umerous people contributed to the making of this book. I am indebted to Captain Carl Keske USN (retired) and his wife, Carol, for applying gentle but steady pressure on me to write this book and for proofreading an earlier version of the manuscript. They, more than anyone else, served as the catalyst for me to put into print what I have long offered in lectures. For the opportunity to give lectures at a variety of venues I am grateful to David Stewardson of Crystal Cruises, Pat Higgins of Silversea Cruises, Marta Marschalko, formerly of the National Geographic Society, and Royal Viking line; also to Lester and Brenda Crain, John and Lynda Shea—all from Memphis, Tennessee; Harvey and Brenda Blatt from Montreal; Robert and Betty Ann Jordan from Tampa, Florida; Bernie and Judy Franklin, Beverly Hills, California; Jonathan O’Brien, Headmaster emeritus, and Robert Stegeman, Dean, emeritus at St. Andrew’s School, Middle-town, Delaware. Finally, I am also grateful to Faruk Loğoğlu, the present Turkish ambassador to the United States, a friend of three decades and, with a Ph.D. from Princeton, one of the best-educated members of the Washington Diplomatic Corps.

Numerous other individuals contributed to the creation of this book. I am especially grateful for advice from friends at the National Gallery of Art, Washington, D.C.: David Alan Brown, curator of Italian Renaissance Art; Ann Bigley Robertson, exhibition officer; and David Bull, formerly the chief restorer and conservator of the National Gallery and currently president of Art Conservation Foundation. Thanks are also due to Carmen Bambach, curator of drawings and prints at the Metropolitan Museum of Art, New York; Thomas Somma, director of the Mary Washington College Art Galleries; and Sarah Trible, his excellent assistant. Special thanks are also due to a good friend, Lindy Hart, widow of the superb sculptor Frederick Hart, for information on her husband’s works, and also to Jamie Wyeth and Beverly Doolittle, two exceedingly talented contemporary artists, for allowing me to include their works. Mr. Wyeth, moreover, was generous with his time in reading the manuscript and offering encouraging words.

Among managers of rare book collections two individuals were immensely gracious in allowing me to examine their treasures: Marilyn Ogilvie, curator of the History of Science Collections at the University of Oklahoma, for allowing me to photograph pages of Galileo’s personal copies of his two books, the Sidereal Messenger and Dialogue on the Two Chief World Systems; and Neal Turtell, executive librarian at the National Gallery of Art, for allowing me to examine and photograph the priceless books De divina proportione and Trattato di pittura, as well as the facsimiles of the Leonardo manuscripts. I am deeply indebted to Andrew Rush and Kate Cooke, computer technologists, who have been generous with their time and skills, and also to Laurie Preston, Instruction and Science/Business Librarian, for assistance in tracking down a variety of crucial sources and references.

My physicist friends have been wonderful foils, listening and commenting on many topics: Nikola Nikolic and George King, both colleagues in physics at Mary Washington College, and Ady Mann, coauthor and colleague at Oxford, the Technion in Haifa, and at the Institute for Advanced Study in Princeton. All three are exceptionally cultivated individuals, conversant in the arts as well as the sciences. I gained insight into symmetry in elementary particle physics and into the structure of quasicrystals from two of Israel’s most eminent scientists, Yuval Ne’eman and Danny Shechtman, while participating in a symposium on various aspects of symmetry (Washington, D.C., 1997). Of immense help also were David Goodstein, professor of physics and vice provost at Caltech; Michael Higattsberger, professor and director emeritus at the Boltzmann Institute of the University of Vienna; Norman Ramsey, professor emeritus of physics at Harvard University; William Phillips, head of Laser Trapping and Cooling at the National Institute of Standards and Technology (and currently serving as the George Eastman Professor at Oxford); and William Ott, deputy director of the physics branch at NIST. All are eminent physicists; Ramsey and Phillips are Nobel Prize-winners. Professor Ramsey supplied wonderful anecdotes on physicists that he has known during his long career. Professor Phillips, a man as gracious as he is brilliant, read the entire manuscript with the inordinate precision that characterizes all his work, and offered valuable suggestions. The others invited me to speak or give colloquia at their respective institutions.

Attempting to follow Leonardo’s model I benefited from consulting academic friends outside physics: professor of religion Mehdi Aminrazavi, for insights into Islamic culture; professor of classics Liane Houghtalin, for information on early Greek philosophers; professor of Italian Clavio Ascari, on enlightening discussions relating to the Italian Renaissance and for expert translations from the early modern Italian; professor of business administration Daniel Hubbard for information on Luca Pacioli’s contributions to double-entry accounting; and professor of art Joseph Dibella, for the mechanics of painting.

On the topics of psychology and physiology I am indebted to Christopher Tyler, Michael Nicholls, Robert “Rick” Ricketts, and Michael Atalay. In February of 2000 we collaborated in a symposium in Seoul, Korea, presenting papers on “Symmetry in its Various Aspects: Search for Order in the Universe.” The four individuals have made seminal contributions in their respective fields, and they are cited in a number of chapters in the book. Aesthetic surgeon Steven Marquardt, whose investigation of facial aesthetics and the divine proportion parallels the work of Dr. Ricketts, has created a mask that gauges human beauty. He has been gracious in allowing me to use the mask in the context of “Art of Nature.” For results of studies of the brain of the artist versus the brain of the nonartist, the topic of Chapter 8, I am grateful to artist Humphrey Ocean; scientists John Tchalenko, Christopher Miall, and Robert Solsa; also to my niece, Billur Tansel, who brought this important work to my attention; her mother, Gülseren Tansel; and to my uncle, Jeff Kokdemir, for helpful advice on so many aspects of the book.

Professor Julian Stanley, founder of the Johns Hopkins Center for Talented Youth (JHCTY), gave me invaluable material on the topic of gifted youth. Over the years I’ve had the opportunity to meet exceptionally gifted students at sessions of the JHCTY, at Thomas Jefferson High School for Science and Technology, and at the Oklahoma School of Science and Math. The interaction with some of these students has been a source of inspiration. I am grateful to the noted psychoanalyst Gerald Aronson of Los Angeles, with whom I have maintained an intellectually edifying correspondence on topics of mutual interest, specifically on physics and the brain. Indeed, Dr. Aronson read the manuscript of the book and advised me on the subject of the tortured genius.

A number of my former students maintained an interest in the project over the years and contributed valuable ideas. I am grateful to Gilbert Schor, who allowed me to read his graduate thesis on the mathematics of the Fibonacci series; to Abbey Delk, who assisted me in selecting Leonardo drawings from the facsimile collection of the National Gallery of Art; and to Betty W. Jones; Lisa L. Wu; Rochele Hirsch, née Betty Stansell; Davis Lee; Bonnie Norris; Mohamed Chakhad; and Matthew Welz for many inspiring discussions and helpful suggestions.

I would like to single out for special gratitude my good friend Keith Wamsley, who in an earlier life trained in classics and English literature at Cornell, but is now training for a career in physics and mathematics. It was when he was enrolled in my graduate course Character of Physical Law during the summer of 2000 that I recognized his insatiable curiosity, his skills as a writer, and his latent talent as an editor. Since first agreeing to serve as my unofficial copy editor, he began to encounter the chapters of the manuscript in the random order in which I wrote them. Nonetheless, he never complained, never argued about that particular inconvenience. He did, however, argue about every other aspect—each sentence, each phrase—until we were both satisfied that the ideas were clearly explained, and the level of the book was consistent and accessible to the intelligent layman. This is appropriate, since Keith is an exceptionally intelligent layman, neither artist nor scientist, but harboring passion for the arts and the sciences.

In the context of unofficial copy editing, I am very grateful to Nick Murray, a wordsmith extraordinaire, who read the entire manuscript and made numerous helpful suggestions. I would also like to express my deepest gratitude to Sherwin Nuland, professor emeritus of surgery at Yale University—winner of the 1994 National Book Award and the author of the recent indispensable short biography of Leonardo da Vinci in the Penguin Lives series—for reading the manuscript of my book and offering inspiring comments.

I am indebted to the former science editor at Smithsonian Books, Vincent Burke, who recognized early the value of a book on Leonardo’s model. Vince, a man of inordinate patience and exceptional editorial skills, guided me in achieving a tight book. He, along with his able assistant Nicole Sloan, held in check my tendency to go off on tangential topics—useful in informal lectures, but not in a well organized book. The book holds together much better thanks to their mediation. In the final phases of the book’s production Mary Christian (copy editor), Robert Poarch (production editor), and Scott Mahler (acquisitions editor and Vince Burke’s successor) were eminently helpful. A trained art historian, Mary especially brought not only her editorial skills, but also her knowledge of art into the scheme.

I am deeply indebted to my extended family members, Roy and Lolly Weinstock, friends of three decades, for putting up with interminable discussions and for offering unfaltering support. Finally, I am most grateful to my immediate family—wife Carol Jean, daughter and son, Jeannine and Michael, and their spouses, Mike Harvey and Elizabeth Atalay, for serving as resilient sounding boards on so many topics in the book and for being infinitely patient. My daughter, who trained as an artist, and my son, a scientist, were both helpful on so many topics in the arts and the sciences.

This book would have been much longer had it not been for the wisdom of true friends (and editors) who admonished me to just stop writing, all ultimately echoing the sentiment of a cartoon appearing in the Chronicle of Higher Education. An editor is penning a letter to his famous author: “Dear Dostoevski—We feel your new manuscript, ‘Crime, Punishment, and Repentance’ is much too long. You should cut it by a third.”