Reviews for Integral Geometry, Radon Transforms And Complex Analysis, Vol. 168

The average rating for Integral Geometry, Radon Transforms And Complex Analysis, Vol. 168 based on 2 reviews is 3.5 stars.

Review # 1 was written on 2013-07-17 00:00:00 Leonor Casadiego A. Key points 1. Newtonian style 2. Transformation of scientific ideas 3. Newtonian Revolution was the most significant revolution in the 16th and 17th 4. Newton's style was the key component of his Revolution (not any new scientific content) B. Summary: 1. This book centers on the scientific life of Newton. Cohen does so to explore the understanding of the "revolution" that Newton's contemporaries believed that they were experiencing. (Thus revolution is not an anachronistic term). 2. This book focuses on the Principia (Newton's science of motion) because it is here where Newton's style is most clearly found. The "Newtonian style" was the ability to separate science into 2 parts: first was the development of mathematics to explore an imaginative system; second was the application of such mathematics to describe reality. This style was Newton's revolution. 3. Three phases of Newtonian style a) An imaginative construct in the mathematical domain where motions of imaginative entities are tested. b) Comparison with experiential data in the real world. c) The relationship of these results to natural philosophy to describe Newton's "system of the world." C. The Newtonian Revolution and the Newtonian Style 1. How was 17 century science different? External factors included scientific communities, journal publishing, research institutions (like the Royal Observatory). Internal factors included aims (science would improve men's life on earth), methods (experimental, induction, quantitative), results (laws of nature). 2. Since the term revolution was used to describe Newton's calculus and his celestial dynamics in his own day there is no need to discuss the meanings of the word revolution. But the word came to be used to describe the Principia which was published one year after the Glorious Revolution. Thus, this was the first recognized scientific revolution, and was not used to describe Galileo, Kepler, or Copernicus. D. Transformations of scientific ideas 1. The word "synthesis" has also been used to describe Newton's work. This usually implies Newton having put together his world view from the contributions of others. But, Cohen argues that this is a misleading word because it masks the creativity Newton used in understanding his predecessors. This section examines how Newton transformed the scientific ideas of his predecessors. 2. Transformation examples: Newton's transformation of Kepler's "inertia" (bodies come to rest when motive force ceases to act) to a "force of inertia" by which a body maintains its motion in the absence of an external force. 3. So Newton's synthesis not only accepted the work of others but also denied the work of others. The creative genius of Newton allowed this transformation of ideas and provides a central component of his revolution. 4. Freud argues that in any case of 'apparent scientific originality' a new idea is first hailed as a discovery, and then its novelty is disputed. 5. This idea of transformation is opposite what Kuhn argues. Kuhn argues for radical transformation, while Cohen argues for gradual shaping and transformation. 6. A lengthy discussion of the stages of transformation leading to universal gravitation (Newton's and Kepler's laws). Cohen argues that Newton did not define universal gravitation until 1684 and then published it quickly. He did not deduce the law from Kepler's laws. In universal gravitation is a radical transformation of Kepler's laws. E. What is a scientific revolution? From Revolution in Science 1. The stages: intellectual revolution, commitment to the new method, dissemination to the world (revolution on paper), other scientists become convinced of it 2. Four tests for the occurrence of a revolution: testimony of witnesses, examine the documentary history of the period, judgment of historians, mythology of the present day

Review # 2 was written on 2014-08-25 00:00:00 Mike Richardson This was very helpful! I especially liked how it tried to relate the math to everyday topics and the story problem themes were very helpful as well!