Flatland door Edwin Abbott Abbott

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  • 23 mei 2015
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Boekcover Flatland
Flatland door Edwin Abbott Abbott
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I had known about Flatland for a while. I don’t know when, but my father told me about it quite long ago, and it always managed to fascinate me.

It was brought up more on various later occasions, but I never actually read it, mainly because I just didn’t read English books in general back then. I definitely had it on my to-read list, though.

Now, when my father departed from the company he had worked for for years, he got lots of gifts and presents. One of those was a DVD of a Flatland adaption. We watched it with the whole family, and it was really cool. By then I realised I could read this book for English literature.

I actually borrowed two copies of this book, because the first one I borrowed had seemed to disappear. Or perhaps it just left the third dimension, and it’s lying somewhere here still, in only two dimensions... but I got a new copy.

I had expected it to be relatively close to the movie. I had also expected it to be a bit tough to read, as I knew it involved a bit of mathematics.

- I should watch out to not spoil anything here, because this is the “before reading” section, and I’m writing it after reading xD –

But when glancing at the contents, I understood that the movie hadn’t been so close to the book, as this one discussed lots of subjects that weren’t discussed in the movie.

I’m going to write a summary now, using only what I remember, only reading the contents.

I This World

1. Of the Nature of Flatland:
Flatland is a world where only the two dimensions exist: width and length. It’s thus completely flat from a 3 dimensions perspective, but to the people in this world, it’s all there is.

2. Of the Climate and the Houses in Flatland:
The houses are made up out of walls, mostly in pentagonal shapes, but other shapes also exist. There are two holes as entrances, one for women, one for men.

3. Concerning the Inhabitants of Flatland:
The more angles a figure in Flatland has, the more respect it gets and the higher it’s placed on the social ladder. Every child gets one angle more than their parents. So with generations, more and more angles get added, until they are pretty much circles. The lowest order are the triangles. They are often not even perfect triangles as we often draw them, and do not have equal angles.

4. Concerning the Women:
The women in Flatland are straight lines. This makes them quite dangerous, as they can really hurt another figure if they walk into it, being so sharp. If they walk outside, they’re obliged to continuously scream, to let other know they’re coming, so nobody will run into them. That’s why you shouldn’t make a woman mad. They aren’t too good at thinking and hardly do anything of use, aside of reproduction.

Dit wil je ook lezen:

5. Of our Methods in Recognizing one another:
While we from the third dimension could easily distinguish a hexagon from a pentagon just by looking at it from above, in Flatland that’s of course an entire different case, as they have no above. To them everything appears as a straight line. But they can recognise each other by feeling. In school, they learn to feel one’s angles, and if they’re good at it, they know if someone is an octagon or a nonagon by only feeling one angle.

6. If Recognition by Sight:
Even though everyone appears as a straight line, the higher educated figures actually recognise by sight. How? Well, if something is farther away, it seems dimmer, because of fog. So by looking at how quickly and with which intervals a line gets dimmer, it’s actually very well possible to distinguish between for example a pentagon and a heptagon.

7. Concerning Irregular Figures:
Irregular Figures are those who have not exactly equal angles. People have little respect for them, and if the angles are off by too much, the figures may actually be executed.

8. Of the Ancient Practice of Painting:
Long ago, someone had found out figures could be painted. It quickly became a craze, as everyone wanted to be coloured. This made distinction by sight much, much easier.

9. Of the Universal Colour Bill:
Because the inventor of this painting thought it was a great way to prevent many problems, everyone was obliged to have themselves painted. However, there was one big problem now: the art of both recognition by sight and recognition by touch decayed quickly.

10. Of the Suppression of the Chromatic Sedition:
This chapter tells how the story that started in chapter eight eventually ended. After lots of debates and almost massacres, the painting got forbidden.

11. Concerning our Priests:
The priests are the circles. Circles? Well, they obviously aren’t actually circles, but they have so many angles they aren’t countable anymore, and the figure appears as a perfect circle. They earn much respect, and rule the land for the most part.

12. Of the Doctrine of our Priests:
In the last chapter of the first part of the book, the teller of the story tells us more about priests, the chief priest, and more stuff that’s too complicated to remember.

II Other Worlds

[Let’s call the protagonist ■ from now on, for the sake of easy referencing]

13. How I had a Vision of Lineland:
In this chapter ■ gets a vision of Lineland. Lineland is a land that has only one dimension. ■ can see everyone in the land, and starts talking with the king. The king is quite baffled, he sees someone appearing and disappearing, after all. But yet he thinks ■ is a magician, and doesn’t believe him when he says he’s from a land with 2 dimensions.

14. How I vainly tried to explain the nature of Flatland:
■ tries lots of things to convince the king, but he just cannot comprehend. He asks the king about lots of subjects, but the king keeps saying things as “such a thing is impossible.” The king explains how Lineland works, and it’s actually quite interesting. Then ■ tells the king who is where in his kingdom, something he couldn’t have known for a 1 dimension perspective. But yet, the king doesn’t get it.

15. Concerning a Stranger from Spaceland:
Back in Flatland a sphere from Spaceland visits ■. Even though ■ has just had the vision of Lineland, where the king didn’t believe him, he doesn’t believe the stranger from Spaceland now, and thinks he’s just a magician when he keeps appearing and disappearing.

16. How the Stranger vainly endeavoured to reveal to me in words the mysteries of Spaceland:
The sphere tries to make clear how Spaceland works by using simple geometry. But yet, ■ can’t comprehend, and eventually tries to squish the sphere.

17. How the Sphere, having in vain tried words, resorted to deeds:
■ obviously doesn’t succeed squishing the sphere, as he just moves up. Now the sphere tries to prove his words by gently touching the insides of ■. It hurts ■ a lot, but only makes him more outrageous.

18. How I came to Spaceland, and what I saw there:
The sphere, knowing nothing else to do, now takes ■ up to Spaceland. Well, he’s  convinced now, obviously. ■ can see his entire house, and when he’s taken up farther, the entire land, from an entirely new perspective.

19. How, though the Sphere shewed me other mysteries of Spaceland, I still desired more; and what came of it:
The sphere tells ■ more about Spaceland. Then ■ asks about the fourth dimension, and the fifth. Because surely, this supreme being must know about them. The sphere doesn’t like those questions at all, though. But ■ keeps going, starting again with Lineland, going to Flatland, Spaceland, al using basic geometry… and then explains the next land, and asks more about it. But the sphere exclaims such a thing doesn’t exist, and with big force ■ gets sent back to Flatland.

20. How the Sphere encouraged me in a Vision:
The sphere once again talks to ■, this time in a vision. He encourages ■ to make these revelations public.

21. How I tried to teach the Theory of Three Dimensions to to my Grandson, and with what success:
■ wanted to share this new theory with someone, but not his wife. He remembered his grandson asking about something quite close to this earlier, when ■ had actually scolded him for it. When ■ asked him again,
he ran away, because he knew every disciple of the 3rd dimension would be prosecuted.

22. How I then tried to diffuse the Theory of Three Dimensions by other means, and of the result:
For a long while, ■ tries to keep it quiet, but he has more and more trouble picturing a cube. Eventually he tries to convince the doctrine of the priests. Without success, though, and ■ was imprisoned. ■ has written this book, and at the time of finishing it he had been imprisoned for seven years.

Because of the way this book is written, I couldn’t find five short, usable quotes, that were actually understandable taken out of context. However, I’ll quote a part from This World and one of Other Worlds.

“The Reader will probably understand from these two instances how - after a very long training supplemented by constant experience - it is possible for the well-educated classes among us to discriminate with fair accuracy between the middle and lowest orders, by the sense of sight. If my Spaceland Patrons have grasped this general conception, so far as to conceive the possibility of it and not to reject my account as altogether incredible - I shall have attained all I can reasonably expect. Were I to attempt further details I should only perplex. Yet for the sake of the young and inexperienced, who may perchance infer - from the two simple instances I have given above, of the manner in which I should recognize my Father and my Sons - that Recognition by sight is an easy affair, it may be needful to point out that in actual life most of the problems of Sight Recognition are far more subtle and complex.”

“Seven years have elapsed and I am still a prisoner, and - if I except the occasional visits of my brother - debarred from all companionship save that of my jailers. My brother is one of the best of Squares, just, sensible, cheerful, and not without fraternal affection; yet I confess that my weekly interviews, at least in one respect, cause me the bitterest pain. He was present when the Sphere manifested himself in the Council Chamber; he saw the Sphere's changing sections; he heard the explanation of the phenomena then given to the Circles. Since that time, scarcely a week has passed during seven whole years, without his hearing from me a repetition of the part I played in that manifestation, together with ample descriptions of all the phenomena in Spaceland, and the arguments for the existence of Solid things derivable from Analogy. Yet - I take shame to be forced to confess it - my brother has not yet grasped the nature of the Third Dimension, and frankly avows his disbelief in the existence of a Sphere.

Hence I am absolutely destitute of converts, and, for aught that I can see, the millennial Revelation has been made to me for nothing. Prometheus up in Spaceland was bound for bringing down fire for mortals, but I - poor Flatland Prometheus - lie here in prison for bringing down nothing to my countrymen. Yet I exist in the hope that these memoirs, in some manner, I know not how, may find their way to the minds of humanity in Some Dimension, and may stir up a race of rebels who shall refuse to be confined to limited Dimensionality.

That is the hope of my brighter moments. Alas, it is not always so. Heavily weighs on me at times the burdensome reflection that I cannot honestly say I am confident as to the exact shape of the once- seen, oft-regretted Cube; and in my nightly visions the mysterious precept, "Upward, not Northward," haunts me like a soul-devouring Sphinx. It is part of the martyrdom which I endure for the cause of the Truth that there are seasons of mental weakness, when Cubes and Spheres flit away into the background of scarce-possible existences; when the Land of Three Dimensions seems almost as visionary as the Land of One or None; nay, when even this hard wall that bars me from my freedom, these very tablets on which I am writing, and all the substantial realities of Flatland itself, appear no better than the offspring of a diseased imagination, or the baseless fabric of a dream.”

Okay, done. I love this book. It’s super deep. Really something to talk more about, and not one that should be easily forgotten. I love the thoughts, and the ways things go. I love how the protagonist tells first about his world, then about his story.

One thing I absolutely love is how the square first tries to convince the monarch from Lineland, and then doesn’t believe the Sphere from Spaceland. After that, the Sphere, who has just convinced the Square, actually throws away the thought of a fourth dimension. So hypocritical, but it sets you to thinking.

I can say, this book differs a lot from the film I saw. For one, it has a completely different ending. Here, his grandson runs away and the protagonist himself is eventually imprisoned. In the film, the grandson is the one who gets taken up to Spaceland, and he is the one who eventually does convince the circles, making the film have a happy ending. I honestly prefer the way Abbot handled it. That also answers the question about it coming up to my expectations: it was much different, but much better than I expected.

I’d definitely recommend reading this book to other people, but not people in my class, I think most of them are too young for something like this. For reading this, you should have no problems reading and understanding scientific English articles. This is no simple English, I assure you. You should be experienced at maths, and be intrigued by the wonders mathematics has to offer. And then you should have a great imagination.

See? That’s a combination of three things not nearly everyone has. But if you do qualify, I’d highly recommend this. It’s tough to read, but oh so inspiring and intriguing. 


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