, or other components, depending on your interests and abilities. Use your imagination!

Homework

Download files: