Geometry, Relativity and the Fourth Dimension

by Rudolf Rucker

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.

Genres: Science, Mathematics, Physics, Nonfiction, Philosophy, Geometry, Popular Science

160 pages, Paperback

First published June 1, 1977

Reviews

[Heather · Rating 4 out of 5]

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.

[Lance · Rating 5 out of 5]

Picks up where Flatland 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.

[ramezan · Rating 5 out of 5]

چی‌شد که خوندم؟
این کتاب رو ۱۰ سال پیش، سال سوم راهنمایی برای رسیدن به جواب سوال‌های بی‌شمارم دربارهٔ ماهیت زمان و ابعاد و... و به پیشنهاد یه معلم ریاضی فوق‌العاده خونده بودم. یه کتاب افستی طلق و شیرازه‌ای بود تو کتابخونهٔ مدرسه. امسال که به عنوان معلم برگشتم به اون مدرسه کلی تو کتابخونه دنبالش گشته‌بودم 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
این‌طور که از رزومه‌ش مشخصه، این آقا بیشتر از اون‌که به ریاضی‌دان بودنش شهره باشه به خاطر داستان‌های علمی و متون ترویجیش مشهوره. این کتاب هم بر خلاف اسمش کتاب خوبیه و نثرش بیشتر شبیه کتاب‌های ترویجیه تا کتاب‌های پژوهشی. یعنی تا جایی که ممکنه از حداقل ریاضیات (فرمول‌ها یا مفاهیم و اسامی) استفاده کرده و حتی اصول هندسهٔ اقلیدسی رو هم از صفر توضیح می‌ده.

زبان و نثر کتاب
شما این‌طور در نظر بگیرید که یه بچهٔ سوم راهنمایی این رو خونده‌بود و تقریبا فهمیده‌بود. حالا شاید یه جاهای کمی که ریاضی داشته و مثلا گفته فلان سطح رو می‌تونید خودتون با این انتگرال حساب کنید و از روش پریده‌بودم اون موقع. ولی اصلا آسیبی نمی‌زنه 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 می‌کرده. البته یه جاهاییش واقعا برام غامض و گنگ بود که جلوتر می‌گم درباره‌ش.
یه نکتهٔ جالب کتاب اینه که ریاضیه و نه فیزیک. یعنی چیزهایی که چندبار (احتمالا) توی کتاب‌های فیزیکی خوندید رو از یه منظر ریاضیاتی توضیح می‌ده و این خیلی می‌تونه 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 می‌گیره و داستان رو جلو می‌بره و مفاهیم مربوط به ابعاد بالاتر و خمیدگی فضا-زمان و امثال این‌ها رو اول روی دنیای دوبعدی و حتی یک‌بعدی نشون می‌ده و بعد راجع به خودمون حرف می‌زنه. 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 همه‌فهمه.
اما یه جاهایی زیادی می‌ره تو فاز فلسفی و... . کتاب رو جذاب می‌کنه ها. ابعاد جدیدی هم برای تفکر باز می‌کنه. 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 می‌شه برام. خصوصا بعد از شاهکار آقا نولان دیگه این حرفا خیلی جذابیت گذشته رو نداره. از اواسط فصل هفت دوباره همه‌چی گل و بلبل می‌شه. به نظر می‌رسه هر چی مباحث به حوزه تخصصی نویسنده نزدیک‌تر باشه راحت‌تر توضیح می‌ده :-)

کتابشناسی
جذاب‌ترین بخش کتاب ولی به نظرم بخش کتاب‌شناسی‌ش بود. آقای راکر کتاب‌شناسی کتابش رو به صورت تفصیلی نوشته یعنی برای هر کتابی حدود یکی-دو صفحه توضیح داده و بررسی کرده و از این جهت می‌تونه برای کسانی که علاقه دارن در این زمینه بیشتر مطالعه کنن، مفید باشه. خصوصا این که همه‌جور کتابی هم توی این بخش معرفی کرده: از نوشته‌های بورخس گرفته تا کتابای پژوهشی انیشتن!

خود کتاب
این کتاب سال ۷۴ تو ایران ترجمه شد و متاسفانه دیگه تجدید چاپ نشد و اگه خوش‌شانس باشید شاید بتونید نهایتا از تو کتابخونه‌ای پیداش کنید. با این حال نسخهٔ انگلیسی کتاب توی اینترنت آرشیو موجوده:
https://archive.org/stream/geometryre...

[Erickson · Rating 5 out of 5]

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.

[Chris Via]

This, 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.

[Amir Hesam · Rating 5 out of 5]

want to know more about fourth dimension!? read this book. By reading this book you will also learn to see things DIFFERENTLY.

[Mary Tierney · Rating 5 out of 5]

Very clear , easily understood by people without mathematical training

[William Schram · Rating 5 out of 5]

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.

[Timothy Morrison]

To 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

[Kitap · Rating 4 out of 5]

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 .

[Yiğit · Rating 4 out of 5]

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.

[Jacob R · Rating 4 out of 5]

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.

[Vanessa · Rating 4 out of 5]

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.

[Raghuveer · Rating 4 out of 5]

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.

[Randy · Rating 3 out of 5]

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.

[Stan · Rating 4 out of 5]

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".

[Eric · Rating 5 out of 5]

Everyone should read this.

[Beside Beside]

great, mind blowing

[Eric Layton · Rating 4 out of 5]

A very interesting little book.

[Connor Lamphier · Rating 3 out of 5]

Neat little tome covering the basics of the understanding we had of spacetime at the time it was written. The diagrams are helpful, and it refreshed my understanding of these concepts, many of which I was familiar with from my astrophysics course in high school.

One thing about learning things like this is that you can ponder and mull over them as you read and for a bit after, but if you think about it all the time, you might go insane. The relativity of everything, including time, simultaneity, and even space, is really hard to reconcile with, and may lead one to a belief that nothing matters or human affairs are futile.

I don’t feel this way at all, I feel as if we are blessed with life, love, emotion, art, and even blessed with this kind of difficult knowledge. Living in a universe in which there is too much to learn in billions of lifetimes is something we shouldn’t take for granted, something that binds us indelibly to everyone that has been and ever will be. I feel lucky to be alive at a time where I can even begin to comprehend some of these things that all of humanity before this most recent period had no conception of. Black holes, the speed of light, antimatter, spacetime distortion, etc, are incomprehensible wonders of the world we have been given.

That being said, certain parts of this book specifically expressed concepts in a way harder to follow manner than others I have interacted with. I often found myself stopping reading to refresh my knowledge using other sources that conveyed this information more clearly and concisely. Some of the diagrams could be better formatted or more clearly drawn, as I was again able to find diagrams of the same concepts that were far more comprehensible. Regardless, I think I was largely able to grasp the concepts and ideas of this book, refreshing my prior knowledge and adding to it, and the questions at the end of each chapter were good for ensuring strong conceptual understanding.

[Christopher C. Fuchs · Rating 5 out of 5]

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.

[Wayker · Rating 4 out of 5]

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.

[Tom Ritman-Meer · Rating 5 out of 5]

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.

[Forked Radish]

An 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.

[Dylan Rock · Rating 5 out of 5]

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

[John Ciubuc · Rating 5 out of 5]

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

[Mike · Rating 3 out of 5]

3.5 stars

[corbdog max · Rating 3 out of 5]

Nothing groundbreaking but mentions a lot of interesting books to read that i would like to check out for further reading

[Jaza42 · Rating 5 out of 5]

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.

[Michelle Sanders · Rating 4 out of 5]

"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."