Innovation Product	Site	Existing System or Actual Need
Financial Checkbook Interface	Home	Checkbook balancing
Spreadsheets	JPL Caltech Jet Propulsion Lab	Space image data handling
Browsers	CERN European Particle Physics Laboratory	Information management

VICAR was the space image data handling software at JPL. It was adapted to manage a workplace football betting pool with many participants. The result is the new general calculating tool called a Spreadsheet. Quicken is INTUIT's product based on a response from one marriage partner to the other's expressed need for a computer assistant to help keep a check book in balance. Finally, the developed world has seen vast change in information management since a prototype program was written for that purpose at CERN. After some expansion it is now the basis of the world wide web browser technology that supports on-line trading of stock, major changes in retail sales (Amazon.com), and many other innovations. In each of these situations only a small number of individuals have changed the way the world works. In many other computer software cases similar radical changes were the result of a few people: Figure 2 lists just a few instances.

Innovation Product	Site	Innovation Description
C, Unix	AT&T Laboratories	Efficient High Level Language, Operating System
APL	Harvard	Array-Oriented Language
Mathematica	Caltech	Comprehensive Mathematical System With Graphics

Many people working with computing have seen the artistic side of writing programs or an engineering aspect of design. Programs of study are called "software engineering". Ambitious multivolume books spanning much of program design begin their title "the art of". Finally, individual and complex digital systems are described in terms of "computer architecture." In all three instances language has been adapted to convey the things that truly contribute to or characterize innovation in digital technology. Innovation requires inspiration and perseverance. Imagination, conceiving of some new thing, is what all the Figure 1 and 2 items have in common. Dedication, continued application of one's self until a recognizable working model appears, fits in well with the common understanding of art, architecture and engineering. A common obstacle to thinking in computer terms is unfamiliarity with notions from Mathematics. Even experts in Math or Computer Science can be overwhelmed by a topic new to them. This creates two sorts of problems for beginners. It is easy for instructors to define a subject in a limiting way, and to teach it inside narrow boundaries. But worse, there is constant change about what is important, and a huge overhead of terms that "everyone" knows. This book answers these possible difficulties with specific activities to energize and involve the reader. If you should find a course or book in Mathematics or Computing dull or boring, try learning and explaining a part of it or some related issue, such as how it relates to a real task. (Galileo worked out the Math that governs how to aim a cannon. Many similar examples exist.) While you could seek out a web site, newspaper or magazine article, or someone to talk with who knows the subject, another possibility involves the bibliography at the end of this chapter. Difficulties recur in a career involving computing. It is good to build into oneself the habit of going around them. Since there are incredible opportunities to develop oneself and a business, it is worthwhile to focus on "the big picture" and regard any Mathematics or Computing difficulty as a minor or temporary obstacle. Many have created new enterprises. They have been built from a mixture of ideas, initiative, and knowledge. While there is always a tendency to think that this is a case of coming on the scene too late (after everything possible - or at least, easy - has been innovated) that is definitely not so. Internet businesses are the latest example. Yahoo/GeoCities, EBay, ICQ, and Blue Mountain Arts are all examples. Figure 3 describes their products and gives universal resource locators for them.

Business Name	Key Product	Universal Resource Locator
Yahoo	Searchable Directory	http://www.yahoo.com
EBay	Electronic Auctions	http://www.ebay.com/
Mirabilis/ICQ	Instant Messaging	http://www.mirabilis.com/
Blue Mountain	Online Greeting Cards	http://www.bluemountain.com/

Some statements from a few of these sites appear in Figure 4.

"What is ICQ? ICQ is a revolutionary, user-friendly Internet tool that informs you who's on-line at any time and enables you to contact them at will."

"Last week's trivia answer - I was born in 1995, conceived by a guy to help his wife collect Pez dispensers. Today, nearly 4 million people use my service, buying and selling everything from Tiffany lamps to Muppet Show lunchboxes. I've facilitated more than 45 million auctions, and average close to a million bids per day. Every day, 250,000 new items are listed for sale with me. I recently bought upscale auction house Butterfield and Butterfield. My average visitor spends more than two hours with me, and I never close. In less than a year my stock has risen more than tenfold. Who am I? (Answer: eBay)"

"Ranking among the 10 most popular Internet destinations, the company's Web site lets visitors send electronic greeting cards free of charge. The Web site (available in English, Spanish, and French versions) is supported by banner ads that appear when users send e-cards. The company also publishes poetry and offers other products such as stationery. Self-described hippies Stephen Schutz (a physicist) and Susan Polis Schutz (a poet) founded Blue Mountain Arts in 1971. The Blue Mountain Web site debuted in 1996 ..."

There are more opportunities now than ever before for innovation using digital computer technology. This is true for several reasons. First, many items, for example the large amount of programs written in older languages like Fortran and Cobol, need to be maintained, improved, adapted to circumstances that were not forseen when they were first created. Second, there are large numbers of people who are not yet users of computers. They represent an opportunity to serve needs that haven't yet been addressed. Finally there are many situations where digital technology could be used where it is not yet in place. This inevitably will change as cost of hardware declines and benefit from digital processes are better understood. To overcome common experience of boredom and difficulty associated with technical aspects of computing, I recommend developing a recreational reading stance. Use the appended book lists and find one you want to read or cover partially. An alternative is to seek out a topic you need to know about, e.g., a new computer language, and find a book about it. Finally consider reading a series of web-sites that are about a topic you care to learn more about. [Most things in the computer world are changing rapidly, so if you seek current information be ready to download and store, or print copies and file, key materials.] Examples of web-based information appear in the third part of the bibliography. Note that some of the sources listed there pertain to electronic mail etiquette, writing style, etc., others to words of wisdom to sustain activity.

Bibliography 1 - Mathematics Books

Enzensberger, Hans Magnus, The Number Devil: A Mathematical Adventure (Translated by Michael Henry Heim, Illustrated by Rotraut Susanne Berner) NY: Metropolitan Books, Henry Holt and Company, 1998. [A children's fairy tale with substance about numbers.]

Chernyak, Yuri B., and Robert M. Rose, The Chicken from Minsk, NY: HarperCollins BasicBooks, 1995. [Preface - ... "If you sign up for this course," said another student, "do not make any other plans. Do not think you will have time to socialize, date, take showers or sleep. If you do sleep, you will have nightmares about the problems-and they will haunt you in the shower too!" ...]

Devlin, Keith, Mathematics: The Science of Patterns, NY: W. H. Freeman and Co., 1994. [A wise and helpful guide to many topics in Mathematics.]

Dunham, William, Journey Through Genius: The Great Theorems of Mathematics, NY: John Wiley & Sons, Inc., 1990. [Historic and fundamental issues.]

Hoffman, Paul, The Man Who Loved Only Numbers - The Story of Paul Erdos and the Search for Mathematical Truth, NY: Hyperion, 1998. [Unimaginable tragedy leads to an itinerant life path.]

Kasner, Edward, and James R. Newman, Mathematics and the Imagination, NY: Simon and Schuster, 1940; ISBN 1-55615-104-7 Redmond: WA, Tempus Books of Microsoft Press, 1989. [A broad survey.]

Kanigel, Robert, The Man Who Knew Infinity - A Life of the Genius Ramanujan, NY: Simon and Schuster, first published Charles Scribner's Sons, 1991. [The giant of twentieth century Mathematics.]

Kline, Morris, Mathematics for the Nonmathematician, New York: Dover, 1985. [A useful compendium with thoughtful examples.]

Beckmann, Petr, A History of Pi, Boulder, Colorado: Golem Press, 1982. [A superb view of Mathematics from ancient and post-renaissance times.]

Dantzig, Tobias, Number The Language of Science, New York, The Macmillan Company, 1930. [A magnificent and inspirational narrative.]

Davis, Philip J., The Thread, A Mathematical Yarn, Second Edition, NY: Harcourt Brace Javanovich, Publishers, 1983, 1989. [Wit and history mingled with detailed information about the founder of approximation theory.]

Bell, Eric Temple, The Last Problem, Washington, D.C.: Mathematical Association of America, 1990. [About Mathematics' greatest amateur.]

Nelsen, Roger B., Proofs Without Words, The Mathematical Association of America, 1993. [Images that show verities.]

Joseph, George Gheverghese, The Crest of the Peacock - Non-European Roots of Mathematics, London UK: I.B. Tauris & Co. Ltd Publishers, 1991. [Roles of non-Europeans in originating Mathematics.]

Adams, James L., Conceptual Blockbusting, San Francisco: W. H. Freeman, 1974. [Thinking and visual reasoning.]

Osen, Lynn M., Women in Mathematics, ISBN 0-262-15014-X, Cambridge MA: The MIT Press, 1974. [Great achievements by women Mathematicians.]

Bibliography 2 - Computing Books

Knuth, D.E., The Art of Computer Programming, I Fundamental Algorithms , Reading, Mass.: Addison-Wesley, 1968, 1981.

Filo, David and Yang, Jerry, et. al., Yahoo! unplugged: your discovery guide to the Web, with Karen Heyman, et. al., Foster City, CA : IDG Books Worldwide, 1995. [Pp. 117-203 on "Computers and Internet" are themselves a wonderful guide to current technology. For example see the text description on p. 123 of "Beginner's Guides" and "Beginner's Guides to Effective Email" http://www.webfoot.com/advice/email.top.html .]

Graham, Ronald L., Knuth, Donald E., and Patashnik, Oren, Concrete mathematics : a foundation for computer science, Reading, Mass. : Addison-Wesley, 1989.

Knuth, Donald E., The Art of Computer Programming, 3rd ed., I Fundamental algorithms, II Seminumerical algorithms, III Sorting and searching, Reading, Mass.: Addison-Wesley, 1997, 1998.

Bentley, Jon L.,Programming pearls, Reading, Mass. : Addison-Wesley, 1989, 1986.

Bentley, Jon L., Writing efficient programs, Englewood Cliffs, N.J. : Prentice-Hall, 1982.

Bentley, Jon L., More programming pearls : confessions of a coder, Englewood Cliffs, N.J. : Prentice-Hall, 1988.

Wirth, Niklaus, Algorithms and data structures, Englewood Cliffs, N.J. : Prentice-Hall, 1986.

Kernighan, Brian W. and Pike, Rob, The UNIX programming environment, Englewood Cliffs, N.J. : Prentice-Hall, 1984.

Brooks, Frederick P. Jr., The mythical man-month : essays on software engineering , Reading, Mass. : Addison-Wesley Pub. Co., 1975; Anniversary ed., 1995.

Bibliography 3 - Writing Items, Universal Resource Locators

Strunk, William Jr., "Elements of Style," 1918 (and still current): http://www.columbia.edu/acis/bartleby/strunk/

Strunk, W. and White, E., The Elements of Style, NY: Macmillan, 1972. (The 1918 classic reissued. Available in paperback; new edition.)

Sherwood, Kaitlin Duck, "A Beginner's Guide to Effective Email," Revision 2.0 : http://www.webfoot.com/advice/email.top.html

Sherwood, Kaitlin Duck, "A Beginner's Guide to Effective Email - Context": http://www.webfoot.com/advice/email.context.html

Klinger, Allen, collected sayings about work: http://www.cs.ucla.edu/~klinger/tenpp/3_work.html

Klinger, Allen, collected sayings about doing: http://www.cs.ucla.edu/~klinger/tenpp/2_do_it.html