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Geometry, Relativity and the Fourth Dimension
This is a highly readable, popular exposition of the fourth dimension and the structure of the universe. A remarkable pictorial discussion of the curved space-time we call home, it achieves even greater impact through the use of 141 excellent illustrations. This is the first sustained visual account of many important topics in relativity theory that up till now have only been treated separately.
Finding a perfect analogy in the situation of the geometrical characters in Flatland, Professor Rucker continues the adventures of the two-dimensional world visited by a three-dimensional being to explain our three-dimensional world in terms of the fourth dimension. Following this adventure into the fourth dimension, the author discusses non-Euclidean geometry, curved space, time as a higher dimension, special relativity, time travel, and the shape of space-time. The mathematics is sound throughout, but the casual reader may skip those few sections that seem too purely mathematical and still follow the line of argument. Readable and interesting in itself, the annotated bibliography is a valuable guide to further study.
Professor Rucker teaches mathematics at the State University of New York in Geneseo. Students and laymen will find his discussion to be unusually stimulating. Experienced mathematicians and physicists will find a great deal of original material here and many unexpected novelties. Annotated bibliography. 44 problems.
Finding a perfect analogy in the situation of the geometrical characters in Flatland, Professor Rucker continues the adventures of the two-dimensional world visited by a three-dimensional being to explain our three-dimensional world in terms of the fourth dimension. Following this adventure into the fourth dimension, the author discusses non-Euclidean geometry, curved space, time as a higher dimension, special relativity, time travel, and the shape of space-time. The mathematics is sound throughout, but the casual reader may skip those few sections that seem too purely mathematical and still follow the line of argument. Readable and interesting in itself, the annotated bibliography is a valuable guide to further study.
Professor Rucker teaches mathematics at the State University of New York in Geneseo. Students and laymen will find his discussion to be unusually stimulating. Experienced mathematicians and physicists will find a great deal of original material here and many unexpected novelties. Annotated bibliography. 44 problems.
160 pages, Paperback
First published June 1, 1977
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Displaying 1 - 30 of 32 reviews
January 25, 2011
A manageable book on an unwieldy topic. While denser than "Flatland" or "A Brief History of Time," it is not beyond the grasp of the casual reader. A few sections of dense mathematics require skimming over, and I confess I could only answer with confidence the chapter-end questions for a single chapter. Still, the chapters are short and generously illustrated, and this kind of book always rewards in direct proportion to the amount of time one is willing to spend with it. One extra feature of note: the annotated bibliography is rich with comment and almost as pleasurable to read as the text itself. At the very least, it offers the reader an idea of other books on this fascinating, but difficult, subject.
May 23, 2008
Picks up where left off and introduces more complex concepts. Aside from the spiritual ramifications, this is a good book for Sci-Fi fans to help them understand things like "hyperspace" travel and time differences. One of my all time favorite books.
April 30, 2018
چی‌ش� که خوندم؟
این کتاب رو ۱۰ سال پیش، سال سوم راهنمایی برای رسیدن به جواب سوال‌ها� بی‌شمار� دربارهٔ ماهیت زمان و ابعاد و... و به پیشنهاد یه معلم ریاضی فوق‌العاد� خونده بودم. یه کتاب افستی طلق و شیرازه‌ا� بود تو کتابخونهٔ مدرسه. امسال که به عنوان معلم برگشتم به اون مدرسه کلی تو کتابخونه دنبالش گشته‌بود� و پیداش نکردم و تا بالاخره به قدری اینترنت رو شخم زدم که اسمش رو یافتم و بعد هم از کتابخونهٔ دانشگاه قرض گرفتمش و خوندم!
رودی راکر
این‌طو� که از رزومه� مشخصه، این آقا بیشتر از اون‌ک� به ریاضی‌دا� بودنش شهره باشه به خاطر داستان‌ها� علمی و متون ترویجیش مشهوره. این کتاب هم بر خلاف اسمش کتاب خوبیه و نثرش بیشتر شبیه کتاب‌ها� ترویجیه تا کتاب‌ها� پژوهشی. یعنی تا جایی که ممکنه از حداقل ریاضیات (فرمول‌ه� یا مفاهیم و اسامی) استفاده کرده و حتی اصول هندسهٔ اقلیدسی رو هم از صفر توضیح می‌د�.
زبان و نثر کتاب
شما این‌طو� در نظر بگیرید که یه بچهٔ سوم راهنمایی این رو خونده‌بو� و تقریبا فهمیده‌بو�. حالا شاید یه جاهای کمی که ریاضی داشته و مثلا گفته فلان سطح رو می‌تونی� خودتون با این انتگرال حساب کنید و از روش پریده‌بود� اون موقع. ولی اصلا آسیبی نمی‌زن� به روند کتاب. بعضی جاهاش هم ممکنه با صبر کردن و فکر کردن و تخیل کردن بهتر جلو بره. ولی عمدتا هر جا عدم شفافیتی داشته بعد از دو-سه صفحه خودش قضیه رو روشن می‌کرد�. البته یه جاهاییش واقعا برام غامض و گنگ بود که جلوتر می‌گ� درباره�.
یه نکتهٔ جالب کتاب اینه که ریاضیه و نه فیزیک. یعنی چیزهایی که چندبار (احتمالا) توی کتاب‌ها� فیزیکی خوندید رو از یه منظر ریاضیاتی توضیح می‌د� و این خیلی می‌تون� کمک کنه به روشن و کامل شدن تصویری که تو ذهنتونه.
چهار فصل اول
توی این چهارفصل که بهترین جای کتابه از نظر من، نویسنده تمثیل پخستان رو می‌گیر� و داستان رو جلو می‌بر� و مفاهیم مربوط به ابعاد بالاتر و خمیدگی فضا-زمان و امثال اینه� رو اول روی دنیای دوبعدی و حتی یک‌بعد� نشون می‌د� و بعد راجع به خودمون حرف می‌زن�. نیازی هم نیست که داستان پخستان رو از قببل خونده باشید که این داستان رو متوجه بشید. این قسمت از کتاب خیلی خوب و ساده نوشته شده و تقریبا همه‌فهم�.
اما یه جاهایی زیادی می‌ر� تو فاز فلسفی و... . کتاب رو جذاب می‌کن� ها. ابعاد جدیدی هم برای تفکر باز می‌کن�. ولی یه جوریه. یعنی انتظار همچین چیزی رو از یه کتاب علمی نداریم قاعدتا.
سه فصل آخر
فصل پنج که راجع به نسبیت خاصه خیلی گنگ شد یه دفعه و فصل بعدش هم که راجع به سفر در زمانه خیلی زبانش غیر علمیه و همه چی تکراری محسوب می‌ش� برام. خصوصا بعد از شاهکار آقا نولان دیگه این حرفا خیلی جذابیت گذشته رو نداره. از اواسط فصل هفت دوباره همه‌چ� گل و بلبل می‌ش�. به نظر می‌رس� هر چی مباحث به حوزه تخصصی نویسنده نزدیک‌ت� باشه راحت‌ت� توضیح می‌د� :-)
کتابشناسی
جذاب‌تری� بخش کتاب ولی به نظرم بخش کتابشناسی� بود. آقای راکر کتاب‌شناس� کتابش رو به صورت تفصیلی نوشته یعنی برای هر کتابی حدود یکی-دو صفحه توضیح داده و بررسی کرده و از این جهت می‌تون� برای کسانی که علاقه دارن در این زمینه بیشتر مطالعه کنن، مفید باشه. خصوصا این که همه‌جو� کتابی هم توی این بخش معرفی کرده: از نوشته‌ها� بورخس گرفته تا کتابای پژوهشی انیشتن!
خود کتاب
این کتاب سال ۷۴ تو ایران ترجمه شد و متاسفانه دیگه تجدید چاپ نشد و اگه خوش‌شان� باشید شاید بتونید نهایتا از تو کتابخونه‌ا� پیداش کنید. با این حال نسخهٔ انگلیسی کتاب توی اینترنت آرشیو موجوده:
این کتاب رو ۱۰ سال پیش، سال سوم راهنمایی برای رسیدن به جواب سوال‌ها� بی‌شمار� دربارهٔ ماهیت زمان و ابعاد و... و به پیشنهاد یه معلم ریاضی فوق‌العاد� خونده بودم. یه کتاب افستی طلق و شیرازه‌ا� بود تو کتابخونهٔ مدرسه. امسال که به عنوان معلم برگشتم به اون مدرسه کلی تو کتابخونه دنبالش گشته‌بود� و پیداش نکردم و تا بالاخره به قدری اینترنت رو شخم زدم که اسمش رو یافتم و بعد هم از کتابخونهٔ دانشگاه قرض گرفتمش و خوندم!
رودی راکر
این‌طو� که از رزومه� مشخصه، این آقا بیشتر از اون‌ک� به ریاضی‌دا� بودنش شهره باشه به خاطر داستان‌ها� علمی و متون ترویجیش مشهوره. این کتاب هم بر خلاف اسمش کتاب خوبیه و نثرش بیشتر شبیه کتاب‌ها� ترویجیه تا کتاب‌ها� پژوهشی. یعنی تا جایی که ممکنه از حداقل ریاضیات (فرمول‌ه� یا مفاهیم و اسامی) استفاده کرده و حتی اصول هندسهٔ اقلیدسی رو هم از صفر توضیح می‌د�.
زبان و نثر کتاب
شما این‌طو� در نظر بگیرید که یه بچهٔ سوم راهنمایی این رو خونده‌بو� و تقریبا فهمیده‌بو�. حالا شاید یه جاهای کمی که ریاضی داشته و مثلا گفته فلان سطح رو می‌تونی� خودتون با این انتگرال حساب کنید و از روش پریده‌بود� اون موقع. ولی اصلا آسیبی نمی‌زن� به روند کتاب. بعضی جاهاش هم ممکنه با صبر کردن و فکر کردن و تخیل کردن بهتر جلو بره. ولی عمدتا هر جا عدم شفافیتی داشته بعد از دو-سه صفحه خودش قضیه رو روشن می‌کرد�. البته یه جاهاییش واقعا برام غامض و گنگ بود که جلوتر می‌گ� درباره�.
یه نکتهٔ جالب کتاب اینه که ریاضیه و نه فیزیک. یعنی چیزهایی که چندبار (احتمالا) توی کتاب‌ها� فیزیکی خوندید رو از یه منظر ریاضیاتی توضیح می‌د� و این خیلی می‌تون� کمک کنه به روشن و کامل شدن تصویری که تو ذهنتونه.
چهار فصل اول
توی این چهارفصل که بهترین جای کتابه از نظر من، نویسنده تمثیل پخستان رو می‌گیر� و داستان رو جلو می‌بر� و مفاهیم مربوط به ابعاد بالاتر و خمیدگی فضا-زمان و امثال اینه� رو اول روی دنیای دوبعدی و حتی یک‌بعد� نشون می‌د� و بعد راجع به خودمون حرف می‌زن�. نیازی هم نیست که داستان پخستان رو از قببل خونده باشید که این داستان رو متوجه بشید. این قسمت از کتاب خیلی خوب و ساده نوشته شده و تقریبا همه‌فهم�.
اما یه جاهایی زیادی می‌ر� تو فاز فلسفی و... . کتاب رو جذاب می‌کن� ها. ابعاد جدیدی هم برای تفکر باز می‌کن�. ولی یه جوریه. یعنی انتظار همچین چیزی رو از یه کتاب علمی نداریم قاعدتا.
سه فصل آخر
فصل پنج که راجع به نسبیت خاصه خیلی گنگ شد یه دفعه و فصل بعدش هم که راجع به سفر در زمانه خیلی زبانش غیر علمیه و همه چی تکراری محسوب می‌ش� برام. خصوصا بعد از شاهکار آقا نولان دیگه این حرفا خیلی جذابیت گذشته رو نداره. از اواسط فصل هفت دوباره همه‌چ� گل و بلبل می‌ش�. به نظر می‌رس� هر چی مباحث به حوزه تخصصی نویسنده نزدیک‌ت� باشه راحت‌ت� توضیح می‌د� :-)
کتابشناسی
جذاب‌تری� بخش کتاب ولی به نظرم بخش کتابشناسی� بود. آقای راکر کتاب‌شناس� کتابش رو به صورت تفصیلی نوشته یعنی برای هر کتابی حدود یکی-دو صفحه توضیح داده و بررسی کرده و از این جهت می‌تون� برای کسانی که علاقه دارن در این زمینه بیشتر مطالعه کنن، مفید باشه. خصوصا این که همه‌جو� کتابی هم توی این بخش معرفی کرده: از نوشته‌ها� بورخس گرفته تا کتابای پژوهشی انیشتن!
خود کتاب
این کتاب سال ۷۴ تو ایران ترجمه شد و متاسفانه دیگه تجدید چاپ نشد و اگه خوش‌شان� باشید شاید بتونید نهایتا از تو کتابخونه‌ا� پیداش کنید. با این حال نسخهٔ انگلیسی کتاب توی اینترنت آرشیو موجوده:
March 3, 2016
Excellent depiction of the topic, and extremely helpful help on visualizing four-dimensionality, stereographic projection and Minkowski diagrams. Will be good even for those who know the topic well, since a brief introduction of tensor notation helps to understand those going into the field.
Read
April 8, 2023This, paired with Hawkins's Brief History of Time, is perhaps the best approach for getting a solid understanding of space-time dimensions. Rucker does a great job balancing crowd-pleasing speculation with sound mathematics.
September 1, 2007
want to know more about fourth dimension!? read this book. By reading this book you will also learn to see things DIFFERENTLY.
July 15, 2014
Very clear , easily understood by people without mathematical training
June 17, 2022
Rudolf Rucker wrote this book in 1976. Surprisingly few things have changed since then, but there are some changes. The book goes straight into the Geometry of four-dimensional spacetime by using the analogies of Flatland.
There is some mathematics in the book, along with problems to solve. The illustrations in the book are illuminating. I guess the worst thing about the book is its length. It covers relativity and geometry in under one hundred fifty pages. Thanks for reading my review, and see you next time.
There is some mathematics in the book, along with problems to solve. The illustrations in the book are illuminating. I guess the worst thing about the book is its length. It covers relativity and geometry in under one hundred fifty pages. Thanks for reading my review, and see you next time.
December 11, 2014
Weird, wonderful, and at times over my head (when the equations came out, my eyes glazed over—and I survived two attempts at college calculus) exploration of the universe as a single geometric object embedded in a higher-dimensional reality. Trippy stuff made trippier (and moderately accessible to smart laypersons) by sf head Rudy Rucker. The annotated bibliography alone is worth the admission, and it doesn't hurt to read this alongside the first novel that Rucker wrote,
Spacetime Donuts
.
September 1, 2019
First 4 chapters were great. Introduction to non-Euclidean geometry was great. Perhaps the best thing about this book was how it referred to general theory of relativity, namely an easy to understand build up that uses curvature of space-time to explain gravitational force-fields or vice versa.
However, personally I did not find the treatment of special relativity and further discussion so easy to follow. Perhaps, the possibility of paradoxes discourages me to delve into the subject fully, irrespective of the author.
Overall, the experience was satisfactory.
However, personally I did not find the treatment of special relativity and further discussion so easy to follow. Perhaps, the possibility of paradoxes discourages me to delve into the subject fully, irrespective of the author.
Overall, the experience was satisfactory.
May 16, 2021
Concise and intuitive explanation of several topics (per the title). On the geometry of space I got some new information. On the fourth dimension, the book didn't go too far (bar discussing the fourth- and higher- dimensions in terms of spacetime or our universe), however, the best (and probably most lengthy) part of the book focused on special relativity. Finally allowed me to get a grasp on the concepts in special relativity without any (too advanced) math.
October 14, 2007
Incredible images flowered in my mind as I read this easy-to-read "book" ("pamphlet" almost seems nearer the mark since it is such a slim volume), which makes concepts like relativity and the shape of timeeasy for the layman to read and understand. It made it a pleasure to think in a very different way about things I am not used to thinking about.
January 22, 2011
For people interested in physics, especially in relativity. The technical/math stuff can be skimmed on first read as long as you get the general idea. Books like Michio Kaku's Hyperspace or implications of Relativity should make more sense after reading this. Edwin Abbott's Flatland is a good book to read BEFORE you pick this one.
January 13, 2011
This book appears to be somewhat of a predecessor, or maybe an earlier draft, of his book "The Fourth Dimension". Not quite a predecessor, sincethis book goes into more mathematical detail (which I liked). I like Rudy Ruckers writing style overall.
June 3, 2016
A fun read for anyone who has an interest in higher mathematics, as well as philosophy or physics. The author explores not only the mathematical fourth dimension, but also those disciplines that have a "higher dimension".
April 16, 2010
Everyone should read this.
Currently reading
June 20, 2010great, mind blowing
January 12, 2017
A very interesting little book.
February 9, 2024
A fascinating book providing a mind-bending romp through ideas on the 4th spatial dimension (not time). Small and well-stocked with conceptual drawings, the book is written in a way that is usually understandable for this non-mathematician. I also appreciated the regular humor and humility of the author, as demonstrated in this quote: “…a pseudosphere is a sphere with imaginary radius, whatever that may mean.� (p50)
The author provides a very open-minded survey of ideas on visualizing, calculating, accessing, and considering the implications of the 4th dimension. This encompasses established mathematics, psychedelics, consciousness, the occult, and fringe theories. The author is methodical about pointing out the difference between what is known and what is speculative while commenting on pseudoscientific ideas. You will find ideas on not only antiparticles, but also antigalaxies and antipeople (p97). And there is plenty on hypercubes and other 4D objects, light, the shape of space-time, gravity, black holes, white holes, geodesics, world lines, singularities, time, and the idea that mass particles could be tiny black holes or hyperspheres (p114).
My only minor complaint is that the book would benefit from an index, and maybe a glossary. But the bibliography for additional reading on the 4th dimension and related topics is extensive, and each chapter is capped with word problems for conceptualizing and calculations.
The author provides a very open-minded survey of ideas on visualizing, calculating, accessing, and considering the implications of the 4th dimension. This encompasses established mathematics, psychedelics, consciousness, the occult, and fringe theories. The author is methodical about pointing out the difference between what is known and what is speculative while commenting on pseudoscientific ideas. You will find ideas on not only antiparticles, but also antigalaxies and antipeople (p97). And there is plenty on hypercubes and other 4D objects, light, the shape of space-time, gravity, black holes, white holes, geodesics, world lines, singularities, time, and the idea that mass particles could be tiny black holes or hyperspheres (p114).
My only minor complaint is that the book would benefit from an index, and maybe a glossary. But the bibliography for additional reading on the 4th dimension and related topics is extensive, and each chapter is capped with word problems for conceptualizing and calculations.
November 6, 2023
This book inspired a lot of what happens in #ChroniclesOfALostTomorrow regarding time travel, even though Rucker does not talk too much about time travel in this book, his ideas are pretty interesting.
"Geometry, Relativity and the Fourth Dimension" explores the fascinating intersection of mathematics, geometry, and physics. In this book, Rucker delves into the concept of the fourth dimension, which is a fundamental aspect of advanced mathematics and theoretical physics.
The book introduces readers to various geometric concepts and principles, helping them understand the nature of higher dimensions and how they relate to our familiar three-dimensional world. Rucker also discusses the theory of relativity, particularly Albert Einstein's groundbreaking work, and how it revolutionized our understanding of space and time.
Through clear explanations and engaging examples, the book guides readers through these complex topics, making them more accessible and comprehensible.
"Geometry, Relativity and the Fourth Dimension" explores the fascinating intersection of mathematics, geometry, and physics. In this book, Rucker delves into the concept of the fourth dimension, which is a fundamental aspect of advanced mathematics and theoretical physics.
The book introduces readers to various geometric concepts and principles, helping them understand the nature of higher dimensions and how they relate to our familiar three-dimensional world. Rucker also discusses the theory of relativity, particularly Albert Einstein's groundbreaking work, and how it revolutionized our understanding of space and time.
Through clear explanations and engaging examples, the book guides readers through these complex topics, making them more accessible and comprehensible.
Read
April 3, 2025To see the universe as a single object is a great thing. We will conclude with a quote on this from one of Einstein’s letters:
A human being is a part of the whole, called by us “Universe,� a part limited in time and space. He experiences himself, his thoughts and feelings, as something separated from the rest—a kind of optical delusion of his consciousness. This delusion is a kind of prison for us, restricting us to our personal desires and to affection for a few persons nearest to us. Our task must be to free ourselves from this prison by widening our circle of compassion to embrace all living creatures and the whole nature in its beauty. Nobody is able to achieve this completely, but the striving for such achievement is in itself a part of the liberation and a foundation for inner security
A human being is a part of the whole, called by us “Universe,� a part limited in time and space. He experiences himself, his thoughts and feelings, as something separated from the rest—a kind of optical delusion of his consciousness. This delusion is a kind of prison for us, restricting us to our personal desires and to affection for a few persons nearest to us. Our task must be to free ourselves from this prison by widening our circle of compassion to embrace all living creatures and the whole nature in its beauty. Nobody is able to achieve this completely, but the striving for such achievement is in itself a part of the liberation and a foundation for inner security
June 21, 2017
Brilliant and entertaining description of Euclidean and non-Euclidean geometry, leading to descriptions of curvature in n-dimensional space, general and special relativity. Lacks Einstein's explicit field equations and tensors but this is one of the best mathematical physics books I have ever read and as an introduction to general relativity I doubt it could be beaten.
reshelved
August 8, 2022An extrapolation of Abbott's excellent Flatland. The problem being that Rucker knows nothing about QM which is an absolutely necessary prerequisite to the understanding of 4-dimensional space.
September 2, 2022
A highly readable book on some extremely high minded concepts and theories. I highly recommend it to any looking to gain an better understanding of Geometry, Realativity,Fourth Dimensional space and what they entail
June 12, 2023
Awesome book. Highly recommend reading flatland before this one. If flatland opened your mind to the understanding of dimensions, this book takes it one more step forward, on how to open your mind to you and the universe around you
November 13, 2017
3.5 stars
December 22, 2024
Nothing groundbreaking but mentions a lot of interesting books to read that i would like to check out for further reading
December 16, 2017
In this wonderful little book, Rucker sets on a quick but thorough journey through what we know and what we don't know about relativity, four dimensional objects and even time travel. It's one of my favourite books on the matter, and the best one in making concepts clear and intriguing. Rudy Rucker is the true heir of Edwin A. Abbot.
May 3, 2017
"The relativity of simultaneity, more than anything else, forces the view that time is not really passing... the idea is that if simultaneity is a relative concept, then it is impossible to think of space-time as being a stack of unique 'nows' that successfully appear and vanish from existence. The past and future really exist."
March 21, 2007
yes it's IMPROBABLE, but not IMPOSSIBLE!
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