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childrens novel - What relationship is there between tesseracts in A Wrinkle in Time and the mathematical object?


It's been a long time since I read A Wrinkle in Time, but I remember the heroes using a phenomenon or device called a tessaract to travel across space, kind of like a stargate. I later learned that the word "tesseract" is a real mathematical term and refers to a four-dimensional cube-like object, also sometimes called a hypercube.


I'm not seeing the connection between these two uses of the term. I know physicists were making hypotheses about extra dimensions before A Wrinkle in Time came out, and I can sort of see the connection between extra dimensions and quick travel through three-dimensional space, but I don't see how a four-dimensional cube enters into the equation.


Is there any connection between how "tesseract" is used in A Wrinkle in Time and how it's used in mathematics?



Answer



In L'Engle's book a tesseract is a five dimensional object. It isn't a physical object but an abstraction used to explain a shortcut through spacetime. Three linear dimensions, plus a time dimension, plus a fifth dimension into which to fold the other four to reduce trip times.



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 top."


"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 round. In other words, to put it into Euclid, or old-fashioned plane geometry, a straight line is not the shortest distance between two points."



Outside L'Engle's work a tesseract is the natural extension of a cube to four dimensions, not five.


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