Math and the Mona Lisa - The Art and Science of Leonardo da Vinci by Bülent Atalay (2004).pdf - Święta geometria - jangan

~T n the late 1950s the British scientist and writer C. P. Snow deliv-

JL ered the Rede Lecture at Cambridge University and identified

two disparate intellectual cultures: the intellectuals among the

humanists (including artists and writers) and the intellectuals

among the scientists (natural scientists and mathematicians). 1

Snow claimed that communication between the two groups was

strained at best and nonexistent at worst. At the beginning of the

twenty-first century we find ourselves still discussing the chasm

dividing Snow's two cultures.

My own passions have always been varied. I am an artist, an

xvi | Prologue

occasional archaeologist, but primarily, a physicist—teaching and

doing research in atomic physics, astrophysics, and nuclear physics.

In art, my works were displayed in a number of exhibitions, includ-

ing one-man shows in London and Washington, D.C., and collec-

tions of my lithographs found their way into Buckingham Palace (a

gift of United States Ambassador Walter Annenberg to the Queen),

the White House, and the Smithsonian Institution. As a theoretical

physicist I have trained or taught at a number of universities—

including Georgetown, Berkeley, Princeton, Oxford, and the In-

stitute for Advanced Study. I am a person, I like to think, who lives

in both cultures.

Five hundred years ago in Italy there were many intellectuals who

developed expertise in diverse fields, and a number of these individ-

uals were spectacularly good in many fields. The expression "Ren-

aissance man" entered the Western vocabulary precisely to describe

such people. One person, Leonardo da Vinci, more than any other,

embodied that spirit, indeed transcended it. He was quite simply the

best in the myriad fields with which he preoccupied himself.

Leonardo was a part-time artist, who might have worked on

twenty paintings, a dozen of which survive; of these, only seven are

of unchallenged provenance. Nonetheless, it is first as an artist that

he is remembered. Indeed, one might argue about who is the third

greatest artist in history—perhaps Rembrandt or Raphael, Monet or

Picasso? About the first two, there is no argument. One can take

Leonardo or Michelangelo, in either order. The level of their influ-

ence, their role as drivers, is that significant. As an engineer,

Leonardo's legacy includes a long list of actual and mental inventions

that foreshadow future technologies by hundreds of years. Leonardo

is inventing the future. Thus, he is the first and preeminent futurist.

The most extraordinary aspect of his genius, however, may just

be that his general modus operandi actually prefigures the method-

ology of modern empirical science. Accordingly, I join in the trum-

Prologue | xvii

peting of a theme beginning to be heard among scientists, that

Leonardo was the first modern scientist. There have been individ-

uals with greater scientific legacies than Leonardo. Certainly

Galileo, Newton, and Einstein are more prominent figures in the

history of science, but science is the only reason for their attain-

ing prominence. They made unprecedented discoveries and they

published their results. In Leonardo's day printing was in its in-

fancy, and he had a relatively minor role in the production of only

one book, De divinaproportione. Had he been able to publish the sci-

entific ruminations found in his manuscripts in his own time, our

present level of sophistication in science and technology might

have been reached one or two centuries earlier.

Leonardo's Model

For Leonardo, the paragon artist-scientist-engineer, the astonishing

variety of his interests are like the knots of a magnificent tapestry.

Uncovering the internal dynamics of each of these interests and

establishing the connections between them were his quest, and sys-

tematic experimentation, his method. Ultimately, in every aspect of

his life—while doing science, engineering, and on the infrequent

occasions when he did art—he was operating as the consummate

scientist. And it was the cross-fertilization of ideas and their seam-

less integration that led to many of his astonishing achievements.

The transcendent unity of science and art, and the expansive cross-

semination, are the essence of Leonardo's model.

Five hundred and fifty years after Leonardo's birth we use

Leonardo's model to seek again the consilience of science and art—

painting, architecture, sculpture, music, mathematics, physics, biol-

ogy, and engineering—and to remedy as far as possible the disasso-

ciation that exists between cultures. We examine common themes

and grounds among the interests of the artist and the scientist and

xviii Prologue

the modes of expression adopted by each. The task involves applying

elements of modern science and mathematics to the analysis of per-

spective, proportion, patterns, shapes, and symmetries underlying

art and nature. It is important to point out at the outset, however, that

in the case of the artist it is almost always unwittingly (but intuitively)

that he imbues his works of art with these technical devices, often

picked up as subliminal messages from nature. But in Leonardo's

case, it was most likely done with total awareness and forethought—

in his art as well as his science. And so it is in the sciences now. The

underlying mathematics and the principles of symmetry are not just

useful, they are indispensable.

The chapters of Math and ibeMona Lisa follow the development

of fundamental science from the dawn of civilization, when num-

bers were invented, to ancient Greece, where science was born. We

shall examine the significant role of Muslim scholars, who not only

served as a conduit for the transfer of knowledge from the philoso-

phers of antiquity to the scholars of the Renaissance, but who also

invented some powerful tools of science and mathematics. The

journey will take us through the Renaissance into the Scientific

Revolution of the seventeenth century, through Galileo's discov-

eries of the law of the pendulum and the law of free-fall and

Newton's discoveries of the universal law of gravitation and the for-

mulation of the calculus. The scientific methodology of Leonardo

continued into the twentieth century with Einstein formulating the

theory of relativity and a number of extraordinarily gifted young

physicists creating quantum mechanics.

Only after we establish the framework of the science and math-

ematics underlying art and science, and the differing approaches the

artist and scientist take in describing nature, will we return to exam-

ine Leonardo's modus operandi and his legacy as artist, scientist, and

engineer. Thus, although Leonardo's system, the "model," serves as

a unifying theme throughout the book, only three chapters are

Math and the Mona Lisa - The Art and Science of Leonardo da Vinci by Bülent Atalay (2004).pdf

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