8.298 Selected Topics in Physics

Lies and Damn Lies: The Art of Approximation in Science

Homepage for an IAP physics course at MIT (2006). Course description:

How far can birds (and 747s) fly without eating? Why are raindrops a few millimeters in radius? How high can animals jump? How tall can mountains grow? How cold is the air at the top of Mt Everest? How hot is the interior of the sun? How much energy do gravitational waves carry? How fast do tsunamis travel? Even when these questions have exact answers, they are buried in the solution of complicated, often nonlinear differential equations. But by skillful lying -- the art of approximation -- you can understand these and other phenomena, and can enjoy the physics, chemistry, biology, and engineering of the world around you.

Problems

These problems (in PDF) cover Chapters 1 through 6. They are optional and are for you to check your understanding. I won't collect them, and they don't count for a grade.

Here are some solutions to the problems above.

Logistics

Meetings : Class: MWF, 2-3pm, Room 2-139. Jan 9, 11, 13, 18, 20, 23, 25, 27, 30; Feb 1, 3. Recitation, W 3pm in Room 1-135. Jan 11, 18, 25; Feb 1. Listeners welcome! (but please do the readings -- see below!)

: Prerequisites : Freshman physics (ask me for other cases).

: Freshman physics (ask me for other cases). Grading: based on reading memos, an idea developed by Prof. Edwin Taylor of MIT. No exams or quizzes that count, but maybe a few strictly for self-assessment so that you know how you are understanding the material.

Readings

These will come from a textbook on approximation that I am writing. For each chapter, turn in a reading memo at the beginning of class on the day listed. We'll discuss any questions and go through more examples.

Listeners/auditors are strongly urged to read the chapters and even do reading memos. First, there's lots more in each chapter (examples, discussion) than we can possibly do in a lecture, so if you don't read the chapters you'll be lost -- which is not good for you or for the class. Second, by doing a reading memo you'll read attentively and learn more.

Why am I so keen that you read the material before class? The short answer is that it's a much better use of class time for us to discuss physics rather than for me to read you a book aloud. Here is a longer answer (1.6MB PDF article), a classic talk by Robert Morrison on 'The lecture system in teaching science.'

More reading

Useful data.

Several books overlap with the themes of this course. My favorites:

Harold McGee. On Food and Cooking: The Science and Lore of hte Kitchen (New York: Scribner, 1984). There's also a newer edition.

(New York: Scribner, 1984). There's also a newer edition. John Harte. Consider a Spherical Cow: A Course in Environmental Problem Solving (Mill Valley, CA: University Science Books, 1988).

(Mill Valley, CA: University Science Books, 1988). John Harte. Consider a Cylindrical Cow: Further Adventures in Environmental Problem Solving (Sausalito, CA: University Science Books, 2001).

(Sausalito, CA: University Science Books, 2001). G. Polya. Induction and Analogy in Mathematics (volume I of Mathematics and Plausible Reasoning ) (Princeton, NJ: Princeton University Press, 1954).

(volume I of ) (Princeton, NJ: Princeton University Press, 1954). Knut Schmidt-Nielsen. Scaling: Why is Animal Size So Important? (Cambridge, England: Cambridge University Press, 1984).

(Cambridge, England: Cambridge University Press, 1984). Craig F. Bohren. Clouds in a Glass of Beer: Simple Experiments in Atmospheric Physics (New York: John Wiley, 1987).

(New York: John Wiley, 1987). Thomas A. McMahon and John Tyler Bonner. On Size and Life (New York: Scientific American Library, 1983).

More problems

There are problems to try at the end of each chapter, of varying difficulty. Try those that interest you, and ask any questions about them either in class or in section (Wednesdays 3pm), send me an email, or just stay after lecture to chat. These problems are for self-assessment -- for you to check your understanding -- not for a grade.