A View from the Back of the Envelope top

Table of Contents

Jump to...
Approximate reasoning
Nice books
Lists of Magnitudes / Landmarks


ASTR 103 - Supplement 1A. Measurement and Computation
`Back-of-the-Envelope' Calculations (Or The Seven Habits of Highly Effective Astronomers)
IUN/FYDE Introductory Physics Notes Especially the Introduction.
"These notes constitute a general, non-calculus introductory physics course. They are based on lectures given through the IUN/FYDE distance education program of the University of Winnipeg, which provides access to university level courses for communities outside of Winnipeg. The material covered comprises the introductory course Physics 1301 offered at the University."
CalTech's Physics 103b: Order of Magnitude Physics (Winter 97)
CalTech's Physics 103c: Order of Magnitude Physics (older)
Physics on the Back of an Envelope Abstract for Physics 309, NEW for Spring 1996, Prof. L. Weinstein
Order-of-Magnitude Astrophysics an informal course taught by Andrew Gould and David Weinberg


Powers of Ten : About the Relative Size of Things in the Universe, and the Effect of Adding Another Zero.
Philip Morrison and Phylis Morrison, and The Office of Charles and Ray Eames.
1982, 1994. Scientific American Library. ~$20. [Amazon]
[The classic.] [** I should add descriptions of films, CD, etc. I though there was a web version, but I can't find it now. **]
Powers Of Ten (the movie) and an early draft.
Powers of Ten Interactive CD-ROM.
A poster and flipbook also exist.

There are lots of links on the `Powers of Ten' scales page.

"Powers Of Ten" was inspired by the 1957 Cosmic View: The Universe in 40 Jumps. Related films include the NASM IMAX Cosmic Voyage, the National Film Board of Canada's Cosmic Zoom and Planetary Vision's Cosmic Zoom. The Eames Office has a www.powersof10.com. PoT is a theme of the Hayden Planetarium Rose Center. A reader says the Film Board's animation is "beautifully hand drawn".

Timescale : an atlas of the fourth dimension
Nigel Calder
1983. Viking Press.
[Apparently out of print. :( ]
This book is a singleminded attempt by one falible but tolerably well-informed person to weave new cloth from other people's yarns.[6]
Timescale begins with an overview of ... dating ... [and] time ..., continues with a narrative [and log timeline] of what has happened to the world, to life, and to humankind, and culminates in a facinating index that cross-references important dates of topics and concepts, from abacus and amphibian to work and Zoroastrianism.[cover flap]

Comparisons of distance, size, area, volume, mass, weight, density, energy, temperature, time, speed
Diagram Group.
1980. St. Martin's Press.
[Apparently out of print? :( ]
[Lots of pictorial scale comparisons. "Young adult" accessible.]

Powers Of Time
Demetrios, Eames
[I have not seen this.]
A reader reports it's also on the Powers of 10 Interactive CD-Rom.
Powers of Time compliments the classic short film, Powers of Ten. Just as Powers of Ten is about spatial scale, Powers of Time is a journey in time. The journey slices time finer and finer, down to the tiniest sliver of time for which we have a name, the attosecond (10-18). Then we see a representation of ever-longer stretches of time, from a single second to over 31 billion years (or 10+18). A brilliant approach to a complex subject. Grades: 9-12, C, A; 9 mins

Seeing Time
Hone, Robert(Bob) and Red Hill Studios (Stuff here.)
[I have not seen this.]
This exhibit exposes museum visitors to the many different natural changes that take place over various time scales - from geologic processes that transend millions of years, to the changes in a forest over forty year, down to microscopic events that are measured in fractions of a second. Supported by a $500,000 grant from the National Science Foundation (Installed at Exploratorium in San Francisco, June '95 and The Science Museum of Minnesota, Summer '95)

Is a Blue Whale the Biggest Thing There Is?
Robert E. Wells
1993. Albert Whitman & Co. [Amazon]
Ages 4-8.

From Quark to Quasar : Notes on the Scale of the Universe
Peter H. Cadogan,
1985. Cambridge University Press.
[Out of print]
[Basically a remake of Powers of Ten, perhaps targeted at a slightly more general audience. Some nice nuances of difference.]

Imagining the Universe : A Visual Journey
Edward Packard.
1994. Perigee Books. 154 pages. [Amazon]
[Some pictorial scale comparisons, centered in a San Francisco ball park. Mainly length (> 1 meter). Some time. First read Powers of Ten and Timescale.]

Approximate reasoning

Consider a Spherical Cow : A Course in Environmental Problem Solving.
John Harte (UCBerkeley).
1988. University Science Books. $25. [Amazon]
"This book should provide a novel, and I hope enjoyable, way of learning how to use relatively simple mathematical methods (often of the "back-of-the-envelope" variety) to understand how planet Earth and its inhabitants interact.
The idea for this text evolved from courses in environmental science I have taught at Yale University and the University of California at Berkeley over the past 15 years. These courses have ranged from the introductory undergraduate to the advanced graduate level. Regardless of the level, I have stressed quantitative problem solving in all my courses, and over the past 15 years I have invented a sizeable repertoire of homework problems. These, along with a few delightful ones contributed by my colleagues, form the basis for this book."
Note also `The Dynamic Environment - Computer Models to Accompany Consider a Spherical Cow'.

Search for Simplicity
Weisskopf, Victor F.
Column in the American Journal of Physics.
Dec 1984 - Feb 1986 (atleast).
[Some notes.]

The Back of the Envelope
Purcell, Edward M.
A column in the American Journal of Physics.
Jan 1993 - July 1984. (atleast)
[Some notes.]

On the Back of an Envelope: A column devoted to encouraging calculation in geology
Triplehorn, Don
A column in the Journal of Geological Education.
1994 v. 42 p. 46, 164, 272, 402, 524; 1995 v. 43 p. 58, 289. (atleast)
[Some notes.]

The Cosmological Milkshake
Robert Ehrlich,
1995. Rutgers University Press.
[From the net: "This is a fun book, written in the spirit of the Fermi problems. There are 135 questions answered, each in about one to two pages. Here are two examples: What is the smallest suction cup you could use to walk on the ceiling ? How fast can chemical rockets travel?"]

Educated guesses
John A. Adam
In "Quantum: The Magazine of Math and Science", Sept/Oct 1995 (v6n1)(pgs 20-24).
[Some Fermi Questions. "Quantum" was difficult to find.]

Nice books

On Size and Life
Thomas A. McMahon and John Tyler Bonner.
1983. Scientific American Library. [Out of print?]
[Scaling issues and patterns, and their impact on the shape of life.]
A central objective of this book is to examine the relation between the size and shape of organisms. [...] we are interested in those instances in which size appears to impose specific constraints on shapes [...] The leg of a 5-kilogram dik-dik differs in shape from the leg of a 500-kilogram buffalo for reasons almost entirely due to the constraints impose by their differing sizes. [...] the same is true of [...] a wheat plan and the thick trunk of an oak tree.[pg 18]

The Science of Measurement
Herbert Arthur Klein
1974. Dover reprint (1988). ~736 pgs. [Amazon]
"The author, during research and writing of several books on recent advances in science, became impressed, and finally almost possessed, by the conviction that modern measurement methods provide the broadest, most natural, least restricted road on which nonscientists can approach modern science."[pg 24]


On Number Numbness
Hofstadter, Douglas R.
Scientific American, May 1982, "Metamagical Themas" column.
reprinted with added "Post Scriptum" (pp 131-135) in book
Metamagical themas : questing for the essence of mind and pattern
New York : Basic Books, c1985.
pp 115-135

Innumeracy: Mathematical Illiteracy and Its Concequences
Paulos, John Allen
1988. Amazon

A Mathematician Reads the Newspaper
Paulos, John Allen

How Much is a Million?
by Schwartz, David M., pictures by Kellog, Steven
1985, (multiple editions/publishers, including Mulberry Books and Scholastic).
36 p. [Amazon]
[A nicely illustrated childrens book.
"If one million kids climbed onto one another's shoulders, they would be...
taller than the tallest buildings,
higher than the highest mountains,
and further up than airplanes can fly.
If you wanted to count from one to one million...
it would take you about 23 days.
If a goldfish bowl were big enough for a million goldfish...
it would be large enough to hold a whale.
Presto! One hundred stars. If this book had a million stars, they would fill seventy pages."
These elements are then repeated for a billion, and a trillion.]

Lists of Magnitudes / Landmarks

Niel Brandt's Timelines and Scales of Measurement Page
Including Evolutionary / Geological Timeline, Cosmological Timeline, Scales of Measurement.

The Magnitudes of Physics
George Goth
An insert in The Physics Teacher vol34, Dec 1996.
[A list of some 500 values.]
Here is a copy.

The Sizesaurus : from hectares to decibels to calories : a witty compendium of measurements
Stephen Strauss
1997, Avon. 1995, Kodansha International.
[I've yet to look at this closely. It seems a science journalist's combination of magnitude lists with discussions of individual units (something like those in Klein's The Science of Measurement). Some additional info can be found on Amazon.com's pages for the 1995 (hardcover) and 1997 ("somewhat revised" paperback) editions. ]

Quest / Science by the Numbers
Scott LaFee
A newspaper column of the Union-Tribune's Quest [links broken].


Things I plan to look at...

Physiology by Numbers: An Encouragement to Quantitative Thinking
Richard Burton Other books

The Dynamic Environment - Computer Models to Accompany Consider a Spherical Cow
Leonard J. Soltzberg
1995. University Science Books.
(I have not seen this.) PR: "Environmental Science has become an interactive experience. Now, you can control the parameters governing environmental systems such as pollutant flows or population dynamics and watch the result unfold on your computer screen. This package combines two books, the ever-popular Consider a Spherical Cow by John Harte and The Dynamic Environment, with the powerful demo version of the STELLA modeling software. Ideal for self instruction and introductory modeling and environmental problem-solving courses.
-Two Books and Software for the Macintosh 0-935702-38-5 $58
-Two Books and Software for Windows 0-935702-37-7 $58 "

Used Math (2nd ed)
Clifford Swartz,
1993. American Association of Physics Teachers.
From the net: "This is great for the student who needs a quick explanation of the mathematics you need in introductory physics. It is also great for the instructor."

Some Misc

Amazon.com's Size perception topical page.

Rule of Thumb[link broken] Some rules. Nice definition.

"general goals regarding feed consumption, feed conversion and egg production or body weight gain for small flocks."
Astronomy stuff

Ad Astra's "Back of the Envelope" column does not have anything to do with BotE calculation.

From the Exploratorium's Structure and Shape Learning Resources

About the Size of It: Film Series Leaps of Scale: The Dimensions of Time
McBean Theater, 2pm In this program, the earth is formed, babies are born, and we travel to the edges of the universe, all in a matter of minutes! The first part of this program explores how film condenses time, helping us to experience great shifts in scale. Films include Baby Booming (1989, 2 min.) by Mary Cybulski and John Tintori; Pasadena Freeway Stills (1974, 5 min.) by Gary Beydler; Delugion (3 min.) by Michael Rudnick and Rock Ross; An American Time Capsule (1969, 3 min.) by Charles Braverman; Going Up (1989, 30 min.) by Gary Pollard; Geologic Time (1989, 7 min.), which tells the entire history of the world in a mere six minutes; Eyes to Earth (1986, 10 min.) by Tom Van Sant; Charles and Ray Eames' classic Powers of Ten (1968, 9 min.), an adventure in magnitudes; and Lew Alquist's Frame (3 min.).
About the Size of It: Film Series Leaps of Scale: Part Two McBean Theater, 2pm Messing around with scale is part of the classical training of an animation artist. Thanks to the animator's charged imagination, peas transform into planets, and we see the world from a fly's perspective. Films include Please Don't Feed the Animals (1988, 4 min.) by J. Stephan Leeper; The Fly (1982, 3 min.) by Ferenc Rofusz; Nose Hair (1994, 5 min.); Academy Award winner Mona Lisa Descending a Staircase (1992, 9 min.) by Joan Gratz; Marv Newland's Black Hoola (1994, 5 min.) and Bambi Meets Godzilla (1962, 2 min.); Max Fleischer's Felix Trifles with Time (1925, 6 min.); the classic Tex Avery short King Size Canary (1947, 7 min.); and Through the Mirror, in which Mickey Mouse experiences his own adventure in Wonderland.

Ruef, K. 1992 The Private Eye. 224 pp., paperback, 8.5x11". ISBN 0-9605434-1-4 The Private Eye Project,
"7710 31st Ave. NW, Seattle, WA 98117; 206-784-8813, FAX 206-781-2172. Teacher's guide (add $3.50 shipping) $18.95
5x loupe 3.95. 10 or more loupes, each 2.30. Kit for class of 36 (with 50x microscope) 570.00 [Amazon]
This is listed as a "curriculum guide" for want of a better place to put it; it's unique. An educator would say that it's a manual that shows how to use a 5x jeweler's loupe to incorporate constructivist science into an integrated curriculum, over the full K-12 grade range. It actually does that, without the use of either scientific or educational jargon (like that in the previous sentence). The central role of imagery in science is used to link science to visual and verbal arts, and magnification is used as the key to observation. Study of simple "found" objects is followed by descriptive analogy and the development of theory. It lacks specific lesson plans with detailed materials lists, but it's a wonderful introduction to the creative use of inquiry science in almost any classroom, by any teacher. Science professionals also can learn from it how to present their specialty in a classroom in a way that will communicate excitement and encourage further inquiry. Grades K-12 and adult."

`Order of Magnitude' Notation From Statistical Thermodynamics. [links broken]

A View from the Back of the Envelope
Comments encouraged. - Mitchell N Charity <mcharity@lcs.mit.edu>

 This page is in serious need of an overhaul.
   (less so now, but still)
 2003-Feb-03  Repaired links - 5 fixed, 3 removed, 5 flagged.
 2002-Jul-17  Fixed "Powers of Time" link.  Mentioned it's on CD. - Thanks to a reader.
 2001-Jul-28  Added `Cosmic Zoom' links - Thanks to a reader.  Fixed a few others.
              This page has drawn little comment over the years, and thus little work.
 2001-Mar-13  Fixed a link.
 2000-Mar-14  Added `Order-of-Magnitude Astrophysics'.
 1999.Nov.25  Added a link.
 1998.Nov.19  Some cleanup.
 1997.Sep.30  Corrected Sizesaurus citation - Thanks to author.
              Put `Size perception' in `recent changes' and `history'.
 1997.Sep.19  Added "Lists of Magnitudes / Landmarks" section,
              and Amazon.com's `Size perception'
 1997.Aug.12  Added "Physiology by Numbers" to the `I plan to look at' section.
 1997.Jul.30  Added "Scientific Companion" note.
 Prior changes were in June 1997.