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RECENT ARTICLES
click titles to read articles
Ripping Apart Einstein
Cutting the threads of the spacetime fabric and reinstating the "aether" could lead to a theory of quantum gravity.
Readers' Choice: Much Ado About Nothing
Does the vacuum regenerate itself to fill the gaps as spacetime is pulled apart? Could a growing vacuum explain dark energy?
Classic Article: Building a Better Black Hole
FQXi essay contest winner Louis Crane explains how artificial black holes might have controlled our universe’s past and could direct humanity’s future, in this classic article from 2007.
Editor's Choice: Taming Infinity
General relativity and quantum mechanics could be perfectly compatible—as long as you know how to handle infinity, that is.
Readers' Choice: True Lies: Why Mathematics is an Illusion
To find a theory of quantum gravity we may have to look through a different logical lens, abandoning conceptions of "truth" and "falsehood" and crossing over to a new "mathematical universe."
E-infinity communications 1-7: "To: Researchers working on El Naschie E-infinity Cantorian-fractal..." in The Beautiful Truth
Dr. Cosmic Ray: "Dear Amean, You said "the parasite is spreading the word everywhere that..." in The Beautiful Truth
Anonymous: "But the assumption would need to be made that no other theoretical..." in Astrotheology: Do Aliens...
Lawrence B. Crowell: "There are long discussions about these faster than light schemes. The..." in Astrotheology: Do Aliens...
Marshall Barnes: "The comment by anonymous about dating twins at a greater distance reminds..." in Quantum Dating Market
Steve Dufourny: "Hi John, Indeed I agree, if people inserts this confusion about the..." in Free Radical
Anonymous: "Anthony: I believe that you're focusing in too much on this hypothetical..." in Quantum Grantmaking
RECENT ARTICLES
click titles to read articles
Ripping Apart Einstein
Cutting the threads of the spacetime fabric and reinstating the "aether" could lead to a theory of quantum gravity.
Readers' Choice: Much Ado About Nothing
Does the vacuum regenerate itself to fill the gaps as spacetime is pulled apart? Could a growing vacuum explain dark energy?
Classic Article: Building a Better Black Hole
FQXi essay contest winner Louis Crane explains how artificial black holes might have controlled our universe’s past and could direct humanity’s future, in this classic article from 2007.
Editor's Choice: Taming Infinity
General relativity and quantum mechanics could be perfectly compatible—as long as you know how to handle infinity, that is.
Readers' Choice: True Lies: Why Mathematics is an Illusion
To find a theory of quantum gravity we may have to look through a different logical lens, abandoning conceptions of "truth" and "falsehood" and crossing over to a new "mathematical universe."
FQXI ARTICLE
March 15, 2010
The Crazy Old Uncle of Algebra
September 13, 2009
Octonions may be the key to understanding the universe, but what are they? There are four number systems in mathematics, each spanning a different number of dimensions, in which division is possible:
* real numbers (1 dimension);
* complex numbers (2 dimensions);
* quaternions (4 dimensions);
* octonions (8 dimensions).
Quaternions are weirder still because they are noncommutative. In mathematics, commutativity is the ability to change the order of terms in your mathematical operation without changing the end result. So, for example, using real numbers, multiplication is commutative because 1 x 2 is the same as 2 x 1. Baez describes quaternions as "the eccentric cousin who is shunned at important family gatherings."
Octonions are worse still because they do not have the property of associativity, which means that you get a different result if you change the order in which you carry out your mathematical operations. Multiplication is associative for the real numbers because, for example, multiplying 1 and 2 together first and then by 3, is the same as multiplying by 1 the product of 2 and 3 (that is, (1 x 2) x 3 = 1 x (2 x 3)). That isn’t true for octonions. "
Return to the main article: "Taking on String Theory’s 10-D Universe with 8-D Math."
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Please read the important Introduction that governs your participation in this community. Inappropriate language will not be tolerated and posts containing such language will be deleted. Otherwise, this is a free speech Forum and all are welcome!