The Babylonians invented it, the Greeks banned it, the Hindus worshipped it, and the Church used it to fend off heretics. For centuries, the power of zero savored of the demonic; once harnessed, it became the most important tool in mathematics. Zero follows this number from its birth as an Eastern philosophical concept to its struggle for acceptance in Europe and its apothThe Babylonians invented it, the Greeks banned it, the Hindus worshipped it, and the Church used it to fend off heretics. For centuries, the power of zero savored of the demonic; once harnessed, it became the most important tool in mathematics. Zero follows this number from its birth as an Eastern philosophical concept to its struggle for acceptance in Europe and its apotheosis as the mystery of the black hole. Today, zero lies at the heart of one of the biggest scientific controversies of all time, the quest for the theory of everything. Elegant, witty, and enlightening, Zero is a compelling look at the strangest number in the universeૼand one of the greatest paradoxes of human thought....more
Paperback, 248 pages
Published
September 2000
by Penguin
(first published 2000)
Michael CurtisYes. Some reviewers quibble over details and rhetoric, but the book covers a lot of math history, offers good explanations, and helped this…moreYes. Some reviewers quibble over details and rhetoric, but the book covers a lot of math history, offers good explanations, and helped this non-mathematician better understand some math concepts.(less)
Ketika Leonardo da Pisa (kelak dikenal juga sebagai Fibonacci) memperkenalkan angka nol ke Eropa, dia banyak dihujat kaum terpelajar di sana. Alasannya, selain angka tersebut berasal dari negeri kaum kafir, Arab (sebenarnya awal mula sejarah angka nol berasal dari peradaban Hindu, tapi diadaptasi, 'dipermudah', dan 'diperluas' oleh ilmuwan arab Al-Khawarizmi), orang2 Eropa juga merasa terancam oleh kehadiran angka ini. Dengan hadirnya angka nol, bisa dikatakan sistem numeral Romawi yang terdisiKetika Leonardo da Pisa (kelak dikenal juga sebagai Fibonacci) memperkenalkan angka nol ke Eropa, dia banyak dihujat kaum terpelajar di sana. Alasannya, selain angka tersebut berasal dari negeri kaum kafir, Arab (sebenarnya awal mula sejarah angka nol berasal dari peradaban Hindu, tapi diadaptasi, 'dipermudah', dan 'diperluas' oleh ilmuwan arab Al-Khawarizmi), orang2 Eropa juga merasa terancam oleh kehadiran angka ini. Dengan hadirnya angka nol, bisa dikatakan sistem numeral Romawi yang terdisi dari abjad (misal I untuk 1, V untuk 5, dll) akan menjadi usang.
Memang, untuk penggunaan luas, sistem bilangan Romawi menjadi ribet dan terlalu panjang. Karena, pada hakikatnya, bilangan Romawi nyaris tidak mengenal nilai tempat. Akibatnya, saat menuliskan angka dengan nilai bilangan besar, sangat sulit untuk menuliskan bilangan tersebut dengan angka Romawi. contohnya, bilangan 1888 jika ditulis dalam bilangan Romawi menjadi MDCCCLXXXVIII. Biar lebih dramatis lagi, coba tulis bilangan 14.792.483.388 dalam bilangan Romawi. Berapa baris yang dibutuhkan? :)
Kedua, bilangan Romawi sama sekali tidak bisa digunakan untuk menyatakan bilangan desimal. Mungkin angka 1/2, 1/4, dsb (jumlahnya sedikit) masih bisa ditulis dengan berupa simbol sederhana, tapi bagaimana jika menulis 11/17? berapa nilai eksaknya? Semua kesulitan itu disebabkan oleh satu hal, sistem bilangan Romawi tidak mengenal angka nol!
Akhirnya, dengan mempertimbangkan hal tersebut, bangsa Eropa menerima penggunaan bilangan nol. Namun, seandainya mereka dapat meramal masa depan dan melihat efek angka nol bagi peradaban modern, niscaya mereka akan mati-matian mempertahankan sistem bilangan Romawi dan menolak kehadiran angka nol.
Apa pasal? ternyata, angka nol tak selugu penampilannya. Meski bentuknya sangat bersahaja, cuma berbentuk lingkaran (0), bahkan di beberapa budaya hanya cukup diwakili tanda titik (.), namun bisa dikatakan, dari angka nol inilah segala mula masalah sains, teknologi, hingga filsafat bermula. Bisa dikatakan, tanpa angka nol, peradaban manusia tidak mungkin memiliki wajah seperti dewasa ini. (komputer dan internet yang jauh lebih ajaib daripada Piramida Mesir tidak akan hadir tanpa angka nol. inget sistem bilangan biner?)
Awal bab buku ini memberikan contoh bagaimana sebuah kapal selam canggih nan mahal nyaris tenggelam dan tak berdaya karena hal sepele, sistem pemrograman pengendali mesinnya ngadat karena dalam pemrograman komputasinya, ada satu kehadiran angka nol yang tidak pada tempatnya. Ajaib. Hanya perlu satu angka nol ntuk menjadikan kapal selam canggih dan mahal itu menjadi rongsokan besi karatan di dasar samudera. Yah, meski pada akhirnya kapal tersebut dapat diperbaiki, tapi itupun perlu usaha ekstra keras, terlambat sedikit saja, bisa fatal akibatnya.
Di lain pihak, fisika (yang pada gilirannya nanti tanpa ampun menyeret dunia filsafat dalam gejolak arus membingungkan) hampir mengalami kematian karena terbentur masalah angka nol. Pada penghujung abad 19, Fisikawan terkenal Inggris, Lord Calvin (John Calvin, terkenal karena kajiannya di bidang kalor, namanya diabadikan menjadi nama satuan standar pengukur temperatur mutlak, derajat Kalvin) mengatakan bahwa ilmu Fisika sudah selesai. teori Mekanika Newton, teori gelombang elektromagnetik Maxwell, (dan secara tidak langsung dia menyebut teori termodinamika Calvin :-p) sudah dapat menjabarkan semua fenomena fisika yang ada. Apalagi yang perlu dipelajari dalam fisika?
Namun, semua mimpi indah fisikawan itu mengalami benturan dahsyat yang nyaris membuat dunia fisika hancur lebur. Mimpi buruk pertama dimulai saat seorang fisikawan ternama, Khircoff, pada tahun 1859, menyelidiki tingkat intensitas radiasi emisi yang dipancarkan oleh benda hitam (Black Body). Namun, hasil radiasi emisi ini sungguh di luar harapan para fisikawan saat itu. Teori elektromagnetik Maxwell yang seharusnya bisa menjelaskan fenomena itu dengan mudah dan indah, menjadi sama sekali tidak berguna. Bahkan teori probabilitas Boltzman yang terkenal canggih pun menjadi kelihatan aus saat digunakan untuk menjelaskan fenomena ini. Fenomena baru ini secara langsung menjadi ancaman baru nan serius bagi fisika. Ucapan Calvin tinggal menjadi sekedar mimpi.
Revolusi fisika pun dimulai. dengan rumus yang bisa dikatakan 'untung-untungan', Wilhelm Wien, menjelaskan fenomena ini dengan melalui hukumnya yang termasyhur, Wien's Law. Dikatakan untung-untungan karena dia membuat rumus baru yang tidak memiliki dasar fisika mantap menurut teori klasik, tetapi rumusnya cocok dengan data hasil pengamatan. Malangnya, Hukum Wien hanya cocok dengan percobaan jika percobaan tersebut dilakukan pada radiasi dengan frekuensi tinggi. Pada frekuensi rendah, rumus tersebut memberikan hasil yang jauh dari harapan. Bantuan kedua datang dari duet Rayleigh-Jeans. Dengan keberuntungan yang sama, mereka berhasil mencocokkan data percobaan dengan rumus 'sederhana'. Namun sekali lagi, mimpi buruk itu belum berakhir. Rayleigh-Jeans's Law, uniknya berkebalikan dengan Wien's Law, rumus ini hanya berlaku pada radiasi benda hitam yang memiliki frekuensi rendah! Jika teori ini diterapkan pada frekuensi tinggi, akan muncul yang namanya "ultraviolet catastrophe" atau "bencana ultraviolet". Arti fisik fenomena ini adalah, ini contoh sederhana saja, jika suatu benda memancarkan radiasi tingkat tinggi, maka radiasi yang dihasilkan akan menjadi tak terhingga yang pada akhirnya akan melampaui batas maksimum, tak penah berakhir. Artinya, jika kita memegang cangkir kopi panas, maka radiasi panas dari kopi akan terus memancar sampai tak terhingga sehingga tangan kita akan hangus terbakar sampai ke taraf atom! Padahal bumi tiap hari disinari matahari! jelas kehidupan akan musnah (bahkan tak akan pernah ada).
Tapi, kita tidak mengalami kejadian mengerikan seperti itu kan? Kajian2 fisikawan berikutnya adalah upaya 'mengawinkan' kedua hukum tadi menjadi teori tunggal. Namun, sekeras apapun mereka berusaha, maka sekeras itu pula tamparan kegagalan yang mereka terima. Seperti terbang, semakin tinggi terbang ke angkasa, maka akan semakin sakit jua saat jatuh terhempas tanah.
Namun, sebelum fisika hancur lebur, Sang Juru Selamat muncul. Fisikawan Jerman, Max Planck menawarkan solusi ajaib sekaligus mengerikan. Melalui sudut pandang yang sama sekali baru (bahkan bisa dikatakan bertentangan dengan teori mapan sebelumnya) Planck merumuskan bahwa problem radiasi benda bisa diselesaikan jika benda tersebut diamati dengan menganggap energi terpancar dari benda tersebut dapat 'dipotong-potong' ('potongannya' disebut kuanta). Gagasan ini sangat radikal dan bisa dikatakan terlepas dari teori mapan sebelumnya (bahkan bisa dikatakan bertentangan). Analogi dari kuanta ini adalah jika kita sedang menyetir mobil dan ingin menaikkan kecepatan dari 30 km/jam menjadi 40 km/jam, maka menurut teori kuantum, speedometer kita TIDAK AKAN PERNAH melewati angka 33 atau 38 km/jam! Dari angka 30, secara ajaib, langsung loncat ke angka 40! Ini karena energi dipancarkan secara paket-an, bukan secara perlahan dan kontinu. Teori klasik jelas tidak mengijinkan hal ini.
Kelak teori ini dengan bantuan Einstein, Born, Heissenberg, Dirac, de Broglie, Schrodinger, Pauli, Bohr, dsb melahirkan cabang baru dalam fisika yang disebut fisika modern, teorinya dikenal sebagai Teori Kuantum. (dan sejak saat itu pula, apa2 yang ada embel-embel 'kuantum'-nya akan dianggap hebat, bahkan hingga saat ini, suatu seminar pelatihan akan tampak hebat jika diberi nama kuantum learning, dll) :-p
Dengan pendekatan jeniusnya tadi, ajaibnya, fenomena radiasi benda hitam tadi dapat dijelaskan Planck dengan sempurna baik itu pada frekuensi tinggi maupun rendah. bahkan 'kesempurnaan'-nya terlalu menakutkan. Data hasil percobaan dan data hasil hitungan rumus Planck sama persis!!!
Apa yang membuat teori Planck sedemikian sukses? Sebelumnya Planck sendiri mengalami keraguan dalam mempublikasikan teorinya. Bagaimana jika potongan tadi sedemikian kecilnya sehingga bisa dikatakan nol? teori sempurna tadi juga akan musnah! Namun, untuk menghindari hal itu, dan inilah kunci keberhasilannya yang gagal dilakukan para pendahulunya (dan juga apa hubungan cerita panjang lebar tadi dengan ripiyu buku ini :-p), adalah dia menghindari angka nol!!! Angka Nol adalah pemusnah! untuk itu dia memperkenalkan suatu konstanta yang menjadi batas minimal agar suatu benda 'berperilaku normal', tidak menimbulkan bencana ultraviolet, yang dikenal dengan nama Konstanta Planck (h), dinamakan demikian untuk menghormatinya.
Sangat kecil tapi BUKAN NOL!!! karena konstanta super mini tadilah kita bisa aman saat meniup lilin ulang tahun atau berjemur sinar mentari pagi. Bersyukurlah pada hal-hal kecil dalam hidup ini.
Belakangan teori kuantum berkembang lebih jauh lagi hingga 'membongkar' habis-habisan struktur atom. Hingga hari ini, milyaran dollar telah terkuras hanya demi 'mengupas' isi atom hingga bagian paling-paling-paling-paling-paling dasar. Bidang kajian Fisika Elementer dewasa ini sudah pada taraf 'tak dapat diungkapkan dengan kata-kata'. namun sekali lagi, mereka terbentur satu hal. Atom tidak dapat dipecah lagi sehingga menjadi nol... Untuk menjadikannya nol, perlu energi tak terbayangkan, perlu biaya lebih mahal dan usaha lebih ekstrem. sekali lagi NOL sang biang kerok! XD
Apa mimpi buruk fisika sudah berakhir? Apakah sudah berakhir kekalahan fisika dari angka nol? belum saudara-saudara! goncangan kedua muncul dari Sang Legenda Termasyhur, Einstein! Dengan teori relativitas (terutama teori relativitas umumnya) Einstein telah mengubah takdir fisika selamanya. Sebelumnya para fisikawan dan (sebagian) kaum filsuf berpendapat bahwa alam semesta bersifat konstan alias steady state. Semesta tidak berawal juga tak berakhir. Semesta sudah ada 'sejak dulu'. Tidak ada perubahan, tidak ada penciptaan, tidak ada Tuhan! Edwin Hubble (namanya diabadikan menjadi nama teleskop ruang angkasa paling terkenal) mengamati bahwa jagat raya sedang mengembang. tapi apa artinya? Nah, di sini Einstein memainkan peranannya. Secara mencengangkan dia bisa membuktikan secara matematis (seperti Planck, data hasil rumus sama dengan data percobaan dengan ketelitian mengerikan) bahwa alam semesta itu mengembang! Artinya, jika waktu diputar ke belakang, alam semesta ternyata 'lahir' melalui proses yang dikenal dengan nama Big Bang.
Alam semesta telah lahir. alam semesta diciptakan. Segalanya memiliki awal. Ada Tuhan.
Oya, alasan mengapa Einstein digelari jenius terbesar sepanjang masa (semua ikon kata 'jenius' pasti mengacu padanya, mulai dr komik hingga film) adalah berbeda dengan teori kuantum yang hasil keroyokan, teori relativitas lahir, diurus, dan dikembangkan sendirian oleh Einstein! nyaris bantuan dari ilmuwan lain hanya berkonstribusi 'secuil'. Bisa dikatakan karya tunggal Einstein!
Lantas bagaimana proses penciptaan alam semesta tersebut dimulai? Meski dengan sukses menerangkan proses pengembangan jagat raya, teori relativitas yang canggih itu mentok saat, sekali lagi si biang kerok muncul, teori itu 'runtuh' jika mengukur jagat raya pada waktu (t) sama dengan NOL!!!!
Belakangan Hawking berusaha memadukan teori relativitas dengan teori kuantum untuk menjelaskan penciptaan jagat raya. Sebelum-sebelumnya, ini ajaibnya, kedua teori super canggih tersebut sama sekali tidak mengalami kecocokan. Seperti teori Wien dan Rayliegh di atas yang tidak ada kecocokannya, kedua teori ini juga sama. Saat alam semesta (yang dapat dipelajari dg relativitas) diciptakan, kan wujud aslinya masih berupa bentuk penyusun atom (yang dipelajari dengan kuantum). seharusnya ada titik temunya kan? Tahun-tahun terakhir hidup Einstein dihabiskan untuk menggeluti titik temu ini yang dia sebut sebagai teori medan gravitasi, sayang sampai meninggal, usaha belum berhasil. 'warisan' Einstein inilah yang menjadi cikal pergolakan intelektual dalam fisika hingga saat ini.
Tapi ternyata titik temu itu tidak semudah seperti yang diperkirakan. Kemudian Hawking 'dianggap berhasil' memadukan kedua teori tsb (secara keliru teorinya disebut Theory of Everything, TOE, padahal belum 'sempurna' dan tidak dapat menjelaskan segalanya) dengan asumsi yang radikal. Alih-alih menganggap alam semesta lahir pada saat t=0, Hawking dengan matematika canggihnya, 'membuktikan' bahwa ada waktu (t) sebelum t=0 atau yang disebutnya waktu imajiner. Artinya ada waktu sebelum waktu. dengan kata lain, tidak ada awal, tidak ada penciptaan. tidak ada Tuhan. Bisa dikatakan Hawking adalah fisikawan atheis terbesar sepanjang masa.
Meski teori Hawking belum final, tapi konsekuensi pergolakan fisika ini tak ayal menyeret kaum filsuf dan agamawan. di satu sisi mereka mengklaim ada penciptaan (ada Tuhan), di sisi lain ada klaim tidak ada penciptaan (tidak ada Tuhan). Perdebatan tanpa akhir ini tidak akan mereda sebelum mereka bisa membuktikan, apa yang terjadi saat waktu sama dengan NOL?!!
Nol! Nol! Nol! Nol dan sekali lagi, Nol!!!!!!!!!! ------------------------------------------------------------------------------------------------------- Okeh, segituh dulu pelajaran Fisikanya :P
nah, 'kegilaan' akibat angka Nol inilah yang dibahas dalam buku ini. Yah, meski gak terlalu mendalam, tapi secara lengkap, buku ini merangkum sejarah kelahiran angka nol dan usaha-usaha manusia dalam mengalahkan angka nol.
Mengapa banyak orang begitu takut pada angka 'sederhana' ini? (banyak pelajar dan mahasiswa takut jika ujian mereka mendapatkan nilai nol XD). Rangkuman usaha pengalahan angka nol inilah yang menjadi tema mendasar buku ini. Begitu panjangnya usaha manusia mengalahkan esensi angka nol ini, namun sejauh ini kita harus mengaku kalah. Hasil yang dicapai bisa dikatakan nol. :-)
Apakah angka nol bisa dikalahkan?
Mengapa dalam kesahajaannya angka Nol justru menimbulkan kekompleksitasan yang mencengangkan?
Apakah angka nol justru merupakan bentuk eksistensi 'Tuhan' sehingga sebegitu dahsyatnya? (Saat membaca buku ini, saya nyaris percaya jika nol adalah Tuhan itu sendiri!)
Jawabannya ada di buku ini (sebagian :D)
Udah ah, whhooaaa... capek juga ternyata :-p
oyah, 'coz latar belakang saia ttg fisika adalah NOL, mohon maap jika ada data/fakta yang diuraikan di atas keliru. yang pernah/sedang menjalani pendidikan di bidang fisika, silakan koreksi.
cmiiw :)
--------------------------------- PS:
sejak dulu kala, angka nol memang dianggap 'mengganggu' bahkan oleh para matematikawan sendiri. sebagai contoh, angka nol bisa membuktikan kekacauan hukum berhitung. Contoh populer dicantumin di bawah ini,
Misal a = b a² = ab ... (kali kedua ruas dengan "a") a² + a² = a² + ab ... (tambahkan kedua ruas dengan a²) 2 a² = a² + ab 2 a² - 2 ab = a² - 2 ab + ab ... (kurangi kedua ruas dengan "2 ab") 2 a² - 2 ab = a² - ab 2 (a² - ab) = 1 (a² - ab) ... (faktor pengali (a² - ab) dicoret) 2 = 1
Hmmm..... jelas kan, dasar matematika menyatakan 2 tidak sama dengan 1?
terus ada aturan aritmatika sederhana menyatakan bahwa jika
a x o = o a / o = ~
Mengapa suatu bilangan harus 'mnyerah' saat dibagi dengan angka nol menjadi ketakberhinggaan? Tampaknya, untuk mengalahkan angka nol, kita harus merubah aturan perhitungan di atas. Artinya? Peradaban kita kembali ke titik nol! Arrrrgggghhhhh....... sekali lagi nol! kita kalah lagi oleh angka nol! T,T...more
I’m not sure if this book quite worked out what it wanted to be. Besides getting to say, ‘and that is the power of zero’, over and over again it wasn’t quite sure where it should pitch itself and the guy writing it was never quite certain how much back knowledge he could rely on his audience actually having. This meant subjects were generally treated too cursory so I was left thinking ‘wait a second, what happened there?’. His discussion of Gauss was very complicated and hard to follow (not nearI’m not sure if this book quite worked out what it wanted to be. Besides getting to say, ‘and that is the power of zero’, over and over again it wasn’t quite sure where it should pitch itself and the guy writing it was never quite certain how much back knowledge he could rely on his audience actually having. This meant subjects were generally treated too cursory so I was left thinking ‘wait a second, what happened there?’. His discussion of Gauss was very complicated and hard to follow (not nearly as interesting as Euclid's Window The Story of Geometry from Parallel Lines to Hyperspace – A book I mentally compared this to throughout) but then, bizarrely, he went into a fairly detailed description of the Doppler effect, for instance. This book would have benefited from being edited by someone who knew virtually nothing about science. And they could have written on the sides of the page either ‘oh, I see’ or ‘WTF?’
There are many interesting little bits to all this that made it worthwhile, though – the stuff on Pythagoras was interesting – I didn’t know he didn’t eat beans because they make people fart and because they look like little genitals (I’ve never really looked closely enough at beans to notice this resemblance, to be honest, but it does sound as good a reason for a food aversion as any other, I guess). I also didn’t know he was killed because he refused to cross a field of beans (makes my rantings about only going into McDonalds to use their toilets – I only make deposits, no withdrawals - sound perfectly enlightened, if you ask me).
There were also interesting bits about vanishing points being zeros and therefore the relationship between space and zero being something non-trivial – but all of that stuff is handled much more interestingly in The Pearly Gates of Cyberspace A History of Space from Dante to the Internet (even if I still have problems with the last bits of that book).
Look, it wasn’t a bad book – but I felt it struggled due to feeling it had to make zero the core concept of all of science. This is a trend in this sort of book – you know, pick something (nutmeg or coffee or space) and show it as the nexus through which all strands of the universe can be understood. Generally, this is handled better than it has been handled here though.
Zero is the story of the number, the time that elapsed before its acceptance, and how the ideas behind it (the void and its opposite, infinity) shook the ideals of religion and science across the globe. The book advances through time chronologically, from the Greek philosophers through Renaissance paintings through Einstein's relativity, ending with speculations on string theory. And yes, all of this is fantasia on the theme of the number zero.
I didn't expect this book to be so math-heavy and soZero is the story of the number, the time that elapsed before its acceptance, and how the ideas behind it (the void and its opposite, infinity) shook the ideals of religion and science across the globe. The book advances through time chronologically, from the Greek philosophers through Renaissance paintings through Einstein's relativity, ending with speculations on string theory. And yes, all of this is fantasia on the theme of the number zero.
I didn't expect this book to be so math-heavy and sort of resented the reintroduction to the Rule of L'Hopital. But overall I found this to be an enjoyable read. My favorite parts were the discoveries of the old Greek musicians and the artists who moonlighted as math dudes. The first section of the book reminded me of that one Donald Duck cartoon [(http://en.wikipedia.org/wiki/Donald_i...)].
In my opinion, the ideal audience for this book is kids who are just about to take calculus, because Zero makes the math is both applicable and fun. But also an interesting read for adults. Just be warned that part of this book involves a journey back to high school math equations....more
A book about numbers that had me laughing out loud while I was on vacation. My wife could not understand how a book about math could make me laugh so much...
But any book that shows the horrible mistake that not having a Year 0 (i.e., 1 BC and 1 AD are adjancent) would have on history as well as subtraction mistakes, how infinity is really is zero's tricky friend, and make almost understandable the reason why the amazing equation "e ^ (pi * i) = -1" is true is pretty fantastic.
I laughed, I cried.A book about numbers that had me laughing out loud while I was on vacation. My wife could not understand how a book about math could make me laugh so much...
But any book that shows the horrible mistake that not having a Year 0 (i.e., 1 BC and 1 AD are adjancent) would have on history as well as subtraction mistakes, how infinity is really is zero's tricky friend, and make almost understandable the reason why the amazing equation "e ^ (pi * i) = -1" is true is pretty fantastic.
Wow! A tremendous amount of information is packed between the cover pages of this little hummer. I had no idea zero created such controversy--in religion and math/science. Who knew!
Fascinating facts about how our calendar system is ahead by a year BECAUSE we should have begun with year zero, not one. So, when December 31, 1999 came around, true mathematicians didn't celebrate the millenium until December 31, 2000. The Mayan's had the calendar system figured out. They started with zero, but didnWow! A tremendous amount of information is packed between the cover pages of this little hummer. I had no idea zero created such controversy--in religion and math/science. Who knew!
Fascinating facts about how our calendar system is ahead by a year BECAUSE we should have begun with year zero, not one. So, when December 31, 1999 came around, true mathematicians didn't celebrate the millenium until December 31, 2000. The Mayan's had the calendar system figured out. They started with zero, but didn't call it that.
Interesting, because we do consider some things as zero, i.e., babies are not born and then automatically considered to be 1 year old. They are 1 month, 24 months, etc, then they are 1. Makes sense.
I enjoyed how the author used examples that I could relate to when explaining thermodynamics, quantum physics, time-travel, black holes (wormholes), etc. Enjoyed the e (calculus), too.
A lot of history of our number system is enclosed in this book. Where the word Algebra came from. Who knew! A lot of names, theories, dates and some interesting stories to help bring the time period(s) to life.
Appendix E: How to Make Your Own Wormhole (time machine) was humorous.
The last chapters dove into physics, time-travel, black holes, our galaxy, how the star distances were measured, how the universe came to be (big bang theory) and how it may end, how we can travel vast distances on little fuel. It was very complicated, but I now understand why we haven't been able to do it yet. The universe is still expanding. The other galaxies are speeding further away from us. There are still large hunks of nothing in space. The author goes into what is going on with our sun. Einstein and his theories are throughout the book.
Interestingly, all this ties right into zero. A black hole is zero. Vast nothingness. How zero and God correlate.... Who knew!
I agree that this was a great book. When I was reading it, I thought what a wonderful experience it would be if the walls between Mathmatics, History, Social Science, and English weren't so high, this type of learning could take place in a middle school setting. If I had read this book when i was in middle school, I would have been wagging my tail in math class every day.
Seife, a science writer, leads us down the rabbit hole we term 'zero'. The mathematical history of the number follows a convoluted path, early on a place-holder in counting systems or a much-feared void forbidden by belief on pain of death. Eventually the path leads to infinity which, like its twin zero, figures the limit of human experience. For Seife this means that nature - described in its native language of mathematics - breaks completely with possible human experience at zero and infinity.Seife, a science writer, leads us down the rabbit hole we term 'zero'. The mathematical history of the number follows a convoluted path, early on a place-holder in counting systems or a much-feared void forbidden by belief on pain of death. Eventually the path leads to infinity which, like its twin zero, figures the limit of human experience. For Seife this means that nature - described in its native language of mathematics - breaks completely with possible human experience at zero and infinity. Yet the need to confront these limits and by increments bring them within the space of the humanly possible is the impulse behind this book. Short as it is, the first two thirds of the work provide an engaging survey of the development and application of 'zero' in mathematics. A substantial part of its current conception is bound up in the development of the calculus which underlies so much of mathematical physics. Relativity theory and the development of thermodynamics spurred further application of the concept in theories of nature. Nonetheless, singularities represent limits to what we know and perhaps can know, as well as what we can do. Zero's enigmatic presence in our thoughts is a gateway to the speculative, sometimes nearly mystical suppositions in a scientific vein that take up the final third of the work. Zero, in Seife's account, is a main character in a story about mathematics and physical science. But his account of the concept as an artifact of culture and of language may offer some additional insight. For example, in common English usage, zero is nothing apart from comparison. The activity of comparing and by extension of measuring is part of this odd number which happens to be even. ...more
Well, well, well, math. So we meet again. I have done a fantastic job avoiding you for the last ten years, but I knew it couldn't last forever. Still, I wasn't expecting you to come for me in the guise of a pick for our book club. Well played, math. Well. Played.
Basically, I think this is probably a fine book and worthy of more than the "It was okay" rating I am giving. It has lots of pictures and illustrations and appendices, and I am assuming that they mean something. One of them, in theory,Well, well, well, math. So we meet again. I have done a fantastic job avoiding you for the last ten years, but I knew it couldn't last forever. Still, I wasn't expecting you to come for me in the guise of a pick for our book club. Well played, math. Well. Played.
Basically, I think this is probably a fine book and worthy of more than the "It was okay" rating I am giving. It has lots of pictures and illustrations and appendices, and I am assuming that they mean something. One of them, in theory, even explains how through the power of the dangerous zero, you can make an equation that proves Winston Churchill is a carrot. I would have truly liked to understand that! However, nowhere in this book does Donald Duck leap out of the pages and explain the The Golden Ratio to you a la Mathmagic Land, and that proved to be the downfall of this book and me. Not gonna lie--when I got to the section about calculus, I was overcome by the the old feeling of having a test the next day and not knowing what a differential equation was, and maybe Mr. Taylor would make it a group test and I could force my ex-boyfriend to be my partner and not have to know? God, that's going be a hard email to write. STRESS. STRESS.
Where was I? Oh yes. All that said, the early chapters did come with some interesting history sprinkled around all of the equations. I never really noticed the links of old-school Judeo-Christian thought to Aristotle and his rejection of the infinite or the void. I also never realized that the Catholic Church was actually embracing new thinkers until Martin Luther decided to upset the apple cart and they went scrambling back to their traditions and finger-pointing at heretics. These sections were a little textbookish and occasionally hyperbolic ("Zero is dangerous! Zero will ROCK YOUR WORLD. Zero may kill your children!") but I think the info will stick with me.
But, in the end, if a=level of book enjoyment, and b=feelings of stupidity, and c=interesting tidbits, then A = c-b will probably give you a negative number . . . which I know we only have thanks to Eastern thought! Also, Winston Churchill is a carrot.
SueYour review is absolutely the BEST EVER!! I was utterly entertained by it and given a good idea of the character and scope of the book as well. ( AndYour review is absolutely the BEST EVER!! I was utterly entertained by it and given a good idea of the character and scope of the book as well. ( And I believe if I did read it, it would end up on my "scan for the interesting tidbits and then give away to my scientist brother" bookshelf.)...more
Oct 27, 2011 06:56AM
drea Marjorie--Merci! I am a big fan of your reviews as well.
Mom--Tell Uncle Charlie/Phil good luck!
Oct 28, 2011 12:48PM
My grade 11 math teacher gave this to me, and I remember reading it and loving it. Here I am, three years later, returning to Zero for a second read. No longer the gullible high school student (now a gullible university student!), I'm apt to be more critical of Zero. Nevertheless, it stands up to a second reading and both inspires and informs.
Imagining a world without zero is probably difficult for most people. It was especially difficult for me, as a mathematician who grew up learning calculusMy grade 11 math teacher gave this to me, and I remember reading it and loving it. Here I am, three years later, returning to Zero for a second read. No longer the gullible high school student (now a gullible university student!), I'm apt to be more critical of Zero. Nevertheless, it stands up to a second reading and both inspires and informs.
Imagining a world without zero is probably difficult for most people. It was especially difficult for me, as a mathematician who grew up learning calculus and understanding that zero is just another number. Even with Charles Seife leading the way in the first chapter, I still have trouble comprehending this idea that entire civilizations rose and fell—and achieved great things in between—without the concept of a mathematical zero.
In that respect, Zero acts as a history of the development of an idea, one that began in Babylonia and spread, via Alexander the Great, to India, where it flourished. Seife's history is necessarily balanced between East and West in this case, as it's impossible to discuss mathematics without discussing India. That being said, I would have liked to learn about how China regarded zero, even if Chinese mathematicians contributed no new developments to the number's importance as their absence from this book seems to imply. This one oversight overlooked, Zero is not your typical history book that starts in ancient Egypt or Greece and insists everything we know flows from there.
What's admirable about Zero is Seife's ability to focus on zero. The story intersects with the lives of many famous mathematicians, but the obvious slimness of this book testifies that Seife managed to distill only what was necessary about their lives in his quest to explain the mystery of zero. I'm not trying to imply, "Short books are easier for non-mathematical people to understand," but that's part of the attraction. Although it's heavier on the equations than I remembered, I would still feel comfortable recommending Zero to my non-mathematically-inclined friends. Firstly, Seife's writing is accessible, even when loaded with equations. As long as you have some basic arithmetic left over from high school, you can follow along. And I'd definitely recommend this book to high school students, like I was when I first read it: it's one of those books that opens the mind. Secondly, the narrow focus acts like a window into the history of mathematics. I have A History of Mathematics sitting next to Zero on my desk, and while the former is more complete, I somehow suspect the latter is more appropriate for a general audience. In other words, Zero is a good gateway drug.
Where Zero starts to show its seams is in Seife's rhetorical ability, which stretches itself thin even over so thin a volume. He's too dramatic for my taste, especially as he recounted the attitudes and fate of the Pythagoreans. And he's always eager to remind us of how "powerful" zero is. While I agree that zero is a pretty cool number, the constant refrain felt somewhat forced after a while, pulling me out of the book instead of keeping me comfortably ensconced in this little tutorial. Seife devotes only cursory glances at the philosophical arguments offered for or against the acceptance of zero; he tells us about Aristotle's rejection of zero but goes into little detail. While I'm sure he wanted to avoid turning the book into a text on Aristotelian philosophy, I feel like there are gaps here that, if not filled, could have been covered with a more attractive carpet.
Not perfect, not as mind-blowing as some mathematical literature I've read, Zero makes it mark because it's adequate at explanation without going overboard. I'm not sure what else to say: if you're interested in the subject, this is a good place to start. And even if you're not, hey, it's only 250 pages. What have you got to lose? Nothing. Zero!...more
An intriguing topic but not a particularly well-told story. The author clearly believes that zero and infinity are somehow dangerous and mystical, and I guess there's some evidence that mathematical philosophers have felt the same way over time. But for the most part, the general vibe of this book was, "Ooh, zero, how *mysterious*," and I wasn't really into that.
I was in the mood for some math (it had been so long since I read some pop-math literature), and Zero seemed like the perfect tome. Unfortunately, Zero is a little TOO pop-math - it hits on the same "interesting" math and physics tidbits that so many other pop-math and science books do. And while it relates all of its ideas to zero, it's not really about zero.
The first half does talk about the historical context of the concept of zero, but it is mostly about philosophy - how the concepts of zeroI was in the mood for some math (it had been so long since I read some pop-math literature), and Zero seemed like the perfect tome. Unfortunately, Zero is a little TOO pop-math - it hits on the same "interesting" math and physics tidbits that so many other pop-math and science books do. And while it relates all of its ideas to zero, it's not really about zero.
The first half does talk about the historical context of the concept of zero, but it is mostly about philosophy - how the concepts of zero and infinity affected science and religion of the time. Just when I was hoping for some math, the book switches to a by-discipline survery of, again, math and phyiscs all-star fun factoids, including Fibonacci sequences, the golden ratio, set theory, numbers larger than infinity, wormholes, etc., etc. There were some ideas in there I had not read about before, like projective geometry, but for the most part, Hawking, Bryson, and popular math authors have covered this.
So, for me, it was rehash. If you have not read much pop-math, this book is very interesting, although it definitely requires a late-high school understanding of algebra and physics to make sense. If you are familiar with the genre, you've seen most of it before....more
0 + ( It's a book about math. And I read it. ) - ( It took me nine months. ) = 0
For three weeks after I finished Zero: The Biography of a Dangerous Idea, its central figure looked out ominously at me. In that way, Charles Seife was entirely successful in this piece of pop-nonfiction, weaving together the creation of the "zero", its role in history of mathematical theory, its religious controversies, its philosophical significance and ultimately, its true place at the heart of the universe. It's t0 + ( It's a book about math. And I read it. ) - ( It took me nine months. ) = 0
For three weeks after I finished Zero: The Biography of a Dangerous Idea, its central figure looked out ominously at me. In that way, Charles Seife was entirely successful in this piece of pop-nonfiction, weaving together the creation of the "zero", its role in history of mathematical theory, its religious controversies, its philosophical significance and ultimately, its true place at the heart of the universe. It's to Seife's credit that he manages to weave out of these eclectic approaches a coherent story that borders at times upon the epic... while never being too important not to include an irreverent tangent about Pythagoras's acute dislike of beans.
If anything, Seife trends too sprightly at times. Though I admire his stance in neither dumbing down the material nor making it intimidating for the casual reader, at some point, no matter how breezily one explains black holes or the Casimir effect- there's no disguising that there are some vast concepts being covered. As it is, I believe you definitely have to at least of heard of some of these ideas (particularly in the last third) to enjoy the new contexts he weaves for them in his narrative. Myself, I sort of managed alright with some first year Calculus and Physics schooling.
I can't say I ever turned down the chance for more trivia, and Zero delivered in spades. Also, know this: the first appendix details a mathematical proof on why Winston Churchill is a carrot. Rating: 4 stars...more
Winner of the PEN/Martha Albrand Award honoring debut nonfiction from American authors, this book traces the history of the number zero from its initial appearances in Babylonian and Mayan mathematics to its widespread acceptance during the Renaissance to its role in advanced sciences. In addition to detailing the history of the number’s usage in the mathematics systems of various cultures, the book attempts to tie the concept of zero to more fundamental philosophical struggles that have accompaWinner of the PEN/Martha Albrand Award honoring debut nonfiction from American authors, this book traces the history of the number zero from its initial appearances in Babylonian and Mayan mathematics to its widespread acceptance during the Renaissance to its role in advanced sciences. In addition to detailing the history of the number’s usage in the mathematics systems of various cultures, the book attempts to tie the concept of zero to more fundamental philosophical struggles that have accompanied the mathematical changes – Aristotelian ethics to Hinduism to the Catholic Church/Copernicus/Galileo debates. The prose does a pretty good job of simplifying major philosophies and major mathematics concepts for the general reader, although about two-thirds of the way through, the history of zero reaches imaginary numbers and proceeds to quantum mechanics, and from then on, the concepts become fairly technical. The biggest problem with the book is that I think Seife doesn’t do an adequate job of convincing me that the number zero is as directly tied to the philosophical struggles of the times as he asserts. He makes the number zero synonymous with “void” and infinity synonymous with “eternity” and therefore mathematical arguments over zero and infinity are the same thing as religious debates over the creation of the universe and eternal destination. It is an extremely large jump that doesn’t come off as convincing. And the last third of the book is more focused on quantum mechanics and cosmology and sort of forgets about the philosophical struggles. An interesting history of the most important number, but not as dangerous an idea as Seife is trying to intimate. Recommended for those who enjoy pop math books....more
ZERO, The Biography of a Dangerous Idea. (2000). Charles Seife. ****. The author here presents a history of zero, from its earliest discovery and use in the ancient East to its ultimate place in the mathematics of today. It started out as a philosophical and religious concept, likely in India, and slowly spread its way west where it encountered the mathematicians more familiar to us. In its early days, the concept of zero ran into its perception as a concept that went athwart religion. It also beZERO, The Biography of a Dangerous Idea. (2000). Charles Seife. ****. The author here presents a history of zero, from its earliest discovery and use in the ancient East to its ultimate place in the mathematics of today. It started out as a philosophical and religious concept, likely in India, and slowly spread its way west where it encountered the mathematicians more familiar to us. In its early days, the concept of zero ran into its perception as a concept that went athwart religion. It also begged the question of its close ally, infinity. The author has managed to draw a relatively simple path for these concepts from their early days to today’s mathematics as used routinely in all branches of science. The author also is able to provide an understanding of these mathematical tools in a way that a non-mathematician can grasp. It is also apparent that Mr. Seife has a keen sense of humor and an appreciation for the trivia of history. Recommended. ...more
Recommends it for: People who can tell the difference between numbers and letters.
Mind-blowing mathematical literature. That is, if you don't mind having your brain fellated formulaically. Okay, stupid joke aside; this book meets minimum prose competency for making the story of zero, and mathematics, interesting and engaging. After finishing the book, I actually spent two hours giving myself basic algebra problems to see if I could still solve them. This is a good book to read on a whim, any intentions for it more serious will result in disappointment. (In other words, it's lMind-blowing mathematical literature. That is, if you don't mind having your brain fellated formulaically. Okay, stupid joke aside; this book meets minimum prose competency for making the story of zero, and mathematics, interesting and engaging. After finishing the book, I actually spent two hours giving myself basic algebra problems to see if I could still solve them. This is a good book to read on a whim, any intentions for it more serious will result in disappointment. (In other words, it's like a really good one-hour History Channel program.)...more
Another one of the best books that I've read recently. Seife does an excellent job of turning zero into a subject. It is a number, and it is an idea; it is a troublemaker, and it is a problem solver. The biography is very interesting, beginning with history and philosophy and ending with science and the modern age. I enjoyed the actual writing of the book: clear and easy to follow, slightly humorous at times (in a Stephen Hawking kind of way), and clever. I like the chapter titles (beginning withAnother one of the best books that I've read recently. Seife does an excellent job of turning zero into a subject. It is a number, and it is an idea; it is a troublemaker, and it is a problem solver. The biography is very interesting, beginning with history and philosophy and ending with science and the modern age. I enjoyed the actual writing of the book: clear and easy to follow, slightly humorous at times (in a Stephen Hawking kind of way), and clever. I like the chapter titles (beginning with Chapter Zero and ending with Chapter Infinity) and the fact that Seife is not biased. He simply conveys historical and scientific fact, not allowing his opinions to leak through his words. I don't like when scientists make it obvious that they're not only proving theories but also trying to disprove God. Seife never does that--he just presents ideas and explains how zero went from being reviled and feared to respected to something that needs to be erased once more. My only critique is that the first part of the book is very easy to understand, but during the second half when Seife discusses modern mathematics and science, the narrative becomes more difficult to follow if the reader isn't a calculus major or a physicist (neither of which I am.... Still, there are nice illustrations that make Seife's points clearer. I highly recommend this book to anyone interested in the idea of zero, its origins and usefulness, its place in the world, or to anyone who loves math and science. ...more
The science geek in me absolutely loved this book. It was fascinating to see how the idea of zero could have such incredible effects on everything from religion to art to physics. I also thought the author did an excellent job of writing this in a way that is accessible to the non-scientific mind. Definitely glad I picked it up!
This book goes through the story of zero, showing the beginnings and the effects it has had on everyday life throughout the years. It goes through the many issues the concept of zero faced in gaining acceptance in the ancient world because of their way of thinking. From the time when the Babylonians first used it, to modern days where we accept and use our knowledge of zero to answer our questions of the universe. Charles Seife is a wonderful author who had me laughing out loud to his funny commThis book goes through the story of zero, showing the beginnings and the effects it has had on everyday life throughout the years. It goes through the many issues the concept of zero faced in gaining acceptance in the ancient world because of their way of thinking. From the time when the Babylonians first used it, to modern days where we accept and use our knowledge of zero to answer our questions of the universe. Charles Seife is a wonderful author who had me laughing out loud to his funny comments and witty humor. He goes in depth, and explains his reasoning with facts and pictures to make sure the reader understands his work. Many of the pictures and figures helped me understand his thoughts and were it not for the pictures I probably wouldn’t have understood many points of the book. As much as it was great, the book could’ve been improved by adding a list definitions of some words at the end of the book. The author also could’ve elaborated more on some of the heavier topics, such as String Theory, and the Quantum Zero. “… you can destroy the entire foundation of logic and mathematics. Dividing by zero – just one time – allows you to prove, mathematically, anything at all in the universe. You can prove that 1 + 1 = 42, and from there you can prove that J. Edgar Hoover was a space alien…” (p. 23). This quote is only one example of the humor included in this book. It allowed the reader a lighter topic to digest, along with the rougher qualities of zero outlined in the book. This one quote had me laughing out loud, causing my siblings to question how I could laugh at a book explaining the origins of zero. ...more
Most of the subject matter--Cantor's discovery of multiple infinities, calculus, big bang vs. steady state models--is related to zero, but Seife's imposition of the zero theme on his explanations makes them muddled at times. There is also simply too much material for a 200-page book. The early chapters about ancient views on the void are the most interesting and focused; Aristotle, tit for tat, may well have (inadvertently) damaged Western thought with his sentimental void-denial more than he prMost of the subject matter--Cantor's discovery of multiple infinities, calculus, big bang vs. steady state models--is related to zero, but Seife's imposition of the zero theme on his explanations makes them muddled at times. There is also simply too much material for a 200-page book. The early chapters about ancient views on the void are the most interesting and focused; Aristotle, tit for tat, may well have (inadvertently) damaged Western thought with his sentimental void-denial more than he progressed it with his achievements....more
One of the most fascinating books I've read. After reading the first two chapters, I knew I wanted to own it, and I will definitely be buying a copy. I never thought I'd say this about any book having to do with science or math, but this is one of those books that I could turn around and re-read immediately after finishing it. In fact, I might wait a couple days before returning it to the library just so I can read at least the first couple chapters again.
As a side note, toward the end of The AOne of the most fascinating books I've read. After reading the first two chapters, I knew I wanted to own it, and I will definitely be buying a copy. I never thought I'd say this about any book having to do with science or math, but this is one of those books that I could turn around and re-read immediately after finishing it. In fact, I might wait a couple days before returning it to the library just so I can read at least the first couple chapters again.
As a side note, toward the end of The Age of Wonder: How the Romantic Generation Discovered the Beauty and Terror of Science, the author says that he believes students learning about science should also learn about the people behind the discoveries of science and how they made their discoveries. I wholeheartedly agree. For one thing, I've found that learning the reasons why people wanted answers to scientific questions has made the science much more interesting. The stories behind the science are also often quite dramatic or even tragic and therefore memorable. These stories give the scientific data a context that makes it easier to remember. And this isn't really too surprising, is it? After all, we've been storytellers for nearly as long as we've been walking upright. We make sense of the world through storytelling, so storytelling seems like an easy way to help make sense of science. ...more
Thanks to the mathematics of zero and infinity, Pascal concluded that one should assume that God exists – from Zero : The Biography of a Dangerous Idea
God’s Debris – by Scott Adams is an interesting novella that tries to in a way put out a belief model where the universe and its constituents are explained as “God’s Debris” – the primordial sea of pre-big bang existence that got sprinkled into living existence as we perceive it today. No one knows or can easily surmise as to what exactly happened Thanks to the mathematics of zero and infinity, Pascal concluded that one should assume that God exists – from Zero : The Biography of a Dangerous Idea
God’s Debris – by Scott Adams is an interesting novella that tries to in a way put out a belief model where the universe and its constituents are explained as “God’s Debris” – the primordial sea of pre-big bang existence that got sprinkled into living existence as we perceive it today. No one knows or can easily surmise as to what exactly happened one second before the big bang took place. In the book “Zero: The Biography of a Dangerous Idea” – author Charles Seife attempts to explain the suffusion of the idea of zero throughout our existence and hints at the possibility of zero being at the beginning as well as at the end of our existence.
If one accepts the universe as a sprinkling of God’s Dust formed out of the primordial sea that existed pre-big bang (which in Charles Seife’s view is nothing but something as close to what Zero signifies), then it can be taken as granted that all forms in perceivable existence today are representations of constituents which when trussed together will be an exact replica of the pre-big bang primordial sea. But as Charles Seife indicates that zero must have existed before and at the beginning of big bang – it leads me to a hypothetical assumption that the sum total of the entire universe must be equal to what Zero signifies – an idea which takes into account the anti-matter argument posed by Stephen Hawkings in “A Brief History of Time” – where the positive matter resulted in the observable universe and the negative matter – i.e., anti-matter exists as non-existence, a concept not easily graspable by our faculties.
Any number divided by Zero can result in infinity. As an example, suppose a packet of 50 toffies is to be distributed. If it is to be distributed to 25 people, then the number 50 is to be divided by 25 to result in 2 toffies in the hands of each individual. But if 0 toffies were to be distributed, then one can go on distributing 50 toffies to as many people as possible (of course in this case, no one will get anything in their hands). Thus a number divided by zero tends to infinity. But Zero is also a number – so can it be argued that 0/0 is equal to infinity? An absurd conclusion of course – because it seems that nothing divided by nothing results in everything : an absurd conclusion – but something which is very close to the nature of existence as we understand it today. We know that the universe is expanding and the discovery of that fact by Hubble led one to the conclusion that the universe was once closely packed into a primordial soup – but what could have caused the explosion and whether the universe will infinitely expand or will there be a limit? An external source of energy or force acting on the primordial soup? Well it would be naïve to argue that propulsion of the primordial soup into an expanding universe is owed to the agency of an external force – since that is a physical law steeped in our earthly surroundings – and which might not have existed in operation at all during pre-big bang. So does that imply, the initiative must have come from within? If the initiative had come from within, then why at that point of time only – and why it all had to come about in the first place? It could have continued as a dense primordial soup?
Could Zero be God? An exact assimilation of the sum-total consciousness in the pre-big bang arrangement but which has got scattered round the universe and now exists as a harmless looking Zero? This concept is not new and thinkers of lore have attempted to discover God in the concept of Zero. In my opinion, offered merely as a thought and not as firm conviction, what Zero signified in the pre-big bang set-up lost its power and energy as it suffused out across the length and breadth of the universe-so much so that it now became worthy of only a concept that exists as a human thought – which leads one to the natural question – whether zero as a concept, not as a numerical entity, but as a thought representing the void – also graspable by animals?
Another interesting thought that can there be is – What value to give to Zero? Should it signify a void – a nothingness? Has Zero been devised to signify a void only because our perceptions of existence imply “not nothingness”. What if the pre-big bang moment is not the Zeroth hour but just another point among several points as denoted by numbers on a numberline? As a personal belief, it is difficult for me to grasp that there was a big bang – but I do not shy away from believing in the possibility of an inter-dimensional change from a certain dimension to the other. As to whether the Universe is infinite or finite, the riddle lies in the resolution of the concept of Time; but Time as we have been thoroughly ingrained to accept is the Solar notion of time based on earth’s rotation/revolution around the Sun. Time as it really exists devoid of a reference point is a difficult concept for me to conjure.
Whoa. This book appealed to the science/math geek in me. Less than 200 pages long, I found Zero to be mostly interesting. I read it quickly after all. For the most part, this book was fairly easy to understand but I may have gotten lost in a few places (like string theory and set theory for example -- and I'm pretty sure I understood the Heisenberg Uncertainty Principle). For the record, it's the ancient Babylonians who are credited with inventing zero, although the Mayans used it too. Sort of.Whoa. This book appealed to the science/math geek in me. Less than 200 pages long, I found Zero to be mostly interesting. I read it quickly after all. For the most part, this book was fairly easy to understand but I may have gotten lost in a few places (like string theory and set theory for example -- and I'm pretty sure I understood the Heisenberg Uncertainty Principle). For the record, it's the ancient Babylonians who are credited with inventing zero, although the Mayans used it too. Sort of. This book touches on many different zero-related subjects such as: Pythagoras (a bit of a tyrant), the golden ratio, Zeno's paradox, the kabbalah, God, calculus, infinity (zero's "twin"), absolute zero, quantum mechanics, the elusive M-theory (a.k.a. the Theory of Everything), gravity potentials, black holes, worm holes, time travel, the Big Bang, and how to prove that Winston Churchill is a carrot. To name a few. Basically, as I understand it, the whole universe started with zero. (I can picture Pinto from Animal House discussing this book with a doobie in hand.) I also have a pretty good idea of how the universe will end. (I'll give you a hint: we're all either going to burn or freeze. Care to guess?) ...more
Δεν ήταν καθόλου αυτό που περίμενα, γι' αυτό και δεν το βαθμολογώ -- περίμενα να είναι κυριολεκτικά μια βιογραφία του νούμερου μηδέν, αλλ' αντί αυτού, αμέσως μετά το 1/3 του βιβλίου, αυτό... σταματάει, και το βιβλίο μπαίνει σε καθαρά μαθηματικό mode. Δεν είμαι ικανός να κρίνω κατά πόσο είναι καλό ή ενδιαφέρον διάβασμα, καθώς οι μαθηματικές μου γνώσεις δεν αρκούν. Όσα κατάφερα να διαβάσω μου φάνηκαν όμορφα και καλά, αλλά περισσότερα από τα μισά μου ήταν ακατανόητα ως μαθηματικός συλλογισμός/πράξειΔεν ήταν καθόλου αυτό που περίμενα, γι' αυτό και δεν το βαθμολογώ -- περίμενα να είναι κυριολεκτικά μια βιογραφία του νούμερου μηδέν, αλλ' αντί αυτού, αμέσως μετά το 1/3 του βιβλίου, αυτό... σταματάει, και το βιβλίο μπαίνει σε καθαρά μαθηματικό mode. Δεν είμαι ικανός να κρίνω κατά πόσο είναι καλό ή ενδιαφέρον διάβασμα, καθώς οι μαθηματικές μου γνώσεις δεν αρκούν. Όσα κατάφερα να διαβάσω μου φάνηκαν όμορφα και καλά, αλλά περισσότερα από τα μισά μου ήταν ακατανόητα ως μαθηματικός συλλογισμός/πράξεις. Το πρώτο τρίτο του βιβλίου είναι ευκολοδιάβαστο και ενδιαφέρον, καθώς δείχνει το πώς η θρησκεία επηρέασε τα μαθηματικά και τούμπαλιν -- από την άρνηση των αρχαίων Ελλήνων να δεχθούν το μηδέν ως το πώς η ανάγκη των μοναχών να μετράνε λεφτά και ώρες προσευχής έφερε την άνθιση των μαθηματικών στη δυτική Ευρώπη.
My students like the introduction about dividing by zero. I want to use mylar strips to make an ellipse and see the light collect in the other focus. I talk about orbital mechanics a lot in my math classes, and the students often ask me what is in the other focus. For instance the sun is in one focus of an ellipse...why is the other one empty, and while this doesn't exactly answer that question...it illustrates the right triangle connection beautifully. So, project for me. 2 thumbtacks, a pieceMy students like the introduction about dividing by zero. I want to use mylar strips to make an ellipse and see the light collect in the other focus. I talk about orbital mechanics a lot in my math classes, and the students often ask me what is in the other focus. For instance the sun is in one focus of an ellipse...why is the other one empty, and while this doesn't exactly answer that question...it illustrates the right triangle connection beautifully. So, project for me. 2 thumbtacks, a piece of string tied in a loop, and some bamboo skewers, and some mylar should do the trick. I need something for a base. Suggestions? Comments? I also think that I will form a math cult next school year. It worked for Pythagoras...up to a point....more
Really interesting book because it tackles a subject I've never seen attempted within the pop-sci genre. Wasn't a thrilling read, but I got a lot out of it, and I can recommend this one for anyone interested in the history of mathematics.
I enjoyed reading this book. Seife has a nice way of writing and the connections between the history, the math, the arts, the sciences are all wonderful to read and think about.
I think it would have been wonderful to have read in high school or college as it connected so many ideas from various classes. It wasn't a quick or easy read especially toward the end with theories of string theory and such but Seife makes it approachable enough with analogies. It was an interesting thing to read since II enjoyed reading this book. Seife has a nice way of writing and the connections between the history, the math, the arts, the sciences are all wonderful to read and think about.
I think it would have been wonderful to have read in high school or college as it connected so many ideas from various classes. It wasn't a quick or easy read especially toward the end with theories of string theory and such but Seife makes it approachable enough with analogies. It was an interesting thing to read since I hadn't studied some of those topics and the connections to snippets of things I've read in the news were interesting to make.
I loved the progress of the idea of zero (and the infinite) from early number systems and philosophy through to string theory and the big bang. The reviewers suggest that the book is accessible to non-mathematicians, but I would think that much of the material is lost to those without some understanding of mathematical ideas. That is the main reason for the score of three.
I always enjoy books that explore the development of ideas. I seem to have a particular interest in the interplay between phI loved the progress of the idea of zero (and the infinite) from early number systems and philosophy through to string theory and the big bang. The reviewers suggest that the book is accessible to non-mathematicians, but I would think that much of the material is lost to those without some understanding of mathematical ideas. That is the main reason for the score of three.
I always enjoy books that explore the development of ideas. I seem to have a particular interest in the interplay between philosophy, religion and scientific development.
I'll avoid the obvious puns and won't say that this was was a Seinfeld book, you know, a book about nothing. ...more
CHARLES SEIFE is a Professor of Journalism at New York University. Formerly a journalist with Science magazine, has also written for New Scientist, Scientific American, The Economist, Science, Wired UK, The Sciences, and numerous other publications. He is the author of Zero: The Biography Of A Dangerous Idea, which won the PEN/Martha Albrand Award for First Nonfiction. He holds an M.S. in mathematCHARLES SEIFE is a Professor of Journalism at New York University. Formerly a journalist with Science magazine, has also written for New Scientist, Scientific American, The Economist, Science, Wired UK, The Sciences, and numerous other publications. He is the author of Zero: The Biography Of A Dangerous Idea, which won the PEN/Martha Albrand Award for First Nonfiction. He holds an M.S. in mathematics from Yale University and his areas of research include probability theory and artificial intelligence. He lives in Washington D.C....more
“Zero is powerful because it is infinity’s twin. They are equal and opposite, yin and yang. They are equally paradoxical and troubling. The biggest questions in science and religion are about nothingness and eternity, the void and the infinite, zero and infinity. The clashes over zero were the battles that shook the foundations of philosophy, of science, of mathematics, and of religion. Underneath every revolution lay a zero – and an infinity.”
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“Where there is the Infinite there is joy. There is no joy in the finite. —THE CHANDOGYA UPANISHAD”
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May 09, 2014 03:07PM
May 10, 2014 09:51AM