The Art of the Infinite: Our Lost Language of Numbers

The Art of the Infinite: Our Lost Language of Numbers Epub
    IGNOU M.Com Study Material, IGNOU Books, Free Download plane of geometry into the unlikely realm where parallel lines meet Along the way, deft character studies of great mathematicians and equally 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 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, and reveals mathematics as one of the most exhilarating expressions of the human imagination."/>
  • Paperback
  • 336
  • The Art of the Infinite: Our Lost Language of Numbers
  • Robert M. Kaplan
  • English
  • 06 April 2018
  • 0141008865

About the Author: Robert M. Kaplan

The Art of the Infinite: Our Lost Language of Numbers Epub infinite: download, lost epub, language pdf, numbers pdf, The Art book, of the free, The Art of the Infinite: Our Lost Language of NumbersArt of the epub, Art of the Infinite: Our kindle, The Art of the Infinite: Our Lost Language of Numbers eBookRobert and Ellen Kaplan have of the PDF/EPUB é taught mathematics to people from six to sixty, at leading independent schools and most recently at Harvard University Robert Kaplan is the author of the best selling The Nothing That Is A Natural History of Zero, which has been translated into languages, and together they wrote The Art of the Infinite Ellen Kaplan is also co author of Chances Are Adventures in Probability and Bozo Sapiens Why to Err is Human, co The Art Epub / written with her son Michael Kaplan.


The Art of the Infinite: Our Lost Language of NumbersThe Art of the Infinite: Our Lost Language of Numbers Epub infinite: download, lost epub, language pdf, numbers pdf, The Art book, of the free, The Art of the Infinite: Our Lost Language of NumbersArt of the epub, Art of the Infinite: Our kindle, The Art of the Infinite: Our Lost Language of Numbers eBookRobert Kaplan s The Nothing of the PDF/EPUB é 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 quotes and allusions from Aquinas via Gershwin to Woolf and The Philadelphia Inquirer 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 The Art Epub / Where The Nothing That Is looked at math through the lens of zero, The Art of the Infinite takes infinity, in its countless 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 Art of the Kindle Ó 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 geometry into the unlikely realm where parallel lines meet Along the way, deft character studies of great mathematicians and equally 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 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, and reveals mathematics as one of the most exhilarating expressions of the human imagination.

You may also like...

10 thoughts on “The Art of the Infinite: Our Lost Language of Numbers

  1. Darcy says:

    Wow I loved this book It really opened my mind around how numbers are represented and constructed.This is one of the best books I have read that explores the foundations of numbers in a very understandable format The approach development of math knowledge in the book was entertaining, with a mix of history and inspiring proofs and examples I wished I read this book when I was in high school Topics I really appreciated include the explanation of number fields In particular, I really enjoye Wow I loved this book It really opened my mind around how numbers are represented and constructed.This is one of the best books I have read that explores the foundations of numbers in a very understandable format The approach development of math knowledge in the book was entertaining, with a mix of history and inspiring proofs and examples I wished I read this book when I was in high school Topics I really appreciated include the explanation of number fields In particular, I really enjoyed the explanation of why a heptagon can t be constructed with compass and ruler through the previously developed understanding of fields Additional tools would be needed Of 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 construct represent numbers exactly.As a side note The book didn t talk about this, but floating point numbers are popular for approximating real numbers Floating point numbers can be problematic because of truncation and rounding errors that occur in calculations This book has inspired me to learnabout Exact Reals and has given me the ability to follow understand papers on various strategies for exact reals as an alternative to floating point numbers

  2. Dmitry Frenkel says:

    Well, simply put, this is NOT a book about mathematics Sure, it has numbers and math as its subject matter, but what authors really wanted you to get out of this book is how wonderfully elitist their English language skills are Combined with a narrator choice straight out of Downton Abbey the upstairs kind, of course , this book is impossible to either read or listen to Even as someone who has a degree in math and loves science, I could not hold on to this book Long winded Shakespearian tir Well, simply put, this is NOT a book about mathematics Sure, it has numbers and math as its subject matter, but what authors really wanted you to get out of this book is how wonderfully elitist their English language skills are Combined with a narrator choice straight out of Downton Abbey the upstairs kind, of course , this book is impossible to either read or listen to Even as someone who has a degree in math and loves science, I could not hold on to this book Long winded Shakespearian tirades and philosophical comparisons are sprinkled throughout the chapters making this book VERY hard to comprehend If authors wanted to wake our natural curiosity when it comes to numbers and math, travel with us from ancient times of Euclid and ratios all the way to modern times to show us amazing process of discovery and beauty and logic of math, they failed utterly All you are left with after reading or listening to this book is their weird words salad

  3. Adam says:

    Somewhere between Flatland A Romance of Many Dimensions and Cosmos, Art of the Infinite is a popularization of mathematics by way of extensive metaphor and cultured references to literature and philosophy I thought this was just a bit cheesy at first, but after a few times around, I got why they were doing this The chief metaphor is spatial math is an exploration into these unimaginably vast vistas in which humans are comfortable with a negligible patch and can imagine only a fraction The K Somewhere between Flatland A Romance of Many Dimensions and Cosmos, Art of the Infinite is a popularization of mathematics by way of extensive metaphor and cultured references to literature and philosophy I thought this was just a bit cheesy at first, but after a few times around, I got why they were doing this The chief metaphor is spatial math is an exploration into these unimaginably vast vistas in which humans are comfortable with a negligible patch and can imagine only a fraction The Kaplans assert that these vistas are full of palaces and treasures and that the pursuit is of some value to humanity The value they present is this heady experience in which the simple propagates along some logical line into infinity, like a door opening to reveal the set of all possible doors These experiences are certainly delightful and make the book enjoyable to read, and I d imagine this would be muchthe case had I followed along with each chapter whichor less corresponded to a continuous line of inquiry trying my hand at the math and making sure I understand what the symbols in each section referred to I m sure I m capable of this, especially since the Kaplans go out of their way to put things in comprehensible terms though it is never oversimplified , but I was merely too lazy.While the Kaplans present this as a sort of valuable service, math as a heady wonder inducer, they don t skirt around the Lovecraftian implications of this The last chapter, in which Cantor plumbs the nature of compound infinities mind blowing revelation in which he proves that there MUST be infinities larger than other infinities, as paradoxical as this is and of course this is only the premise of the chapter , ends up with his gradual descent to disgrace and insanity The brilliant thing about this all is that whereas Cantor, it is implied, went insane because of his frustration with the unprovability of the Continuum theorem, i.e., because he hit some limit in the comprehensibility of this shit, the authors end by pointing out that Kurt Godel resolved Cantor s final issue rather handily he proved that it was neither provable or disprovable The historicity of the discipline is heartening it suggests that there is no aspect of this boggling system that is inherently beyond human grasp, that it isn t really the hostile and unmasterable force Lovecraft s nightmares conjure it as Which doesn t help Cantor or any of us who exist at a fixed point on the timeline we are stuck with the paradoxes of our day, not privy to the brilliant answers around the corner I did think it was a bit unfortunate if ultimately satisfying that the Kaplans decided to end the book on a resolution, not its consequent question It d be interesting and tantalizing to know what problems are presently driving mathematicians insane.And this is what I took away from the book a greater sense of math as a discipline parallel to science In the first chapter, the Kaplans lay out the plane of imaginary numbers intersecting with the plane of real numbers They make the story of math equal in the same way to the history of science Scientists have been doing things in the world to make things about itclear, always clearing awaycobwebs and opening new doors, etc Mathematicians have been doing the same thing, exploring the seemingly real properties of this other world, not precisely intersecting with ours, or exactly including it It is just a different thing that they are investigating, with different tools, to be sure, but with the same process of discovery, despite the abstraction and lack of the empiricism we often define as integral to science

  4. Chris Herdt says:

    Prose so purple I claim it was abused This book needed an editor to cut out the blathering that the authors thought clever The references to Rimbaud and Proust, to cite just a couple, were completely unnecessary and distracting.I 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 theorist I was excited when I read this in the introduction Many small things estrange math fro Prose so purple I claim it was abused This book needed an editor to cut out the blathering that the authors thought clever The references to Rimbaud and Proust, to cite just a couple, were completely unnecessary and distracting.I 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 theorist I was excited when I read this in the introduction Many small things estrange math from its proper audience One is the remoteness of its machine made diagrams These reinforce 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 reader to think he is seeing the things themselves rather than pixellated approximations to them An insightful remark, if somewhat overwrought Hand drawn diagrams will make the text feel less imposing and let the reader know that, however true, they are humble human calculations Brilliant, right Unfortunately, the text is ridiculously remote A sample Have negative numbers definitively moved mathematical thought into abstraction, where the dance of 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 is because, like squaredances in the confines of a barn, little room to maneuver leads to intricate patterns Theelaborate these become, each linking onto the last, thesuch patterns will all seem to lodge in a sense at onceancestral andabstract than sight It is as if the predominance in our brains of the visual cortex masked a different, deeper apprehension of time, then, or something akin to music structure itself There s a lot to make fun of in that paragraph, but for me, I have to say Squaredances Really This was published in 2003 Note 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 returned on 30 March 2007 I m going to assume that was a faculty member

  5. TheGriffinReads says:

    Though I was only able to follow about two thirds of the math in The Art of the Infinite, it was extremely informative I found most interesting the principles of shifting from perspective to perspective, using techniques and processes of one branch of mathematics to interpret techniques and processes of another, the use of mathematical substitutions from seemingly unrelated contexts to sidestep mathematical deadends and the varying styles of thought used to approach math I especially enjoyed t Though I was only able to follow about two thirds of the math in The Art of the Infinite, it was extremely informative I found most interesting the principles of shifting from perspective to perspective, using techniques and processes of one branch of mathematics to interpret techniques and processes of another, the use of mathematical substitutions from seemingly unrelated contexts to sidestep mathematical deadends and the varying styles of thought used to approach math I especially enjoyed the revelations of deep pattern throughout mathematical concepts very satisfying Finally, a great moment for me many years ago I came across the term Cantorian transfinites in a science fiction short story In intervening years other reading confirmed the existence of a mathematician named Cantor and my suspicion that the transfinites were real, and, as they hinted at numbers beyond infinity, I was fascinated Math teachers I questioned were unfamiliar with the idea through fourteen years of teaching But, there it is in the last chapters of The Art of the Infinite.The text is challenging at best and can be overwhelming to the layman, but the patterns, principles and often bizarre coincidence of numbers makes it quite worthwhile

  6. Marty says:

    Mathematics is something that I find interesting, but definitely wish I knewabout 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 wrong.The book is written in this weird, florid prose, and just the way it was written made it impossible to read I tried really hard, but I couldn t get past the first few pages Finally, I took it back to the library and lo Mathematics is something that I find interesting, but definitely wish I knewabout 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 wrong.The book is written in this weird, florid prose, and just the way it was written made it impossible to read I tried really 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 andtechnical If you can handle the flowery prose, then you might enjoy this book, but I just couldn t handle it

  7. Christian Duerig says:

    Beautiful Mathematic Book for college students THE GREAT CONTROVERSE isimportant to know than all other stuff The question Where do we get our knowledge from and how do we know, that that is it John von Neuman said In Mathematics we never understand things but we just get used to them That can t be quite right yet our understanding must be stretched to the breaking point before it becomes flexible enough to adjust to the unthinkable page 024 Paul Erd s said about The B Beautiful Mathematic Book for college students THE GREAT CONTROVERSE isimportant to know than all other stuff The question Where do we get our knowledge from and how do we know, that that is it John von Neuman said In Mathematics we never understand things but we just get used to them That can t be quite right yet our understanding must be stretched to the breaking point before it becomes flexible enough to adjust to the unthinkable page 024 Paul Erd s said about The Book You don t have to believe in God, but you do have to believe in The Book I myself understand these proofs The New Scientist meant This is mathematics for the Soul just the way it should be I can only agree

  8. Roberto Rigolin F Lopes says:

    The essence of mathematics lies entirely on its freedom , said Georg Cantor THE man who figured out that 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 muchThe whole thi The essence of mathematics lies entirely on its freedom , said Georg Cantor THE man who figured out that 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 muchThe 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

  9. Robbie D says:

    One of my favorite books on math.

  10. Jeff says:

    Husband and wife team Robert Kaplan and Ellen Kaplan have written a rich exploration of several aspects of the expansive field of mathematics Through the book they cover the foundations of number and arithmetic, the rigors of mathematical proof, the nature of mathematical insight, the primes, infinite sequences, Euclidean geometry, building algebra from geometry, complex numbers, projective geometry this was completely new for me , and finish with the nature of different infinities and the lif Husband and wife team Robert Kaplan and Ellen Kaplan have written a rich exploration of several aspects of the expansive field of mathematics Through the book they cover the foundations of number and arithmetic, the rigors of mathematical proof, the nature of mathematical insight, the primes, infinite sequences, Euclidean geometry, building algebra from geometry, complex numbers, projective geometry this was completely new for me , and finish with the nature of different infinities and the life of Georg Cantor In many ways, this book is a nice companion to Jerry P King s books The Art of Mathematics and Mathematics in 10 Lessons In The Art of Mathematics, King argues that mathematics is an art form that can be appreciated through its own theory of aesthetics built on precision and concise elegance Both Mathematics in 10 Lessons and this book attempt to give to the interested but lay reader a taste of the art form.I really enjoyed both of King s books, but found The Art of the Infinite a little less accessible First, the Kaplan s write with a style rich in complex, ornamental language, a bit surprising for a math text, but apparently they both studied linguistics at one point What this means is there are lots of literary references and clever metaphors It took me a while to get used to this style of writing, and found it distracting in parts Particularly, when it comes to my second criticism That is I had a hard time understanding a few of the chapters because the math was new to me andcomplex requiring me to reread sections to make sure I followed Not fully following all of the intricacies of the mathematics is frustrating, but I generally feel like if I spend enough time with it I ll start to get it With this work, it took longer because of the gloss of the language.I m happy to have read The Art of the Infinite, but I can t say that it will be a book I reference when I need an explanation of some bit of math That said, they have a good bit on the nature of play and creative exploration in mathematics, and this insight alone is worth the reading of this book