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Calculating the Cosmos Lib/E: How Mathematics Unveils the Universe
Ian Stewart's up-to-the-minute guide to the cosmos moves from the earth and the planets to the galaxy and the universe. He describes how galaxies, stars and planets form, why stars implode, how everything began, and how it's going to end. He considers parallel universes, fine-tuning of the cosmos, whether life on earth will be snuffed out by a comet, and what extra-terrestrial life may be like. He provides crystal clear accounts of gravity, spacetime, relativity and quantum theory, and how they relate to each other.
Mathematics has been the driving force in astronomy and cosmology since the ancient Egyptians. Professor Stewart shows how Kepler's work on the planets led to Newton's law of gravity, which in turn inspired Einstein's theories of relativity. He examines current challenges to Big Bang Theory and how the next scientific revolution may once again transform understanding of the universe and our place within it.
Mathematics has been the driving force in astronomy and cosmology since the ancient Egyptians. Professor Stewart shows how Kepler's work on the planets led to Newton's law of gravity, which in turn inspired Einstein's theories of relativity. He examines current challenges to Big Bang Theory and how the next scientific revolution may once again transform understanding of the universe and our place within it.
Audio CD
First published October 25, 2016
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About the author
Ian Stewart
261 books750 followersIan Nicholas Stewart is an Emeritus Professor and Digital Media Fellow in the Mathematics Department at Warwick University, with special responsibility for public awareness of mathematics and science. He is best known for his popular science writing on mathematical themes.
--from the author's website
Librarian Note: There is more than one author in the GoodReads database with this name. See other authors with similar names.
--from the author's website
Librarian Note: There is more than one author in the GoodReads database with this name. See other authors with similar names.
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Displaying 1 - 30 of 72 reviews
September 20, 2016
(I actually reviewed the UK hardback, with this cover.) This is a weird one - it's a book where I'm really struggling to identify who it's for and what it is supposed to do. The only conclusion I can draw is that Calculating the Cosmos is intended for people who like Ian Stewart's excellent maths books, but who don't usually read popular science books, so need a maths-driven introduction to astronomy, astrophysics and cosmology.
The particularly odd thing is that despite the subtitle 'how mathematics unveils the universe' there is very little explicit maths in the book - it's mostly just straightforward physics with little prominence given to the mathematical side. And the physics is put across in a fairly heavy handed 'fact, fact, fact...' way - the book is light on narrative throughout. Where it does stray into history there are one or two examples that don't quite get the story straight - for instance, when talking about Newton's development of his gravitational work, Stewart tells us that it took a 'stroke of genius' to see that the Moon is both falling and moving sideways so it misses. What he doesn't point out was that the genius in question was Robert Hooke, not Isaac Newton. This is one of the few points where Newton explicitly says the idea had not occurred to him until Hooke wrote to him about it.
Where the book does stand out is where Stewart delves into something that is usually glossed over in a popular science book. Sometimes this content feels a touch 'so what?' - for example in describing the method used to simulate the formation of the Moon - but in other cases, for example the analysis of how comet 67P got its 'rubber duck' shape, the route of the Rosetta probe, and in probably the best explanation of curved spacetime and manifolds I've seen. Best of all, Stewart explains how dark matter could not exist at all, simply being a matter of making the wrong assumptions in combining the interactions of stars in a galaxy and the way he eloquently dissects the many worlds hypothesis (many of the best bits are towards the end of the book). However, these are standout moments amongst a whole collection of information we've seen so many times before, and when he does explain the science, the approach taken is often not easy to grasp - for example his impenetrable use of Penrose diagrams in talking about black holes.
The story of the Rosetta probe is probably the closest we come to having some narrative to engage us, but even here the storytelling is bland, and, from a mathematical standpoint, we miss the opportunity to look at a different kinds of mathematical involvement, as there was interesting work done on the scheduling of Rosetta's experiments to deal with the very limited communications bandwidth.
This isn't a bad book, but apart from those handful of highlights where something is explained better than elsewhere, most of it fails to bring in anything new and lacks the engaging writing style of, say, Stewart's books written with Terry Pratchett. Here Stewart rarely makes use of mathematical insights to tell us anything different to straightforward familiar astronomy and cosmology, which is a shame as he is so excellent at making maths interesting. For the science, though, we get this distinctly 'here's a fact, here's another fact, here's yet another fact' style of writing. It might work as a book for that maths-based space newcomer, but I'm afraid its not for me.
The particularly odd thing is that despite the subtitle 'how mathematics unveils the universe' there is very little explicit maths in the book - it's mostly just straightforward physics with little prominence given to the mathematical side. And the physics is put across in a fairly heavy handed 'fact, fact, fact...' way - the book is light on narrative throughout. Where it does stray into history there are one or two examples that don't quite get the story straight - for instance, when talking about Newton's development of his gravitational work, Stewart tells us that it took a 'stroke of genius' to see that the Moon is both falling and moving sideways so it misses. What he doesn't point out was that the genius in question was Robert Hooke, not Isaac Newton. This is one of the few points where Newton explicitly says the idea had not occurred to him until Hooke wrote to him about it.
Where the book does stand out is where Stewart delves into something that is usually glossed over in a popular science book. Sometimes this content feels a touch 'so what?' - for example in describing the method used to simulate the formation of the Moon - but in other cases, for example the analysis of how comet 67P got its 'rubber duck' shape, the route of the Rosetta probe, and in probably the best explanation of curved spacetime and manifolds I've seen. Best of all, Stewart explains how dark matter could not exist at all, simply being a matter of making the wrong assumptions in combining the interactions of stars in a galaxy and the way he eloquently dissects the many worlds hypothesis (many of the best bits are towards the end of the book). However, these are standout moments amongst a whole collection of information we've seen so many times before, and when he does explain the science, the approach taken is often not easy to grasp - for example his impenetrable use of Penrose diagrams in talking about black holes.
The story of the Rosetta probe is probably the closest we come to having some narrative to engage us, but even here the storytelling is bland, and, from a mathematical standpoint, we miss the opportunity to look at a different kinds of mathematical involvement, as there was interesting work done on the scheduling of Rosetta's experiments to deal with the very limited communications bandwidth.
This isn't a bad book, but apart from those handful of highlights where something is explained better than elsewhere, most of it fails to bring in anything new and lacks the engaging writing style of, say, Stewart's books written with Terry Pratchett. Here Stewart rarely makes use of mathematical insights to tell us anything different to straightforward familiar astronomy and cosmology, which is a shame as he is so excellent at making maths interesting. For the science, though, we get this distinctly 'here's a fact, here's another fact, here's yet another fact' style of writing. It might work as a book for that maths-based space newcomer, but I'm afraid its not for me.
November 23, 2016
Vispār jau ir ļoti, ļoti grūti paiet garām grāmatai ar šādu nosaukumu. Kādu dienu biju nokāpis Jāņa Rozes grāmatnīcas pagrabstāvā un ieraudzīju šo grāmatu. Autoram, neskatoties uz to, ka regulāri sekoju viņa jaunumiem, atkal bija izdevies izdot grāmatu, kuru es biju palaidis garām. Nevar teikt, ka man ar viņa grāmatām būtu labas attiecības. Lielākoties tā esmu novērtējis visnotaļ viduvēji, jo viņam reizēm pietrūkst pacietības visu izskaidrot līdz galam. Taču katrā no viņa grāmatām ir atrodamas pāris nodaļas, kuras atsver visu. Cerot uz šādu nodaļu, grāmatu nopirku.
Matemātika jau no Babilonas laikiem ir bijusi astronomijas un kosmoloģijas dzinējspēks. Balstoties uz Keplera darbu, Ņūtons radīja savu gravitācijas teoriju. Taču arī tā nebija precīza, un divus gadsimtus vēlāk, novērojot planētu orbītu neatbilstību aprēķiniem, Einšteins iedvesmojās savas Vispārējās Relativitātes teorijai. Pirms astoņdesmit gadiem tika atklāts, ka Visums izplešas, un tas radīja Lielā sprādziena teoriju, vēlāk tam klāt pievienojās inflācija, tumšā matērija un tumšā enerģija. Un visiem šiem atklājumiem apakšā slēpjas matemātika un matemātiskie modeļi.
Katru reizi, kad es kādā populārzinātniskajā grāmatā izlasu par to, ka pēc miljards gadiem Jupiters būs izmetis Zemi no orbītas un aiztrieks to vai nu uz sauli vai uz atklātu kosmosu, man ir radies jautājums, kā viņi to paveic? Teorētiski es saprotu, atrisinām vienādojumu sistēmu kvadriljons reizes un gatavs! Taču ir tāda lieta, ka kļūdas sākotnējos datos, kas akumulējas pēc katras iterācijas, nemaz nerunājot par vairāk nekā divu ķermeņu savstarpējo dinamiku, kura jau ir haosa teorijas lauciņā. Autors mani pārliecināja, ka var- galvenais vajag vienkāršot, jo citādi nepietiks nekādas datoru jaudas. Taču analizējot rezultātu pēc būtības, ir jāņem vērā arī visi vienkāršojumi. Un te bieži tiek grēkots, šīs novienkāršotās lietas reti kad tiek pastāstītas.
Piemēram, Mēness rašanās simulācijas. Sākot no pārtveršanas līdz Theias hipotēzei ir balstītas uz vienkāršotiem matemātiskiem modeļiem, kuriem mainot bāzes parametrus mēģina iegūt situāciju, kura atbilstu mūsdienu Zemes Mēness sistēmai. Tā kā nav iespējams simulēt katru daļiņu, kas radusies protozemei saduroties ar kādu citu protoplanētu, tad tiek simulēts tikai neliels daudzums, pieņemot, ka kopējā dinamika no tā nemainās un, lai padarītu lietu vēl vienkāršāku, tad trīsdimensiju telpas vietā tiek ņemta divdimensiju un tā tālāk. Tādēļ nav ko brīnīties, ka pieaugot datoru jaudām mainās arī teorijas un aprēķinu rezultāti.
Šoreiz nodaļa, kuras dēļ bija vērts pirkt grāmatu, bija veltīta Starpplanētu Lielceļiem jeb trajektorijām, ar kuru palīdzību ar minimālu enerģijas daudzumu var aizceļot uz jebkuru Saules sistēmas objektu. Viss, kas vajadzīgs ir jaudīgs dators un spēja saprast, ka reizēm labāk ir nedoties pa taisno, bet izmantot planētu palīdzību. Daudz tiek stāstīts par Lagranža punktiem, par to cik viegli tur ir mainīt orbītu, piesaukti piemēri no dzīves. Viss, kas ir vajadzīgs, ir precizitāte.
Beigās tiek uzbraukts inflācijas modelim, autors iedziļinājies jautājumā un ir izvilcis tā matemātiskās nepilnības, apšaubījis daudzus pamatpieņēmumus. Pats gan vaļsirdīgi atzīstas, ka, iespējams, viņam nav taisnība, bet matemātiku šeit vajadzētu pieslīpēt. Izrādās, ka arī Reliktā starojuma modelis īsti neatbilst novērotajam, bet zinātnē tāpat kā visās citās nozarēs ir neliela inerce un nav lielas vēlmes atmest puslīdz strādājošu modeli, lai pārmestos uz kaut ko jaunu.
Kā kronis visam bija autora argumenti par to, kādēļ tumšā matērija visticamāk ir fikcija, jo tās pamatpieņēmums, ka zvaigznes neriņķo ap galaktikas centru kā prognozēts un tādēļ ir jāpastāv tumšās matērijas mākonim, kurš kā halo apņem visu galaktiku, tādējādi mainot matērijas sadalījumu galaktikā un izskaidrojot zvaigžņu dīvaino kustību. Āķis ir tajā, ka šāds halo neko neizskaidro.
Ja interesē astronomija un kosmoloģija, ja vēlies zināt, kā viņi to visu ir aprēķinājuši, tad noteikti lasiet! Varbūt šī grāmata nav tik saistošā valodā kā darbi, kuri radīti kopā ar Teriju Prečetu, te nav daudz matemātisku vienādojumu un vairāk autors ir pievērsies tieši fizikai. Lielākoties lietas tiek pasniegtas kā gatavi fakti un paģērē no lasītāja nelielas priekšzināšanas. Vietām autora vēstures zināšanas nav pietiekoši dziļas, lai nepielaistu muļķīgas kļūdas. Taču tas viss ir sīkums salīdzinot ar tēmām, kuras autors apskata. Ne viss, ko lasām, ir atklāts līdz galam un neapstrīdami, ir vēl daudz vietas diskusijām. Lieku 9 no 10 ballēm. Lasiet, nenožēlosiet, es pusaudža gados būtu dvēseli apmainījis pret šo grāmatu!
Matemātika jau no Babilonas laikiem ir bijusi astronomijas un kosmoloģijas dzinējspēks. Balstoties uz Keplera darbu, Ņūtons radīja savu gravitācijas teoriju. Taču arī tā nebija precīza, un divus gadsimtus vēlāk, novērojot planētu orbītu neatbilstību aprēķiniem, Einšteins iedvesmojās savas Vispārējās Relativitātes teorijai. Pirms astoņdesmit gadiem tika atklāts, ka Visums izplešas, un tas radīja Lielā sprādziena teoriju, vēlāk tam klāt pievienojās inflācija, tumšā matērija un tumšā enerģija. Un visiem šiem atklājumiem apakšā slēpjas matemātika un matemātiskie modeļi.
Katru reizi, kad es kādā populārzinātniskajā grāmatā izlasu par to, ka pēc miljards gadiem Jupiters būs izmetis Zemi no orbītas un aiztrieks to vai nu uz sauli vai uz atklātu kosmosu, man ir radies jautājums, kā viņi to paveic? Teorētiski es saprotu, atrisinām vienādojumu sistēmu kvadriljons reizes un gatavs! Taču ir tāda lieta, ka kļūdas sākotnējos datos, kas akumulējas pēc katras iterācijas, nemaz nerunājot par vairāk nekā divu ķermeņu savstarpējo dinamiku, kura jau ir haosa teorijas lauciņā. Autors mani pārliecināja, ka var- galvenais vajag vienkāršot, jo citādi nepietiks nekādas datoru jaudas. Taču analizējot rezultātu pēc būtības, ir jāņem vērā arī visi vienkāršojumi. Un te bieži tiek grēkots, šīs novienkāršotās lietas reti kad tiek pastāstītas.
Piemēram, Mēness rašanās simulācijas. Sākot no pārtveršanas līdz Theias hipotēzei ir balstītas uz vienkāršotiem matemātiskiem modeļiem, kuriem mainot bāzes parametrus mēģina iegūt situāciju, kura atbilstu mūsdienu Zemes Mēness sistēmai. Tā kā nav iespējams simulēt katru daļiņu, kas radusies protozemei saduroties ar kādu citu protoplanētu, tad tiek simulēts tikai neliels daudzums, pieņemot, ka kopējā dinamika no tā nemainās un, lai padarītu lietu vēl vienkāršāku, tad trīsdimensiju telpas vietā tiek ņemta divdimensiju un tā tālāk. Tādēļ nav ko brīnīties, ka pieaugot datoru jaudām mainās arī teorijas un aprēķinu rezultāti.
Šoreiz nodaļa, kuras dēļ bija vērts pirkt grāmatu, bija veltīta Starpplanētu Lielceļiem jeb trajektorijām, ar kuru palīdzību ar minimālu enerģijas daudzumu var aizceļot uz jebkuru Saules sistēmas objektu. Viss, kas vajadzīgs ir jaudīgs dators un spēja saprast, ka reizēm labāk ir nedoties pa taisno, bet izmantot planētu palīdzību. Daudz tiek stāstīts par Lagranža punktiem, par to cik viegli tur ir mainīt orbītu, piesaukti piemēri no dzīves. Viss, kas ir vajadzīgs, ir precizitāte.
Beigās tiek uzbraukts inflācijas modelim, autors iedziļinājies jautājumā un ir izvilcis tā matemātiskās nepilnības, apšaubījis daudzus pamatpieņēmumus. Pats gan vaļsirdīgi atzīstas, ka, iespējams, viņam nav taisnība, bet matemātiku šeit vajadzētu pieslīpēt. Izrādās, ka arī Reliktā starojuma modelis īsti neatbilst novērotajam, bet zinātnē tāpat kā visās citās nozarēs ir neliela inerce un nav lielas vēlmes atmest puslīdz strādājošu modeli, lai pārmestos uz kaut ko jaunu.
Kā kronis visam bija autora argumenti par to, kādēļ tumšā matērija visticamāk ir fikcija, jo tās pamatpieņēmums, ka zvaigznes neriņķo ap galaktikas centru kā prognozēts un tādēļ ir jāpastāv tumšās matērijas mākonim, kurš kā halo apņem visu galaktiku, tādējādi mainot matērijas sadalījumu galaktikā un izskaidrojot zvaigžņu dīvaino kustību. Āķis ir tajā, ka šāds halo neko neizskaidro.
Ja interesē astronomija un kosmoloģija, ja vēlies zināt, kā viņi to visu ir aprēķinājuši, tad noteikti lasiet! Varbūt šī grāmata nav tik saistošā valodā kā darbi, kuri radīti kopā ar Teriju Prečetu, te nav daudz matemātisku vienādojumu un vairāk autors ir pievērsies tieši fizikai. Lielākoties lietas tiek pasniegtas kā gatavi fakti un paģērē no lasītāja nelielas priekšzināšanas. Vietām autora vēstures zināšanas nav pietiekoši dziļas, lai nepielaistu muļķīgas kļūdas. Taču tas viss ir sīkums salīdzinot ar tēmām, kuras autors apskata. Ne viss, ko lasām, ir atklāts līdz galam un neapstrīdami, ir vēl daudz vietas diskusijām. Lieku 9 no 10 ballēm. Lasiet, nenožēlosiet, es pusaudža gados būtu dvēseli apmainījis pret šo grāmatu!
December 5, 2019
I absolutely loved this one. Stewart's writing style is easy to understand for the layman (such as I) without ever being condescending. It's even funny in places and he gets bonus points from quoting both Red Dwarf and the Discworld books.
There's not as much mathematics in here as I was expecting, given the title, but I can't bring myself to knock a star off for that. Highly recommended.
There's not as much mathematics in here as I was expecting, given the title, but I can't bring myself to knock a star off for that. Highly recommended.
February 6, 2017
I don't recommend this book for everyone, but it was a perfect fit for me. The last time I read a physics/astronomy book that taught me profound new things was Michio Kaku's Hyperspace. While I can definitely recommend Kaku's work for anyone, this book was more technical. I would say it speaks to a graduate level audience in either math, physics, or astronomy. While these aren't my areas professionally, I am passionately interested in them, so this book spoke my language. Every chapter took a subject with which I was familiar and laid out a laundry list of all the things I didn't know about it, and all the underlying assumptions that aren't set in concrete. I was floored to read about the subtleties and intricate structures within Saturn's rings, for example, a treasure trove of lessons from Mother Earth about how gravity works, and far from settled science. I was equally exhilarated to hear doubts about what Stewart calls "bolt-ons" to the Big Bang theory: Inflation, Dark Matter, and Dark Energy. Not because I don't want to "believe in them," whatever that means in a scientific context, but because they are so counter intuitive they cry out for either a better explanation or some measured degree of doubt.
The greatest lesson of the book is that science is always provisional. Every theory we have (even the seemingly settled, orthodox ones) are only as good as the observations they match. And every theory we have really only matches 98% of observations. Science is a continual process of improvement and the occasional overhaul. It's a great pleasure to read an author with both expertise and humility, who can illuminate while at the same time casting doubt.
The greatest lesson of the book is that science is always provisional. Every theory we have (even the seemingly settled, orthodox ones) are only as good as the observations they match. And every theory we have really only matches 98% of observations. Science is a continual process of improvement and the occasional overhaul. It's a great pleasure to read an author with both expertise and humility, who can illuminate while at the same time casting doubt.
February 14, 2017
The first half of the book is a nice survey of our solar system, it's formation, and discovery.
The second half goes off the deep end with bizarre dark matter denial, and crank alternatives to the Big Bang. He also gives a totally incorrect description of Schrodinger's cat.
The author seems to see himself as an outsider as a Mathematician. He constantly attacks a straw man of the physics community. He says things like, "nobody thinks about the boundary conditions" (which is simply false) and "there's also a tenancy to overstate the implications of the latest idea or discovery" (which is true about the media, but not about the scientific community).
This book is a good example of Max Planck's maxim "Science progresses one funeral at a time." This author just can't seem to accept scientific discoveries made after ~1950.
The second half goes off the deep end with bizarre dark matter denial, and crank alternatives to the Big Bang. He also gives a totally incorrect description of Schrodinger's cat.
The author seems to see himself as an outsider as a Mathematician. He constantly attacks a straw man of the physics community. He says things like, "nobody thinks about the boundary conditions" (which is simply false) and "there's also a tenancy to overstate the implications of the latest idea or discovery" (which is true about the media, but not about the scientific community).
This book is a good example of Max Planck's maxim "Science progresses one funeral at a time." This author just can't seem to accept scientific discoveries made after ~1950.
January 29, 2024
Overall, a really nice book exploring some fundamental concepts behind the universe! A nice introductory book for people wanting to understand more about the cosmos with some intermediate concepts explained in the second half of the book.
Despite claiming ‘how mathematics unveils the universe’, the book focused less on mathematical equations and more on mathematical concepts. It would have been nice to have seen some equations explained but the concepts were described nicely :)
Despite claiming ‘how mathematics unveils the universe’, the book focused less on mathematical equations and more on mathematical concepts. It would have been nice to have seen some equations explained but the concepts were described nicely :)
November 29, 2016
I am not exactly sure what to say about this book. The first 4/5 of it were slow going and didn't seem to bring anything new to the table. I expected this book to have the passion and insight his book Fearful Symmetry, which dealt with patterns found on Earth, did. When this book came out, I rushed to get it, thinking it, like Fearful Symmetry, would open my eyes to the wonderful patterns not just on Earth but in the entire universe. I was mostly disappointed. However, it picked up significantly toward the end when Stewart took an analytical sledgehammer to the Big Bang theory, dark matter, and inflation. That alone made the rest of the book worth reading. Also, Stewart's descriptions of star type (what determines a red dwarf, brown dwarf, neutron, etc) and the evolution of stars was the best I have read yet.
April 2, 2023
I can't think of any book on mathematics that I have actively enjoyed listening too before.
The book traces the evolution of mathematics and its links to astronomy starting with the Babylonian integration of mathematics into the study of astronomy and cosmology and working up to the modern day. New readers beware, this book will awaken dormant parts of your brain, blossoming concepts and reinvigorating the old while giving you a love of the beauties of existence. If you're into that sort of thing.
My only major caveat to the quality is that the constantly building material makes it approachable at first but a bit incoherent later in the book, but I attribute that to my own inexperience if nothing else.
The book traces the evolution of mathematics and its links to astronomy starting with the Babylonian integration of mathematics into the study of astronomy and cosmology and working up to the modern day. New readers beware, this book will awaken dormant parts of your brain, blossoming concepts and reinvigorating the old while giving you a love of the beauties of existence. If you're into that sort of thing.
My only major caveat to the quality is that the constantly building material makes it approachable at first but a bit incoherent later in the book, but I attribute that to my own inexperience if nothing else.
December 29, 2017
I'm so sorry I finished this - I just wanted it to go on and on and now I don't want to give it back to the library. I found it a new (for me) perspective on cosmological ideas and that helped me learn a lot. In the end I'm neither a mathematician nor a cosmologist so I have no worry about things being true or false at this stage and I can just enjoy the ideas.
September 5, 2020
A journey by the means the mathematics and physics, starting from the Earth to the remotest possible place in the universe.
Ian Stewart explain enough of almost everything, not much in depth for the novices nor too shallow to makes one who already knew somethings bored.
Best introductuon to the astrophysics I've read so far.
The amount of knowledge that has been cover properly in this book is enough for one to feel the satisfaction of it at the end.
Ian Stewart explain enough of almost everything, not much in depth for the novices nor too shallow to makes one who already knew somethings bored.
Best introductuon to the astrophysics I've read so far.
The amount of knowledge that has been cover properly in this book is enough for one to feel the satisfaction of it at the end.
December 21, 2021
Mathematics in the universe, universe in mathematics..
October 3, 2023
In “Calculating The Cosmos”, Ian Stewart takes us on a journey through the history of cosmology and astrophysics, and how mathematics has been used to unveil the mysteries of the universe.
Stewart’s writing style is engaging and accessible, making complex concepts easy to understand for the layperson. He uses analogies and metaphors to explain difficult concepts, such as comparing the curvature of space-time to the surface of a trampoline.
One of the strengths of this book is that it doesn’t shy away from the technical details. Stewart provides an excellent, non-technical survey of the mathematical bases of the historical development of cosmology and astrophysics. He explains how Kepler’s laws of planetary motion led Newton to formulate his theory of gravity, and how Einstein’s theory of general relativity was inspired by tiny irregularities in the motion of Mars.
Stewart also delves into some of the more esoteric aspects of cosmology, such as dark matter and dark energy. He describes how these mysterious substances were first hypothesized to exist, and how they have been used to explain some of the more puzzling observations in astrophysics.
The book concludes with a discussion on the current big bang orthodoxy and Stewart’s concerns about it. He makes a carefully formulated case for why he believes that there may be a scientific revolution on the way that will challenge long-held scientific orthodoxy and once again transform our understanding of the universe.
Overall, “Calculating The Cosmos” is an excellent book that provides an exhilarating guide to the cosmos.
Stewart’s writing style is engaging and accessible, making complex concepts easy to understand for the layperson. He uses analogies and metaphors to explain difficult concepts, such as comparing the curvature of space-time to the surface of a trampoline.
One of the strengths of this book is that it doesn’t shy away from the technical details. Stewart provides an excellent, non-technical survey of the mathematical bases of the historical development of cosmology and astrophysics. He explains how Kepler’s laws of planetary motion led Newton to formulate his theory of gravity, and how Einstein’s theory of general relativity was inspired by tiny irregularities in the motion of Mars.
Stewart also delves into some of the more esoteric aspects of cosmology, such as dark matter and dark energy. He describes how these mysterious substances were first hypothesized to exist, and how they have been used to explain some of the more puzzling observations in astrophysics.
The book concludes with a discussion on the current big bang orthodoxy and Stewart’s concerns about it. He makes a carefully formulated case for why he believes that there may be a scientific revolution on the way that will challenge long-held scientific orthodoxy and once again transform our understanding of the universe.
Overall, “Calculating The Cosmos” is an excellent book that provides an exhilarating guide to the cosmos.
January 4, 2019
A fascinating tour of how we understand the cosmos. Stewart has the ability to expound, without getting bogged down in technical details, on the most interesting subjects, like chaos, galaxies, comets, moon, and stars. He puts each part in its historical context and then unveils more recent discoveries which are often much more complex and elegant than what imagined. I appreciate his scientific flexibility and he writes with a sense of a continual process of discovery. The book has its thumb on the pulse of lively research.
May 29, 2022
A very interesting read. 4.5 stars.
June 9, 2018
Nice book, great for those who are wondering what is mathematics for and how the whole cosmos can be simplified to equations and numbers.
December 8, 2018
Diving into an astrophysics publication so cleverly titled as Calculating the Cosmos: How Mathematics Unveils the Universe, readers would expect a lengthy and complex account of the vitality of mathematics in the astrophysical world filled with heavy scientific terminology. However, University of Warwick professor and popular-science author Ian Stewart effectively constructs his book on the relationship between math and astronomy in a way that is comprehensible and enjoyable even for the average reader lacking any prior knowledge of astrophysics. From a mathematician’s perspective he explores the various ways and specific instances in which the use of math helps find answers to scientific questions or to bring scientists one step closer to finding answers.
Such questions include: What is the likelihood of intelligent life existing outside of planet Earth? What might such extraterrestrials look like? What alternative theories are there to the big bang? What is the shape of the universe? Why are we here? Is it possible that there are more universes than the one we inhabit? Stewart explores these concepts as well as gravity, the formation of the moon, the content of Saturn’s rings, spectroscopy, and black holes - all of which have some relation to mathematical principles, as difficult as it may be to believe. There’s even a mathematical explanation for the gap between planetary orbits - a pattern, in fact! Since ancient times, astronomers and mathematicians have utilized components of geometry and calculus to gain a better understanding of how the world works. In Calculating the Cosmos, Stewart emphasizes the absolute necessity of these mathematical techniques in order to obtain answers.
Although Stewart’s purpose of the book is evidently to convince readers of the importance of math in scientific discovery, specifically in relation to astrophysics, the majority of the math explained in the book is not explicit. He does offer a few equations and calculations that may leave the mathematically-challenged with a headache, but for the most part, the physics is fairly straightforward and demonstrated concisely with the experience and knowledge of the general public in mind. Therefore, much of the science is understandable for readers who have a high school education and therefore a foundation for comprehending the more complicated concepts. Still, some points of description went a little overboard with basic physics such as the concept of momentum, while at other points, short passages of complex science might deserve a quick re-read. In that respect, there was some inconsistency, albeit little of it. Moreover, he emphasizes how intricate and complicated the math can be, and simultaneously expensive and time-consuming.
One wouldn’t expect much on the narrative side of things, but Stewart delves into the history of currently accepted theories and chronicles the discoveries that led to our modern understanding of the universe. For some readers, these tidbits may even be more engaging than all the numbers and calculations. In addition, Stewart includes a few pop culture references - from a Joni Mitchell song about stardust to science fiction’s portrayal of humanoid aliens - in order to add a bit of humor to his writing. He keeps his diction simplified to ensure understanding among the everyday readers, although when it is necessary to use astronomical jargon he includes a synonym alongside the vocabulary. For example, libration is a fancy term for wobbles (Stewart 42). To help with comprehension of some of the more difficult concepts, Stewart offers sufficient analogies such as comparing the search of trojan asteroid blips in light curves to the search of lion tracks in a game reserve (194). Stewart writes with exceptional flair and takes advantage of various sentence structures, especially very short sentences for emphasis. He keeps an upbeat and slightly subjective tone throughout the book that almost makes one forget that they are reading a book about science.
A few passages were slow, but in general, the book was fast-paced. A few topics were not explored fully in depth as much as they could have been, such as the gravitational evidence for dark matter, although that can be respected as an artistic choice. There is a lot of information already presented throughout the chapters, evidently more about breadth than depth. Ideas seem to become more outlandish as the book progresses, partially chronological in the history of discoveries and partially working from small scale to large scale in terms of celestial objects (from talking about asteroids to planets to galaxies to the universe itself).
It is admirable that Stewart addresses the nature of astronomy and science itself. Although not as explicit, it is clear that he encourages readers to think critically and not accept theory as fact as he would often repeat the notion of scientists correcting other’s (or even their own) mistakes and always trying to prove things wrong. That’s how science works. As Stewart says himself, “if no one is allowed to get things wrong, no progress will ever be made” (261). He acknowledges this fundamental idea while remaining skeptical of some of astronomy’s most recent theories, such as the multiverse theory. At the same time, he encourages readers to never doubt what is possible in the realm of astrophysics because there was once a time when spaceflight was believed to be impossible and people could not fathom the idea of landing on the moon.
Sure, Stewart makes some phenomena such as comets and extraterrestrial life not as exciting and dramaticized as they are in science fiction films. However, it is important to know the basis for the mathematical principles and scientific theories behind such phenomena in order to understand why accurate, precise measurements and careful calculations are important. In cases such as sending a space shuttle full of humans into orbit, misunderstandings and miscalculations can be costly - even deadly. In general, the book is very well written and serves as an excellent source for both information and entertainment for any reader who is interested in the ever intertwining relationship between math and science. Ian Stewart’s Calculating the Cosmos allows readers to gain a deeper understanding of the significance of mathematics as well as develop an appreciation for all it has contributed - not only to astrophysics, but to the world as a whole.
Such questions include: What is the likelihood of intelligent life existing outside of planet Earth? What might such extraterrestrials look like? What alternative theories are there to the big bang? What is the shape of the universe? Why are we here? Is it possible that there are more universes than the one we inhabit? Stewart explores these concepts as well as gravity, the formation of the moon, the content of Saturn’s rings, spectroscopy, and black holes - all of which have some relation to mathematical principles, as difficult as it may be to believe. There’s even a mathematical explanation for the gap between planetary orbits - a pattern, in fact! Since ancient times, astronomers and mathematicians have utilized components of geometry and calculus to gain a better understanding of how the world works. In Calculating the Cosmos, Stewart emphasizes the absolute necessity of these mathematical techniques in order to obtain answers.
Although Stewart’s purpose of the book is evidently to convince readers of the importance of math in scientific discovery, specifically in relation to astrophysics, the majority of the math explained in the book is not explicit. He does offer a few equations and calculations that may leave the mathematically-challenged with a headache, but for the most part, the physics is fairly straightforward and demonstrated concisely with the experience and knowledge of the general public in mind. Therefore, much of the science is understandable for readers who have a high school education and therefore a foundation for comprehending the more complicated concepts. Still, some points of description went a little overboard with basic physics such as the concept of momentum, while at other points, short passages of complex science might deserve a quick re-read. In that respect, there was some inconsistency, albeit little of it. Moreover, he emphasizes how intricate and complicated the math can be, and simultaneously expensive and time-consuming.
One wouldn’t expect much on the narrative side of things, but Stewart delves into the history of currently accepted theories and chronicles the discoveries that led to our modern understanding of the universe. For some readers, these tidbits may even be more engaging than all the numbers and calculations. In addition, Stewart includes a few pop culture references - from a Joni Mitchell song about stardust to science fiction’s portrayal of humanoid aliens - in order to add a bit of humor to his writing. He keeps his diction simplified to ensure understanding among the everyday readers, although when it is necessary to use astronomical jargon he includes a synonym alongside the vocabulary. For example, libration is a fancy term for wobbles (Stewart 42). To help with comprehension of some of the more difficult concepts, Stewart offers sufficient analogies such as comparing the search of trojan asteroid blips in light curves to the search of lion tracks in a game reserve (194). Stewart writes with exceptional flair and takes advantage of various sentence structures, especially very short sentences for emphasis. He keeps an upbeat and slightly subjective tone throughout the book that almost makes one forget that they are reading a book about science.
A few passages were slow, but in general, the book was fast-paced. A few topics were not explored fully in depth as much as they could have been, such as the gravitational evidence for dark matter, although that can be respected as an artistic choice. There is a lot of information already presented throughout the chapters, evidently more about breadth than depth. Ideas seem to become more outlandish as the book progresses, partially chronological in the history of discoveries and partially working from small scale to large scale in terms of celestial objects (from talking about asteroids to planets to galaxies to the universe itself).
It is admirable that Stewart addresses the nature of astronomy and science itself. Although not as explicit, it is clear that he encourages readers to think critically and not accept theory as fact as he would often repeat the notion of scientists correcting other’s (or even their own) mistakes and always trying to prove things wrong. That’s how science works. As Stewart says himself, “if no one is allowed to get things wrong, no progress will ever be made” (261). He acknowledges this fundamental idea while remaining skeptical of some of astronomy’s most recent theories, such as the multiverse theory. At the same time, he encourages readers to never doubt what is possible in the realm of astrophysics because there was once a time when spaceflight was believed to be impossible and people could not fathom the idea of landing on the moon.
Sure, Stewart makes some phenomena such as comets and extraterrestrial life not as exciting and dramaticized as they are in science fiction films. However, it is important to know the basis for the mathematical principles and scientific theories behind such phenomena in order to understand why accurate, precise measurements and careful calculations are important. In cases such as sending a space shuttle full of humans into orbit, misunderstandings and miscalculations can be costly - even deadly. In general, the book is very well written and serves as an excellent source for both information and entertainment for any reader who is interested in the ever intertwining relationship between math and science. Ian Stewart’s Calculating the Cosmos allows readers to gain a deeper understanding of the significance of mathematics as well as develop an appreciation for all it has contributed - not only to astrophysics, but to the world as a whole.
August 29, 2021
An interesting read, but a couple of points didn't quite click for me: 1) it was written a few years ago, so inevitably some of the ideas are already a few years old, but mostly 2) it didn't quite flow as a story in the way that the very best popular science books I've read do (eg Marcus Chown). It was well written, and undoubtedly Ian Stewart is highly intelligent and incredibly well respected. I particularly liked him explaining different opposing theories with some pros and cons and then giving his personal view only afterwards. But somehow it was a bit heavy going in places, a little too much like an academic paper than a popular science book. Whilst I still followed along, it wasn't exactly a light holiday read to indulge my interest, which I thought was a shame. Perhaps part of it was not having internet access to look up the references and online visualisations to go alongside some of the passages - only my own fault for a reader in 2021.
June 21, 2017
An utterly fascinating discussion of all things cosmological. Ian Stewart explains all of the various aspects of the cosmos in such a clear and concise way that it makes the incomprehensible understandable. He also describes the math behind these mindblowing concepts in such a way that even someone as mathematically challenged as myself can almost grasp it. Truly a remarkable book.
May 27, 2017
A really nice overview of modern cosmology. My only cavil with the book is that it is more "Cosmos" than "Caclulating". Don;t read it for the math, read it for the astrophysics.
November 17, 2023
Animal, para quem gosta do tema em detalhes.
April 13, 2018
Si algo queda completamente claro en este libro es que no sabemos una castaña sobre el universo. No estamos ni siquiera en la orilla de la playa cósmica, como dijo Carl Sagan, sino bien en el interior, y encima en medio de montañas harto escabrosas.
Pese al título en el libro no aparece ninguna ecuación relevante. Más bien se trata de una descripción de la física, astrofísica y cosmologías actuales pero desde un punto de vista matemático, por lo que resulta un análisis bastante original y refrescante, haciendo hincapié en lo limitado de las técnicas matemáticas asociadas a dichas explicaciones.
De hecho me ha dejado bastante estupefacto, porque cuando los astrónomos, astrofísicos y cosmólogos explican sus teorías, se muestran mucho más seguros sobre los cálculos realizado que Ian Stewart, que refleja las limitaciones y las simplificaciones que han sido necesarias para poder explicar dichas teorías.
Hasta el punto de dejar bien claro que casi casi toda la astronomía actual no es más que un endeble entramado de ecuaciones matemáticas simplificadas hasta la saciedad. Y algo de lo que ya era consciente desde hace tiempo: muchos artificios para encajar partes que no cuadran.
Esto lleva al autor a dar un buen rapapolvo hasta a las teorías supuestamente establecidas como la del Big Bang, rozando la cuántica y hasta la Relatividad. Y no os digo si hablamos de la Teoría de Cuerdas o del Multiverso.
—
Una cosa que me ha impactado, y no poco, es el concepto de “tuberías” respecto al movimiento de los astros. Es decir, los astros se mueven dentro de una serie de tubos que delimitan el camino que pueden seguir, en lugar de hacerlo por trayectorias completamente definidas hasta cierto grado de exactitud.
Con eso no quiero decir que los tubos existan, sino que se trata de una serie de autopistas virtuales que marcan el camino de los objetos astronómicos, incluyendo intersecciones y cambios de rumbo como si los objetos pudieran tomar salidas a voluntad.
Hay más cosas interesantes en este libro, que creo vale la pena leer para recibir un jarro de agua todavía más fría que el de Smolin, o más bien el mismo enfriamiento que The Trouble with Phisics arroja sobre la física.
Como resumen del libro, me ha quedado bien clara la idea de que no tenemos ni repajolera idea de cómo funciona nuestro universo, ni siquiera cómo pudo crearse nuestro sistema solar, y que todas esas moderneces más allá de la Relatividad no son más que teorías con muchos fallos y más intentos de ocultar debajo de la alfombra las inconsistencias más flagrantes.
September 12, 2020
In my attempts to read this book, I had about five false starts. I kept giving up. I’d make it, like, twenty pages in and just throw my hands up. I returned it to the library and checked it out again and again, trying to get through it. I was a probe sent to land on a faraway planet and mission control back home just couldn’t get the knack.
Then, after the early days when the coronavirus began to affect our lives, I made a final dash to our local library and I picked this book up—again.
Briefly, Stewart’s book is an absolute kick. Somehow, even though the language is often about as over-my-head as Voyager 1 (or 2, I forget), the amount of material discussed is just plain awe inspiring. But there were many, many sections I had to just sprint through. I could reread this book twenty times and still not understand most of it.
This varies from a lot of other physics books I’ve read, like those written by Carl Sagan, Steven Hawking or Carlo Rovelli.
Just the same, Ian Stewart’s English humor and sensibility was a huge plus.
Toward the end of the book, the author started tearing through a bunch of different theories about the origins and fate of the universe and raising questions about them all. I sense that even he was sprinting to the end.
In conclusion, Stewart completely leaves the door open for subsequent scientific work on the subject. And that was refreshing and reassuring to read.
Then, after the early days when the coronavirus began to affect our lives, I made a final dash to our local library and I picked this book up—again.
Briefly, Stewart’s book is an absolute kick. Somehow, even though the language is often about as over-my-head as Voyager 1 (or 2, I forget), the amount of material discussed is just plain awe inspiring. But there were many, many sections I had to just sprint through. I could reread this book twenty times and still not understand most of it.
This varies from a lot of other physics books I’ve read, like those written by Carl Sagan, Steven Hawking or Carlo Rovelli.
Just the same, Ian Stewart’s English humor and sensibility was a huge plus.
Toward the end of the book, the author started tearing through a bunch of different theories about the origins and fate of the universe and raising questions about them all. I sense that even he was sprinting to the end.
In conclusion, Stewart completely leaves the door open for subsequent scientific work on the subject. And that was refreshing and reassuring to read.
June 15, 2020
The book moves from the formation of the Earth and the Moon to the planets and asteroids of the solar system and then to the wider universe. The architecture of space and time, how galaxies form, why stars implode, how everything began and how it will all end - are described by the author. Beginning with the Babylonian integration of mathematics into the study of astronomy and cosmology, the book traces the evolution of our understanding of the cosmos - how Kepler’s laws of planetary motion led Newton to formulate his theory of gravity, how the motion of Mars led to Einstein formulating his general theory of relativity, how the discovery of the fact of expanding universe led to the development of the Big Bang theory and, in turn, led to theorize new components like inflation, dark matter and dark energy. The author also finally highlights the inconsistencies that have developed and the still unexplained observations and leaves us with the question whether a new theory and thinking is required.
A great book but may be somewhat technical especially related to some mathematical concepts.
A great book but may be somewhat technical especially related to some mathematical concepts.
March 7, 2021
I don't know where to start. Reading this book was the best experience when it comes to reading books in the recent years. It is well researched and written. Considering that the author is a renowned cosmologist, no one should be surprised. But the amount of effort put in is admirable.
I especially appreciate the comprehensive review of the origin of a problem, the hypothesis posed and all the effort and argument around it, leading the latest stage of research. If you are tired of hearing the buzzwords "multiverse", "dark matter", "event horizon" but never get the chance to truly understand it. Then this book does its work perfectly.
I have drawn 10+ mind maps for this book and it is worthy of it. Although it slowed down my reading progress in the meantime.
It felt so difficult to say goodbye to this book although I swear during the reading I can't wait to rush to the end. Well, what we know about the universe is just at the beginning. So I am looking forward to the "sequel" of this one.
I especially appreciate the comprehensive review of the origin of a problem, the hypothesis posed and all the effort and argument around it, leading the latest stage of research. If you are tired of hearing the buzzwords "multiverse", "dark matter", "event horizon" but never get the chance to truly understand it. Then this book does its work perfectly.
I have drawn 10+ mind maps for this book and it is worthy of it. Although it slowed down my reading progress in the meantime.
It felt so difficult to say goodbye to this book although I swear during the reading I can't wait to rush to the end. Well, what we know about the universe is just at the beginning. So I am looking forward to the "sequel" of this one.
December 26, 2016
This is a very readable account of the mathematics that underlie several of the most important concepts and phenomena in modern astrophysics. Stewart is at his best when dissecting the current theories of galaxy formation as well as the theories of our own moon's formation; these sections are not only very readable but also quite thorough and captivatingly written. Additionally, his brief discussion at the end of book surrounding the fundamental flaws in notions of the, "fine-tuning," of our universe's cosmological constants is an excellent précis to the more thorough work on this subject by Victor Stenger. His disagreement with multiverse theory is presented well though much too briefly and a greater amount of material here would have made for extremely interesting reading. This is an important book that I would recommend to those with a background in the math and theories behind the subjects discussed.
September 11, 2024
70%
Calculating the cosmos. The reason I gave this book 70% is because I do enjoy it, but how much new stuff did I actually learn from this? I don't think I learned anything new from this. I was reminded of several pieces of content, and I was like, okay, cool. I love hearing about space, learning about space, but did I learn anything? No. We went over quantum mechanics, physics, gravitational constants, quantum constants, multiple different theories, and I was already informed of all this stuff. And this would have been a great book if it was placed as a general overview earlier on in my journey. But since it wasn't, we're to this point where it's like, hey, it's already told all this stuff. So there's nothing I can do here, which left me feeling kind of disappointed. But I still enjoyed the content.
Calculating the cosmos. The reason I gave this book 70% is because I do enjoy it, but how much new stuff did I actually learn from this? I don't think I learned anything new from this. I was reminded of several pieces of content, and I was like, okay, cool. I love hearing about space, learning about space, but did I learn anything? No. We went over quantum mechanics, physics, gravitational constants, quantum constants, multiple different theories, and I was already informed of all this stuff. And this would have been a great book if it was placed as a general overview earlier on in my journey. But since it wasn't, we're to this point where it's like, hey, it's already told all this stuff. So there's nothing I can do here, which left me feeling kind of disappointed. But I still enjoyed the content.
March 15, 2023
How can we know anything about Cosmology when it's all up there? Thanks to the power of mathematics and other tools, we are well-equipped to discover many facets of knowledge. For example, what is the Sun? Spectroscopy makes finding the composition of stellar objects a walk in the park.
Ian Stewart brings his usual lucid prose and explains how we perform these mini-miracles. Although the target audience is the layperson, Stewart drops some jargon in the text. He answers so many questions that I can't summarize them well.
One issue with the book is how few equations get included within the pages. Despite that, there are plenty of graphs.
I enjoyed the book. Thanks for reading my review, and see you next time.
Ian Stewart brings his usual lucid prose and explains how we perform these mini-miracles. Although the target audience is the layperson, Stewart drops some jargon in the text. He answers so many questions that I can't summarize them well.
One issue with the book is how few equations get included within the pages. Despite that, there are plenty of graphs.
I enjoyed the book. Thanks for reading my review, and see you next time.
September 16, 2024
Ian Stewart’s “Calculating the Cosmos: How Mathematics Unveils the Universe” (2016) traces the evolution of our understanding of the cosmos and (to some extent) how mathematics played a role in that development. There are chapters on topics such as the theory of gravity and planetary motion, the sizes and distribution of moons, comets, asteroids, exoplanets, the Big Bang, dark matter, and dark energy. Some chapters are difficult to follow, but others are relatively straightforward. The chapter on dark matter is extremely interesting and is a nice critique of theories about, and evidence for and against the existence of dark matter. Recommended if you are interested in astronomy and cosmology.
July 17, 2022
This is a book about cosmological discoveries driven by mathematics. Runs the gamut from geocentric vs heliocentric to predicted orbits of planets to gravitic lensing, black holes and dark matter.
I read this as an audio book, and I hope the printed version has references and equations for some of the math in the end notes. This is definitely an interesting approach to looking at historical science.
The audio book was also a problem for the reader, Dana Hickox. He frequently mispronounced mathematical terms and the names of mathematicians and other scientists; this ranged from cringeworthy to laugh-out-loud absurdity. Would highly recommend skipping this format.
I read this as an audio book, and I hope the printed version has references and equations for some of the math in the end notes. This is definitely an interesting approach to looking at historical science.
The audio book was also a problem for the reader, Dana Hickox. He frequently mispronounced mathematical terms and the names of mathematicians and other scientists; this ranged from cringeworthy to laugh-out-loud absurdity. Would highly recommend skipping this format.
January 19, 2023
Excellent read. The author did a good job of explaining some basic concepts and some very complex topics. I was able to understand most of it, although the description of rotating black holes kind of lost me. The book also inspired me to go back and learn some math and physics that i haven't thought about since the seventies. The good news is that it doesn't seem as hard now as it did then and there are some great on line lectures on the topic to support self study.
If your hobby is reading about astrophysics or cosmology, this book will be a great addition to your library.
If your hobby is reading about astrophysics or cosmology, this book will be a great addition to your library.
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