What do you think?
Rate this book
Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace
The British edition. Through Euclid's Window, Leonard Mlondinow brilliantly and delightfully leads us on a journey through five revolutions in geometry, from the Greek concept of parallel lines to the latest notions of hyperspace. This new, refreshing, alternative history of maths reveals how simple questions anyone might ask about space in the living room or in some other galaxy have been the hidden engine of science's highest achievements.
322 pages, Kindle Edition
First published January 1, 2001
195 people are currently reading
3639 people want to read
About the author
Leonard Mlodinow
29 books1,184 followersLeonard Mlodinow is an American theoretical physicist and mathematician, screenwriter and author. In physics, he is known for his work on the large N expansion, a method of approximating the spectrum of atoms based on the consideration of an infinite-dimensional version of the problem, and for his work on the quantum theory of light inside dielectrics.
He has also written books for the general public, five of which have been New York Times best-sellers, including The Drunkard's Walk: How Randomness Rules Our Lives, which was chosen as a New York Times notable book, and short-listed for the Royal Society Science Book Prize; The Grand Design, co-authored with Stephen Hawking, which argues that invoking God is not necessary to explain the origins of the universe; War of the Worldviews, co-authored with Deepak Chopra; and Subliminal: How Your Unconscious Mind Rules Your Behavior, which won the 2013 PEN/E. O. Wilson Literary Science Writing Award. He also makes public lectures and media appearances on programs including Morning Joe and Through the Wormhole, and debated Deepak Chopra on ABC's Nightline.
He has also written books for the general public, five of which have been New York Times best-sellers, including The Drunkard's Walk: How Randomness Rules Our Lives, which was chosen as a New York Times notable book, and short-listed for the Royal Society Science Book Prize; The Grand Design, co-authored with Stephen Hawking, which argues that invoking God is not necessary to explain the origins of the universe; War of the Worldviews, co-authored with Deepak Chopra; and Subliminal: How Your Unconscious Mind Rules Your Behavior, which won the 2013 PEN/E. O. Wilson Literary Science Writing Award. He also makes public lectures and media appearances on programs including Morning Joe and Through the Wormhole, and debated Deepak Chopra on ABC's Nightline.
Ratings & Reviews
Friends & Following
Create a free account to discover what your friends think of this book!
Community Reviews
Displaying 1 - 30 of 194 reviews
July 16, 2009
I’ve done what I never do – before starting this review I’ve read some of the other reviews on this site. I’m quite surprised at the negative reviews this book has received. Someone has even complained that this is quite an ‘anti-Christian’ book. I guess this is because the author was clearly less than impressed with the ‘Dark Ages’ which he introduces by discussing Hypatia. So, yes, I can understand why that might annoy a Christian. But this would be like a Marxist complaining when people mention Czechoslovakia in 1968 or Stalin’s purges. Complaining that people point at the bones in the cupboard hardly makes those bones disappear.
Another says that it is an odd book because it is a book on geometry and yet it has virtually no diagrams. Again, I can see why this would seem odd, but I thought the writing was so clear and so engaging that the somewhat surprising lack of diagrams hardly seemed to matter.
Others complained about the humour – and yes, I can also understand this. But compared to the ‘humour’ I’ve read in other pop-science books, this guy is Douglas Adams. I mean, The God Particle If the Universe Is the Answer, What Is the Question? was considered a funny book according to the blurb… God, save us…
I’m going to tell you why I really liked this book.
The thing that I liked most about it was that it started by saying that many people really have negative memories of high school geometry and the author thinks that this is a real pity. His point in writing the book is to explain why geometry is interesting and what is its place in science and mathematics. This is why the criticism about the lack of diagrams somewhat misses the point – this book isn’t really seeking to teach geometry, but to inspire readers to go back and learn more about geometry themselves.
Basically, this is not only a history of geometry, but also a history of our understanding of space itself. It starts in the ancient world with Egyptians and Babylonians marking out the ground, building pyramids and calculating approximations for Pi. It ends with a discussion of string theory and the possible multi-dimensional space that is predicted in that. He takes us on this grand tour in a light-hearted and easy to follow narrative. You literally do not need to even remember any of your high school geometry to enjoy this book. It fits into that class of books, like The Pearly Gates of Cyberspace A History of Space from Dante to the Internet or Fermat's Enigma The Epic Quest to Solve the World's Greatest Mathematical Problem that take quite difficult scientific and mathematical ideas and presents them in a way a general audience will understand.
This also did something else I love – it gave lots of background to the lives of many of the scientists and mathematicians mentioned. I thought this was a wonderful introduction to the history of the development of geometry and one that provided simple to understand summaries of the main ‘questions’ in the development of geometry. Here is a guy who understands that science progresses with questions, rather than answers. For instance, the discussion of the question of whether there is a law of parallel lines and if so is it possible to state this law in a way that is not circular – was simply phrased and the many ‘attempts’ to solve this problem given in the history of the subject was done with both humour and intelligence.
This book is worthwhile just for the information on the lives of Gauss and Riemann. Parts of this book, particularly the chapter on Gauss’ life, would almost make you weep. There is a beautiful and beautifully simple explanation of non-Euclidian geometry and why these ‘spaces’ became necessary – and also how Einstein used these ideas in his General Theory of Relativity.
Naturally, the section on string theory is the hardest part of the book – I had hoped to be able to report that the author’s exceptional skills at presenting complex ideas in beautifully simple prose would extend to this most complex of ideas, but that was far too much to hope for.
This was still a wonderful introduction to geometry and one that does more than make you think about triangles and such things – but that really helps non-specialists (and even those with virtually no knowledge of the subject at all) get an idea of just why having a means of describe space is so important not just in mathematics and science, but in philosophy as well.
This book also has some lovely throwaway lines on science that I really enjoyed and which can’t be said too often. For example, at one point he says that Occam’s Razor (the idea that a theory should try to use as few ‘bits’ as it can get away with to explain what it is trying to explain) is referred to as science’s chief aesthetic principle – isn’t that lovely? The other thing I liked was at the end when he asked (in reference to String Theory) if science was about pointing a searchlight at the world to discover its ‘truths’ or if it was about building a tower with as many blocks as possible to see if it will stand or fall. The conclusion he seems to draw is that it is a bit of both.
So, will you come away from this book being able to solve complex geometrical problems? Well, no. Will you come away from this book amused and with a much better understanding of the role played by geometry in the history and development of science? Absolutely. If you are after the first you might want to find another book, otherwise, this really is worth a read.
Another says that it is an odd book because it is a book on geometry and yet it has virtually no diagrams. Again, I can see why this would seem odd, but I thought the writing was so clear and so engaging that the somewhat surprising lack of diagrams hardly seemed to matter.
Others complained about the humour – and yes, I can also understand this. But compared to the ‘humour’ I’ve read in other pop-science books, this guy is Douglas Adams. I mean, The God Particle If the Universe Is the Answer, What Is the Question? was considered a funny book according to the blurb… God, save us…
I’m going to tell you why I really liked this book.
The thing that I liked most about it was that it started by saying that many people really have negative memories of high school geometry and the author thinks that this is a real pity. His point in writing the book is to explain why geometry is interesting and what is its place in science and mathematics. This is why the criticism about the lack of diagrams somewhat misses the point – this book isn’t really seeking to teach geometry, but to inspire readers to go back and learn more about geometry themselves.
Basically, this is not only a history of geometry, but also a history of our understanding of space itself. It starts in the ancient world with Egyptians and Babylonians marking out the ground, building pyramids and calculating approximations for Pi. It ends with a discussion of string theory and the possible multi-dimensional space that is predicted in that. He takes us on this grand tour in a light-hearted and easy to follow narrative. You literally do not need to even remember any of your high school geometry to enjoy this book. It fits into that class of books, like The Pearly Gates of Cyberspace A History of Space from Dante to the Internet or Fermat's Enigma The Epic Quest to Solve the World's Greatest Mathematical Problem that take quite difficult scientific and mathematical ideas and presents them in a way a general audience will understand.
This also did something else I love – it gave lots of background to the lives of many of the scientists and mathematicians mentioned. I thought this was a wonderful introduction to the history of the development of geometry and one that provided simple to understand summaries of the main ‘questions’ in the development of geometry. Here is a guy who understands that science progresses with questions, rather than answers. For instance, the discussion of the question of whether there is a law of parallel lines and if so is it possible to state this law in a way that is not circular – was simply phrased and the many ‘attempts’ to solve this problem given in the history of the subject was done with both humour and intelligence.
This book is worthwhile just for the information on the lives of Gauss and Riemann. Parts of this book, particularly the chapter on Gauss’ life, would almost make you weep. There is a beautiful and beautifully simple explanation of non-Euclidian geometry and why these ‘spaces’ became necessary – and also how Einstein used these ideas in his General Theory of Relativity.
Naturally, the section on string theory is the hardest part of the book – I had hoped to be able to report that the author’s exceptional skills at presenting complex ideas in beautifully simple prose would extend to this most complex of ideas, but that was far too much to hope for.
This was still a wonderful introduction to geometry and one that does more than make you think about triangles and such things – but that really helps non-specialists (and even those with virtually no knowledge of the subject at all) get an idea of just why having a means of describe space is so important not just in mathematics and science, but in philosophy as well.
This book also has some lovely throwaway lines on science that I really enjoyed and which can’t be said too often. For example, at one point he says that Occam’s Razor (the idea that a theory should try to use as few ‘bits’ as it can get away with to explain what it is trying to explain) is referred to as science’s chief aesthetic principle – isn’t that lovely? The other thing I liked was at the end when he asked (in reference to String Theory) if science was about pointing a searchlight at the world to discover its ‘truths’ or if it was about building a tower with as many blocks as possible to see if it will stand or fall. The conclusion he seems to draw is that it is a bit of both.
So, will you come away from this book being able to solve complex geometrical problems? Well, no. Will you come away from this book amused and with a much better understanding of the role played by geometry in the history and development of science? Absolutely. If you are after the first you might want to find another book, otherwise, this really is worth a read.
July 1, 2014
Well, I loved this book (reading it as a layman who knows very little about geometry, physics and mathematics in general!)
It broadened my horizons - I want to read books about physics now. I want to read about Feynman and Gauss and string theory.
I loved how the author interwove other parts of history with the discoveries in geometry. I appreciated the way in which he explained complex mathematical concepts in an almost anecdotal style.
I noticed how when describing theoretically what a physicist might notice or discover at different times he switched between sayng 'he' and 'she'.
The last few chapters on string theory lost me almost completely and blew my mind. I swear, it's taken me 5 months to read this book on and off. I'd read for 10 seconds, then gaze off into space for 10 minutes thinking about what I'd just read.
I can't comment on accuracies or anything like that, but I have a base understanding and enthusiasm to build on now. Who would ever have thought that a book on geometry could open up so many doors of thought and stimulation for someone once mostly indifferent to the ideas and studies within its pages?
That's deserving of 5 stars from me.
It broadened my horizons - I want to read books about physics now. I want to read about Feynman and Gauss and string theory.
I loved how the author interwove other parts of history with the discoveries in geometry. I appreciated the way in which he explained complex mathematical concepts in an almost anecdotal style.
I noticed how when describing theoretically what a physicist might notice or discover at different times he switched between sayng 'he' and 'she'.
The last few chapters on string theory lost me almost completely and blew my mind. I swear, it's taken me 5 months to read this book on and off. I'd read for 10 seconds, then gaze off into space for 10 minutes thinking about what I'd just read.
I can't comment on accuracies or anything like that, but I have a base understanding and enthusiasm to build on now. Who would ever have thought that a book on geometry could open up so many doors of thought and stimulation for someone once mostly indifferent to the ideas and studies within its pages?
That's deserving of 5 stars from me.
March 5, 2012
Euclid's Window is an unremarkable tour of a very specific line of reasoning that is neither refreshing nor fleshed out. The narrative is supposed to span the progress of ideas coming from the advent of space as a notion to modern multidimensional brane theory but the path drawn by the author is not clear.
Writing - The writing itself is fine. The prose is concise, the jokes are acceptable, and the anecdotes are quaint. Definitions are usually good with periodic reminders.
Organization - Strictly chronological. There is little tying back of concepts to their origin as well as indicating where an idea will go except for a rapid change back and forth regarding events at the turn of the previous century. It is not obvious why a given topic is include or why others excluded.
Breadth - This is where the book falls flat. Whole tracts of geometry are excluded liked most of Islamic math, Vedic math, and large bits of contemporary geometry. Embedding, manifolds, and compacting are very briefly mentioned.
Writing - The writing itself is fine. The prose is concise, the jokes are acceptable, and the anecdotes are quaint. Definitions are usually good with periodic reminders.
Organization - Strictly chronological. There is little tying back of concepts to their origin as well as indicating where an idea will go except for a rapid change back and forth regarding events at the turn of the previous century. It is not obvious why a given topic is include or why others excluded.
Breadth - This is where the book falls flat. Whole tracts of geometry are excluded liked most of Islamic math, Vedic math, and large bits of contemporary geometry. Embedding, manifolds, and compacting are very briefly mentioned.
September 1, 2015
Још мало популарне науке. Еуклидов прозор се, као и већина научнопопуларних књига, бави модерним теоријама које би требало да представљају пут ка Теорији свега, при чему се наравно на првом мјесту налази фамозна теорија струна. Разлика је (ваљда!) у томе што се овде много више пажње посвећује геометрији из које све то проистиче, како еуклидској, тако и нееуклидској. Нажалост, Леонард Млодинов је кобила, тако да оно што је у теорији могло да представља предивно читање добија једва пролазну оцјену и то чисто због тематике која је инхерентно фасцинантна.
Прва ствар: Леонард Млодинов је атеиста, што је наравно лијепо и немам проблем с тим. Међутим, имам проблем с тим да неко нон-стоп сервира своја религијска увјерења (па макар она била и атеистичка) у књизи која нема (или бар не би требало да има) никакве везе с религијом. Нормално, ако читам рецимо Крај вјере Сема Хериса или нешто слично, читам управо зато да видим која замјерке аутор има на коју религију. Али кад читам књигу о Еуклиду и Ајнштајну, онда очекујем причу о Еуклиду и Ајнштајну, а не о томе како је грозно хришћанство увалило свијет у мрачно доба хиљаду година и како бисмо, само да тога није било, већ одавно колонизовали обод познатог свемира и живјели по три хиљаде година захваљујући нанотехнологији и побољшаној репликацији ћелија. Наравно, "хришћанска руља" је та која је растргала Хипатију и спалила александријску библиотеку (иако је ово посљедње најблаже речено дискутабилно). Сад, за Хипатију не кажем да то није тачно, међутим чак и кад говорите истину, начин на који је говорите може много да открије. Претпостављам да Млодинову, као америчком Јевреју чији су родитељи преживјели Холокауст, не би било право да неко почне да прича о "јеврејској руљи" која је крива за Исусову смрт, или о "америчкој руљи" која је истријебила Индијанце. А, Млодинове? Поред овога, ту је маса извитоперености и тенденциозности у биографијама научника које спомиње (првенствено кад је ријеч о Декарту), али тога стварно има превише да овде све редом наводим, па вас упућујем да за много ширу и објективнију слику прочитате и књигу Мен оф Матхематицс аутора Е.Т. Бела, која је очигледно и овде кориштена као један од извора.
Друга ствар: Млодинов је заправо мрзитељ Еуклидове геометрије (!). Помало необично од некога ко је књигу назвао Еуклидов прозор, али тако испада. Не пропушта ниједну прилику да спомене како је та геометрија превазиђена, нетачна, непрецизна, како не описује простор (замало да напишем "прозор") како треба, итд. итд. итд. Човјек влажи гаће на хиперболичку и сферну геометрију, што је лијепо и сигуран сам да му је донијело много поентирања на забавама, али то није објективна слика стања ствари. То што ми не можемо да повучемо праву линију по површини Земље није кривица праве линије него површине Земље. Исто и за зрак свјетлости, који се савија под утицајем гравитације или неког сличног чуда. Јел му Еуклид крив што се савија? На оптужбе против Еуклида ја одговарам једноставно: Зрак свјетлости, ако се савија, није права линија. И носите се. Даље, аутор ове књиге у свом типичном неразумијевању даје себи за право да критикује Еуклидове дефиниције појмова који се данас сматрају за основне, па каже нпр. да је дефиниција тачке (која гласи: "Тачка је оно што нема дијелове"), пазите добро, "на рубу бесмислице" (!!!!!?!?!??!). Да је то рекао пред мојим покојним професором геометрије Стевановићем, добио би такву шљагу да би се три дана окретао око своје осе. Ова дефиниција не само да није "на рубу бесмислице", већ је напросто генијална, бриљантно феноменална за вријеме у коме ј�� настала. Проблем није у ономе што садржи (осим тог незгодног појма "оно"), већ у томе што би се могла назвати малчице некомплетном (ништа такође нема дијелове, тако да је само некако требало разликовати тачку и ништа).
Четврта ствар: Комплетне заслуге за развој нееуклидске геометрије Млодинов приписује Гаусу и нешто мало Риману. Да ми је неко рекао да ћу читати књигу у којој нееуклидска геометрија игра главну улогу, а да се Јанош Бољај и Николај Лобачевски спомињу укупно у три реченице, од којих је једна потрошена да се Лобачевски назове ПЛАГИЈАТОРОМ (!?!?!?!?!?!?!?!?), рекао бих му да је луд и да није нормалан. Међутим, то је управо случај са овом књигом. Не знам како би мој покојни професор Стевановић реаговао на ово, али имајући у виду да смо ми унутар геометрије радили нешто што се звало "геометрија Лобачевског", сигуран сам да не би баш благонаклоно гледао на овакво хуљење. Наравно, свака част Гаусу за све што је урадио, али негирати заслуге великих математичара само зато што је неко идиот (при чему мислим на аутора ове књиге, а не на Лобачевског), то стварно није лијепо.
Пета ствар: Ово је врло ситна замјерка, а можда заправо и није. Опште је познато да у научнопопуларним књигама морате да имате мноштво примјера којима ћете тешке појмове приближити просјечно образованом читаоцу. Од одабира тих примјера практично зависи имате ли успјешну књигу или не. Не улазећи сад у саму суштину примјера (о томе нешто касније, кад завршим са закерањем), морам да споменем да се они скоро сви одликују једном прилично бизарном особином. Наиме, Млодинов има два сина под називима Алексеј и Николај и они фигуришу у скоро свим примјерима у књизи (!). Већ на самом почетку имамо правоугли троугао, у коме је хипотенуза названа Хипотенуза (не зезам се), а катете - Алексеј и Николај. Онда, мало послије тога, нека жена шаље неке своје минионе да измјере неке удаљености - миниони су наравно Алексеј и Николај. Нешто касније, илустрација релативности кретања, у возу се налазе, погодили сте, Алексеј и Николај. Једном је океј, можда чак и двапут, али кад имате десет или петнаест оваквих примјера, онда се већ запитате за ментално здравље књигописца. Тек пред сами крај књиге удостојио се да умјесто својих синова спомене Ајнштајновог. Не знам из ког разлога.
На крају баладе, поставља се питање има ли у овој књизи ишта вриједно? Ако сте атеиста и бесмислице о хришћанству вас не нервирају, можете комотно да додате пола бода или бод на горњу оцјену. Прича је интересантна, питка, примјери углавном успјешни и сликовити (ако можете да сварите Алексеја и Николаја, што постаје све теже како се приближавате крају књиге), а био бих врло непоштен ако не бих рекао да ништа нисам сазнао из књиге. На примјер, до сада сам имао потпуно погрешно разумијевање ентропије, које је сада исправљено. Онда, сазнао сам зашто је у једној од првобитних варијанти теорије струна било неопходно да простор има двадесет шест димензија. И има још неких ситница, углавном везаних за физику. Док математички дио оставља доста простора за поправку, на онај са физиком немам замјерки, можда зато што немам појма о физици.
Закључак: Да ли читати ову књигу? Препоручујем да је прочитате, али све информације, како о математици, тако и о биографијама научника који се спомињу, морате да узмете са зрном соли, а понегдје и са паковањем од пола киле. То наравно ако књигу планирате да искористите исправно, односно за оно за шта популарна наука иначе и служи - дакле да вам прошири видике на неке ствари о којима мало знате и да вас упути на дубљу и стручнију литературу ако вас та тематика занима. Аутор нажалост не наводи ту литературу, али што се тиче биографија незаобилазно штиво би требало да вам буде књига Мен оф Матхематицс (аутор: Е.Т. Белл), која је и Млодинову послужила као извор (нарочито у поглављу о Гаусу, гдје је позајмљивао шаком и капом). За физику нисам стручан, али сигурно не можете погријешити са радовима самих научника поменутих у књизи. То је то. Популарна наука НЕЋЕ вас направити стручњаком нити вас учинити паметнијима, мада може да вам донесе популарност на забавама, а ако сте Атеиста Србије, онда можете и да је користите као обрачун са неистомишљеницима, као неки лик што је прије неки дан рекао да су фанатични хришћани спалили александријску библиотеку, а кад сам га питао за извор, упутио ме на Космос Карла Сагана. Тру стори.
Прва ствар: Леонард Млодинов је атеиста, што је наравно лијепо и немам проблем с тим. Међутим, имам проблем с тим да неко нон-стоп сервира своја религијска увјерења (па макар она била и атеистичка) у књизи која нема (или бар не би требало да има) никакве везе с религијом. Нормално, ако читам рецимо Крај вјере Сема Хериса или нешто слично, читам управо зато да видим која замјерке аутор има на коју религију. Али кад читам књигу о Еуклиду и Ајнштајну, онда очекујем причу о Еуклиду и Ајнштајну, а не о томе како је грозно хришћанство увалило свијет у мрачно доба хиљаду година и како бисмо, само да тога није било, већ одавно колонизовали обод познатог свемира и живјели по три хиљаде година захваљујући нанотехнологији и побољшаној репликацији ћелија. Наравно, "хришћанска руља" је та која је растргала Хипатију и спалила александријску библиотеку (иако је ово посљедње најблаже речено дискутабилно). Сад, за Хипатију не кажем да то није тачно, међутим чак и кад говорите истину, начин на који је говорите може много да открије. Претпостављам да Млодинову, као америчком Јевреју чији су родитељи преживјели Холокауст, не би било право да неко почне да прича о "јеврејској руљи" која је крива за Исусову смрт, или о "америчкој руљи" која је истријебила Индијанце. А, Млодинове? Поред овога, ту је маса извитоперености и тенденциозности у биографијама научника које спомиње (првенствено кад је ријеч о Декарту), али тога стварно има превише да овде све редом наводим, па вас упућујем да за много ширу и објективнију слику прочитате и књигу Мен оф Матхематицс аутора Е.Т. Бела, која је очигледно и овде кориштена као један од извора.
Друга ствар: Млодинов је заправо мрзитељ Еуклидове геометрије (!). Помало необично од некога ко је књигу назвао Еуклидов прозор, али тако испада. Не пропушта ниједну прилику да спомене како је та геометрија превазиђена, нетачна, непрецизна, како не описује простор (замало да напишем "прозор") како треба, итд. итд. итд. Човјек влажи гаће на хиперболичку и сферну геометрију, што је лијепо и сигуран сам да му је донијело много поентирања на забавама, али то није објективна слика стања ствари. То што ми не можемо да повучемо праву линију по површини Земље није кривица праве линије него површине Земље. Исто и за зрак свјетлости, који се савија под утицајем гравитације или неког сличног чуда. Јел му Еуклид крив што се савија? На оптужбе против Еуклида ја одговарам једноставно: Зрак свјетлости, ако се савија, није права линија. И носите се. Даље, аутор ове књиге у свом типичном неразумијевању даје себи за право да критикује Еуклидове дефиниције појмова који се данас сматрају за основне, па каже нпр. да је дефиниција тачке (која гласи: "Тачка је оно што нема дијелове"), пазите добро, "на рубу бесмислице" (!!!!!?!?!??!). Да је то рекао пред мојим покојним професором геометрије Стевановићем, добио би такву шљагу да би се три дана окретао око своје осе. Ова дефиниција не само да није "на рубу бесмислице", већ је напросто генијална, бриљантно феноменална за вријеме у коме ј�� настала. Проблем није у ономе што садржи (осим тог незгодног појма "оно"), већ у томе што би се могла назвати малчице некомплетном (ништа такође нема дијелове, тако да је само некако требало разликовати тачку и ништа).
Четврта ствар: Комплетне заслуге за развој нееуклидске геометрије Млодинов приписује Гаусу и нешто мало Риману. Да ми је неко рекао да ћу читати књигу у којој нееуклидска геометрија игра главну улогу, а да се Јанош Бољај и Николај Лобачевски спомињу укупно у три реченице, од којих је једна потрошена да се Лобачевски назове ПЛАГИЈАТОРОМ (!?!?!?!?!?!?!?!?), рекао бих му да је луд и да није нормалан. Међутим, то је управо случај са овом књигом. Не знам како би мој покојни професор Стевановић реаговао на ово, али имајући у виду да смо ми унутар геометрије радили нешто што се звало "геометрија Лобачевског", сигуран сам да не би баш благонаклоно гледао на овакво хуљење. Наравно, свака част Гаусу за све што је урадио, али негирати заслуге великих математичара само зато што је неко идиот (при чему мислим на аутора ове књиге, а не на Лобачевског), то стварно није лијепо.
Пета ствар: Ово је врло ситна замјерка, а можда заправо и није. Опште је познато да у научнопопуларним књигама морате да имате мноштво примјера којима ћете тешке појмове приближити просјечно образованом читаоцу. Од одабира тих примјера практично зависи имате ли успјешну књигу или не. Не улазећи сад у саму суштину примјера (о томе нешто касније, кад завршим са закерањем), морам да споменем да се они скоро сви одликују једном прилично бизарном особином. Наиме, Млодинов има два сина под називима Алексеј и Николај и они фигуришу у скоро свим примјерима у књизи (!). Већ на самом почетку имамо правоугли троугао, у коме је хипотенуза названа Хипотенуза (не зезам се), а катете - Алексеј и Николај. Онда, мало послије тога, нека жена шаље неке своје минионе да измјере неке удаљености - миниони су наравно Алексеј и Николај. Нешто касније, илустрација релативности кретања, у возу се налазе, погодили сте, Алексеј и Николај. Једном је океј, можда чак и двапут, али кад имате десет или петнаест оваквих примјера, онда се већ запитате за ментално здравље књигописца. Тек пред сами крај књиге удостојио се да умјесто својих синова спомене Ајнштајновог. Не знам из ког разлога.
На крају баладе, поставља се питање има ли у овој књизи ишта вриједно? Ако сте атеиста и бесмислице о хришћанству вас не нервирају, можете комотно да додате пола бода или бод на горњу оцјену. Прича је интересантна, питка, примјери углавном успјешни и сликовити (ако можете да сварите Алексеја и Николаја, што постаје све теже како се приближавате крају књиге), а био бих врло непоштен ако не бих рекао да ништа нисам сазнао из књиге. На примјер, до сада сам имао потпуно погрешно разумијевање ентропије, које је сада исправљено. Онда, сазнао сам зашто је у једној од првобитних варијанти теорије струна било неопходно да простор има двадесет шест димензија. И има још неких ситница, углавном везаних за физику. Док математички дио оставља доста простора за поправку, на онај са физиком немам замјерки, можда зато што немам појма о физици.
Закључак: Да ли читати ову књигу? Препоручујем да је прочитате, али све информације, како о математици, тако и о биографијама научника који се спомињу, морате да узмете са зрном соли, а понегдје и са паковањем од пола киле. То наравно ако књигу планирате да искористите исправно, односно за оно за шта популарна наука иначе и служи - дакле да вам прошири видике на неке ствари о којима мало знате и да вас упути на дубљу и стручнију литературу ако вас та тематика занима. Аутор нажалост не наводи ту литературу, али што се тиче биографија незаобилазно штиво би требало да вам буде књига Мен оф Матхематицс (аутор: Е.Т. Белл), која је и Млодинову послужила као извор (нарочито у поглављу о Гаусу, гдје је позајмљивао шаком и капом). За физику нисам стручан, али сигурно не можете погријешити са радовима самих научника поменутих у књизи. То је то. Популарна наука НЕЋЕ вас направити стручњаком нити вас учинити паметнијима, мада може да вам донесе популарност на забавама, а ако сте Атеиста Србије, онда можете и да је користите као обрачун са неистомишљеницима, као неки лик што је прије неки дан рекао да су фанатични хришћани спалили александријску библиотеку, а кад сам га питао за извор, упутио ме на Космос Карла Сагана. Тру стори.
July 31, 2012
History of math more than actualfacts math, with a minimally annoying authorial voice as these things go. Except for the teeny weeny culture/race centrism problem – I’m neither a historian nor a mathematician, but even I know it’s pretty freaking suspect when your history doesn’t include the advancements of, um, the Arab world, the South/Central American empires, or, you know, Asia, except for that one paragraph that one time. I mean, write a history of European geometry, by all means, I did like it, but let’s maybe call it that next time so as to look less like clueless Eurocentric twits, yeah?
Anyway. Last third of the book swung into modern physics, and convinced me yet again that in the absence of advanced math, it really does sound like these guys are just making shit up. I mean, vibrating strings? Oh rilly. Shame I stopped at calculus, because no matter how many metaphors you throw at me, I still have a hard time taking this stuff seriously without the fundamental grocking I don’t have the tools for.
Anyway. Last third of the book swung into modern physics, and convinced me yet again that in the absence of advanced math, it really does sound like these guys are just making shit up. I mean, vibrating strings? Oh rilly. Shame I stopped at calculus, because no matter how many metaphors you throw at me, I still have a hard time taking this stuff seriously without the fundamental grocking I don’t have the tools for.
March 25, 2014
Firstly, a disclaimer: as the author was a writer for "Star Trek: The Next Generation" (which I totally loved), I am naturally inclined to give a favourable review to whatever he writes :).
Back to the book: basically, this book is a history of our understanding of the structure of space (dimensions, curvature etc., in other words its "geometric" properties) starting from the Ancients (usual culprits, Pythagoras and Euclid) up to the latest scientific developments.
This book provides beautifully simple explanations of non-Euclidian geometries and how they have been used in Relativity and subsequent physical theories. His lucid and clear explanation of how the mass/energy distribution relates to the metric of four-dimensional space-time is really nice. The section on string theory is also a great pleasure to read, and equally explained in a very nice manner. His explanation of how in string theory the most basic properties of space (such as the number of dimensions) determine the laws of nature and the properties of matter/energy is outstanding.
And his enthusiasm for science and understanding of the Universe is totally contagious (the short epilogue is beautiful), and I am very happy that I had the opportunity to read this book.
The author's sense of humour is also quite good (but, being myself a bit of a nerd, I am probably not greatly qualified to judge other people's sense of humour), and this makes the reading of this book even more pleasurable.
The only (small) sin of this book is in the naïve and outdated treatment of the so-called "Dark Ages" - here the author really should have received advice from a real historian.
But, apart from this small sin, this book is an absolute pleasure to read. 5 stars.
Back to the book: basically, this book is a history of our understanding of the structure of space (dimensions, curvature etc., in other words its "geometric" properties) starting from the Ancients (usual culprits, Pythagoras and Euclid) up to the latest scientific developments.
This book provides beautifully simple explanations of non-Euclidian geometries and how they have been used in Relativity and subsequent physical theories. His lucid and clear explanation of how the mass/energy distribution relates to the metric of four-dimensional space-time is really nice. The section on string theory is also a great pleasure to read, and equally explained in a very nice manner. His explanation of how in string theory the most basic properties of space (such as the number of dimensions) determine the laws of nature and the properties of matter/energy is outstanding.
And his enthusiasm for science and understanding of the Universe is totally contagious (the short epilogue is beautiful), and I am very happy that I had the opportunity to read this book.
The author's sense of humour is also quite good (but, being myself a bit of a nerd, I am probably not greatly qualified to judge other people's sense of humour), and this makes the reading of this book even more pleasurable.
The only (small) sin of this book is in the naïve and outdated treatment of the so-called "Dark Ages" - here the author really should have received advice from a real historian.
But, apart from this small sin, this book is an absolute pleasure to read. 5 stars.
April 7, 2011
Interesting discussion of history of geometry from the time of the ancient Greeks through geometry's role today in String Theory and M-Theory. It covers what it considers to be the major events of the history of geometry, starting with Euclid's organizing Greek knowledge of geometry into the Elements, Descartes bringing the coordinate system to geometry, Gauss and Riemann moving geometry beyond Euclidean space, Einstein with his theory of relativity, and finally Ed Witten and his contributions to String and M-Theory. I felt like the book might have been a little rushed at the end, but that is probably because String theory and M-theory are both still young and in the process of being developed.
August 7, 2015
Ich kann nicht behaupten, alles in diesem Buch verstanden zu haben. Gerade die letzten 100 Seiten über Relativitäts- und Stringtheorie wurden zusehends unverständlich, teils auch, weil die Forschung auf letzterem Gebiet in vollem Gange ist und die Experten selbst noch nicht wissen, was Sache ist.
Aber allein die ersten 150 Seiten waren für mich ein ganz neuer Blick auf ein Feld, das mich nie interessiert hat. Mlodinow schreibt äußerst unterhaltsam und liefert viele Einblicke in kulturelle und gesellschaftliche Entwicklungen und wie sie mitverantwortlich für mathematische Entdeckungen oder einen Stillstand in der Forschung sind.
Das Buch ist aufgeteilt in Kapitel über Euklid, Descartes, Gauß, Einstien und Witten und erzählt so von den zunehmend komplexen Theorien über Raum und später auch Zeit.
Faszinierend und unterhaltsam. Würde ich auch jedem Schüler empfehlen. Die Lehrer erzählen nämlich nur den langweiligen Kram: Warum kann Schule nicht ein wenig mehr wie dieses Buch sein?
Die deutsche Übersetzung "Das Fenster zum Universum" ist übrigens sehr frei übersetzt. Da wurde umgestellt, gestrichen und hinzu erfunden. Und weniger pointiert ist es auch noch. Also empfehle ich jedem, der flüssig Englisch versteht, das Original.
Aber allein die ersten 150 Seiten waren für mich ein ganz neuer Blick auf ein Feld, das mich nie interessiert hat. Mlodinow schreibt äußerst unterhaltsam und liefert viele Einblicke in kulturelle und gesellschaftliche Entwicklungen und wie sie mitverantwortlich für mathematische Entdeckungen oder einen Stillstand in der Forschung sind.
Das Buch ist aufgeteilt in Kapitel über Euklid, Descartes, Gauß, Einstien und Witten und erzählt so von den zunehmend komplexen Theorien über Raum und später auch Zeit.
Faszinierend und unterhaltsam. Würde ich auch jedem Schüler empfehlen. Die Lehrer erzählen nämlich nur den langweiligen Kram: Warum kann Schule nicht ein wenig mehr wie dieses Buch sein?
Die deutsche Übersetzung "Das Fenster zum Universum" ist übrigens sehr frei übersetzt. Da wurde umgestellt, gestrichen und hinzu erfunden. Und weniger pointiert ist es auch noch. Also empfehle ich jedem, der flüssig Englisch versteht, das Original.
December 27, 2011
Book was great from the beginning with small stories that engage and keep you interested. When the book goes further on it takes too much time to describe Einstein and String Theory and moves too slowly. Half the book is the history of geometry, the other half is Einstein. It turned me off at the end.
January 16, 2009
An extremely poor approach to the historical development of mathematics. The book is replete with historical inaccuracies and a clear anti-Christian bias throughout. Try Kline's "Mathematics for the Nonmathematician" instead.
April 11, 2016
In passing, Mr Moldinow mentioned the art perfected by schools and colleges in presenting Geometry as one of the most boring subjects. And also how he is going to change that view for his readers. That too with the help of minimal number of diagrams. Before I start, let me say that I belong to the same category of people who have been bored with Geometry. And so, when I read this passage, where he promises to show how interesting a subject Geometry is, I was naturally very excited. Even though I am not a big fan of Geometry, elementary and high school Maths was always my go to subject. When I fared poorly in other subjects, I could point at Maths and be contended.
And my modest proficiency in elementary and high school maths helped me rush through the first few chapters. The details on how Greeks were the forefathers who laid the cornerstone for Maths and about various day to day activities for which they employed Maths. Then he talks about the great Pythagoras and other well known Greek mathematicians. The way he explained Pythagoras theorem in words were commendable. It awed me when I found that this was the way how Pythagoras came up with the all famous equation. I felt some sort of electricity passing through me when I realized that I was made to think the same way Pythagoras did albeit he did it a couple hundred decades back. At times, the book gave the vibe of the ever famous book Cosmos by Carl Sagan. There were even same incidents mentioned in both the books.
Till now all was well. Then came the Euclidean theory. The author pens down his postulates and starts explaining it one by one. I could stay up with him till then. Then he starts talking about other mathematicians who later found flaws in these same postulates. Some are easy to understand while the rest make up for this easiness by making it much more difficult to comprehend. I was left open mouthed not knowing what was going around. I thought this would get better. But it went from worse to a complete train wreck. Author started explaining the high end stuff in mere words and I was completely bamboozled. He went from one mathematician to another (Descartes to Gauss to Einstein and finally at Witten) and I was still stuck in Euclid's parallel postulates. Then I decided to let it be and started picking up words and how these eminent personalities lived. This attitude was what carried me till the end of the book. Or else I would have left the book half way. This lasted till he finished off with string theory, super string theory and M theory.
In spite the book remaining something too much to understand, there were instances when I was left reeling on the floor laughing. The author is so good and spot on with his humor. When you feel dejected about not being able to follow what he is trying to say, he cracks a well timed joke which rejuvenates me and fuels me to read the next few pages. And the fact that he is an atheist was another factor which kept me going. There were a couple of instances in which he takes swipe at "GOD" and its so fucking hilarious. He even gave roles to his sons Nicolai and Alexei.
P.S. Paul Curry's trick was magnificent.
And my modest proficiency in elementary and high school maths helped me rush through the first few chapters. The details on how Greeks were the forefathers who laid the cornerstone for Maths and about various day to day activities for which they employed Maths. Then he talks about the great Pythagoras and other well known Greek mathematicians. The way he explained Pythagoras theorem in words were commendable. It awed me when I found that this was the way how Pythagoras came up with the all famous equation. I felt some sort of electricity passing through me when I realized that I was made to think the same way Pythagoras did albeit he did it a couple hundred decades back. At times, the book gave the vibe of the ever famous book Cosmos by Carl Sagan. There were even same incidents mentioned in both the books.
Till now all was well. Then came the Euclidean theory. The author pens down his postulates and starts explaining it one by one. I could stay up with him till then. Then he starts talking about other mathematicians who later found flaws in these same postulates. Some are easy to understand while the rest make up for this easiness by making it much more difficult to comprehend. I was left open mouthed not knowing what was going around. I thought this would get better. But it went from worse to a complete train wreck. Author started explaining the high end stuff in mere words and I was completely bamboozled. He went from one mathematician to another (Descartes to Gauss to Einstein and finally at Witten) and I was still stuck in Euclid's parallel postulates. Then I decided to let it be and started picking up words and how these eminent personalities lived. This attitude was what carried me till the end of the book. Or else I would have left the book half way. This lasted till he finished off with string theory, super string theory and M theory.
In spite the book remaining something too much to understand, there were instances when I was left reeling on the floor laughing. The author is so good and spot on with his humor. When you feel dejected about not being able to follow what he is trying to say, he cracks a well timed joke which rejuvenates me and fuels me to read the next few pages. And the fact that he is an atheist was another factor which kept me going. There were a couple of instances in which he takes swipe at "GOD" and its so fucking hilarious. He even gave roles to his sons Nicolai and Alexei.
P.S. Paul Curry's trick was magnificent.
October 10, 2012
Mlodinow tackles what some people would think would be a dry topic and manages to infuse some wit into it. You can tell that he really loves his topic and wants the reader to as well. He explains the math and gives you examples to help you understand. And they are very helpful (although I must say that his examples using his sons start to get a little annoying after a while.) He explains the beginnings of geometry and how it progressed and reasons why it was, at times, held back due to politics and religion and other things (which puts a lot of history in the book that you normally wouldn’t think of as having anything to do with math.) It starts out with things I learned in school, like the Pythagorean Theorem and coordinates on a x/y graph and other things I recognized and then moved on to more complex things like string theory which I had no prior knowledge of. I started out fine and could follow well enough but as the book went on and the theories got more complex I had a harder and harder time keeping up and often had to reread a passage to understand it (and sometimes never totally did.) It is obviously a book for a particular audience and is not for everyone but if you are interested enough to pick up the book in the first place I don’t think you will be disappointed. It is well written and Mlodinow knows his stuff and his love of the topic comes through and infects the reader.
January 16, 2016
It's called Euclid's Window, but the view isn't really so inspiring in the opening chapters. My version had a glaring mistake on the first page! The previous borrower had helpfully (and amusingly) annotated my library copy. Makes me wonder if I could perhaps make it as a professional editor. I mean, how hard can it be?
Typos aside, this is a fairly pedestrian stroll through the key (European) developments in geometry from antiquity to the 20th century. The anecdotes are quite dry, and the explanations aren't immediately elucidating. To me, popular science books should be easy enough to understand in a single pass. Once I find myself having to re-read a page several times to work out what the author is trying to say, my enjoyment level begins to decline rapidly. If you want to feel inspired by mathematics or physics, I can heartily recommend Fermat's Last Theorem or Alex's Adventures in Numberland.
However, this book does spark stutteringly into life at the turn of the 20th century. It's readily apparent where the author's interests lie, and I found the sections from Einstein's paradigm-shifting theories to string theory to be entertaining and educating in just the right proportions.
Typos aside, this is a fairly pedestrian stroll through the key (European) developments in geometry from antiquity to the 20th century. The anecdotes are quite dry, and the explanations aren't immediately elucidating. To me, popular science books should be easy enough to understand in a single pass. Once I find myself having to re-read a page several times to work out what the author is trying to say, my enjoyment level begins to decline rapidly. If you want to feel inspired by mathematics or physics, I can heartily recommend Fermat's Last Theorem or Alex's Adventures in Numberland.
However, this book does spark stutteringly into life at the turn of the 20th century. It's readily apparent where the author's interests lie, and I found the sections from Einstein's paradigm-shifting theories to string theory to be entertaining and educating in just the right proportions.
December 19, 2022
Too many problems with the book :-
a) Very few diagrams. Difficult to understand advanced geometry and relativity and space-time curvature blah blah blah as-it-is.
b) The examples he used were badly worded and didnt add to the understanding. And irritated by the supposedly cute references to his family again and again.
c) Despite the above problems, the book was a decent read till the half-way mark. It just went over my head after the introduction of Gauss and "curved-space".
Far better books have been written on Einstein's relativity (which forms a crucial part of the book). Would suggest reading Quantum: Einstein, Bohr and the Great Debate About the Nature of Reality . Not a breezy read, but atleast you get some of it !
PS:- This was my 5th book by the author and all read this year. Happy that this wasnt the first I picked else would certainly have missed out on the superlative "The Drunkard's Walk" and the excellent "The Upright Thinkers".
a) Very few diagrams. Difficult to understand advanced geometry and relativity and space-time curvature blah blah blah as-it-is.
b) The examples he used were badly worded and didnt add to the understanding. And irritated by the supposedly cute references to his family again and again.
c) Despite the above problems, the book was a decent read till the half-way mark. It just went over my head after the introduction of Gauss and "curved-space".
Far better books have been written on Einstein's relativity (which forms a crucial part of the book). Would suggest reading Quantum: Einstein, Bohr and the Great Debate About the Nature of Reality . Not a breezy read, but atleast you get some of it !
PS:- This was my 5th book by the author and all read this year. Happy that this wasnt the first I picked else would certainly have missed out on the superlative "The Drunkard's Walk" and the excellent "The Upright Thinkers".
August 21, 2009
Nach dem Drunkard's Walk war das eine herbe Enttäuschung. Keine überraschenden Erkenntnisse, mehr Kurzbiographien als Erläuterungen der wissenschagtlichen Fortschritte selbst und ziemlich viel aufdringliche Beispiele, in denen Alexej und sein Bruder vorkommen. Ich hatte nicht die Illusion, dass ich diesmal Einsteins Theorien verstehen würde (das wird mir sicher nie gelingen), aber von diesem Ziel bin ich jetzt eher weiter entfernt als näher dran. Ich habe nichts dagegen, wenn Wissenschaft locker und entspannt dargestellt wird, aber der Versuch in jedem Absatz einen Witz zu erzählen, ist auf Dauer ermüdend. Meistens beruhen diese Witze auf Hinweisen darauf, dass Newton keinen iPod hatte und Einstein kein Skatboard.
June 12, 2010
I read Mlodinow’s The Drunkard’s Walk and thought this would be a great book on the history of mathematics. It started out good and then just fizzled out for me toward the end. His explanations were sometimes a little hokey and sometimes confusing. I think if you worked hard you could probably make sense of what he was trying to explain, but I’ve read better explanations of relativity, quantum mechanics, and string theory so I skimmed through the last half of the book pretty fast. It just didn’t seem worth it to spend a lot of time on poorly thought out narratives. I got the feeling he was more interested in promoting string theory than explaining the history of mathematics.
July 30, 2011
The book goes off-topic.
The premise is excellent and the book starts off well. However, the standard tendency of such books of the era to bring everything to relativity, quantum physics and superstring theory - may be because of far easier availability of topics in the space - means the book loses its interesting and unique subject quite quickly.
As a result, when it is compared with other books on either history of maths/science or that try to explain cosmology theoretically, it comes up with neither too many new things nor interesting insights. Good introduction for anyone into the first few books on the subject, all that said.
The premise is excellent and the book starts off well. However, the standard tendency of such books of the era to bring everything to relativity, quantum physics and superstring theory - may be because of far easier availability of topics in the space - means the book loses its interesting and unique subject quite quickly.
As a result, when it is compared with other books on either history of maths/science or that try to explain cosmology theoretically, it comes up with neither too many new things nor interesting insights. Good introduction for anyone into the first few books on the subject, all that said.
April 12, 2013
I had high hopes for this book given the love and interest I have for the topic, but I was very disappointed. The book tends to look at classical work through a modern and distorting lens, and the historical component leans toward lurid tales.
Rather than raising the subject matter to the height I think it deserves, it is diminishing. I found myself more frustrated by this than anything else. Given what an easy audience I am, there is no reason for me to pick a math book that I find frustrating.
Rather than raising the subject matter to the height I think it deserves, it is diminishing. I found myself more frustrated by this than anything else. Given what an easy audience I am, there is no reason for me to pick a math book that I find frustrating.
August 30, 2016
The problem I have with this book is that the author adds in a lot of made up speculative stories about times and people that are not only extraneous and misleading; they are also detrimental to the book in that they are fictious and along the lines of mean-spirited, snarky humor that doesn't work. They don't help hold the story or transition to the next part making them mentally jarring to read through.
September 2, 2019
If you have a background in math & science, this will surely move you. Many stories of extraordinary individuals and their invaluable insights. I laughed and cried. Leonard Mlodinow is a great story teller.
June 12, 2013
charming, inspite of sometimes a little bit too much of unceremoniousness.
and yes, it makes the brain work and get amazed. and excited.
and all in all: a person loving his|her subject just can't possibly write a vapid book, i believe.
and yes, it makes the brain work and get amazed. and excited.
and all in all: a person loving his|her subject just can't possibly write a vapid book, i believe.
November 24, 2014
Probably the worst popular science/math book I've read. He distorted and sensationalized history in an effort to be shocking and entertaining. It's less a history of geometry than a tabloid like account of the lives and discoveries of famous mathematicians and physicists.
October 24, 2015
Interesting. Funny. At times too cutesy for my taste.
April 14, 2021
Liked it a lot, but the book is not perfect. As many students, I spent a lot of time with the details of mathematics, and this story was a great way to zoom out and enjoy the overview of, in this case, geometry. Combined with the historical context it beautifully showcases what makes mathematics unique: Ingenuity and creativity, but with a strong sense of inevitability.
That being said, I feel like a big part of the subtleties of the explanations in the latter part (on physics) were hindered by the writing style. Don't get me wrong, the writing style is hilarious: it does a great job at making math accessible and not scary. But this accessibility comes at a cost, as Mlodinow does not mention a single equation in the whole book. I think it was Stephen Hawking's publisher who said: "For every equation you include in the book, the number of readers is halved". Still, Hawking chose to include some. Mlodinow does not, sadly. I can imagine that a reader who is not familiar with the equation of the uncertainty principle, would have a significantly harder time following this part in the book.
Of course, as the book goes over the cutting edge 2o years ago (string theory with all its optimism), this is too complicated to be condensed into simple, intuitive explanations. If string theory and supersymmetry would have since become the revolution it promised, this would have been forgiven. But it did not, thus this was by far the weakest chapter of the book. (Side note: this is a fun chapter to read if you have also read "Lost In Math" by Sabine Hossenfelder. This chapter suffers from just about every problem she describes).
I would recommend the first 3 parts (on Euclid, Descartes, Gauss) to anyone who has taken high school geometry for granted. It shows the progression of western mathematical thinking in a captivating way. The 4th part (on Einstein) is fascinating on its own. The 5th part (on Witten), you should really only read to throw around a few cool words at parties.
That being said, I feel like a big part of the subtleties of the explanations in the latter part (on physics) were hindered by the writing style. Don't get me wrong, the writing style is hilarious: it does a great job at making math accessible and not scary. But this accessibility comes at a cost, as Mlodinow does not mention a single equation in the whole book. I think it was Stephen Hawking's publisher who said: "For every equation you include in the book, the number of readers is halved". Still, Hawking chose to include some. Mlodinow does not, sadly. I can imagine that a reader who is not familiar with the equation of the uncertainty principle, would have a significantly harder time following this part in the book.
Of course, as the book goes over the cutting edge 2o years ago (string theory with all its optimism), this is too complicated to be condensed into simple, intuitive explanations. If string theory and supersymmetry would have since become the revolution it promised, this would have been forgiven. But it did not, thus this was by far the weakest chapter of the book. (Side note: this is a fun chapter to read if you have also read "Lost In Math" by Sabine Hossenfelder. This chapter suffers from just about every problem she describes).
I would recommend the first 3 parts (on Euclid, Descartes, Gauss) to anyone who has taken high school geometry for granted. It shows the progression of western mathematical thinking in a captivating way. The 4th part (on Einstein) is fascinating on its own. The 5th part (on Witten), you should really only read to throw around a few cool words at parties.
July 7, 2022
From the title of the book you will be confused that what is this book about really? But when you will start reading the book, you will understand slowly. This book will not get you interested in math but who are already interested in math and have some kind of background in physics or math, they should read it.
This book talks about 3000 year old journey of mathematics and how it influenced physics and other sciences. The book talks about geometry and how geometry is the key to understand the universe. How Euclid who was the father of geometry started his geometry and his ideas are no longer in use today in modern physics. Today scientist use non Euclidean geometry like hyperbolic geometry, spherical geometry etc to understand the universe. But one thing is pretty clear that Greek civilization started studying patterns in numbers and geometry in order to understand the universe. This book is divided into 5 parts and each part have 6-8 chapters. I like the format of the book. The book starts with the story of Euclid. This book also covers history of math at first and then it tells the story about the discoverer and ends it with a question so that we can find out the answer in the next part. This book tells us to look at the world from the lens of geometry and how geometry is still prevailing like in string theory in order to understand the reality and we don't know how far we can go with the help of geometry.
Read this book of you want to perceive the world from mathematician's or theoretical physicist's perspective.
This book talks about 3000 year old journey of mathematics and how it influenced physics and other sciences. The book talks about geometry and how geometry is the key to understand the universe. How Euclid who was the father of geometry started his geometry and his ideas are no longer in use today in modern physics. Today scientist use non Euclidean geometry like hyperbolic geometry, spherical geometry etc to understand the universe. But one thing is pretty clear that Greek civilization started studying patterns in numbers and geometry in order to understand the universe. This book is divided into 5 parts and each part have 6-8 chapters. I like the format of the book. The book starts with the story of Euclid. This book also covers history of math at first and then it tells the story about the discoverer and ends it with a question so that we can find out the answer in the next part. This book tells us to look at the world from the lens of geometry and how geometry is still prevailing like in string theory in order to understand the reality and we don't know how far we can go with the help of geometry.
Read this book of you want to perceive the world from mathematician's or theoretical physicist's perspective.
This entire review has been hidden because of spoilers.
September 23, 2021
I stupidly read this book about geometry as an audio book. I figured that I know enough about geometry that I would be able to understand it without the aid of pictures. I was right about that part. I was already familiar with all of the geometric ideas discussed in this book so I didn't have trouble following the discussion. But the beauty of geometry, at least at the introductory level, is deeply connected to the visual imagery. I would have enjoyed the ideas much more, familiar though they may have been, if I had been looking at the pictures and had paused with pencil and paper to work through some of the concepts. The way that I did it was like going to an art museum wearing sunglasses. You can still see the art, but the glasses only diminish the experience.
February 19, 2023
Good overall read showing how mathematics and physics have developed over the last 3000 years. Could have used more illustrations. Many on the concepts are difficult to understand with just text explanations. Also wish he had spent more time on the pre-20th century work. There are tons of current books on relativity and quantum mechanics.
September 9, 2020
Shows how geometry is related to physics. Starts from the time physics and philosophy were same and discusses the contributions of different scientists through the history. From Thales to Witten. From Euclidean geometry to M-theory.
March 18, 2024
I was surprised at how negative some reviews were. I have an MS in Applied Math and I found the book delightful. It definitely helped me understand what Einstein accomplished.
February 7, 2017
It may not be an overstatement to say that I learned more science from this book than I did in my secondary education. (Big picture, key concept knowledge...not little details like distance equals rate times time.) Gravity is a matter of perspective? Space and time, in one sense, don't really exist? There is no absolute distance...of anything. Space may actually have 11 dimensions? Oh yeah, and time is different on the earth than it is on the sun. Since I graduated after this book was published, it seems like someone really should have mentioned this. Thanks to further studies in math, I did know that space is curved and that the geometry of high school doesn't really describe the universe (only locally, at some level). A triangle in space doesn't have 180 degrees in its angles...imagine that.
However, in the event that these are new ideas for my students, I'm looking forward to assigning this book this semester. The writing was incredibly entertaining, and I loved the author's sense of humor. Some reviews accuse the book of an anti-Christian, Euro-centric bias. As a Christian, I bridled at a few statements, but there's no reason not to enjoy the book just because some statements were written from a different worldview. Instead, there's room for discussion here. As for the Euro-centric perspective, this is probably correct. Sadly I am the product of a Euro-centric education, so I can't really say whether or not other cultures' contributions to geometry were minimized.
Other criticisms of the book attacked its historical inaccuracies and tendency to sensationalize key characters' biographies. I didn't find this to be overly true. I've read worse, and I felt like the author did a good job qualifying his interesting stories ("legend has it," "he may have remarked something like"....). This style certainly suits my purposes: assigning the book to a group of non-math-major, possibly disinterested, undergrads in an attempt to introduce the larger historical narrative of geometric progress.
Favorite aspects of the book: a host of interesting biographical anecdotes (some of lesser known mathematicians), a clear structure broken down into manageable parts (five revolutions in geometry), literally laugh-out-loud invoking descriptions, the most beautifully written epilogue for a math book that I've read to date.
Least favorite aspects: some wordy descriptions of difficult concepts that REALLY could have used a picture or diagram, excessive family illustrations featuring Alexai and Nicolai over and over and over (apologies to the author, as his love for his sons is admirable). Also, I really hoped to see a stronger connection in the last chapter between string theory and non-Euclidean geometry. This is just my own personal wish, as I'm using the book for a geometry class.
While the book isn't perfect, I absolutely loved it and would recommend it to anyone wanting to learn more about geometry: the real story, including messy complications and unanswered questions and possibly shaky philosophical foundations, not the nicely packaged everything-is-proved sort you may have previously learned.
However, in the event that these are new ideas for my students, I'm looking forward to assigning this book this semester. The writing was incredibly entertaining, and I loved the author's sense of humor. Some reviews accuse the book of an anti-Christian, Euro-centric bias. As a Christian, I bridled at a few statements, but there's no reason not to enjoy the book just because some statements were written from a different worldview. Instead, there's room for discussion here. As for the Euro-centric perspective, this is probably correct. Sadly I am the product of a Euro-centric education, so I can't really say whether or not other cultures' contributions to geometry were minimized.
Other criticisms of the book attacked its historical inaccuracies and tendency to sensationalize key characters' biographies. I didn't find this to be overly true. I've read worse, and I felt like the author did a good job qualifying his interesting stories ("legend has it," "he may have remarked something like"....). This style certainly suits my purposes: assigning the book to a group of non-math-major, possibly disinterested, undergrads in an attempt to introduce the larger historical narrative of geometric progress.
Favorite aspects of the book: a host of interesting biographical anecdotes (some of lesser known mathematicians), a clear structure broken down into manageable parts (five revolutions in geometry), literally laugh-out-loud invoking descriptions, the most beautifully written epilogue for a math book that I've read to date.
Least favorite aspects: some wordy descriptions of difficult concepts that REALLY could have used a picture or diagram, excessive family illustrations featuring Alexai and Nicolai over and over and over (apologies to the author, as his love for his sons is admirable). Also, I really hoped to see a stronger connection in the last chapter between string theory and non-Euclidean geometry. This is just my own personal wish, as I'm using the book for a geometry class.
While the book isn't perfect, I absolutely loved it and would recommend it to anyone wanting to learn more about geometry: the real story, including messy complications and unanswered questions and possibly shaky philosophical foundations, not the nicely packaged everything-is-proved sort you may have previously learned.
Displaying 1 - 30 of 194 reviews