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Great Calculations: A Surprising Look Behind 50 Scientific Inquiries
Science is based not only on observation and experiment, but on theory as well. As Einstein said, "Theory tells us what to measure." And theories are often crystallized into succinct calculations, like those made using Einstein's famous E = mc2. This book looks at fifty such great calculations, exploring how and why they were developed and assessing their impact on the history of science.As the author shows, many significant scientific calculations are quite simple and fairly easy to understand, even for readers will little math background. But their implications can be surprising and profound.For example, what links a famous comet and the cost of an annuity? Why do scientists claim there is "dark matter" in the universe if it can't be observed? How does carbon-based life on Earth depend on a quirk of nuclear physics? The answer to each question is an illuminating calculation.This accessible, engaging book will help you understand these breakthroughs and how they changed our view of life and the world.
330 pages, Kindle Edition
First published July 7, 2015
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Displaying 1 - 5 of 5 reviews
February 2, 2020
The author suggests that one might like to make one's own list. Mine would be: what the fuck do I know? Certainly not enough to be waxing on about the greatest calculations. In any case, this was an insightful and engaging way to present a mix of history and mathematics, and well worth the time I spent with it. It was also a bit depressing in that it brought into stark clarity just how much math I don't know anymore. I don't think there was anything here I didn't learn in college, and most of it I once understood on at least on some level, but now... not so much. I would have to go back and relearn broad swaths of math to really get it. But putting that aside, I liked the authors exercise of attempting to rank the calculations, his scholarship seemed deep, and he was adept at communicate some difficult concepts.
August 22, 2022
This book looks closely at fifty “great calculations”, as judged by the author, who has produced other works in the area of mathematics popularization. The significant scientific calculations and formulae are presented simply and with historical context, including careful observation of the often tangled claims of priority. Readers are not required to have a significant mathematics background to understand the stunning implications and elegant innovation behind each of the fifty. The result is an accessible and engaging book covering a spectrum of mathematical breakthroughs that solved mysteries of our world, such as measuring the solar system, or revealed new mysteries, such the existence of dark matter and dark energy in our universe.
The historical context brings in key persons and often interesting side alleys. Thus is the balletic choreography of planetary epicycles reviewed in the chapter on the “Solar System: First Mathematical Models” is a part of the act, leading to the stunning, resolving scene featuring Kepler. Here also is the beautiful, if misguided, astronomical model based on the Platonic solids. As part of classical mathematics, Eratosthenes’ visionary seeing of the circumference of the globe in the bottom of a well is also here. So is Andrija Mohorovičić peering in to see Earth’s very bones with the aid of seismic waves.
The attempt to reach readers without high levels of mathematical sophistication brings the author to evaluate some equations for almost subjective aesthetics. Maxwell’s equations can be daunting even for accomplished undergraduates, but the author calms the reader with pragmatism and superlatives, “It is not necessary to understand the mathematics… these wonderful equations do tell us how the electromagnetic fields can vary in space and time.” Thus is the lead-in to “Maxwell’s Miraculous Calculation”.
Can such a list be compiled without criticism for some oversight? Probably not. I encourage you to read it yourself and come up with your own necessary additions. What would you part with to keep it to fifty? For me, in a list that includes (and rightly so) Archimedes’ insightful approximation of π must find room for Euler’s number e. I would even say this could replace the entry for Euler solving the Basel Problem, since that, essentially, could be a footnote to the exploration of π. Or, let it replace the valuation of annuities as calculated by Halley, better known for predicting his eponymous comet.
This is the class of thoughts the book will raise with any reader, and rightly it should. The author directly tackles the subject of necessary omissions, both generally and at the conclusion of the topical chapters. The end of Chapter 8 “About Us” suggests there could have been more on DNA, modeling nervous system signal transmission and Turing’s “mathematically elegant work on pattern formation”. Of course, there are many surprising and appealing entries, such as the World War II D-Day tide calculations based on work done by Lord Kelvin seven decades previous.
As can be expected, this work has an extensive, supporting bibliography. I very much appreciate an author that elevates titles out of the sterile appendix listing to make qualitative assessments of favored works. This author does that often and boldly, which resulted in new additions to my own “to-read” list. In a run up to time dilations, Right Hand, Left Hand: The Origins of Asymmetry in Brains, Bodies, Atoms and Cultures by Chris McManus is called “entertaining”. The same adjective is applied to the paper “Lambda: The Constant That Refused to Die“ (John Earman) when linking Einstein’s Λ to a discussion of dark energy. We are also assured that Fred Hoyle’s autobiography Home is Where the Wind Blows: Chapters from a Cosmologist's Life is “captivating”. In this way nearly every page offers departure points for further exploration assessed as “fascinating” or another superlative descriptor. The journey this book takes the reader on is full of stunning vistas and promising side treks.
[My review is also posted on MAA Reviews.]
The historical context brings in key persons and often interesting side alleys. Thus is the balletic choreography of planetary epicycles reviewed in the chapter on the “Solar System: First Mathematical Models” is a part of the act, leading to the stunning, resolving scene featuring Kepler. Here also is the beautiful, if misguided, astronomical model based on the Platonic solids. As part of classical mathematics, Eratosthenes’ visionary seeing of the circumference of the globe in the bottom of a well is also here. So is Andrija Mohorovičić peering in to see Earth’s very bones with the aid of seismic waves.
The attempt to reach readers without high levels of mathematical sophistication brings the author to evaluate some equations for almost subjective aesthetics. Maxwell’s equations can be daunting even for accomplished undergraduates, but the author calms the reader with pragmatism and superlatives, “It is not necessary to understand the mathematics… these wonderful equations do tell us how the electromagnetic fields can vary in space and time.” Thus is the lead-in to “Maxwell’s Miraculous Calculation”.
Can such a list be compiled without criticism for some oversight? Probably not. I encourage you to read it yourself and come up with your own necessary additions. What would you part with to keep it to fifty? For me, in a list that includes (and rightly so) Archimedes’ insightful approximation of π must find room for Euler’s number e. I would even say this could replace the entry for Euler solving the Basel Problem, since that, essentially, could be a footnote to the exploration of π. Or, let it replace the valuation of annuities as calculated by Halley, better known for predicting his eponymous comet.
This is the class of thoughts the book will raise with any reader, and rightly it should. The author directly tackles the subject of necessary omissions, both generally and at the conclusion of the topical chapters. The end of Chapter 8 “About Us” suggests there could have been more on DNA, modeling nervous system signal transmission and Turing’s “mathematically elegant work on pattern formation”. Of course, there are many surprising and appealing entries, such as the World War II D-Day tide calculations based on work done by Lord Kelvin seven decades previous.
As can be expected, this work has an extensive, supporting bibliography. I very much appreciate an author that elevates titles out of the sterile appendix listing to make qualitative assessments of favored works. This author does that often and boldly, which resulted in new additions to my own “to-read” list. In a run up to time dilations, Right Hand, Left Hand: The Origins of Asymmetry in Brains, Bodies, Atoms and Cultures by Chris McManus is called “entertaining”. The same adjective is applied to the paper “Lambda: The Constant That Refused to Die“ (John Earman) when linking Einstein’s Λ to a discussion of dark energy. We are also assured that Fred Hoyle’s autobiography Home is Where the Wind Blows: Chapters from a Cosmologist's Life is “captivating”. In this way nearly every page offers departure points for further exploration assessed as “fascinating” or another superlative descriptor. The journey this book takes the reader on is full of stunning vistas and promising side treks.
[My review is also posted on MAA Reviews.]
April 8, 2019
I was very impressed by Pask's scholarship. He has a remarkable knowledge of the history of science. This book is a like a tourist guide through the highlights of the scientific past. I enjoyed the book a lot. Well worth the read. My only disappointment was that at times he only gave a superficial description of the calculations on the grounds that the reader might not understand the math. This is a common failing of books aimed at a broad audience. However, with a title that includes the word "Calculations" it is reasonable to expect that anyone who buys this book understands enough math to follow a calculation in some detail. That being said, I do recommend the book.
August 19, 2023
This is an enthralling overview of the history of science. The book distinguishes itself from similar books by including a fair number of formulas and equations. The interested reader can thus get a clearer understanding of the great scientific achievements of the past. From ancient greeks to the scientific revolution and modern physics, you will understand how humanity has used science to make sense of the world we live in.
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January 28, 2016My judging a book from this cover , it looks good !
Displaying 1 - 5 of 5 reviews