In high school, I had a reading assignment given to me over the book Flatland: A Romance of Many Dimensions by Edwin A. Abbott. This book was very challenging to read and definitely stretched my find on the concepts of dimensions. The plot of the story seems really simple but the concepts go far beyond the plot, sometimes making it hard to wrap to your mind around ideas. The story makes you think!
The square lives in a place called Flatland, where all two-dimensional objects live. In the story the square wants to travel and learn about the one-dimensional land filled with many points called Lineland. As he is searching for Lineland he ends up meeting a sphere. He doesn’t understand the sphere at first until he travels to Spaceland. Spaceland is where all the three-dimensional shapes live. In Flatland it is illegal to talk about and try to learn about Spaceland because the leaders of Flatland do not want the community to know that Spaceland exist. During all of his travel to Spaceland, Abbott brings in new ideas and concepts about all shapes that are genius and make you think of dimensions on a whole other level. I would explain more but then I would ruin all the thinking involved when trying to read this type of work. The book is made for YOU to stretch your thinking realm. You will never think of dimensions in the same way after reading this book. I encourage you to read it. I have posted a link with my blog if you would like to read some of the story or all of it if you would like.
Brief sections of the book (Figures and Descriptions from the Link Above):
Fig. 1 represents the Tradesman as you would see him while you were bending over him from above; figs. 2 and 3 represent the Tradesman, as you would see him if your eye were close to the level, or all but on the level of the table; and if your eye were quite on the level of the table (and that is how we see him in Flatland) you would see nothing but a straight line.
Fig. 2 Now in the case of (I) the Merchant, what shall I see? I shall see a straight line one day, in which the middle point (A) Will be very bright because it is nearest to me; but on either side the line will shade away rapidly into dimness, because the sides AC and AB recede rapidly into the fog and what appear to me as the Merchant’s extremities, viz. D and E, will be very dim indeed.On the other hand in the case of (2) the Physician, though I shall here also see a line (D’ A’ E’) with a bright centre (A’), yet it will shade away less rapidly into dimness, because the sides (A’ C’, A’ B’) recede less rapidly into the fog: and what appear to me the Physician’s extremities, viz. D’ and E’, will not be not so dim as the extremities of the Merchant.
Fig. 3 If for example, when my Father, the Triangle, approaches me, he happens to present his side to me instead of his angle, then, until I have asked him to rotate, or until I have edged my eye round him, I am for the moment doubtful whether he may not be a Straight Line, or, in other words, a Woman. Again, when I am in the company of one of my two hexagonal Grandsons, contemplating one of his sides (AB) full front, it will be evident from the accompanying diagram that I shall see one whole line (AB) in comparative brightness (shading off hardly at all at the ends) and two smaller lines (CA and BD) dim throughout and shading away into greater dimness towards the extremities C and D.
Fig. 4 View of Lineland
After you read this book try to put yourself in the position of the square. What would happen if we traveled to a world of four-dimensions.
Credits to the book Flatland. Not all my work. I do not take credit.