David Garfinkle

from the sun to black holes to the mystery of dark matter

Three steps to the universe

Richard Garfinkle

X Marks the Spot is written from the point of view of the users of mathematics. Since the beginning, mathematical concepts and techniques (such as arithmetic and geometry) were created as tools with a particular purpose like counting sheep and measuring land areas. Understanding those purposes leads to a greater understanding of why mathematics developed as it did. Later mathematical concepts came from a process of abstracting and generalizing earlier mathematics. This process of abstraction is very powerful, but often comes at the price of intuition and understanding. This book strives to give a guided tour of the development of various branches of mathematics (and what they're used for) that will give the reader this intuitive understanding. Features Treats mathematical techniques as tools, and areas of mathematics as the result of abstracting and generalizing earlier mathematical tools Written in a relaxed conversational and occasionally humorous style making it easy to follow even when discussing esoterica. Unravels how mathematicians think, demystifying math and connecting it to the ways non-mathematicians think and connecting math to people's lives Discusses how math education can be improved in order to prevent future generations from being turned off by math.

The Lost Inheritance of Mathematics

X Marks the Spot

X Marks the Spot is written from the point of view of the users of mathematics. Since the beginning, mathematical concepts and techniques (such as arithmetic and geometry) were created as tools with a particular purpose like counting sheep and measuring land areas. Understanding those purposes leads to a greater understanding of why mathematics developed as it did. Later mathematical concepts came from a process of abstracting and generalizing earlier mathematics. This process of abstraction is very powerful, but often comes at the price of intuition and understanding. This book strives to give a guided tour of the development of various branches of mathematics (and what they’re used for) that will give the reader this intuitive understanding. Features Treats mathematical techniques as tools, and areas of mathematics as the result of abstracting and generalizing earlier mathematical tools Written in a relaxed conversational and occasionally humorous style making it easy to follow even when discussing esoterica. Unravels how mathematicians think, demystifying math and connecting it to the ways non-mathematicians think and connecting math to people’s lives Discusses how math education can be improved in order to prevent future generations from being turned off by math.

If scientists can’t touch the Sun, how do they know what it’s made of? And if we can’t see black holes, how can we be confident they exist? Gravitational physicist David Garfinkle and his brother, science fiction writer Richard Garfinkle, tackle these questions and more in Three Steps to the Universe, a tour through some of the most complex phenomena in the cosmos and an accessible exploration of how scientists acquire knowledge about the universe through observation, indirect detection, and theory. The authors begin by inviting readers to step away from the Earth and reconsider our Sun. What we can directly observe of this star is limited to its surface, but with the advent of telescopes and spectroscopy, scientists know more than ever about its physical characteristics, origins, and projected lifetime. From the Sun, the authors journey further out into space to explore black holes. The Garfinkle brothers explain that our understanding of these astronomical oddities began in theory, and growing mathematical and physical evidence has unexpectedly supported it. From black holes, the authors lead us further into the unknown, to the dark matter and energy that pervade our universe, where science teeters on the edge of theory and discovery. Returning from the depths of space, the final section of the book brings the reader back down to Earth for a final look at the practice of science, ending with a practical guide to discerning real science from pseudoscience among the cacophony of print and online scientific sources. Three Steps to the Universe will reward anyone interested in learning more about the universe around us and shows how scientists uncover its mysteries.

From the Sun to Black Holes to the Mystery of Dark Matter

Three Steps to the Universe

Why this book? -- Sticks and stones -- Abstraction, mistrust, and laziness -- Algebra, geometry, analysis : the mathematical mindsets -- Analytic geometry -- Calculus : motion and size -- The language of motion -- Sound, notes, and harmonics -- Probability and statistics -- Other geometries : not so straight, these sticks -- Algebra and the rise of abstraction -- The smith and the knight -- Building the theoretical universe -- Computers -- The theoretical universe of modern physics : toolkit included -- Math education & math in education.

David Garfinkle

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