If they disparage me as an inventor, how much more they, who never invented anything but are trumpeters and reciters of the works of others, are open to criticism. Moreover, those men who are inventors are interpreters of nature.

—Leonardo da Vinci

eonardo was a master scientist and a master engineer-inventor. In his scientific investigations he often used technology, anticipating a process that was to begin over a century later, but not coming to full realization for several hundred years. The investigations of water pressure, the phenomenon of friction, the trajectories of projectiles, and countless others are all experimental in nature, all carried out using the apparatus he designed for each experiment.

The discovery of fire and the chipping of stones in order to create cutting tools are monumental developments in early technology, dating back to our distant ancestors roaming the savannas of Kenya and Tanzania or dwelling in caves of South Africa 70–80,000 years ago. At the end of the last Ice Age (10,000–9000 B.C.) in Asia Minor and the Middle East farming and domestication of animals were just emerging. Several thousand years later followed the landmark innovations of ceramics, metallurgy, and writing. Each of these developments, each an example of technology sans science, was critical for the birth and rise of civilization. Technology once learned is rarely unlearned.

In contrast to technology, science is a system of knowledge—the orderly and systematic comprehension, description and explanation of natural phenomena, constrained by logic and mathematics. Pure science was an invention of the Pre-Socratic Ionian Greek philosophers. According to Aristotle’s own explanation in the fourth century B.C., the first great philosopher was Thales of Miletus, who had flourished two to three centuries earlier. Thales and his followers had practiced natural philosophy, working with the conviction that there exist natural laws governing the behavior of natural processes, and that future physical events could be predicted by understanding these laws. One did not have to examine animal bones and chicken entrails in order to understand the vagaries and whims of the gods who ultimately determined these events. The only certain date we have for Thales is a solar eclipse that he predicted in 585 B.C.

Echoing the message of Thales, the pre-Socratic philosopher Protagoras (485–415 B.C.) wrote “Man is the measure of all things … of the being of things that are and [the] nonbeing of things that are not.”¹ In Athens of the fourth century B.C., however, empirical science held little appeal (although Aristarchus and Eratosthenes in Alexandria, and Archimedes in Sicily were still to continue to comply with Thales’s dictum, putting more emphasis on observation and logic than speculation and introspection). Socrates had an aversion to natural philosophy. Plato celebrated mathematics but opposed any form of experimentation in natural philosophy. Aristotle was far more receptive to natural philosophy but practiced minimal experimentation or observation.

Science, unlike technology, has progressed in fits and starts, its course sometimes entirely retrograde in direction. The Romans were technologists and made little contribution to pure science; then from the fall of Rome to the Renaissance science regressed. Through these times science and technology had clearly evolved independently, and to a large extent one could have science without technology, and technology without science.

In the Renaissance science was reinvented, and in the Scientific Revolution of the seventeenth century, science and technology began a courtship. The full-scale coupling of the two systems became permanent in the next two centuries. By the nineteenth century electricity and magnetism were developed both at the technological and the scientific levels. Electric generators, motors, and transformers could be created, and the underlying physics could be invoked to explain why they worked and how to improve them. The peak in the coupling, however, came in the atomic age of the twentieth century. Ultimately, it is the interaction of science and technology that led to unprecedented acceleration in the progress of both. The Industrial Revolution, beginning in the eighteenth century, can be regarded as one of the most significant fruits of this interaction. The cross-fertilization between science and technology produced the nuclear, aerospace, and computing revolutions of the twentieth century. Modern science cannot be carried out effectively without technology, and modern technology cannot proceed very far without science.

In the stratified structure that exists in the sciences, physics—the most fundamental and mathematical of the sciences—underlies chemistry, which in turn underlies the life sciences. Astride them all are the social sciences—including psychology, sociology, and anthropology. There are even interfaces such as physical chemistry, biochemistry, psychobiology, and other fields that suggest a seamless progression among the sciences. Evocative of the dynamics of a tree, the nutrients move upward. This simple paradigm explains why the physicist generally lags behind the mathematician in invoking the newest mathematical tools; why chemists adopt some of the techniques of the physicist a generation or two after the physicist has developed them, and indeed why the biologist gets to these tools after the chemist. (To be sure, each science develops some of its own techniques, but the more fundamental concepts flow upward from the more mathematical strata below.) In the first quarter of the twentieth century the preeminent experimental nuclear physicist, Lord Rutherford, expressed his disdain for those sciences higher in the strata than his own, when he made the pronouncement, “In science, there is only physics. The rest is stamp collecting.” By 1953, when x-ray diffraction was being applied to biology to decipher the structure of the DNA molecule, biology would have earned Rutherford’s respect as a legitimate science. Finally, underlying the entire structure is mathematics, not a science itself, but essential for the sciences, providing them with both a powerful tool and a language. Its function is to lend rigor, effectiveness, and predictability to the scientific theories explaining the behavior of natural phenomena.

Archimedes, the greatest scientist and mathematician of antiquity, had made significant strides in connecting mathematics and physics. One hears among historians of mathematics that if the Greeks had possessed a better mathematical notation, Archimedes might have invented calculus eighteen centuries before its formal development in the Europe of the Scientific Revolution. The Greeks lacked the zero, yet new evidence has surfaced of Archimedes having achieved familiarity with infinite sets, at the other end of the numerical spectrum from the zero.²

The publication by Copernicus of his monumental book De revolutionibus in the mid-sixteenth century signaled the real beginning of the revolution. In a more consistent and comprehensive manner the connection of mathematics and natural law came to full fruition in the seventeenth century, starting with Galileo and Kepler, and culminating with Newton.

The journey that brought us to our present understanding of science has taken over two and a half millennia. Experimental and theoretical research are ongoing, with the unification of physical laws—those governing the submicroscopic universe (quantum mechanics) and those governing the large scale universe (general relativity)—representing the ultimate quest of physics.

Leonardo discovered anew some of the scientific principles first developed by the ancients and subsequently forgotten, and he invented entire fields of science and technology that would not be reinvented for centuries. He may have been a prisoner of his time, but his restive mind wandered over scientific and technological problems encountered by the natural philosophers of the distant past and still to be faced by the scientists of the distant future.