Mathematics and the Development of the Physical Science (Vol. VI)

Nothing in life is to be feared; it is only to be understood.

Now is the time to understand more, so that we may fear less.

Marie Curie

The selections in this volume were chosen to be accessible, interesting, informative, and to highlight the attitudes, habits, confidence, persistence and humanity of great problem solvers. The scientists' insatiable desire to learn and to know drove them to ask the right questions and to search for solutions, undaunted by the obstacles that appeared before them. Most of the problems found in this volume took years to solve. There were no answers in the back of the book and more importantly no one, other than nature itself, they could look to for a hint.

The readings are selected from the physical sciences and mathematics[1], arranged in a chronological order that serves to illustrate to some extent the history of thought and discovery from the sixteenth century to present day. The beginning of the scientific revolution finds Copernicus arguing for a sun-centered universe rather than the Earth-centered universe as demanded by church dogma. Galileo's discovery of the moons of Jupiter further argued against the belief that everything in the universe orbited around the Earth. His arguments addressed to the Grand Duchess Christina, along with his careful observations using the newly developed telescope, clearly positioned him in conflict with the church, but clarified the sun as the center of the universe. Newton's pioneering work discovering gravity and in developing calculus showed the relationship between falling objects on Earth to the motion of the moon about the Earth. Poetry, written in the twentieth century by Siv Cedering honors the early astronomers reflecting great admiration for their work and contributions to human understanding.

The sixteenth and seventeenth century scientists discovered the ordered universe. The universe could now be explained by mathematics which could be used to develop models to show a predictable and understandable world, known as the mechanistic view,[2] which prevails to modern times. Buoyed by technological advancement, including the discovery of electricity, the telescope to see into the heavens, and the microscope to make visible cellular structures to identify many more species not visible to the naked eye, this age of enlightenment fostered the belief that science could explain, even solve, all human problems.

The eighteenth and nineteenth centuries were marked by even more scientific discoveries that set the stage for twentieth century discoveries in mathematics, physics, chemistry, and biology. Individuals, such as Michael Faraday, who discovered a number of new organic compounds and wrote a manual of practical chemistry, added to the scientific literature. His lectures, designed for young people, on the workings of the candle, stands as an important contribution to the scientific understanding for a larger circle of citizens. James Clerk Maxwell, a man of wide ranging interests, was the first person to propose that light is an electromagnetic phenomena and that visible light forms only a small part of the whole spectrum of possible electromagnetic radiation. He developed four equations, now called the Maxwell Equations, which completely describe classical electromagnetism. These equations are considered the greatest contributions to nineteenth-century mathematics. His work also set the stage for quantum mechanics and led to modern atomic theory. The mechanized views of Newton began to be more pervasively applied to social and political life. Edwin Abbott, a progressive Anglican clergyman who, in 1884, published a book titled Flatland, is included in our volume for the first time. This text, a brilliant mathematical description of Euclidean space, is also a pure social satire of the Victorian times in which Abbott lived. The work satirizes the Victorian era's preoccupations with class distinctions, social Darwinism, and resistance to the rights of women and others, all issues which have relevance today.

The science world in the twentieth century was a very different place from the sixteenth, seventeenth, and even the eighteenth or nineteenth centuries. The issue of the Earth-centered versus the sun-centered universe was resolved, single cell organisms were commonly understood, and concern for bacteria and germs became the focus of study in the early part of the twentieth century, as did the very important discovery of radiation, and later the development of the atomic bomb. The integrated areas of study in the sciences fractioned into separate disciplines for a good part of the century only to come together again in new fields of study by the end of the twentieth century. Early in the century, Louis Pasteur uncovered the mysteries of rabies and the story of the beginnings of inoculations are recounted in this volume. He also identified the treatments for anthrax, chicken cholera, and contributed to the development of the first vaccines. His work ushered in modern biology and biochemistry. With the process of pasteurization, he gave us the scientific basis for fermentation, wine-making, the brewing of beer, and the careful processing of milk to keep it from spoiling, all pioneering discoveries that enhanced human health and entrepreneurship. Marie and Pierre Curie discovered the phenomenon of radioactivity (a word that she invented) following their discovery of the radioactive elements polonium and radium. Years later, her daughter, Irene, and son and in-law, Frederic, discovered radioisotopes. During World War I, she and Irene developed mobile radiography units for the treatment of wounded soldiers and after the war she devoted herself to developing the medical uses of radiation. Her lifelong focus was the understanding of radioactivity and its potential uses in medicine.

The twentieth century saw chemistry, physics, astronomy, biology, and mathematics become established independent fields of scientific study, oftentimes leading scientists and mathematicians to eschew applied over theoretical studies, each side claiming to address the more important issues. G. H. Hardy, a man of strong, individualistic opinions, argues in The Mathematicians Apology, that mathematics is beautiful and important for its own sake, and that one should not be concerned about direct applications. His views should be compared to those of Mary Cartwright, a theoretical mathematician who collaborated in the development of chaos theory (see "Mathematics and Thinking Mathematically") who argues that applied applications can be informed and advanced by theoretical mathematics, and that theoretical mathematics can, in turn, be developed from applications. More than twenty years earlier, George Pólya, another theoretical mathematician, who in three books on problem solving, provided general heuristics for solving problems of all kinds, not simply mathematical ones. Written for teachers, his focus was on the teaching of problem solving in all areas of human endeavor.

Linus Pauling dominated much of the middle and latter years of the twentieth century with his pioneering work in several fields, especially chemistry. In 1947 he published General Chemistry, a book used by generations of undergraduates around the world. As scientific knowledge advanced, more specialized fields of investigation emerged. Pauling is generally credited with establishing molecular biology which serves as the foundation for the emerging field of biotechnology. Following World War II, he became a strong advocate for peace around the world. He devoted his time and energy to establishing world peace and arguing against the further use of the atomic bomb, for him an unfortunate application of scientific know-how. By the end of the century, knowledge gained from in-depth study of many fields within the arts and sciences came together under the umbrella of the cognitive sciences and artificial intelligence. Work by such contemporary thinkers as Douglas Hofstadter is focused on the building of computer models of human thinking. Students will enjoy studying the "MU Puzzle" as an illustration of complex problem solving. The reading by Richard Feynman from his book, QED: The Strange Theory of Light and Matter (QED), explains the parameters of QED, or the interactions between electrons and light.

The readings in this volume are appropriate for, but certainly not limited to, introductory and upper level science courses and the history of the sciences. However the selections were chosen so that no scientific background is required to read them. Thus, they would be appropriate for a much wider variety of courses limited only by the instructor's creativity.

Students and faculty are invited to explore how the discovery of new information informed the creation of the various disciplines over the centuries and to contemplate the many contributions to our understanding of our place in the universe.