Gödel - L'eccentrica vita di un genio

by John L. Casti, Werner DePauli, Marcello D'Agostino (Translator)

Kurt Godel è stato intellettualmente un gigante. Ma è stato anche un uomo tormentato e bizzarro che, per la sua paura dei germi, arrivò a digiunare fino alla morte. Il libro di Casti e Depauli ci dà un ritratto di questa figura leggendaria, ripercorrendone la vita a partire dalla giovinezza nella Vienna degli anni Venti fino all'ultima fase trascorsa a Princeton, in cui l'amicizia con Einstein costituì l'unico sollievo dagli incubi ai quali la sua instabilità psichica lo condannava

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

180 pages, Paperback

First published September 20, 2000

About the author

John L. Casti (born 1943) is an author, mathematician, and entrepreneur.

As a mathematician and researcher, Casti received his Ph.D. under Richard Bellman at the University of Southern California. He worked at the RAND Corporation in Santa Monica, CA, and served on the faculties of the University of Arizona, New York University and Princeton University, before moving to Vienna in 1973 to become one of the first members of the research staff at the International Institute for Applied Systems Analysis (IIASA) in Laxenburg, Austria. In 1986, he left IIASA to take up a position as a Professor of Operations Research and System Theory at the Technical University of Vienna. He also served as a member of the External Faculty of the Santa Fe Institute in Santa Fe, New Mexico, USA, from 1992-2002, where he worked extensively on the application of biological metaphors to the mathematical modeling of problems in economics, finance and road-traffic networks, as well as on large-scale computer simulations for the study of such networks.

His primary research interests have shifted somewhat in recent years from the natural sciences to the exploration of questions in the social and behavioral realm. One thread has been exploration of the relationship between the social "mood" of a population its biasing effect on actions and behaviors. In this direction, his 2010 book, Mood Matters: From Rising Skirt Lengths to the Collapse of World Powers, published by Copernicus Books, NY, addresses the directions and patterns of social causation and their implications for future trends and collective social events, such as styles in popular culture, the outcome of political processes, and even the rise and fall of civilizations. His most recent book is X-EVENTS: The Collapse of Everything, which addresses the underlying cause of extreme events generated by human inattention, misunderstanding, error, stupidity and/or malevolent intent. The English original edition was published in June 2012 by HarperCollins/Morrow, New York. The book now exists in 15 foreign editions, as well, including German, Japanese, Russian, Dutch, Korean and Portuguese.

As an entrepreneur, Casti formed two companies in Santa Fe and London in 2000, Qforma, Inc. and SimWorld, Ltd, respectively, devoted to the employment of tools and concepts from modern system theory for the solution of problems in business and finance, as well as health care. Qforma merged with SkilaMederi in June 2013. In early 2005 he returned to Vienna where he co-founded The Kenos Circle, a professional society that aims to make use of complexity science in order to gain a deeper insight into the future than that offered by more conventional statistical tools.

For several years, Professor Casti was a Senior Research Scholar at the International Institute for Applied Systems Analysis in Laxenburg, Austria, where he created an initiative for the study on Extreme Events in Human Society. In January 2012 he left IIASA to form a new research institute in Vienna, The X-Center, devoted to the study of human-caused extreme events. The X-Center has now expanded to a network of affiliated X-Centers in Helsinki, Tokyo, Seoul, New York and Singapore. Since early 2013, Dr. Casti has been serving as a Senior Research Fellow at the Center for Complex Systems and Enterprises at the Stevens Institute of Technology in the USA.

As an author, Casti has written more than 120 scientific articles and seven technical monographs and textbooks on mathematical modeling. In addition, he was formerly editor of the journals Applied Mathematics & Computation (Elsevier, New York) and Complexity (Wiley, New York). In 1989 his text/reference works Alternate Realities: Mathematical Models of Nature and Man (Wiley, 1989) was awarded a prize by the Association of American Publishers in a competition among all scholarly books published in mathematics and the natural sciences. In 1992, he also published Reality Rules (Wiley, New York), a t

Reviews

[David · Rating 3 out of 5]

Two tiny books for the price of one: one a biography about Godel and the other a list of subjects inspired by or related to Godel's work.

This is not a great biography. Perhaps there just isn't that much to learn about the somewhat depressing life of Kurt Godel (particularly in his deteriorating later years)? I don't think this book is a particularly great explanation of Godel's work, either. In particular, I appreciated the attempt to explain Incompleteness using a "chocolate cake machine" analogy, but it didn't do anything for me in terms of making the concept of Incompleteness any more clear. Strip away the cake and it's just a crummy run-of-the-mill explanation. I also get the impression that the authors wish they could just forget about Godel after he did his initial work early in life.

Any mention of giants like von Neumann or Einstein are always interesting, but here it felt more like name dropping than real substance. Certainly it's impressive that the greatest of his peers felt Godel was a towering genius - but this book does a poor job of giving us a sense of why they did.

To my surprise, I enjoyed the second half of the book much more than the biography. The related topics about the work of Turing and Church are things I'm already interested in since they are fundamental topics for computer science. Algorithmic information theory and Kolmogorov complexity are largely unexplored topics for me (though they would certainly have come up in the Claude Shannon biography I read not that long ago...) and I found them highly interesting and entertaining.

By the end of the book I was enjoying myself. It also helped me discover a book by one of my favorite SF authors and mathemetician, Rudy Rucker, called "Mind Tools: The Five Levels of Mathematical Reality" (I immediately secured a paperback copy and will read it soon). However, a crappy biography is a crappy biography and I stand by my 3 star review.

[Barak · Rating 3 out of 5]

2.5 stars.

I had several issues with this book.

First of all, the book was suggested to me by someone claiming Gödel was the great genius of all times, and the authors also claim that he was the greatest logician ever.

Now, I am not trying to say he was not extremely smart, or even a genius, whatever this description denotes exactly. He did after all arrive at an important breakthrough/milestone in mathematics at the age of 25, and his later work on relativity theory is also quite imaginative and interesting. However, these discoveries, important as they may be, still do not convince me that he was not just a very smart mathematician like many others were in human history. Let alone the many geniuses in completely separate areas, that were much more prolific than him (Kant, Peirce, Shakespeare etc)

In fact, most of the book is not really about Gödel, but rather about indirect results of his work and parallel sentences to his incompleteness theorem in other fields; which really goes to show I think that one way or another, sooner or later, this would have been discovered by someone. The claim that all those that discovered it would have had to rely on Gödel's work, or that basically all discoveries in computer science and adjacent areas are just consequences of his work is equivalent to my mind to the equally ridiculous claim that the guy who invented the wheel should be credited for the invention of cars.

Lastly, I had the nagging feeling that many of the explanations about his theory and the mathematics/logic are inaccurate. Since I am not a mathematician I would have to leave it at this level, but I did detect inaccuracies in areas relating to philosophy, AI and chess for example. On top of that, I found the "cake" and other such "helpful" analogies to be silly and confusing at best, whereas on the flip side of it, the explanations that stuck to the mathematical level to be very brief and hence abstruse.

[Stephie Williams · Rating 2 out of 5]

The book was okay. I've read about most of the stuff in the book before. One cute thing about the book was the analogy of a Chocolate Cake Machine (CCM) and Godel's incompleteness theorem. Douglas Hofstadter does a much better job in Godel, Escher, Bach presenting Godel's theorem. What would you expect from a Pulitzer Prize book. I have read other books by John Casti, and they were better by far. I guess for someone unfamilar with the topic it would be a good starting place. The presentation is pretty understandable. But, for someone already familiar with Godel and his works it's not much worth it.

[Ami Iida · Rating 4 out of 5]

it is written about "Gödel's incompleteness theorems" and all his life.
Then Gödel solved Einstein General relativity and he found Godel's answer.
it lead time travel and it is explained for "time travel".

[Jessada Karnjana · Rating 4 out of 5]

ดูจากชื่อปกครั้งแรก หลงคิดว่าเป็นหนังสือประวัติของ Gödel แต่ภายในเล่มมีพูดถึงประวัติของเกอเดลแค่ 3 บทเองครับ คือ บทที่ 1 Since Aristotle เป็นบทเกริ่นนำให้เห็นความสำคัญของเกอเดล Hermann Weyl กับ John von Neumann ชื่นชมว่าเกอเดลเป็นนักตรรกศาสตร์ผู้ยิ่งใหญ่ที่สุดนับตั้งแต่ไลบ์นิซหรืออริสโตเติลเลยทีเดียว บทนี้แสดงภาพบรรยากาศทางความคิดร่วมสมัยกับเกอเดล ก่อนทีเกอเดลที่ตอบคำถามสำคัญเรื่องความไม่สมบูรณ์ของ formal system ของฮิลแบร์ต ความคิดที่ฟุ้งกระจายในคณะ Vienna Circle และอิทธิพลความคิดเรื่องขีดจำกัดภาษาของวิทเก้นชไตน์ (ภาษาไม่สามารถจับหรือบรรยายบรรดาสิ่งทั้งหมดที่มีอยู่ในโลกได้) บทที่ 4 Young Gödel กับบทที่ 5 Life in Princeton ชีวิตของเกอเดลในวัยเด็ก และชีวิตของเกอเดลที่พรินซ์ตันตามลำดับ สองบทนี้นำเสนอประวัติอย่างย่อ เนื้อความส่วนหนึ่งนำมาจากบันทึกของรูดอล์ฟพี่ชาย แม้จะเป็นบทที่เกี่ยวกับประวัติสั้น ๆ ที่เราก็พอซาบซึ้ง เห็นใจ กับชีวิตรันทดของเขาในบั้นปลาย กลัวคนจะวางยาพิษ ถึงขั้นขาดสารอาหารตาย เกอเดลตายด้วยท่าเดียวกับท่าของทารกในครรภ์ หนังสือไม่ได้ให้รายละเอียดความพยายามวิเคราะห์เชิงจิตวิเคราะห์ แต่ก็เล่าว่า ถึงแม้จะมีการวิเคราะห์เชิงจิตวิเคราะห์ แต่หมอก็บอกว่าการตายด้วยท่านี้ในคนแก่ที่มีปัญหาเกี่ยวกับการย่อยอาหารไม่ถือว่าแปลกอะไร บทชีวิตในพรินซ์ตันยังเน้นความสัมพันธ์ระหว่างเกอเดลกับไอน์สไตน์ และเพื่อนที่มีอยู่เพียงน้อยนิด รวมถึงความสนใจเรื่องการกลับชาติมาเกิดของจิต (transmigration of soul) เกอเดลเชื่อในชีวิตหลังความตายนะครับ แต่ก็ไม่เกี่ยวอะไรกับพระเจ้าของชาวคริสต์

เนื้อหาในบทที่ 2 กับ 3 ผู้เขียนอธิบายความคิดเกี่ยวกับทฤษฎีบทความไม่สมบูรณ์ สรุปด้วยภาษาและการเปรียบเทียบง่าย ๆ ที่พอเข้าใจได้ว่า truth ใหญ่กว่า proof มีข้อความที่เป็นจริงที่เราไม่สามารถพิสูจน์ได้ว่าจริงภายในระบบ พูดในโวหารของบทที่ 2 Forever Incomplete ผู้เขียนเปรียบเทียบกับเครื่องทำเค้กช็อกโกแลตว่า "จะต้องมีเค้กช็อกโกแลตที่เห็นอยู่ว่าเป็นเค้กช็อกโกแลตจริง ๆ ซึ่งไม่สามารถเขียนสูตรทำเค้กช็อกโกแลตออกมาได้เสมอ" นั่นคือเมื่อเราไม่สามารถเขียนสูตรออกมาได้ เราก็สร้างเครื่องทำเค้กช็อกโกแลตที่สามารถผลิตเค้กช็อกโกแลตทุกชนิดที่มีอยู่ออกมาได้

บทที่ 6 Mechanism and Mathematics ผู้เขียนพาไปสำรวจปัญหา Decision และวิธีที่ทัวริงใช้แก้ปัญหา ซึ่งในเชิงนามธรรมแล้วมันก็เป็นวิธีการแก้ปัญหาเดียวกับวิธีที่เกอเดลใช้ในทฤษฎีบทความไม่สมบูรณ์นั่นแหละครับ บทที่ 7 Thinking Machines and the Logic of Incompleteness พูดถึง AI และเชื่อมโยงกับเกอเดลนิดเดียว ตรงที่ว่า John Lucas (รวมถึง Roger Penrose) ค้านว่าไม่สามารถมี AI ในแบบที่คิดเหมือนมนุษย์ได้โดยอ้างทฤษฎีบทของเกอเดล เหตุผลหลักคือ มี arithmetical truth ที่มนุษย์สามารถเห็นว่าจริงได้ แต่ machine ไม่สามารถพิสูจน์ได้ หนังสือยังพูดถึงสำนักคิดที่ค้าน AI อีก 2 กลุ่มคือ anti-behaviorism ของ John Searle และการทดลองทางความคิด Chinese Room ที่โด่งดังของเขา (คนที่อยู่ในห้อง รู้ภาษาจีนที่ไหนล่ะ? แล้วเราจะเรียกว่ามันคิดเป็นได้เหรอ?) กับ phenomenology มี Hubert กับ Stuart Dreyfus เป็นหัวหอก โดยอิงกับปรัชญาของ Heidegger, Husserl และ Merlau-Ponty (สำหรับผู้ขับรถที่เชี่ยวชาญแล้ว เขาไม่ต้องอาศัยชุดของกฎเหมือนกับมือใหม่อีกต่อไป อีกทั้งการขับรถยังหมดสภาพของการเป็นปัญหา แต่ machine ไม่สามารถแก้ปัญหาโดยทิ้งชุดของกฎ หรือทำให้หมดสภาพของการเป็นปัญหาได้!)

บทที่ 8 Time and Time Again บทนี้ไม่เกี่ยวอะไรกับ logic เลย แต่พูดถึงเหตุการณ์ที่เกอเดลหาผลเฉลยของชุดสมการในทฤษฎีสัมพัทธภาพทั่วไปของไอน์สไตน์ในกรณีเฉพาะ (เอกภพเฉพาะ) กรณีหนึ่ง (เป็นเอกภพที่อนุญาตให้เราเดินทางย้อนอดีตได้ด้วยนะ) บทที่ 9 The Complexity of Complexity นำเสนอการตีความทฤษฎีบทของเกอเดลในมุมมองต่าง ๆ เช่น มีจำนวนที่มีความซับซ้อน (complexity) สูงมากกระทั่งไม่มีโปรแกรมคอมพิวเตอร์ใดสามารถสร้างพวกมันออกมาได้, มีสมการไดโอแฟนไทน์ที่ไม่มีผลเฉลย แต่ไม่มีทฤษฎีทางคณิตศาสตร์ใดสามารถพิสูจน์มันได้

[Len · Rating 3 out of 5]

My first reaction was, not enough Gödel and too much logic. As a biography of Kurt Gödel, genius, logician, mathematician, admired by Einstein, yet capable of ultimate self destruction, it is lacking in substance and detail; as a study of the use made by others of his work it is a fascinating if brief analysis.

Two parts of Gödel's life are treated with such brevity as to make them embarrassing in a biography. Gödel's and his wife's move to Princeton from Vienna in 1940 is described in two sentences and yet this involved travelling from Vienna (in the Third Reich), through Czechoslovakia and occupied Poland into the Soviet Union to Moscow, obtain tickets for the Trans-Siberian railway to Vladivostok, sail to Japan – it was only in 1939 that the Soviet Union and Japan fought each other in Mongolia – sail to San Francisco and then by train across America to reach Princeton. All in two sentences. It would take more than two paragraphs to describe a day trip to the seaside. Then there is Gödel's poisoning phobia and fear of infections held in food prepared by anyone other than himself, which led to his death from “malnutrition and inanition.” It is all covered in a few short paragraphs which leave so much unsaid and unquestioned. The publisher could have also spent a little more money on the reproduction of photographs, those that there are are so small as to almost require a magnifying glass.

The value of the book is pulled through by the discussions on the influence of Gödel's work. The importance of Alan Turing in computing stands out. Chapter 7, Thinking Machines and the Logic of Incompleteness, may push the reader into re-reading Philip K. Dick's Do Androids Dream of Electric Sheep? There were parts of Chapter 8, Time and Time Again, discussing travelling through space and a spacetime continuum that made me think if Gödel had been on the Starship Enterprise he would have questioned, analysed, explained, questioned again so many times that Kirk and Spock would never have ventured further than the space-dock. All entertaining stuff – in its own way – if only the authors had pulled in a biographer to help them.

[Kazım Cansever · Rating 4 out of 5]

Gödel, teoremi ile insanlığı salt matematik kullanarak bir gün kadiri mutlak olabilme ve hakikate hükmedebilme rüyasından uyandırdıktan sonra elimizde kalan en iyi açıklama muhtemelen Orhan Veli’nin şu şiiri olsa gerek:

Bir yer var, biliyorum;
Her şeyi söylemek mümkün;
Epeyce yaklaşmışım, duyuyorum;
Anlatamıyorum.

Kitabın kendisine gelince bence yazarlar güzel bir iş çıkarmış ve böyle derin bir konuyu farklı başlıklara bölerek gayet tadında anlatmış. Fakat iş çeviri kısmına geldiğinde Türkçe’nin hala bu anlatılan konular ile ilgili oturmuş bir kelime hazinesini üretememesi gerçekten üzücü.

[Aaro Salosensaari · Rating 3 out of 5]

Kelvollinen lyhyt elämänkerta Gödelistä ja hänen matematiikastaan (sekä Gödelin tuloksista itsestään että sen sovelluksista).

Matematiikkona olen hieman kahden vaiheilla miten arvioisin teosta. Populaariteoksena ehkä ei toimi: matemaattiset asiat käsitellään tekohauskalla tavalla ("suklaakakkukone"-metafora) joka ei ehkä kuitenkaan välttämättä valaise tarpeeksi ja luultavasti on kuivempi kuin kirjoittajilla ollut tarkoitus. Toisaalta varsinainen eksakti esitys on hieman puolittainen.

Vahvin puoli on että tarkastellaan sekä Gödelin elämää että matemaattista työtä ja sen merkitystä.

[Fabio · Rating 3 out of 5]

Metaphor-based explanations of great mathematical ideas are always problematic and this is no exception. Granted, this gave a nice historical context of Goedel's Vienna , a truly a special time and place (I stumbled upon his house by mere chance walking the streets on the way to Freud's! ) and emphasizes the importance of Goedel's impact, but it still seems far more satisfying to spend the time understanding the mathematical formulation.

[Frank Rensen · Rating 3 out of 5]

Fun book, but primarily as an introduction to (some breakthroughs in) twentieth century logic. As a biography (which the book's subtitle would lead you to believe it is) it falls short spectacularly, derailing halfway through the book into ramifications of Gödel's theorem and not coming back to his life at all. Still, as I was new to Gödel and his place in academia during his lifetime, I did learn new things.

[José Augusto · Rating 4 out of 5]

It is more than a simple biography. The book introduces Godel's life in both contexts mathematical and philosophical, and It explains the Godel's theorems in a ludic way. Despite its clarity, potential readers will need some background in mathematics, logic, computers, and philosophy.

[隻眼簽到 · Rating 2 out of 5]

本書主要在介紹哥德爾「不完備定理」，以及它在圖靈機、AI、複雜性理論等方面的關聯、啟發和最終意義等。至於哥德爾的生平則是其次。他介紹的方式，我猜，應該是一種用數學的形式來表達邏輯推論的所謂形式系統方法。因此大概只適合對邏輯學有造詣的人看。反正我是看不明白的。因此，就個人觀感而言，本書既不是一本好傳記，也不是一本好的介紹不完備定理的書，在介紹圖靈機、AI等更是連輪廓都不清，實在失敗。我唯一的收獲大概是關於不完備定理的各種結論。例如，在第二章，作者說：「撇開枝節、就其精義而言，哥德爾定理所導致的後果，是徹底粉碎了『真理與證明之間並無二致』的信念。」用通俗的話來說就好比，每個案件都有真相，但不是所有真相都能被找到的意思。挺悲觀的！

[Yannis Charalabidis · Rating 4 out of 5]

I could give it less than 4 stars, if it was on another subject. But the theorem of being incompleteness always fascinated me.

Not for the expert, the book reads easily and lights both the life and the works of G.

Nice last section in AI and related issues.

[Peter]

A fun to read biography of Godel. The authors present the general outline a very difficult proof in logic, breaking it down and illuminating the basic insights of the theorem. I cannot remember the proof very well myself (it has been nearly 30 years since I went through it) but the book seems to do a pretty good job. Godel's proof is really quite difficult to follow. They link some of the ideas on which Godel was working with some of what was going on in Vienna in the beginning of the century, particularly with the Vienna Circle. The book also tries to say something about how this important theorem was received. There are some interesting discussions of complexity and the relationship between Turning Machines, the halting problem and the incompleteness theorem. The book runs very quickly over some very difficult material and does so without doing too much damage. I could do without some of the extended metaphors, but who knows? Maybe someone else would find them helpful. I found them distracting.

[Jesse · Rating 3 out of 5]

This is a decent introduction to Godel that moves a bit too quickly, and covers too many loosely connected topics for its slim length. I only understood the portion discussing early twentieth century philosophy because I had a background in the area, and the portion on advanced physics was largely greek to me. The language was concise and clear, but the development of the book was a bit too scattered, and certain sections needed further explanation.

[Vegnesh · Rating 3 out of 5]

This is the first biography that I read in a long time. I don't know if its because of this, but this book is not extremely well written. There are sections where the writing is incredibly awesome and there are sections I could not understand clearly. But a concise book to gain an insight into the life of Godel.

[Waffles · Rating 1 out of 5]

This book filled me scadenallemeinverbrechen. I hate the universal chocolate cake machine. I don't want Sachertorte, I want Sachertod!

[Tom]

Some interesting material, but the book is short, somewhat disorganized, and there's relatively little biographical profile (save early life) of Godel.

[Jesus Cruz · Rating 5 out of 5]

a real good book, I had no expectation at all, but I finally found it quite good, clear and interesting.

[Saurabh Shrivastava · Rating 2 out of 5]

A little complex to read. But opens new areas of reading

['Izzat Radzi · Rating 4 out of 5]

Great brief stoy on Godel works.
Obviously need further and advanced readings on his works

[Kerem · Rating 4 out of 5]

A good summary of life and works of Kurt Gödel.