Robert Kasman, Charlotte, NC.|
In this classic children's adventure story,
"time travel is explained as a tesseract, a five dimensional figure. By
traveling along the tesseract, one bypasses the space in between."
Usually, the term
"tesseract" refers to the four dimensional equivalent of a cube (see,
for example, this very nice description including Java applets provided by the MAA.) In the book it is not used so rigorously:
|(quoted from A Wrinkle in Time)|
"Now," Mrs. Which said. "Arre wee rreaddy?" "Where are we going?"
Calvin asked. Again Meg felt an actual physical tingling of fear as Mrs. Which spoke. "Wwee musstt ago bbehindd thee sshaddow."
"But we will not do it all at once," Mrs. Whatsit comforted them. "We will do it in short stages." She looked at Meg. "Now we will
tesser, we will wrinkle again. Do you understand?" "No," Meg said flatly. Mrs. Whatsit sighed. "Explanations are not easy when
they are about things for which your civilization still has no words. Calvin talked about traveling at the speed of light. You
understand that, little Meg?" "Yes," Meg nodded. "That, of course, is the impractical, long way around. We have learned to take
short cuts wherever possible." "Sort of like in math?" Meg asked. "Like in math." Mrs. Whatsit looked over at Mrs. Who. "Take your
skirt and show them.' "La experiencia es la madre de la ciencia. Spanish, my dears. Cervantes. Experience is the mother of
knowledge." Mrs. Who took a portion of her white robe in her hands and held it tight. "You see ," Mrs. Whatsit said, "if a very small
insect were to move from the section of skirt in Mrs. Who's right hand to that in her left, it would be quite a long walk for him if he
had to walk straight across."
Swiftly Mrs. Who brought her hands, still holding the skirt, together. "Now, you see," Mrs. Whatsit said, "he would be there, without
that long trip. That is how we travel."
Charles Wallace accepted the explanation serenely. Even Calvin did not seem perturbed. "Oh, dear," Meg sighed. 'I guess I am a
moron. I just don't get it." "That is because you think of space only in three dimensions," Mrs. Whatsit told her. "We travel in the fifth
dimension. This is something you can understand, Meg. Don't be afraid to try. Was your mother able to explain a tesseract to you?"
"Well, she never did," Meg said. "She got so upset about it. Why, Mrs. Whatsit? She said it had something to do with her and
Father." "It was a concept they were playing with," Mrs. Whatsit said, "going beyond the fourth dimension to the fifth. Did your
mother explain it to you, Charles?" "Well, yes." Charles looked a little embarrassed. "Please don't be hurt, Meg. I just kept at her
while you were at school till I got it out of her." Meg sighed. "Just explain it to me.""Okay," Charles said. "What is the first
dimension?" "Well-a line: "Okay. And the second dimension?"
"Well, you'd square the line. A flat square would be in the second dimension. "And the third?"
"Well, you'd square the second dimension. Then the square wouldn't be flat any more. It would have a bottom, and sides, and a
"And the fourth?" "Well, I guess if you want to put it into mathematical terms you'd square the square. But you can't take a pencil
and draw it the way you can the first three. I know it's got something to do with Einstein and time. I guess maybe you could call the
fourth dimension Time." "That's right," Charles said. "Good girl. Okay, then, for the fifth dimension you'd square the fourth, wouldn't
you?" "I guess so.""Well, the fifth dimension's a tesseract. You add that to the other four dimensions and you can travel through
space without having to go the long way around. In other words, to put it into Euclid, or old-fashioned plane geometry, a straight
line is not the shortest distance between two points." For a brief, illuminating second Meg's face had the listening, probing
expression that was so often seen on Charles's.
"I think that this was one of the
books I read as a child and it
certainly inspired me as an adult."
Marcia L. Barr|
Madeleine L'Engle's books distort the nature of scientific research and use mathematical concepts as though they were metaphors. I have only one word for her work: meretricious. Two generations of readers in my family have detested and despised her work.
Entertaining and thought-provoking. While the math and science involved may be a bit fuzzy, it can definitely generate some ideas for discussion. I read this as a child, and it still remains one of my favorite books.
sir annom I. nis|
Quite a good book as far as entertainment value, but it was a little vague about the tesseract. It did, however, spark my mind to the idea of multidimensional space.
I liked this story a lot as a preteen but it didn't inspire in a mathematical way. I liked that the main character, a preteen girl, who is intimidated by a younger brother's sheer genius is encouraged to do math by her mother. While I didn't have any genius siblings growing up, I did get intimidated by a few genius kids I met at math contests and appreciated my parents' similar encouragement. So I strongly recommend this book and the whole trilogy to preteens who like math and science and those who maybe think they don't.
I think the model tesseract as constructed by the brother is correct. It was a pretty common science fair project when I was in junior high. I don't think the rest of the fantasy really added to an understanding of higher dimensions at all. Just that one can travel in time.
I REALY LIKED [THIS] BOOK IT IS VERY INTERESTING TO ME AN 11 YEAR OLD BUT I WANT TO LEARN MORE ABOUT THE 1 2 3 4 5 DEMENSIONS AND TESSERACTING
Quang (yeah i know its wierd)|
This book was really great. It makes you ponder about space and out beyond.
A young teenage girl (Meg) and her baby brother Charles Wallace go off traveling through space time and dimentions. Along the way Meg learns about the dangers of conformity. Time travel is achieved through the use of a tesseract.
Mathematics, are used in such a creative way as to add understanding to the possibilities of other dimensions unexplored. The “tesseract” is one example. “In geometry, the tesseract, also called 8-cell or octachoron, is the four-dimensional analog of the cube, which is in turn the three dimensional analog of the square. The tesseract is to the cube as the cube is to the square; or, more formally, the tesseract can be described as a regular convex 4-polytope whose boundary consists of eight cubical cells. A generalization of the cube to dimensions greater than three is called a “hypercube”, “n-cube” or “measure polytope”. The tesseract is the four-dimensional hypercube or 4-cube (Wikipedia)”.
Every character in this outstanding novel is identified as either good or evil. Some of the good characters include Meg, who is the protagonist of "A Wrinkle in Time", Charles Wallace, Megs baby brother, and their family, Calvin O'Keefe, the three Mrs. W.'s,--Mrs. Whatsit, Mrs. Who, Mrs. Which, Aunt Beast and the Happy Medium; the evil characters include IT, the dark thing and the man with the red eyes. In the absence of any ambiguities or shades of gray, the book's central conflict is clearly and starkly dramatized in order to make the reading easier to understand its teams and its message. There is a light and dark balance. Contrast is an important theme, if the ending were to be changed, this could interrupt the balance and the darkness could win, thus making the entire plot superfluous. It must end happily; the “Happy Medium”.
I read this book in first grade and it has kept me intrigued my entire life.
Believe it or not, this book has been a seminal work in regard to many career choices in science by baby boomers.
Since our knowledge of mathematics has been limited to Euclid, Newton and Einstein (quantum mechanics), new knowledge will eventually appear in the mainstream thought of mathematics.
Succinctly, we will eventually understand the fourth, fifth and sixth dimensions as well as others in the future.
I am in eighth grade and I have read a wrinkle in time until the cover was about ready to fall off. Physics and math really never interested me until I read this book. I now really enjoy learning about motion and trying to think about ho it applies to a tesseract. I read multiple wikipedia articles and watched many animations of a geometrical tesseract. I think that not only is this book about math but also about the science involved in it. I was not looking forward to doing physical science this year, but after seeing how many of Madeleine L'engle's ideas had to do with movement and really physics, it seems this year is going to be great. I think this book simply explains five dimensions in a clear and easy to understand way, which is perfect for all ages. This is a must-read in my opinion.
This book is amazing. I don't see why it isn't in the "highly rated" category. This is about as highly rated as a book can get, in my opinion- further shown by the amount of positive comments.
Ella, it is a wonderful book and it does have a very high rating for literary quality. However, the "highly rated" tag on this Website is applied only to those works that have high rankings in both their literary quality and the amount of mathematical content. Of course, there are some books I really love that have no mathematics in them at all, but this database is here specifically to address the mathematics that appears in fiction. Therefore, the fact that A Wrinkle in Time does not have the "highly rated" tag should not be interpreted as an insult to this work of fiction, but rather simply an acknowledgement that it only has the barest of connections to mathematics.
This is a novel for 5th-6th graders and is apparently a classic (it was banned in some places in the US “for challenging religious beliefs”; see here and here) . There are movie and drama adaptations as well).
An evil “brain”, referred to as “IT” and which appears as a large, black cloud draping over multiple planets, is on a mission to dominate the universe. IT is housed on a planet called “Comaztose”, which has fallen under ITs sway. IT is being battled all across the cosmos by beings who have special psychic powers. In the current story, a physicist working on government black-project (Institute For Advanced Studies is called Institute For Higher Learning) on FTL motion is trapped on Comaztose during one of his experimental travels. His telepathic son, Charles, and a mathematically gifted daughter, Meg, try to rescue him with the help of Centaur-like aliens who take the form of 3 elderly women with quirky names. The aliens know the art of “tessering”, which is a form of bending space-time at will and transporting across galaxies. It appears that exceptionally strong minds like that of the Physicist and Charles can “tesser”. In the end, the family escapes the clutches of IT, though the novel is left incomplete (There are 4 other novels involving these characters but they do not form a finishing sequel).
There are some math pieces strewn around in the novel. Meg explains the concept of tessering and a tesseract with some geometrical diagrams. While resisting the rhythmic pulsing and coercing of IT, Meg falls into computing square root of 5 and 7 to disrupt IT’s hold on her brain since reciting the Table of Elements is not taxing enough for her mental faculties (IT, on the other hand, falls into reciting multiplication tables of 1 and 2 to start their conditioning…). She also mentions that every rational number has an infinitely repeating decimal expansion.
In regards to Vijay Fafat's last comment above, some question has been raised as to whether L'Engle's discussion of the decimal expansions of rational numbers is accurate. She gives, as an example, the decimal expansion of 3/7, which is just 0.428571427571... which the string "427571" repeated indefinitely, but this statement may not appear to be true of some other fractions. In fact, the decimal expansion of a rational number necessarily takes the form of an infinitely repeated finite string of digits from some point onwards. There are subtleties like that it can be an infinitely repeating string of zeroes (i.e. and terminating sequence), and that a non-repeating portion of the decimal representation prior to the repeating part can be arbitrarily long, etc. However, I think it is correct to state that "every rational number has an infinitely repeating decimal expansion" and moreover that this property characterizes the rational numbers among the reals.
The math is there to get you places and to show Meg that she is quite gifted.
Today when I think of that story it makes me wonder if Madeleine L’Engle had a premonition of computers taking over the world. When they get to the planet all the houses look the same. I think of the suburbs that became popular in the 60's. The brain that controls the people is called “It”. That reminds me of Information technology (IT) the application of computers and telecommunications equipment to store, retrieve, transmit and manipulate data. Just her mention of the tesseract inspired an appreciation of math that I never had before reading her book. To me the book was more about the future of our own planet than it was about the math.
Math is wrong. The third dimension (cube) is the second dimension squared? What?! A line is represented as x. A Square as x^2. So the cube is (x^2)^2? Isn't that x^4? Which is NOT a cube!!! So frustrating!!! And how is it that a book that's suppose to give girls power by representing a female character who is good at math and science have her being the slowest and most confused compared to her preschool brother and future husband?!!! HATE, HATE, HATE this book. Also super boring and took me years to get through!! Forced myself to read to see what all the hype was about.
Dear Anonymous Reader, you are certainly entitled to your own opinions regarding how much you like (or "HATE, HATE, HATE") this book. One thing to keep in mind when judging it is that it was written in 1962 and indeed many works of fiction from that time which were truly progressive for their day can seem racist or sexist by today's standards. And, as for math being wrong and a cube being connected x4, I'm honestly not sure what you mean. Just as the area of a square with sides of length x is x2, the volume of a cube with sides of length x is x3. As you seem to want, the geometric object called a cube is associated with cubing a number. I cannot think of any way in which the cube is associated to x4 and I think it is likely you have misunderstood something. (Note that a key idea in the book is the existence of a 4-dimensional analogue of a cube which is called a tesseract. The tesseract is not a cube, it is just the 4-dimensional analogue of a cube just as a cube is the 3-dimensional analogue of a square. Moreover, it is associated to x to the fourth power in the same way that a square is associated with x squared and a cube is associated to x cubed. But, you need at least four dimensions in which to realize a tesseract. It seems to me that you may have thought they were talking about a cube when it was a tesseract that was actually being discussed.) Hoping my comments were helpful. -Alex