Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else
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- Type：Epub+TxT+PDF+Mobi
- Create Date：2021-06-04 06:51:30
- Update Date：2025-09-14
- Status：finish
- Author：Jordan Ellenberg
- ISBN：1984879057
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Summary
From the New York Times-bestselling author of How Not to Be Wrong—himself a world-class geometer—a far-ranging exploration of the power of geometry， which turns out to help us think better about practically everything。
How should a democracy choose its representatives？ How can you stop a pandemic from sweeping the world？ How do computers learn to play Go， and why is learning Go so much easier for them than learning to read a sentence？ Can ancient Greek proportions predict the stock market？ （Sorry， no。） What should your kids learn in school if they really want to learn to think？ All these are questions about geometry。 For real。
If you're like most people， geometry is a sterile and dimly remembered exercise you gladly left behind in the dust of ninth grade， along with your braces and active romantic interest in pop singers。 If you recall any of it， it's plodding through a series of miniscule steps only to prove some fact about triangles that was obvious to you in the first place。 That's not geometry。 Okay， it is geometry， but only a tiny part， which has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel。
Shape reveals the geometry underneath some of the most important scientific， political， and philosophical problems we face。 Geometry asks: Where are things？ Which things are near each other？ How can you get from one thing to another thing？ Those are important questions。 The word "geometry，" from the Greek for "measuring the world。" If anything， that's an undersell。 Geometry doesn't just measure the world—it explains it。 Shape shows us how。
How should a democracy choose its representatives？ How can you stop a pandemic from sweeping the world？ How do computers learn to play Go， and why is learning Go so much easier for them than learning to read a sentence？ Can ancient Greek proportions predict the stock market？ （Sorry， no。） What should your kids learn in school if they really want to learn to think？ All these are questions about geometry。 For real。
If you're like most people， geometry is a sterile and dimly remembered exercise you gladly left behind in the dust of ninth grade， along with your braces and active romantic interest in pop singers。 If you recall any of it， it's plodding through a series of miniscule steps only to prove some fact about triangles that was obvious to you in the first place。 That's not geometry。 Okay， it is geometry， but only a tiny part， which has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel。
Shape reveals the geometry underneath some of the most important scientific， political， and philosophical problems we face。 Geometry asks: Where are things？ Which things are near each other？ How can you get from one thing to another thing？ Those are important questions。 The word "geometry，" from the Greek for "measuring the world。" If anything， that's an undersell。 Geometry doesn't just measure the world—it explains it。 Shape shows us how。
Reviews
Brian Clegg
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I really enjoyed Jordan Ellenberg’s earlier book How Not to be Wrong， so looked forward to Shape with some anticipation。 In principle what we have here is a book about geometry - but not seen from the direction of the （dare I say it） rather boring， Euclid-based geometry textbooks some of us suffered at school。 Instead Ellenberg sets out to show how geometry underlies pretty much everything。Along the way， we are given some nice turns of phrase。 I enjoyed， for example， Ellenberg’s remark on the ph I really enjoyed Jordan Ellenberg’s earlier book How Not to be Wrong， so looked forward to Shape with some anticipation。 In principle what we have here is a book about geometry - but not seen from the direction of the （dare I say it） rather boring， Euclid-based geometry textbooks some of us suffered at school。 Instead Ellenberg sets out to show how geometry underlies pretty much everything。Along the way， we are given some nice turns of phrase。 I enjoyed， for example， Ellenberg’s remark on the philosopher Thomas Hobbes， where Ellenberg remarks Hobbes was ‘a man whose confidence in his own mental powers is not fully captured by the prefix “over”’。 Whether or not what we read about here is really all geometry is a matter of labelling （as is the ‘number of holes in a straw’ question that Ellenberg entertainingly covers）。 Arguably， for example， there is some material that is probability that can be looked at in a geometric fashion， rather than geometry that produces probabilistic results - I find the probability viewpoint a lot simpler and more interesting。 In the end， despite his efforts， unless you are a mathematician， some aspects of geometry （and maths in general） feel laboured and uninteresting。 But the marvel of this book is that he does make a surprising amount of it quite the opposite。 Unfortunately， Ellenberg can go into far too much detail sometimes （which may be why the book is a bit of a doorstop at 463 pages） - for example， a story that starts with the mosquito’s random walk seems to go on and on for ever and I rather lost the will to continue， in a topic that interests me a lot more than geometry does。 In a different way， I struggled to get my head around the lengthy section on US electoral district gerrymandering which seemed only of interest to someone with in-depth enthusiasm for US politics， while some of the final meandering final chapter should certainly have been lost in the edit。I do wonder if the success of the earlier book meant this one was not given the editorial scrutiny it needed。 Although Ellenberg failed to convince me that geometry is the foundation of many of the topics he discusses， there is material to interest the reader here - and it’s certainly a far cry from those laborious proofs and QEDs。 。。。more
Mike Wagner
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Terrific book， accessible， funny， thought-provoking and informative。 This book is helping to 。。。 reshape 。。。 my thinking。
Miranda
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I am not sure you can possibly understand how high my expectations were for this book。 Jordan Ellenberg's How Not To Be Wrong is my favorite book of all time about mathematics and I have been waiting for him to write another since I read it。 I have read How Not To Be Wrong at least three times and I have badgered everyone I know into reading it。 "If you want to understand me，" I tell my friends， "you need to read this book。" Ellenberg gives people a short cut to getting a mathematician's view of I am not sure you can possibly understand how high my expectations were for this book。 Jordan Ellenberg's How Not To Be Wrong is my favorite book of all time about mathematics and I have been waiting for him to write another since I read it。 I have read How Not To Be Wrong at least three times and I have badgered everyone I know into reading it。 "If you want to understand me，" I tell my friends， "you need to read this book。" Ellenberg gives people a short cut to getting a mathematician's view of the world。 He's funny， he knows great stories。 You'll laugh， you'll gasp。 Read this book， see the world differently。 Learn。 Understand。 。。。more
Ali
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A glorious intellectual feast & mind-expanding brain workout， exuberantly presentedOnce upon a time， back in college， there was a kid who was winning not just all the awards in mathematics （and by "awards" I mean "top prizes in worldwide competition"）， but also in writing。 How can anyone be that good at both？ That kid has since been teaching math as a college professor for 20+ years， and written a new book。 Would you be interested in reading a book on math by the best combination mathematician-w A glorious intellectual feast & mind-expanding brain workout， exuberantly presentedOnce upon a time， back in college， there was a kid who was winning not just all the awards in mathematics （and by "awards" I mean "top prizes in worldwide competition"）， but also in writing。 How can anyone be that good at both？ That kid has since been teaching math as a college professor for 20+ years， and written a new book。 Would you be interested in reading a book on math by the best combination mathematician-writer I know？ I think you should， 'cause it's pretty damn good！ Note that Shape is probably not beach reading for most people。 It's the mental equivalent of a high-intensity interval training workout: challenging and rewarding。 I initially felt myself protesting when I started reading it because Jordan was actually making my brain do work。 How dare you make me think！ But gradually， I came to appreciate the magnitude of the intellectual journey he was taking us on， and merrily hopped on the train。At its core， Shape is about the underlying patterns of how the world works， and the beauty of how they connect together。 Take the shape of a tree， for example。 It underlies not just the familiar family tree and company org chart， but also decision trees that allow you to craft winning strategies in real-life games and magically effective tools like artificial intelligence。 （Also， trees。）What I appreciated most about Shape was that it forced me to dust off the intellectual cobwebs in my brain and fill holes in my incomplete education。 I didn't even realize that I only had half-assed notions of what squaring the circle， Markov chains， neural networks and eigenvalues meant — a case of the "it sounds familiar and I kind of studied it therefore I must know it" fallacy。 Now， not only do I have a much better understanding of these concepts， but I also know whence they came and how they fit into the world。That's because Ellenberg also provides the whole historical matrix of who came up with an idea， whose work motivated it in the first place， who else came up with the idea in another context， and how it's relevant today。 This makes for a strangely satisfying intellectual tapestry， a visual representation of which Ellenberg is kind enough to provide。 Other things I like about this book:• Ellenberg is not afraid of going into the historical weeds。 He leaves no stone unturned， probably digging up original programs from the 1904 St Louis World Fair， finding an obscure letter in the 1905 issue of "Nature"， and scoring an interview with Euclid himself even though he's been dead 2000 years。 He places a host of richly-drawn characters in their historical context， bringing their ideas to life: Ronald Ross， the cantankerously egotistical biostatistician; Paul Erdös， the supremely eccentric itinerant mathematician; Henri Poincaré， the math god who sparked a revolution in physics; Marion Tinsley， the nigh-invincible checkers player; Einstein， Claude Shannon， Emmy Noether， and （surprise！） geometry fanboy Abraham Lincoln。 • A sense of puckish humor permeates the book。 While reading， I registered a steady rate of 3。618 cph （chuckles per hour）， often in response to pop & literary references: Survivor， Talking Heads， and most important， Akbar and Jeff。 A skilled literary stylist， Ellenberg also threw in some well-crafted neologisms that cracked me up。 Do NOT skip the footnotes; that's where 80% of the funny lives。I will not attempt to summarize the book's content， because it is so dense with ideas as to be incompressible。 Want to learn about machine learning， epidemics， biostatistics， game theory， Google search algorithms， Heisenberg's Uncertainty Principle， neural nets， cryptography， and how they're all interconnected？ It's all in there， explained in a way that felt like encountering the ideas for the first time， usually because I was。 This is because Ellenberg is an educator at heart， and a very skilled one。 In the spirit of his prior book， How Not to Be Wrong， Shape is a paean to rigorous thinking: "The ultimate reason for teaching kids to write a proof is not that the world is full of proofs。 It’s that the world is full of non-proofs， and grown-ups need to know the difference。 It’s hard to settle for a non-proof once you’ve really familiarized yourself with the genuine article。" In a world overrun by disinformation and sloppy thinking， Shape is the antithesis: the genuine article。 It joyously （and rigorously） guides you down paths of bullshit-proof reasoning with precise language， delivering you to the Land of A-ha。 The book expanded my mind， giving me a whole new paradigm for looking at the world — think geometry， baby！ In the process， it awakened parts of my brain so dormant from disuse， I didn't even know they still existed。 Get into Shape to get your own brain in shape。 -- Ali Binazir， M。D。， M。Phil。， Happiness Engineer and author of The Tao of Dating: The Smart Woman's Guide to Being Absolutely Irresistible， the highest-rated dating book on Amazon， and Should I Go to Medical School？: An Irreverent Guide to the Pros and Cons of a Career in Medicine 。。。more
Lou
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Shape is University of Wisconsin math professor and bestselling author Ellenberg’s far-ranging exploration of the power of geometry， which turns out to help us think better about practically everything。 How should a democracy choose its representatives？ How can you stop a pandemic from sweeping the world？ How do computers learn to play Go， and why is learning Go so much easier for them than learning to read a sentence？ If you're like most people， geometry is a sterile and dimly remembered exerci Shape is University of Wisconsin math professor and bestselling author Ellenberg’s far-ranging exploration of the power of geometry， which turns out to help us think better about practically everything。 How should a democracy choose its representatives？ How can you stop a pandemic from sweeping the world？ How do computers learn to play Go， and why is learning Go so much easier for them than learning to read a sentence？ If you're like most people， geometry is a sterile and dimly remembered exercise you gladly left behind in the dust of ninth grade， along with your braces and active romantic interest in pop singers。 If you recall any of it， it's plodding through a series of miniscule steps only to prove some fact about triangles that was obvious to you in the first place。 That's not geometry。 Okay， it is geometry， but only a tiny part， which has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel。Shape reveals the geometry underneath some of the most important scientific， political， and philosophical problems we face。 Geometry asks: Where are things？ Which things are near each other？ How can you get from one thing to another thing？ Those are important questions。 The word geometry， from the Greek for measuring the world。 If anything， that's an undersell。 Geometry doesn't just measure the world--it explains it。 Shape shows us how。 It's an interesting， informative and accessible exploration of the way geometry touches our everyday lives without us giving it a second thought。 I admit， I used to not be that fond of anything relating to maths in school many moons ago， but I found this easily digestible and rather compelling to read。 Showing exactly how geometry applies to real-life situations， Ellenberg pens a fascinating book even to those of us who are rather maths-averse， which is quite the feat。 Highly recommended。 。。。more
Richard Kerver
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Was referred to this perfect diamond of a book by https://www。nytimes。com/2021/05/18/bo。。。 Was referred to this perfect diamond of a book by https://www。nytimes。com/2021/05/18/bo。。。 。。。more
Jeff
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Love Song To Geometry - And A Look At How It Is Truly Everywhere。 This is a mathematician showing just how prevalent geometry is in our every day lives - and why modern math classes tend to ruin it for most people。 As a mathematics oriented person myself （got one math-derived degree， very nearly got two others almost at the same time， former math teacher， current active software developer）， this was fairly easy to follow - Ellenberg mentions some advanced concepts without actually *showing* many Love Song To Geometry - And A Look At How It Is Truly Everywhere。 This is a mathematician showing just how prevalent geometry is in our every day lives - and why modern math classes tend to ruin it for most people。 As a mathematics oriented person myself （got one math-derived degree， very nearly got two others almost at the same time， former math teacher， current active software developer）， this was fairly easy to follow - Ellenberg mentions some advanced concepts without actually *showing* many of them， though there *is* more actual equations in here than some might like in a "popsci" level book。 Thanks to Ellenberg's explanations of said equations and concepts， this *should* be an easy enough follow for most anyone。 And he really does do a great job of showing how even advanced ideas really do come down to the most basic principles - just applied in particularly interesting ways。 Indeed， the only real critique I have here is that when Ellenberg gets off the math specifically and into more political and social commentary - even when ostensbily using the math as a shield - it gets much closer to "Your Mileage May Vary" level。 Overall， those moments weren't quite pervasive enough nor did they stray far enough from the central premise to warrant dropping a star， and thus the book maintains the full five stars that all books start with for me。 Very much recommended。 。。。more
Natalia
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