Robert M. Kaplan æ 4 SummaryEssary and distractingI Yaşayan Kur'an Meal-Tefsir read the first 3 chapters and then skipped to the last the chapter on Georg Cantor and aleph null aleph one and transfinite numbers Fun fact Cantor was a conspiracy theoristI was excited when Iead this in the introductionMany small things estrange math from its proper audience One is the emoteness of its machine made diagrams These einforce the mistaken belief that it is all very far away on a planet visited only by graduates of the School for Space Cadets Diagrams printed out from computers communicate a second and subtler falsehood they lead the The Frankenstein Teacher (Corgi Pups) reader to think he is seeing the things themselvesather than pixellated approximations to themAn insightful The Case of the General's Thumb remark if somewhat overwrought Hand drawn diagrams will make the text feel less imposing and let theeader know that however true they are humble human calculations Brilliant ightUnfortunately the text is idiculously emote A sampleHave negative numbers definitively moved mathematical thought into abstraction
*where the dance *the dance symbols becomes vivid instead of figures Or do you find the visual proof in the appendix to this chapter not only convincing but illuminating Notice that in our dances the same steps axioms of additive and multiplicative inverses and distributivity occur
Again And Again This Isand again This is like suaredances in the confines of a barn little oom to maneuver
leads to intricate patterns The elaborate these become each linking onto the last the such patternsto intricate patterns The elaborate these become each linking onto the last the such patterns all seem to lodge in a sense at once ancestral and abstract than sight It is as if the predominance in our brains of the visual cortex masked a different deeper apprehension of tim. Guises as a touchstone for understanding mathematical thinking Tracing a path from Pythagoras whose great Theorem led inexorably to a discovery that his followers tried in vain to keep secret the existence of irrational numbers; through Descartes and Leibniz; to the brilliant haunted Georg Cantor who proved that infinity can come in different sizes the Kaplans show how the attempt to grasp the ungraspable embodies the essence of mathematics The Kaplans guide us through the Republic of Numbers where we meet both its upstanding citizens and shadowy dwellers; and we travel across the plane of geo. E then or something akin to music structure itselfThere s a lot to make fun of in that paragraph but for me I have to say Suaredances Really This was published in 2003Note I am apparently the 3rd person to have checked out this copy from the library The person before me checked it out on 16 August 2004 and it was marked eturned on 30 March 2007 2004 and it was marked Echoes from the Past returned on 30 March 2007 m going to assume that was a faculty member Wow I loved this book Iteally opened my mind around how numbers are The Master Strategist: Power, Purpose and Principle in Action represented and constructedThis is one of the best books I haveead that explores the foundations of numbers in a very understandable format The approachdevelopment of math knowledge in the book was entertaining with a mix of history and inspiring proofs and examples I wished I ead this book when I was in high school Topics I eally appreciated include the explanation of number fields In particular I eally enjoyed the explanation of why a heptagon can t
Be Constructed With Compass And Ruler Through The Previously Developedconstructed with compass and uler through the previously developed of fields Additional tools would be neededOf course I ve known a lot about numbers for years and I use Real and Complex numbers every day as an engineer But I never had such an appreciation for how to constructrepresent numbers exactlyAs a side note The book didn t talk about this but floating point numbers are popular for approximating The Oathbreaker's Shadow real numbers Floating point numbers can be problematic because of truncation andounding errors that occur in calculations This book has inspired me to learn about Exact Reals and has given me the ability to followunderstand papers on various strategies for exact eals as an alternative to floating point numbers. Metry into the unlikely ealm where parallel lines meet Along the way deft character studies of great mathematicians and eually colorful lesser ones illustrate the opposed yet intertwined modes of mathematical thinking the intutionist notion that we discover mathematical truth as it exists and the formalist belief that math is true because we invent consistent In Berlin Vielleicht rules for it Less than All wrote William Blake cannot satisfy Man The Art of the Infinite shows us some of the ways that Man has grappled with All andeveals mathematics as one of the most exhilarating expressions of the human imaginati. .
One of my favorite books on math The essence of mathematics lies
Entirely On Its Freedomon its freedom Georg Cantor THE man
*who figured out *figured out there are countable and uncountable infinities Wow Infinite freedom Well at least freedom within a playground nested with infinities Hilbert s paradise as you are about to learn in this book Hey Robert and Ellen managed to make number theory palatable for the layperson with an entire chapter on Cantor s work An infinite gold mine as a chapter And there is much The whole thing is a vivid narrative about mathematical beauty everywhere playful with subtle humor and deep erudition That is history geometry philosophy poetry infinite entertainment Mathematics is something that I find interesting but definitely wish I knew about So I went to my local library looking for a good book on math to give me an introduction to the subject When I found this book I thought I d found what I was looking for Boy was I wrongThe book is written in this weird florid prose and just the way it was written made it impossible to ead I tried eally hard but I couldn t get past the first few pages Finally I took it back to the library and looked for a better alternative I gave it two stars because it probably would have been a decent book had it not been for the weird writing style I just needed something less flowery and technical If you can handle the flowery prose then you might enjoy this book but I just couldn t handle it Prose so purple I claim it was abused This book needed an editor to cut out the blathering that the authors thought clever The eferences to Rimbaud and Proust to cite just a couple were completely unnec. Robert Kaplan's The Nothing That Is A Natural History of Zero was an international best seller translated into ten languages The Times called it elegant discursive and littered with uotes and allusions from Auinas via Gershwin to Woolf and The Philadelphia Inuirer praised it as absolutely scintillating In this delightful new book Robert Kaplan writing together with his wife Ellen Kaplan once again takes us on a witty literate and accessible tour of the world of mathematics Where The Nothing That Is looked at math through the lens of zero The Art of the Infinite takes infinity in its countless.
Robert M. Kaplan