What insights can Flatland offer about understanding higher dimensions?

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In summary: I think it's significant that he chose a square as his protagonist. A sphere may have been harder to relate to, but I think the square was an excellent choice, heh.In summary, Flatland is a must-read for anyone interested in freeing themselves from "common" beliefs and understanding higher dimensions. The book presents a story of a square living in a two-dimensional world and his journey to try and understand the third dimension. It also explores the frustrations of trying to imagine higher dimensions and the role of religion in understanding the unknown. Overall, Flatland is a thought-provoking and entertaining read that will leave readers with a new perspective on the limitations of our understanding.
  • #1
Mentat
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This may be considered a Science Fiction book, but it is (IMO) very important to anyone who wants to free themselves of "common" belief, and try to understand higher dimensions.

Your narrator is a square (the actual geometric shape).

The first Part of the book deals with life in "Flatland". The inhabitants of Flatland are two-dimensional, and believe that this is all there is to the Universe. Nature (along with certain laws and regulations) is set a certain way, in Flatland, so that the inhabitants can go about there normal lives, without need of another dimension.

In the second Part, your narrator (the Square) has a dream about Lineland, a place where all of the people are lines, and move along one dimension only. They only see each other as points (much like inhabitants of Flatland only see each other as lines), and believe that there is nothing more to the Universe than the "line". When the Square tries to explain the second dimension to the Kind of lineland, the King dismisses him as a fool (among other things).

Later, as the second Part continues, the Square is visited by a Sphere. The Sphere tries to get the Square to visualize the third dimension, but the Square just couldn't do it. Finally, once the Square gets to understand the third dimension, he (the Square) tries to get the Sphere to imagine dimensions higher than the third one.

I recommend this book to everyone, but particularly those with an interest in knowing the unknowable (like me).
 
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  • #2
Flatland is a book worth reading. It's short and I believe can be bought brand new in stores for like 2 dollars.

It attempts basically to make the statement that "as hard as it is for you in a 3 dimensional space to imagine a 4 dimensional space is the same difficulty it is for a 2 dimensional character to imagine a 3 dimensional space."

However, it doesn't make it any easier for you to imagine a 4 dimensional space, heh. So, I get it's purpose surely, but we're just not going to be able to understand it!

At the moment we disocver 4 dimensional space, the entire population of humanity we'll see how easy it is and go DOH!
 
  • #3
This sounds like a fun read. I'll look for a copy (if I can remember not to forget to remember).
 
  • #4
Originally posted by LogicalAtheist
Flatland is a book worth reading. It's short and I believe can be bought brand new in stores for like 2 dollars.

It attempts basically to make the statement that "as hard as it is for you in a 3 dimensional space to imagine a 4 dimensional space is the same difficulty it is for a 2 dimensional character to imagine a 3 dimensional space."

However, it doesn't make it any easier for you to imagine a 4 dimensional space, heh. So, I get it's purpose surely, but we're just not going to be able to understand it!

At the moment we disocver 4 dimensional space, the entire population of humanity we'll see how easy it is and go DOH!

Yeah, that's something that I really appreciated about it: it showed people's (typical) frustration at their inability to visualize higher dimensions. As a matter of fact it showed different attitudes that people take:

The 0d creature: Perfect Complacency
The 1d King: Dismissing the idea of higher dimensions as foolish.
The Square: Going pretty well mad.
The Sphere: Getting angry, and trying to get the Square to just shut up about such foolishness.

Another point: It doesn't help you visualize higher dimensions, but it does give you an urge to try. It fills you with an awe for how much you just can't see.

P.S. It's also kind of funny, around the ending.
 
  • #5
Yes, a great book. :) And it's available online, for free! That's how I read it.

http://promo.net/pg

Search title for "flatland".
 
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  • #7


It attempts basically to make the statement that "as hard as it is for you in a 3 dimensional space to imagine a 4 dimensional space is the same difficulty it is for a 2 dimensional character to imagine a 3 dimensional space."

Interestingly, Abbott, a clergyman, wrote Flatland as a geometric analogy to theology, to suggest that we should entertain the possibility of aspects of reality that we, as limited beings, cannot directly apprehend.
 
  • #8


Originally posted by Ambitwistor
Interestingly, Abbott, a clergyman, wrote Flatland as a geometric analogy to theology, to suggest that we should entertain the possibility of aspects of reality that we, as limited beings, cannot directly apprehend.

I believe it. He surrounded the presence of the "sphere" with lots of religious hubub. I think that his use of religious metaphor, in this book, is almost as good as that of Orson Scott Card, who has some religious metaphor (usually about a "savior" who is worshipped in spite of not deserving or asking for that worship) in practically all of his science-fiction.
 
  • #9
who's read Flatterland? it's the story of A. Square's great-great granddaughter (yes, she's a line who lives in 20th century Flatland) who goes on an adventure very much like her ancestor before her. I'm currently about half way through and find it to be slightly disappointing when compared to Flatland. it fails to blend the mathamatics and the fiction together as artfully as Abbot was able to, so I've had to give up thinking of it as such and instead imagine it as more of a very poorly written mathamatics lesson. still worth a look though.
 
  • #10
Flatland is an excellent book. You may not be able to visualize more than 3 dimensions at once but after reading this book, you can get damn close. When considering a 4-D construct, you can still examine 3 dimensions at a time. I've found it extremely helpful in my understanding of four-dimensional space-time and definitely recommend it to anyone interested in physics or philosophy.

Flatland is also social satire, poking fun at Victorian society.

http://mathforum.org/mam/00/master/people/abbott/satire.html

It's also fascinating to contemplate 3-dimensional shadows that a 4-dimensional cube, or other shape, would cast. The 3D shadow will undergo curious changes as the 4D object rotates in certain directions. Imagine a clear cube. At the right angle, the shadow cast by the cube will look like a square inside a slightly larger square. The relative size of the squares will depend on the projection, ie how far the light source is away from the cube and/or how far the cube is away from the projection surface. As you rotate the cube around different axes, the projected squares will undergo curious changes in relation to each other. Extrapolating that to a 4D hypercube, at the right angle, it's shadow will appear to be a cube within a larger cube. As the hypercube rotates, the 3D shadow does amazing things.

Check out this Java applet for a hypercube:

http://dogfeathers.com/java/hyprcube.html

This is what a 3D shadow of a rotating hypercube would look like.

It helps if you have a pair of red-blue 3d glasses. There are different modes to use, however, that don't require the glasses. One mode displays two images that you can focus together similar to the way one focuses on a stereogram.
 
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  • #11
Sounds like about a 100 page thought experiment, and I like that. I really enjoy books like these, but you hardly ever encounter them unless someone recommends them. Thanks Mentat!

I am off to the bookstore to procure a copy.
 
  • #12
Look for Rudolph Rucker's books that extend the concepts in Flatland. I recommend them highly, as well as Thomas Banchoff's Beyond the Third Dimension.
 

1. What is "Recommend this book Flatland" about?

"Recommend this book Flatland" is a science fiction novel written by Edwin Abbott Abbott. It is a social satire that explores the concept of higher dimensions through the perspective of a two-dimensional world.

2. Who is the author of "Recommend this book Flatland"?

Edwin Abbott Abbott was an English schoolmaster and theologian who wrote "Recommend this book Flatland" under the pseudonym "A Square". He is also known for his work in mathematics and theology.

3. What inspired the author to write "Recommend this book Flatland"?

The author was inspired by the growing interest in the concept of higher dimensions in the late 19th century. He wanted to use his writing to explore the limitations of human perception and the social hierarchy in Victorian society.

4. Is "Recommend this book Flatland" considered a classic?

Yes, "Recommend this book Flatland" is considered a classic in both science fiction and literature. It has been praised for its unique perspective and thought-provoking themes, and has been referenced in various media and academic discussions.

5. What can readers take away from "Recommend this book Flatland"?

"Recommend this book Flatland" offers a commentary on society, human perception, and the limitations of knowledge. It encourages readers to think critically about their own perspectives and the world around them, and to question the societal norms and hierarchies that may limit their understanding.

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