## Singing Logarithms and Physical Constants

Calculating logarithms using musical intervals (PDF)

Constants for back-of-the-envelope calculations (PDF)

## Required Text

### Updated Version (2014)

The notes used in this course have now been enhanced and published in book form by The MIT Press. The complete book is available as a free download from the OCW website:

The book is also available in paperback for purchase:

• Mahajan, Sanjoy. The Art of Insight in Science and Engineering: Mastering Complexity. MIT Press, 2014. ISBN: 9780262526548.

### As Used in This Course (2008)

The course readings were based on an early draft of the above published book. Those course readings are provided below as a single file, or broken down in the subsequent table by discrete topics for each class session. Chapter 3 in Part 1 is unavailable.

Complete course notes (PDF - 1.2 MB)

## Readings by Session

Readings given in the table below were designed to be read after that session's discussion and are taken from the manuscript above.

Introduction:

1 Preview (PDF)

Managing complexity (PDF)

Pit spacing (PDF)

Managing complexity:

Heterogeneous hierarchies:
2 Tree representations (PDF)

Oil imports (PDF)
3 Gold or bills? (PDF)
4 Random walks (PDF)

Random walks for accuracy (PDF)
5 UNIX (PDF)

Removing spurious complexity:

Proportional reasoning:
6 Triangle bisection (PDF)
7 Pentagonal heat flow (PDF)

Introduction plus spring mass period (PDF)

Mountain heights (PDF)
8 Animal jump heights (PDF)

Calculus (maximizing a quadratic) (PDF)

Jump heights (PDF)
9 Calculus (maximizing gain of a second-order system) (PDF)

Power limits to jumping (PDF)
10 Falling cones (PDF)

Calculus (maximizing a quadratic) (PDF)
11 Drag and jumping (PDF)
12-14 Cycling, swimming, flying (PDF)
Conservation/box models:
15 Conservation cube (PDF)
16 Flight (PDF)
17 Flight (scaling) (PDF)
18 Flight (explicit range and speed) (PDF)
Dimensions and afterword:
19 Algebraic symmetry (PDF)
20 Economics example; pyramid example (PDF)
21 Dimensionless groups (PDF)

Hydrogen size (PDF)
22 Densities (PDF)

Hydrogen size by physics (PDF)
23 Long-lasting learning 1 (PDF)
24-25 Bending of light (PDF)
26-29 Long-lasting learning 2 (PDF)

Buckingham Pi Theorem (PDF)