Flatland
Thanks again to Ms. Price's class... for asking about the fourth dimension and reminding me about one of my favorite books Flatland by Edwin Abbott. (Which was introduced to me many years ago by my favorite entomologist/linguist/zoologist/voyager/writer/artist/musician/explorer/definition-defying friend.)
Flatland is the tale of a Square who lives, surprisingly enough, in Flatland, a two dimensional world. He has a dream about visiting Lineland, a one dimensional world, and trying to explain to the King of Lineland that there existed space outside of the single (although infinitely long) line on which he lived. The King of Lineland perceives the Square as a point. Later the Square is visited by a sphere from Spaceland, the land of three dimensions. Of course, when the Sphere visits the Square in Flatland, the Square can only see the Sphere as a Circle of varying diameter depending on which slice of himself the Sphere has in the plane of Flatland. Technically, the Square can only see the Sphere as a line but uses depth perception and touch to know he's a circle. The Sphere manages to show and explain three dimensions to the Square.
The Square then offends the Sphere by taking it one step further and asking to see the fourth dimension. The Sphere insists that there is only three dimensional space and that a fourth dimension is inconceivable. A reminder not to get so complacent with what we know that we think there's nothing left to learn.
Even written in 1884, this is still probably the best introduction to the concept of multiple dimensions. Although Flatland does have an extremely strict caste system based on someone's number of sides and angular regularity (everyone in this book is a geometric figure). And he uses ridiculous phrases to describe the inhabitants of Flatland such as,
"Thus, in the most brutal and formidable of the soldier class-- creatures almost on a level with women in their lack of intelligence..."
That's the book I just read and now, in addition to skiing, I've been trying to visualize the fourth dimension.
Flatland is the tale of a Square who lives, surprisingly enough, in Flatland, a two dimensional world. He has a dream about visiting Lineland, a one dimensional world, and trying to explain to the King of Lineland that there existed space outside of the single (although infinitely long) line on which he lived. The King of Lineland perceives the Square as a point. Later the Square is visited by a sphere from Spaceland, the land of three dimensions. Of course, when the Sphere visits the Square in Flatland, the Square can only see the Sphere as a Circle of varying diameter depending on which slice of himself the Sphere has in the plane of Flatland. Technically, the Square can only see the Sphere as a line but uses depth perception and touch to know he's a circle. The Sphere manages to show and explain three dimensions to the Square.
The Square then offends the Sphere by taking it one step further and asking to see the fourth dimension. The Sphere insists that there is only three dimensional space and that a fourth dimension is inconceivable. A reminder not to get so complacent with what we know that we think there's nothing left to learn.
Even written in 1884, this is still probably the best introduction to the concept of multiple dimensions. Although Flatland does have an extremely strict caste system based on someone's number of sides and angular regularity (everyone in this book is a geometric figure). And he uses ridiculous phrases to describe the inhabitants of Flatland such as,
"Thus, in the most brutal and formidable of the soldier class-- creatures almost on a level with women in their lack of intelligence..."
That's the book I just read and now, in addition to skiing, I've been trying to visualize the fourth dimension.
Labels: math
posted by LAV at 19:06
3 Comments:
I really should be doing some Geohydrology homework right about now rather than discussing Flatland, but seeing as how Ive read the book, I cannot help but chime in.
The first question we must pose is whether we are addressing the 4th dimension as Minkowski space, in which Einstein based his relativity theory and is essentially viewing the 4th dimension as time, or whether we are actually going to work with true Euclidean 4-space, and can be more easily understood by the standard basis of the vector : ||x|| = (p^2+q^2+r^2+s^2)^(1/2)
which is just the natural generalization of the Pythagorean Theorem to the 4th dimension. Im sure you are familiar with this already, but I just need to write things down myself to understand them (I suck at vectors).
Personally, I prefer to view my 4th dimensions as Minkowski space, as I tend to spend most of my time in classes projecting pollutants modeled as plumes or spheres and projecting dispersion throughout time and space, which is just the third integral of the given function.
and now, back to the homework dimension.
EDM
strike that, should be 4th integral....no wonder Im doing so badly in my classes.
Right now I'm preferring the Euclidean 4-space.
Good luck with the hw.
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