Great Calculations: A Surprising Look Behind 50 Scientific Inquiries

I found this a fascinating book, though I’m not sure how many others will. Science and math don’t seem to be that popular with most people, but this is really well written, and while equations and the like are given, it’s not necessary to really dig into them to gain some new appreciation for how we have been able to learn a great deal about how the universe works by using mathematical techniques developed over the millennia. All fifty of the calculations that he chooses to write about have been important, and he acknowledges that there are probably 500 more that would also be worthy and that a different chooser might have chosen with as much validity as he chose his. At the end he does pare his list down further, to what he considers the ten most important calculations over the course of human history, and listing those will give you an idea of the kind of thing he covers. In more or less chronological order:1. Archimedes Bounds π. Approximating the circumference of a circle by the perimeters of circumscribing and inscribing polygons of ever-increasing number of sides2. Production of Tables of Logarithms. In the last 50 years electronic calculators have made logarithms obsolete, but those of us who did calculations of any complexity before that mightily appreciated them.3. Seismic Rays Reveal the Earth’s Interior. Until the mid-1920s it was generally believed that it was impossible to know much about the interior of the earth. (Tales like Burroughs’ Pellucidar series even made it hollow.) Then a female geologist had an inspiration and succeeded in showing how to use the timing of vibrations from earthquakes to learn a great deal about it.4. Kepler’s Astronomical Calculations. Kepler took the very accurate measurement of apparent planetary motions that Tycho Brahe had recorded and worked back from them to establish his three laws of planetary motion.5. Predicting the Return of Halley’s Comet. Comets had been viewed as omens that appeared from nowhere and had a powerful influence on the world. Newton believed that they were just other bodies, like the planets, that orbited the sun, only with long periods. Edmund Halley did a calculation of the orbit of the comet that appeared in the early 18th century and predicted that it would appear again some 70-odd years later. He was right.6. Rotating Orbits. Newton’s law of gravitation assumed that gravitation attraction was proportional to the inverse square of distance. This would make a planetary orbit an ellipse. If the force was not exactly inverse square, the orbit would still be an ellipse, but the ellipse would rotate with respect to inertial space. The orbit of Mercury did in fact have such a rotation, which was explained by Einstein’s general theory of relativity.7. Harvey Establishes Blood Circulation. The ancient belief about blood was that it was created in the heart and eliminated in the liver; arterial and venous blood were not believed to be the same substance. Harvey did some fairly basic calculations that proved that there was no way blood could be created and eliminated fast enough to deal with the volume in question; it had to circulate as we currently understand.8. Light and Electromagnetism. Establishing the nature of light was one of the great crusades in physics. Treating light as wave motion led to highly successful results, but the question of what kind of waves they were was unknown until James Clerk Maxwell worked out a theory combining electrical and magnetic forces, proving that the nature of light (and other radiation) was electromagnetic.9. The New Mechanics Explains Atoms. Developing quantum mechanics was essential to the understanding that we now have of the nature of matter and energy. It leads to results that to a considerable degree defy common sense, but using the equations works to predict what actually happens in the real world.10. Simply Chaos. The development of chaos theory, where small perturbations of initial conditions cause large effects—e.g. the butterfly that sets off a hurricane on the other side of the world.

There have been countless "great calculations" through history, but it is nonetheless interesting to read Pask's take on the best of the best. He presents each calculation in terms that can be appreciated by the non-expert, even when the underlying methodology would be pretty esoteric. His choices of great calculations are very good, and very interesting, and well-justified. His writing style in very comfortable. You can read the book for a while, put it down and pick it up later without losing the thread of the "story."

Beautifully written and in-depth on various topics of interest.

Lot of more important events were left out of this history. At least it got me looking for a bettr way to calculate logarithms.A

Did you ever wonder how we know the distance to the sun, or the force of gravity, or the mass of Mars, or that submicroscopic atoms are mostly empty space with almost all the mass concentrated in tiny nuclei composed of neutrons and protons, …? The answer is by making ingenious calculations that greatly extend our knowledge beyond what we can actually measure. The author, a mathematician with a wide interest in the applications of his subject, tells fascinating stories of 50 calculations that have literally changed our understanding of the universe about us and of the often fascinating characters who have made them. A sampling of the topics described--Mathus on growth of populations, Eratosthenes on the measurement of the earth’s size and Kelvin’s calculation of its age, Newton’s determination of the laws of planetary motion and tide predictions, Hoyle’s and Bethe’s calculations of how the matter in the universe was synthesized from primordial hydrogen, Maxwell’s determination that light is an electromagnetic wave, how the sun shines,…. This material is presented in a reader-friendly style that should be accessible to anyone willing to open his or her mind to breathtaking insights resulting from calculations that define our knowledge of the universe in which we live.

In clear, friendly, lively and most captivating prose, the author describes 50 calculations (scientific investigations) that have been performed during the course of recorded human history. The calculations selected are what the author considers to be particularly important in the evolution of scientific progress. However, very few of these calculations are presented in detail. Most of them are described in their historical contexts along with the people who performed them. Key equations are liberally included and discussed but very few are actually derived – only a few very simple ones. However, ample references are given for readers who want to delve deeper into the details. Throughout the book, the author mentions other important calculations that could also have been included in his book because of their groundbreaking significance; however, as he mentions, he had to draw the line somewhere and those included in the book are his own personal choices. In making those choices, the author has used a more quantitative method which he describes in the last chapter.I thoroughly enjoyed this marvellous book. It contains so much scientific history dating from Ancient Greece up to the twentieth century. I found the author’s expertise and his friendly writing style to be particularly great assets in making the material so gripping and widely accessible. Needless to say I found the book almost impossible to put down. I believe that anyone can enjoy this excellent book. Those who are mathematically challenged may skip the more mathematical passages and still glean much about the history and evolution of science. However, science enthusiasts are likely to relish this superb book the most.