Zero: The Biography of a Dangerous Idea

by Charles Seife

A NEW YORK TIMES NOTABLE BOOKThe Babylonians invented it, the Greeks banned it, the Hindus worshipped it, and the Christian Church used it to fend off heretics. Today it's a timebomb ticking in the heart of astrophysics. For zero, infinity's twin, is not like other numbers. It is both nothing and everything.Zero has pitted East against West and faith against reason, and its intransigence persists in the dark core of a black hole and the brilliant flash of the Big Bang. Today, zero lies at the heart of one of the biggest scientific controversies of all the quest for a theory of everything. Within the concept of zero lies a philosophical and scientific history of humanity.Charles Seife's elegant and witty account takes us from Aristotle to superstring theory by way of Egyptian geometry, Kabbalism, Einstein, the Chandrasekhar limit and Stephen Hawking. Covering centuries of thought, it is a concise tour of a world of ideas, bound up in the simple notion of nothing.

Genres: Nonfiction, Science, History, Mathematics, Philosophy, Physics, Biography

266 pages, Kindle Edition

First published February 7, 2000

About the author

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 mathematics from Yale University and his areas of research include probability theory and artificial intelligence. He lives in Washington D.C.

Reviews

[Chadi Raheb · Rating 4 out of 5]

[از سری ریویو-استوری های بی ربط]

یک.
به دلیلی, اعداد همیشه یه فصل از داستان زندگی من بودن. اما این فصل در کلاس دوم دبستان بی رحمانه بسته شد. به خاطر اون معلم ریاضی
بیشعوری که یه بچه هفت ساله ی به شدت درونگرا رو پای تخته جلوی کلی بچه و بعد توی دفتر مدیر جلوی کلی آدم بزرگ تحقیر میکنه که چرا اعداد رو به اون شکل ابتدایی و احمقانه ای که خودش درس میده نمی نویسه و چرا راه حل هاش فرق میکنه حتا با اینکه جواب نهایی لعنتی همیشه همیشه همیشه درسته. فقط برای اینکه من بیشتر از سنم ریاضی بلد بودم و اینکه دلم میخواست به روش آدم بزرگا حساب کتاب کنم و شکل نوشتن اعدادم هم مثل اونا باشه. و اصلا چه ایرادی داشت من گاهی اعداد رو لاتین بنویسم وقتی جواب همیشه درست بود؟ من در هفت سالگی یاد گرفتم اگه متفاوت باشی باید تحقیر بشی و کسی دوستت نداره و به خودش زحمت پیگیری ارزش های تو رو نمیده, حتا اگه حق با تو باشه. حتا اگه بدونن حق با توئه.
وقتی برای مامان تعریف کردم, روز بعدش اومد مدرسه و کاری کرد که اون معلم جلوی جمع از من عذرخواهی کنه. زخم دل من اما هیچوقت خوب نشد. از اون روز من از ریاضی متنفر شدم و مغزم با قدرت تمام رد میکرد که هر فرمولی رو به خاطر بسپره. جواب های نهایی من اما هنوزم درست بودن هرچند عملکرد من در طول سالها ریاضی خوندن افتضاح بود. ذهن من به من میگفت تو بی استعدادترین موجود در ریاضی هستی و حتا یک حلزون از تو بهتر بلده حساب کنه.

دو.
من آدم سرسختی ام. من بارها یواشکی کتابهای ریاضی سختتر از حدم رو پیدا میکردم و میخوندم. کتابای تست المپیاد رو میخوندم. و چند بار توی المپیاد ریاضی شرکت کردم در حالیکه معلم هام پوزخند میزدن. سر تمام امتحان های المپیاد من با ایمان به بی استعداد و خنگ بودنم سوالات رو اشتباه جواب میدادم. موقع انتخاب رشته دبیرستان با حماقت تمام ریاضی رو انتخاب کردم. حسابان و ریاضیات پایه و هندسه و معادلات و جبر و احتمال تنها کورسهایی بودن که من مجبور بودم به خاطرشون کلاس های اضافه تری برم. و تنها کورسهایی که معلم هام همیشه تهش با ناامیدی نگاهم میکردن. ترم یک دانشگاه که به اجبار ریاضی داشتیم, وقتی موقع امتحان پایان ترم یه سری سوالا لو رفته بود, من به خاطر حفظ قوانین اخلاقی خودم (شما امروز بخونین حماقت) قبول نکردم به سوالا نگاهی بندازم. خب من اون درس رو افتادم. و این میتونست بهترین اتفاق زندگیم باشه شاید وقتی تصمیم گرفتم انصراف بدم و برم یه رشته هنری بخونم. اما استاد احمقتر از من, در لحظه آخر منو پاس کرد و من به غرق شدن توی اعداد ادامه دادم.

سه.
قبلا اعتقاد سفت و سختی داشتم که سیستم هرچقدر مشکل داشته باشه اگه شخص نتونه پیشرفت کنه مشکل خودشه. باید اونقدری قوی باشه که بتونه راهشو باز کنه و جلو بره حتا به سختی. بعد چیزهای بیشتری یاد گرفتم. بعد فهمیدم که سیستم قسمت بزرگی از تقصیر رو به گردن داره. مخصوصا در هفت سال اول زندگی یک انسان. اما من هنوز آدم سرسختی بودم. وقتی فهمیدم مشکل بیشترش از سیستمه نه از توانایی و هوش من, شروع کردم فقط به خاطر لذتش هندسه و جبر و احتمال یاد گرفتن. از چند تا کورس آنلاین روی یکی از مشهورترین پلتفرمای آموزش.
edX
خب من اون کورس ها رو با نمره کامل پاس شدم. به اضافه ی یه کورس آنلاین دیگه از دانشگاه آریزونا. و وقتی ایمیل آریزونا اومد که نمره مو تبریک میگفت و تشویقم میکرد که برای دپارتمان ریاضی اپلای ام رو بفرستم, یه زخم باز عمیق قدیمی در من جوش خورد. من بلخره یاد گرفته بودم که یاد بگیرم. من یاد گرفته بودم چطور یه انسان رو میشه آموزش درست داد و اولین تجربه, خودم بود. من اولین معلم و اولین شاگردِ خودم بودم و در تمام طول پروسه ی یادگیری ای که مغزم تمام تلاششو میکرد بهم ثابت کنه نمیتونم, با خودم مهربون بودم و اشتباهاتمو دوست داشتم.
چند روز پیش یه سخنرانی تد دیدم که میگفت از اشتباه کردن توی محاسبات نترسید چون هر اشتباهی که در حل مسیله های ریاضی میکنین به توانایی مغزتون اضافه میکنه. گفت که علم اینو بررسی و ثابت کرده که با هر اشتباه مغز بازتر و متمرکز تر میشه. اگه فرض کنیم که حرفاش درست بوده, پس من در طول سالها جنگیدن با مسایل ریاضی حتما مغزم ورزیده تر از چیزی شده بود که حالا پاداشم نامه تشویقی غولی مثل آریزونا بوده.
حالا در من ایمانی وجود داره که چیزی نیست که از پسش بر نیام اگه درست, اصولی, پله پله, و سرسختانه مراحل یادگیریشو دنبال کنم حتا اگه سالها و سالها طول بکشه چون هیچ راهی نیست کان را نیست پایان.
حالا من یک بار دیگه به علوم پایه برگشتم. به خاطر دل خودم. و به خاطر اینکه بی نهایت ضروری میدونم که هر آدمی حتا به شکل بیسیک علوم پایه رو که بیس ساختار زندگی و جهانه مطالعه کنه. اثرش در دیدگاه آدم نسبت به مسایل مختلف واقعا عمیق و شگفت انگیزه.

چهار.
این کتاب به طور خلاصه و جمع و جور به قسمت کوچیکی از اولین فصل های داستان زندگی من میپردازه. به اعداد. به تاریخشون . از کجا اومدن. از راز و رمزهاشون. بیشترین تمرکزش هم همونجوری که از اسم کتاب برمیاد روی عدد صفره. برای خیلیا ممکنه عجیب باشه وقتی توی این کتاب بخونن که فیلسوفان و ریاضیدانان اون زمان چه وحشتی از بعضی اعداد و نسبت ها و مخصوصا عدد صفر داشتن و بعضی کسرها و نسبتهای کشف شده داخل انجمن های سری برای زمانی طولانی به شکل شفاهی حفظ میشده.
یکی از جذاب ترین قسمت های یادگیری در هر مبحثی به نظرم دونستن منشا اون موضوعه. از کجا اومد و چی شد که این شد. اول باید توجه رو جلب کرد. اگه من معلم ریاضی بودم حتما و حتما در اولین جلسات این کتاب رو با شاگردام میخوندم و سعی میکردم حس رازآلود بودن ریاضی رو درشون با این کتاب به وجود بیارم و وقتی اون شور رو دیدم یه جوری راهی پیدا میکردم به ربط دادن کتابای جذابی که در کنار درس میخونیم به اون موضوع درسی.
کاری که معلم جدید ریاضی توی کتاب "اقیانوسی در ذهن" در مورد عدد پای کرد. (به فارسی میگیم عدد پی. همون 3.14) کودک درونِ وحشتزده از علوم من با خوندن این کتاب مورمور خوبی شد و حتا یه لحظه آرزو کرد کاش ریاضی رشته تخصصیش میشد. شاید اگه موفق میشد به شکل یه متخصص روزی حرفی برای گفتن داشته باشه, اون روز داستانشو تعریف میکرد و این همه فشار و تفکر اشتباه رو از دنیا پاک یا کمی تعدیل میکرد. چون فکر میکنم این چیزیه که در نهایت ما به خاطرش اینجا هستیم. هدفمون از زندگی. اینکه یه مهره موثر باشیم تا کل این جریان به سمت بهتری بره. هربار ذره ای بهتر از قبل. هر نسل کمی کم اشتباه تر از نسل قبل. فکر میکنم توی علم میتونیم این رو عملی کنیم. اگه سیستم تمام فشارش رو روی ذهن های خلاق و متفاوت هفت ساله هامون نمیذاشت...
حتا اگه به ریاضی و اعداد علاقه ندارین این کتابو بخونین.
شاید یه جوری علاقه پیدا کردین به این راز و رمز آلود بودنش که حتا متمایل شدین چیزای بیشتری بخونین و بیشتر ازش بدونین
بعد شاید علاقه پیدا کردین که توی وقتای آزادتون چند تا کورس آنلاین بگذرونین و شروع کنین به کشف نقش ریاضی در زندگی روزمره مون
و بعد شگفت زده بشین از اینکه بفهمین حیوانات دیگه و حتا گیاهان هم از ریاضی استفاده میکنن
شاید اصلا ریاضی تبدیل شد به یه قسمت ثابت و تاثیرگذار زندگی تون
آدم هیچوقت نمیدونه توی پیچ بعدی چی منتظرشه. اینو پاپا لنگ درازم بهم گفت. من اضافه میکنم که بهتره بلد باشه با یه حساب کتاب ذهنی بر پایه علوم از اون پیچ با بیشترین ضریب اطمینان بگذره

پنج.
اگه مدرس ریاضی هستین/اگه مدرس ریاضی دارین/ اگه مدرس ریاضی اطرافتون میشناسین این کتابو بهشون پیشنهاد کنین و این روند داستان گویی در کنار درس رو.
نمیدونم این کتاب ترجمه شده به فارسی یا نه. اگه نشده, اگه مترجم هستین/ اگه مترجم اطرافتون میشناسین بهش پیشنهاد کنین این رو ترجمه کنن و این روند ترجمه کتابهای علمی-داستانی رو.
انسان برای یادگیری اول به شگفت زده شدن احتیاج داره
مایی که دیگه وقت توجه به طبیعت رو نداریم, حداقل بذاریم کتابها این کار رو برامون انجام بدن.

[Bharath · Rating 4 out of 5]

This book was recommended to me by a friend quite some time back, and I finally got around to reading it now. If you are curious about how zero became mainstream, this is a great book. There are some slow sections especially in the second half though. I listened to the audiobook on Audible and the narration was very good.

Zero has had a tough time. Though many times mathematicians seemed to veer towards it, they pulled back as it was considered dangerous territory which mortals should not go towards. The clergy wielded control and for a period grew to be very powerful all across Europe. The problem is that zero symbolized nothingness – a void, and was considered the realm of the divine. Nor was it initially considered necessary for everyday life. Infinity (who the author refers to as Zero’s twin) had much the same problem – nothing & everything are matters to stay away from. Numbers can get smaller & smaller or bigger & bigger but not reach zero or infinity.

The East, including India had the advantage that these concepts were intrinsically part of philosophy and hence zero was accepted with no resistance. Zero travelled then to Africa and the Middle East where European mathematicians met it and grudgingly accepted that it is critical for completeness & advancement. The golden ratio too went from India to the rest of the world (credited though to Fibonacci for the series he published, rarely acknowledging its antecedents). There continued to be resistance to zero for a time though and there was a period when mathematicians lost support & respect among the clergy in Europe.

The initial discussions which cover the history and acceptance of zero are fascinating. The later sections are devoted to outlining the importance of zero in the sciences, especially physics, significantly on cosmology. Without zero, we wouldn’t have got to many concepts such as relativity, black holes, big bang, end state simulations of the universe etc.

An interesting book, but should have been more concise, especially in the later sections.

My rating: 3.75 / 5.

[Trevor · Rating 2 out of 5]

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 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.

PS - I hadn't realised this is the same guy who wrote Decoding the Universe How the New Science of Information Is Explaining Everything in the Cosmos, from Our Brains to Black Holes - suddenly, things make much more sense.

[Usha · Rating 4 out of 5]

It's a fascinating and an affirming read. It's difficult to understand any regiment of mathematics and physics without the number zero. Seife reveals, how it's acceptance took time, overcoming of religious and cultural preconceptions and other serious appraisals and tribulations. Without zero, there be no calculus, algebra, astronomy, quantum physics nor understanding of space, beginning and end of the universe, black holes, vacuum and the list goes on into infinity.

[Δx Δp ≥ ½ ħ · Rating 4 out of 5]

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 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.

Berapa nilai h?

h = 6.626 068 96(33) × 10^−34 = 0.0000000000000000000000000000000006260689633 Js !!!

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!!!!!!!!!!
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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

[Gene · Rating 5 out of 5]

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. Amazing book.

[Tania · Rating 4 out of 5]

Zero is quite an undertaking - the author attacks this microhistory with an ambitious goal: to explain how zero came to be, and how it has factored into math and science, and even the dawn of the universe, from the beginning of time. That's a lot to cover. I respect Seife's attempts to make the text more interesting to the layman, but in my opinion the infused excitement is a bit much. Still, there's a ton of information to be found in this book, and it is pretty interesting to see how drastically math and science changed over the centuries.

[Kathrynn · Rating 5 out of 5]

Wow! A tremendous amount of information is packed between the cover pages of this little book. I had no idea zero created such controversy--in religion and math/science.

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, 6 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 historical information about our number system is enclosed in this book, e.g., where the word Algebra came from. There are also 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. Some 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, too.

Interestingly, all this ties right into zero. A black hole is zero. Vast nothingness. How zero and God correlate.

Great book!

5 Star Favorite!

[TK Keanini · Rating 5 out of 5]

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.

[Prakriti Regmi · Rating 4 out of 5]

The range of the book, BRILLIANT!

It opened with the use of numbers, logics for tallying, and closed with mankind’s attempt to better understand the cosmos.

And every chapter, reasonably, screamed the power of zero. It's substantiality in solving some ground-breaking scientific theories to the ability to sabotage a whole branch in science!

A descriptive and fascinating read.

[Ashok Krishna · Rating 3 out of 5]

Expected a lot only to get disappointed. Lacks coherence in some places. At times tends to get too textbook like. The small font is quite a strain too. An okayish read overall. 2.5 stars!

[Unholy Latin Republic · Rating 2 out of 5]

I'm a sucker for esoteric information surrounding sacred numbers, arithmetic, and geometry. So when I first heard of this book, I was hooked. The content therein explores the history of the number zero, how it developed over time, and the philosophical implications of it. My expectations for this book were high...too high perhaps. This book delivered on its main purpose, but I must say I was left disappointed. Most of my malcontents surround the author's interpretation of western philosophy and religion. The concept of zero began in Babylon as a simple placeholder value when counting on an abacus, and from there it spread east and west. India embraced the concept, Europe and Asia minor dismissed it. The author claims that the concept of Zero violated Aristotle's idea that nothing in nature is truly a void, and so the idea of true nothingness presented by the value of zero was illogical (a belief that has been vindicated by quantum physics, I must add...). I did not appreciate the author's tone when comparing the European philosophers to the eastern ones. He basically came across as implying that the backwards and bigoted Europeans were impermeable to reason but the noble and brilliant Indians accepted it without hesitation. Furthermore, as the historical account moved forward into the Medieval period, the author's perception on classical Christianity also fell into similar academic snobbery. Once again, he implied that the backwards clergymen of Europe were terrified of the concept of oblivion and thus censored any idea of zero. At first, I assumed that this author didn't know about the idea of "Creatio ex nihilo" that has been in Christianity since its inception, but later he actually cited that doctrine. There were many instances in his historical account where he dunks on European philosophy in one chapter, only to quickly concede that such classical ideas weren't so illogical in later chapters. I honestly felt like I was reading a massive text-post from the front page of Reddit during some parts of the earlier chapters regarding philosophy and religion. Thankfully, the author later moved more into his element with the introduction of Newton and calculus. Prior critiques aside, the mathematical facts presented in this book and the later explanation of physics were much more tolerable. Regardless, by the end of the book I didn't feel like I had a lot to take away from it, other than a few short fun-facts and a rather unreliable historical account. All things considered, this book wasn't "bad" per se but it just wasn't what I was expecting and the hauteur I perceived in the author left a sour taste in my mouth.

[Melissa Jeanette · Rating 5 out of 5]

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 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.

[Jenny · Rating 4 out of 5]

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 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.

[Steve · Rating 5 out of 5]

With his engaging book "Zero: The Biography of a Dangerous Idea", author Charles Seife embarks on an intellectual adventure exploring the history and meaning behind the number zero. From its origins in ancient Babylonian mathematics to its indispensable role in modern physics and computer science, Seife shows how this seemingly simple concept contains layers of complexity and paradox.

Seife argues that zero is more than just a placeholder or mathematical symbol. It represents a dangerous idea that has constantly challenged our understanding of reality and the nature of existence. The ancient Greeks rejected zero as an absurdity and evidence of mankind's flawed understanding of the cosmos. Philosophers like Aristotle saw zero as an affront to reason itself. How can "nothing" be something? For centuries, zero languished on the fringe of respectable mathematics.

It took visionaries like the Indian mathematician Brahmagupta to fully incorporate zero into the decimal system we use today. As zero found acceptance, it enabled the development of calculus, expanded our scientific knowledge, and led to advancements like computer programming. Yet still it remained controversial. Seife points out many leading thinkers, from Pascal to Heidegger, rejected zero as mystical, contradictory or sinister.

As an audiobook, "Zero" benefits greatly from Bob Souer's engaging narration. He brings energy and enthusiasm to the historical events and mathematical concepts covered. The storytelling style makes the ideas not just understandable, but gripping. The book mixes humor and metaphor effortlessly, capturing the listener's interest.

Some of the most fascinating parts of "Zero" are Seife's explorations into the philosophical dilemmas posed by the concept of nothingness. He uses vivid examples like baseball players' batting averages and parallel universes. These make abstract notions tangible. Seife also has a gift for conveying the drama behind key mathematical breakthroughs like the formal definition of zero.

Seife stresses that zero is still a dangerous idea today. Its unintuitive nature leads people to misunderstand concepts like statistical uncertainty and vaccine efficacy. He ties our uneasiness with zero to cognitive biases like our inability to reason correctly about probability. Seife's discussions of these modern issues are insightful, showing the continued relevance of zero's contradictions.

For all its scope, "Zero" remains accessible to a general audience. Seife excels at finding resonating entry points into complex math and philosophy. The pacing moves briskly, touching on topics like infinity, vacuum physics and logarithms without getting bogged down. Seife has a true passion for his subject that keeps the narrative energetic from start to finish.

Occasionally Seife's style can veer towards the sensational, emphasizing superlatives like most important, greatest, and dangerous. But overall he succeeds admirably in bringing an esoteric concept to vivid life. Anyone curious about the intellectual history behind one of math's simplest but most profound ideas will find "Zero" an enjoyable and illuminating listen. With his absorbing biography, Seife proves that zero really is something.

[Karin · Rating 3 out of 5]

Siefe is a writer with an MS in mathematics, so the good thing is he understands much of what he's writing. The history of zero, which isn't something that has always existed and was resisted in Europe (the Greeks hated the idea) is interesting, but then he goes off into philosphy and sciences. I'm not going to delve into this, but suffice it to say that it gets rather technical times.

However, Siefe lost an entire star for times when he left his lane into things he is apparently quite ignorant of. One example is that in the bit in italics before one of the chapters, he played with a Bible verse by inserting the mathematical definition of the Greek Word Logos from and older Greek into the Koine Greek of the Bible for ratio. Clever? It took me less than five minutes, including the time to log into my computer, to confirm that Pythagoras lived before the standardized Koine Greek of the Bible had been established; both then and later the only place the word "logos" meant ratio is in mathematics. ie, what he did was nonsensical.

[drea · Rating 2 out of 5]

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.

[Tung · Rating 2 out of 5]

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 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.

[Shankar · Rating 5 out of 5]

A wonderful book on a math subject by a great journalist. A lot of interesting information about the evolution of zero from the ages and along the journey I got a lot of learnings.

For example Pythagoras the square of the hypotenuse.. rule was already old hat before his time. He was known more for his teachings and philosophy. Of course there were other math contributions that he did but his prescriptions on silence, diet etc ( not discussing right or wrong ) were eye openers to me.

As always I am late to the party and here is one more. But I am glad I now know what I didn’t.

[David · Rating 4 out of 5]

This book made me want to actually learn calculus. At least until the brain fever wore off. :)

[huydx · Rating 5 out of 5]

Very cool book, it covers many interesting facts.

[Lily M · Rating 4 out of 5]

a re-read from high school math class and genuinely an enjoyable interesting read, though pretty technical at times (i do not understand general relativity sorry charles). really made me think about Science as a fallible human process - the author does a good job of emphasizing how much trade/conquest/politics/religion/interpersonal drama shaped how information was accessed and valued even for things we take as truth now.

[Stefan Mitev · Rating 3 out of 5]

Нулата е опасна идея.

Римските цифри не съдържат нула. Дълго време европейците са отричали и дори са се страхували да възприемат философската идея за нищо, за липса, за празнина. Едва през Средновековието в Европа навлизат арабските цифри (които всъщност са възникнали в Индия) и ползите от нулата стават очевидни за всеки.

Основните причини за отхвърлянето на нулата са догматични и заслужават интерес:
-Влиянието на Аристотел и неговата философия, отричаща хаоса и нищото
-Християнската религия, която се пази от всякакъв ��ид противоречащи научни аргументи

Нулата има много сходни характеристики с безкрайността. Възприемането на странните свойства на нулата води до фундаментални открития като Големия Взрив, разширяващата се вселена, черните дупки и общата теория на относителността.

Книгата ни показва, че нещата, които сега приемаме за даденост някога са били опасни идеи.

[Maximilian Wolf · Rating 5 out of 5]

It is not a book for scientists and engineers only.
All people with a curious and open mind should read it and spread their views on the world and universe.

I did enjoy it.

[Kara Babcock · Rating 4 out of 5]

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 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!

[Frank Davis · Rating 4 out of 5]

Zero is not only an interesting concept generating surprising consequences but it also has a fascinating history. Humans are weird and the conceptual difficulty of accepting zero to one side, it was our ancestors' stubborn refusal to adopt it that I found most peculiar. Having studied a little mathematics it is difficult to imagine a number system that doesn't include zero, but a society that doesn't acknowledge zero is disappointingly and recognisably human.

Inevitably the story of zero involves many other mathematical and scientific concepts. We cover a fairly broad history of mathematics herein but it is a considerably small book so much of this felt like the sidenotes were usurping the lead role. Seife eventually managed to illuminate a significant relationship with zero for each diversion and he did so in a relatively accessible manner but it will help to have some basic maths.

Seife comes across as having some contempt for the Romans, claiming at least twice that they made no mathematical contributions whatsoever. I'm not a historian but that seemed implausible so I did a very brief Google which seemed to agree that the Romans made no major theoretical advancements but noted that they did take many significant steps in the application of mathematics that have left a legacy in a variety of areas.

I first read this book about 6 years ago when I borrowed it from a friend, when I found it on my shelf a few days ago I realised I ought to return it to its rightful owner and because my memory is fairly sieve-like and I could only remember that I enjoyed it, I decided to read it again lest my friend ask for my thoughts when I finally hand it back.

This is a good book but I probably wouldn't have read it twice if not for the circumstance of having accidentally book-napped it for 6 years. The significance of zero in mathematics and society is well worth reading about and I enjoyed doing so.

[Tim · Rating 4 out of 5]

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.

[Philip Mann · Rating 5 out of 5]

You have to love a book that has a section giving instructions on how to build your own wormhole-time machine. All you need to do is build a wormhole and attach one end of it to something very heavy and attach the other end to something travelling at 90% of the speed of light. It gets easier from there, although you do have to wait forty six years and haul the thing to another planet.
The author takes a seemingly simple topic, then tells us how incredibly complex it really is, and then simplifies it again. Yes, there are pages of equations, some of which I actually understood. But it was a fun read, and he shows how the infinite can be unimaginably large or infinitely small, and how they need each other.
The author tells us how this mathematical debate becomes one with the religious debate about the nature of God, and whether He has limits. We see how the ancients Greeks took their debates seriously indeed, and the price of having an unpopular opinion was far worse that getting hateful text messages.
Seife tells us about that ancient riddle, about some creature walking one half the distance to a certain point, one jaunt at a time, and in theory can never reach the end, and shows us the single flaw in that argument. Otherwise, we could never get anywhere.
As I said, this is a very entertaining book, and the equations shouldn't stop the curious reader.

[Tom Quinn · Rating 3 out of 5]

I think the whole spirit of this book can be demonstrated with a single quote: "See appendix A for a proof that Winston Churchill was a carrot." It's kind of fun, but mostly educational.

2.5 stars out of 5. A step above textbook-level dryness but a step below pop-science narrative, this one stops being pleasurable to read after about 75 pages when it begins to retread similar ground (how zero was/wasn't explored as a concept in various ancient civilizations). Later the author shifts from cultural history and towards summaries of much drier mathematical concepts and their development, at which point we're really straining the use of "biography" in the title. But I will say this book's got the most concise and comprehensible explanation of string theory that I've ever come across, and that's certainly worth your time.

(Read in 2017, the twenty-sixth book in my Alphabetical Reading Challenge)

[Paul · Rating 1 out of 5]

Simply terrible. It's a mishmash of different things - it tries to teach you a bit of calculus (but not enough that you'd understand it!) and history (but not in any rigorous or, frankly, interesting way), and it runs out of steam on the whole "zero" idea pretty immediately and starts just going off on random tangents.

The worst part is when Seife drops the math stuff entirely and makes the incredibly tenuous connection to popular science and physics. He is a perfect exemplar of an awful science writer - everything in his writing is the HIGHEST drama. If you want to know about this sort of thing, you're MUCH better off going with The Great Courses course Zero to Infinity: A History of Numbers by Edward Burger. It's about a billion times more grounded.