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Sphereland: A Fantasy about Curved Spaces and an Expanding Universe

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A short Science Fiction novel by a distinguished Dutch mathematician which entertains and instructs in the multi-dimensional geometries of curved space and the expanding universe.


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A short Science Fiction novel by a distinguished Dutch mathematician which entertains and instructs in the multi-dimensional geometries of curved space and the expanding universe.

30 review for Sphereland: A Fantasy about Curved Spaces and an Expanding Universe

  1. 5 out of 5

    Jafar

    The sequel to Flatland. This one was written by a Dutch mathematician in 1960. Flatland was written in 1881, before relativity and quantum, and while ingenious in concept, its physics and geometry had obvious flaws. However, the first thing that Burger feels compelled to correct in this book is the status of women. This story is told by the grandson (a Hexagon) of the Square who narrated Flatland. He goes to great length ensuring us that things have changed in Flatland, and women, even though st The sequel to Flatland. This one was written by a Dutch mathematician in 1960. Flatland was written in 1881, before relativity and quantum, and while ingenious in concept, its physics and geometry had obvious flaws. However, the first thing that Burger feels compelled to correct in this book is the status of women. This story is told by the grandson (a Hexagon) of the Square who narrated Flatland. He goes to great length ensuring us that things have changed in Flatland, and women, even though still humble straight lines, are no longer considered deprived of intelligence, and an isosceles can now freely associate with a high polygon, etc. I really didn’t care much for this book and its political and scientific correctness. Burger has taken somebody else’s book and just retouched it. The main theme of this story is that space is curved. It turns out that Flatland is not a flat plane, but the surface of a sphere. The poor 2D Flatlanders can’t imagine how this could be because the third dimension is beyond their comprehension. They can’t see how their universe can be finite, but still have no boundaries. We have the same problem imagining our universe being finite but without boundaries. However, we can easily see how this could be the case for the surface of a sphere. We just can’t imagine the 4D hyper-sphere whose surface is our universe. And then we learn about the wicked things that a visitor from a fourth dimension can do in our 3D world. He can come out of nowhere and disappear into nowhere. He can see inside enclosed spaces, and can touch the inside of any 3D object. He can remove objects from completely enclosed areas without breaking anything. He can take a left shoe, turn it in the fourth dimension, and bring it back as a right shoe. He can take a chain and turn its links in the fourth dimension, thereby opening the chain without breaking the links. More mischievously, he can take you, turn you in the fourth dimension, and when you come back your entire world will be the mirror image of what it was before. Only if I had access to the fourth dimension!

  2. 4 out of 5

    Kenny

    Using our view of a two-dimensional world as a model, Burger attempts to show us what we cannot see about the limitations of our own 3-D world from the perspective of a 4-D one. Moving constantly between the 1-D world (Lineland) to the 2-D world (Flatland), our current experience in the 3-D world (Sphereland) is the jumping-off point to begin comprehension of the 4-D world. Unfortunately, like the characters in the novel, we too are limited in our ability to visualize the dimension above us, but Using our view of a two-dimensional world as a model, Burger attempts to show us what we cannot see about the limitations of our own 3-D world from the perspective of a 4-D one. Moving constantly between the 1-D world (Lineland) to the 2-D world (Flatland), our current experience in the 3-D world (Sphereland) is the jumping-off point to begin comprehension of the 4-D world. Unfortunately, like the characters in the novel, we too are limited in our ability to visualize the dimension above us, but we can easily see the one below. Fascinating (if verbose) experiment in physics-storytelling. Next I'm reading Rudy Rucker's "Spaceland," which I gather is an attempt to more fully explain the 4th dimension, General Relativity, and beyond. What I hope to learn is whether space is curved around a universe-sized sphere or simply undulating like the waves on the ocean, the gravity wells caused by the mass of bodies.

  3. 4 out of 5

    Nick Black

    Edwin Abbott ought step up from his musty grave and administer a crushing curby on Dionys Burger for raping his quaint Flatland: A Parable of Many Dimensions. Let this be a lesson to all of us about trusting people with such ridiculous first names. Dionys? GOMBIZ.

  4. 5 out of 5

    Shawn M.

    An interesting book that I thought wanted to do way too many things but rarely sticked to one thing. I liked the parts with the Sphere and the king of Lineland though. It was a likable book just pales in comparison to its predecessor Flatland.

  5. 5 out of 5

    Greg

    As a sequel, and expansion (no pun intended) on the ideas presented in Flatland I thought, eventually, this book had something to offer. It did provide me some insight into the ideas of curved space and an expanding universe. My critique is that it took too long to get there and there was a lot of superfluous elements like the reselling of fairy tales. I didn't think it used the Flatland setup in an inventive way. It essentially copied what happened in that book, multiple times over, changing th As a sequel, and expansion (no pun intended) on the ideas presented in Flatland I thought, eventually, this book had something to offer. It did provide me some insight into the ideas of curved space and an expanding universe. My critique is that it took too long to get there and there was a lot of superfluous elements like the reselling of fairy tales. I didn't think it used the Flatland setup in an inventive way. It essentially copied what happened in that book, multiple times over, changing the knowledge component each time so that was disappointing but their wise it is a good follow up.

  6. 4 out of 5

    Jc

    In the 1960s a Dutch mathematician, Dionys Burger, decided to attempt updating E.A.Abbott's 1890s classic fantasy on dimensional mathematics. Not quite as surprising and fun as the original Flatland, Sphereland nonetheless works well as a sequel. Burger attempts to include some of the changes in our view of spatial geometry since Einstein, while keeping to the simple dialogue approach of Abbott. If Flatland hadn't already seen the light of day nearly a century earlier, Sphereland would still sta In the 1960s a Dutch mathematician, Dionys Burger, decided to attempt updating E.A.Abbott's 1890s classic fantasy on dimensional mathematics. Not quite as surprising and fun as the original Flatland, Sphereland nonetheless works well as a sequel. Burger attempts to include some of the changes in our view of spatial geometry since Einstein, while keeping to the simple dialogue approach of Abbott. If Flatland hadn't already seen the light of day nearly a century earlier, Sphereland would still stand well on its own. To quote another GoodReads reviewer, "this book is ridiculously cool."

  7. 4 out of 5

    Yatharth Agarwal

    “Light doesn’t travel in straight lines,” you may have heard, but this book will develop the motivation as well as your intuition for the concepts. There is no better way to understand the nature of our space than to follow Hexagon along on his journey. The serious, almost forceful tone of the ‘updated’ social commentary seems to miss that the original was a satire (and quite a clever one at that), but even with the interspersed fairy tale adaptations, the book remains short and easy to read with “Light doesn’t travel in straight lines,” you may have heard, but this book will develop the motivation as well as your intuition for the concepts. There is no better way to understand the nature of our space than to follow Hexagon along on his journey. The serious, almost forceful tone of the ‘updated’ social commentary seems to miss that the original was a satire (and quite a clever one at that), but even with the interspersed fairy tale adaptations, the book remains short and easy to read with a satisfying ending.

  8. 5 out of 5

    Dru

    This is about the only GOOD sequel to "Flatland". It takes the next logical step, which was to take the flat 2-D world of "Flatland" and have the denizens begin to infer, from large surveys, that their world is "curved" (on a sphere). They can't SEE the curvature, but can see that their largest triangles don't add up to 180 degrees. Brilliant! It helps understand how we 3-D creatures could "infer" that our world is curved in 4-D but not be able to SEE that curvature.

  9. 5 out of 5

    Jean-Luc

    The main character here is descended from the main character in "Flatland" by Edwin A. Abbott and the story picks up soon after the end of the first book. This time the inhabitants, with the help of the Sphere from before, learn their world isn't flat at all, it's curved. o_O More educational and much more entertaining than the excreble "An Episode of Flatland" by Charles Howard Hinton. If you enjoyed Flatland, you will love this one.

  10. 4 out of 5

    Hannah Givens

    Not as clever or as much fun as Flatland, or as well-written as The Planiverse. It doesn't address the concept with the witty social satire of Flatland, or the serious consideration of what two-dimensional science might look like in The Planiverse. The second half is rather interesting and has more of a storyline, dealing with the actual sphereland concept of the title, but the first half is random and boring.

  11. 5 out of 5

    Adina

    If this sounds like a sequel to Flatland, it’s because it is - a sequel written by a Dutch guy in 1965, so exploring some more updated and exciting math/physics (although not quite up to the modern day). Plus, it has a nice expansion on some other aspects of Flatland, such as fashion, geography, and biology. And it has dogs! I found this book super charming. I loved the exploration of Flatland society and how their day to day lives worked.

  12. 4 out of 5

    Bill

    At the time of me writing this review, I have not yet read "Flatland" except for a few parts. This sequel to "Flatland," written in 1960, is quite a worthy one. It expands on the Flatland universe, giving much better thought to gender roles, societal roles, and the notion of the real-world Big Bang Theory and the expanding universe, showing that our worlds, whether Flatland or the real universe, are more than what we see.

  13. 5 out of 5

    Joe Labriola

    Further building upon the canon of modern geometrical fantasy as established by the brilliantly insightful Edwin A. Abbott in his classic, "Flatland", "Sphereland" is a daring sequel by Dionijs Burger Jr. - a story that creatively if sometimes confusingly challenges what we think we know about the physical reality of the world around us, including our own dimension as well as those far beyond our limited perceptions as "3D" beings.

  14. 4 out of 5

    Malli

    A good, honest sequel to Edwin Abbott's Flatland. Dionys Burger uses the same characters A Square and Sphere plus adds a few new ones, including the hexagon, Puncto. The development of the plot sharpens one's understanding of the 4th dimension as well as builds an understanding of the Expanding Universe. At times it does get tedious in the middle and hence the 3 star

  15. 4 out of 5

    Jaime K

    This was a bit slower and not as entertaining as "Flatland" especially with the last 30 pages or so. The square's grandson is the writer now, explaining that his grandfather's views of a 3rd dimension are now allowed, but his views of an expanding world on a curved plane are not. This delves into non-Euclidean geometry, so that was fun.

  16. 4 out of 5

    Kyrie

    Another cute spin off from Flatland. It really should be read before "Flatterland". I liked his descriptions of life in Flatland and his histories and fairy tales. The math and science themselves, not so much.

  17. 4 out of 5

    Noel

    slow going, because seemed to repeat the premise and beginning plot of Flatland, but it finally got going around 3/4 through! Fun analogies to our 3-dimensional space, and a fun not-so-metaphorical look at our own grapple with space-time.

  18. 5 out of 5

    EAL

    Amusing and readable. The social commentary parts were somewhat heavy-handed; the math parts were most excellent. Non-Euclidean space is interesting; when I set out to learn more about it I'll be glad to have this accessible tome to refer to.

  19. 5 out of 5

    Liz

    flatland started it... sphereland really stretches your imagination's flexibility and the language it is written in is much more accessible. for dreamers, artists, mathematicians and anyone interested in being alive and musing about it!!!!!

  20. 5 out of 5

    Terelyn

    Building on Abbott's Flatland, this one expanded my horizons regarding the third dimension, the fourth, and beyond.

  21. 5 out of 5

    Lea Patrick

    If you liked Flatland, you will LOVE Sphereland!!! Open your mind when you open this book and your perception will open with it! Truly an awe inspiring read!

  22. 5 out of 5

    Eric

    I enjoyed the novel. I liked the expansion on non-Euclidean geometry and the thought of an expanding sphere at the end. The way the book intertwines various well known stories was a nice touch.

  23. 5 out of 5

    Hamed

    don

  24. 5 out of 5

    Janos

    Tedious, teaching the wrong idea about how scientific discovery works, and entirely missed the point of the social commentary of the original. Asimov's intro to both was way off the mark.

  25. 4 out of 5

    Laura

    So far, I've learned that they feel badly about the negative portrayal of women and Flatland....and space is curved...

  26. 5 out of 5

    Ton van Gessel

    Een vervolg op flatland de flatlanders realiseren zich dat ze op het oppervlak van een 3 dimensionaal oppervlak leven ..... je ziet de analogieën al denk ik.

  27. 4 out of 5

    Steven

    Follow up to Flatland.

  28. 4 out of 5

    Tatra

    Still more interesting stuffs.

  29. 4 out of 5

    Helaina Wilkerson

  30. 4 out of 5

    Michael Rimer

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