MADELEINE L ENGLE (MAGDALENA-"A WRINKLE IN TIME")-NEXO CON EL HIPERCUBO	2	BARILOCHENSE6999	28/02/2017 18:04
	PLAZA DE SAN PEDRO (VATICANO)=HIPERCUBO ("MAQUINA DEL TIEMPO")	103	BARILOCHENSE6999	26/02/2017 22:21
	¿HIPERCUBO ES LA CUADRATURA DEL TORO GEOMETRICO?	52	BARILOCHENSE6999	26/02/2017 21:47
	TESSERACT 32 LADOS (HIPERCUBO)	16	BARILOCHENSE6999	26/02/2017 21:46
	TEMPLO DE EZEQUIEL="MAQUINA DEL TIEMPO"=HIPERCUBO	38	BARILOCHENSE6999	26/02/2017 21:46
	¿EL HIPERCUBO ES LA CUADRATURA DEL TORO GEOMETRICO?	15	BARILOCHENSE6999	26/02/2017 21:43
	MARCOS 15:33 (NEXO CON EL HIPERCUBO Y LA CUARTA DIMENSION-MERCURIO-ORION-ISHTAR	126	BARILOCHENSE6999	16/02/2017 22:16
	¿HIPERCUBO ES LA CUADRATURA DEL TORO GEOMETRICO?	26	BARILOCHENSE6999	16/02/2017 22:15
	EXAGONO/ESTRELLA DE 6 PUNTAS/ROMBO/HIPERCUBO	74	BARILOCHENSE6999	27/11/2016 22:23
	AJEDREZ="AGUJERO DE GUSANO"=HIPERCUBO	89	BARILOCHENSE6999	23/11/2016 21:27
	¿QUE RELACION TIENE VESCICA PISCIS CON EL HIPERCUBO?	31	BARILOCHENSE6999	30/09/2016 11:45
	HIPERCUBO INTERRELACIONADO CON EL NUMERO 19	36	BARILOCHENSE6999	30/09/2016 11:44
	Hipercubo	47	BARILOCHENSE6999	30/09/2016 11:44
	NUMERO 44=RESURRECCION DE LAZARO=44 HS VATICANO=HIPERCUBO=GESTACION BEBE	20	BARILOCHENSE6999	30/09/2016 11:43
	NUMERO 44=RESURRECCION DE LAZARO=44 HS VATICANO=HIPERCUBO=GESTACION BEBE	1	BARILOCHENSE6999	02/06/2016 18:03
	MARCOS 15:33 (NEXO CON EL HIPERCUBO Y LA CUARTA DIMENSION-MERCURIO-ORION-ISHTAR	1	BARILOCHENSE6999	30/10/2014 14:05
	TEMPLO DE EZEQUIEL="MAQUINA DEL TIEMPO"=HIPERCUBO	1	BARILOCHENSE6999	25/10/2014 23:00

http://geekmom.com/tag/a-wrinkle-in-time/

 

Tesse-whatsit? The Science-ish of Tesseracts in Science Fiction

Tony Stark (Robert Downey, Jr.) examines a holographic representation of Marvel’s version of a tesseract in The Avengers. Image: © Marvel/Disney.

Coining the word “tesseract” is generally credited to Charles Howard Hinton, a 19th century scientist and science fiction writer who had a particular interest in the concept of a fourth dimension. In 1880, he wrote an article called “What is the Fourth Dimension?,” in which he suggests that the fourth dimension a) exists and b) could be time-related.  He then introduced the idea of visualizing this fourth dimension with cubes. He tried out different words to describe it and came up with “tesseract” for his 1888 book A New Era of Thought.

The tesseract—both the word and concept—have since been adapted into fiction repeatedly.

But before we dive into those, let’s break it down, geometrically speaking, to see what we’re talking about. We exist in three dimensions, so that’s pretty easy to imagine. We all understand length, width, and depth. If you want to hang out in two dimensions for a while, read Flatland: A Romance of Many Dimensions. If you’re ready to move to four, that’s when we have to get more creative with the visualizations and get to start talking science fiction.

A square is two-dimensional; we need two coordinates to describe a location on it. A cube is a square’s three-dimensional counterpart; we need three coordinates for a location. A tesseract is the four-dimensional counterpart, also called a hypercube or cube-within-a-cube:

Public domain animation visualizing a geometrical tesseract.

Now let’s look at how that geometrical concept and the fourth dimension as time translate into fiction.

A Wrinkle In Time

The first time I saw the word “tesseract” was in elementary school when I read A Wrinkle In Time. When Madeleine L’Engle was writing it around 1960, she was interested in particle physics and quantum mechanics. She once wrote about the book’s history:

I wrote A Wrinkle in Time when we were living in a small dairy farm village in New England. I had three small children to raise, and life was not easy. We lost four of our closest friends within two years by death—that’s a lot of death statistically. And I really wasn’t finding the answers to my big questions in the logical places. So, at the time I discovered the world of particle physics. I discovered Einstein and relativity. I read a book of Einstein’s, in which he said that anyone who’s not lost in rapturous awe at the power and glory of the mind behind the universe is as good as a burnt-out candle. And I thought, “Oh, I’ve found my theologian, what a wonderful thing.” I began to read more in that area. A Wrinkle in Time came out of these questions, and out of my discovery of the post-utopian sciences, which knocked everything we knew about science for a loop.

In the novel, she says that time is the fourth dimension, and the fifth dimension is a tesseract, which they travel through by tessering. The characters fold space and time to travel through it—the titular “wrinkle in time,” conceptually similar (though not identical) to wormholes or warp travel. The novel’s characters explain:

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.”

In her autobiography, A Circle of Quiet, L’Engle says that there are two types of time.: Chronos is the sort of time we generally think of as time, while Kairos is God’s time, a less linear sort of time without a past or present. Her tesseract is a way of time travel achieved by jumping from Chronos to Kairos back to Chronos.

If you read much more about L’Engle’s ideas in A Wrinkle In Time, you see more and more of her vision of God and religion in science. (She was surprised when it often ended up on banned books lists for being a challenge to Christianity, while she considered the three Mrs. to be angels.)

In Leonard S. Marcus’ Listening for Madeleine: A Portrait of Madeleine L’Engle in Many Voices, Thomas Banchoff (mathematician and professor at Brown University who even teaches a course called “Exploring the Fourth Dimension“) speaks of meeting her at a dinner in Feburary 1984 and discovering she had a completely different view of the science of the tesseract than he did. When asked if he thought she didn’t understand it, he replied, “No, not at all. It was just that she had an alternative view of the science. Hers was more like Star Trek, you know: ‘Beam me up, Scotty!'”

He goes on to clarify that her version of a tesseract was based on her belief that the world we live in has three dimensions of space and a fourth that is time, and tessering involved moving through the fifth dimension. In the end, he supports, though with hedging, the math and science of the book—emphasizing the fiction part of “science fiction”—and confirming that Dr. Murray is trapped in a hypercube (i.e., the cube-within-a-cube tesseract as it is more commonly known) in Camazotz.

Cube 2: Electric Boogaloo

Fine, you caught me. It’s not called “Cube 2: Electric Boogaloo.” Seems like it should have been. It’s actually Cube 2 – Hypercube (familiar word yet?). We’re not talking the finest cinema ever, scoring a 45 percent from Rotten Tomatoes with 37 percent of the audience saying they were into it. But it has “hypercube” in the name, which means it meets the qualifications for talking about tesseracts in fiction.

Spoilers ahead… because I know you’re dying to rush out and watch this right now.

In the original movie, Cube, a guy wakes up trapped in a cube (we often call this “a room”) with hatches on each face, each of which lead to other rooms. In Cube 2, a woman is again trapped in the cube, but when she goes through a hatch, gravity is reversed. Others trapped in the rooms discover gravity is different in each room, things are just plain wacky in all of them, and declare that they’re in a hypercube/tesseract. In one room, they find a square floating, which turns into a tesseract. The tesseract sucks in one of the trapped victims and rips him apart. Then things get weird.

They discover the computer nerd who created the tesseract. It’s imploding. One of them jumps into the imploding tesseract. Look, I want to talk about the science of tesseracts in fiction, but I feel like it’s just not going to happen here. You can watch the trailer instead. It has lots of Matrix-style drippy numbers, so you know there are computers involved.

April 4, 2007

Tesseracts: Cubes Get Hyper

Madeleine L'Engle, who wrote these words in A Wrinkle in Time, used tesseract to mean a shortcut through space and time. In her story, space-time wrinkles, or folds onto itself, creating new paths that allow characters to tesser, or travel from one end of the galaxy to the other in an instant.


Mathematicians also use the word tesseract, but they mean something different. A tesseract is another name for a four-dimensional cube, or a hypercube.

Here's one way to picture what this strange object might look like. You can start by imagining a point floating in space. A mathematical point has no length or width. Mathematicians say the point has no dimension. Moving the point along a straight path to a new position traces out a line. That line is a one-dimensional object. Shifting the line at right angles to its length traces out a square, and a square is a two-dimensional object. Moving the square at right angles to its flat surface traces out a cube—a three-dimensional object.


Here's the mind-boggling part. You have to try to imagine what would happen if you could move the cube in a new, fourth dimension at right angles to the three you've already used. Any drawing or model you might make of the resulting object would look horribly distorted. But you can still get an idea of what a tesseract would look like and even sometimes "see" it in flashes.

How might you recognize a tesseract if you ever encountered one in your multidimensional travels? Well, in our three-dimensional world, it might look something like a large cube that seemed to be spitting out a smaller one.

Even though L'Engle's concept of a tesseract is different, her book has inspired many readers to think more deeply about time and space and mathematics.

---

Muse, September 2000, p. 18.

You can learn more about dimensions, tesseracts, and even Madeleine L'Engle at http://www.mathaware.org/mam/00/918/index.html.

http://musemath.blogspot.com.ar/2007/04/tesseracts-cubes-get-hyper.html