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RECENT ARTICLES
click titles to read articles
The Cosmic Family Tree
Mapping the ancestral history of spacetime in an effort to unite quantum mechanics and general relativity.
Behind the Shadows
Imagining Schrödinger’s cat peering out from behind a black hole could lead to a theory of quantum gravity.
Why Did Nature Choose Quantum Theory?
Schrödinger’s cat may help reveal while some physical theories are better at describing reality than others.
Video Article: Through a Glass Darkly
Eight-dimensional numbers could be needed to handle string-theory’s 10-dimensional physics. This classic article, with new video content, also tackles the mystery of why elementary particles come in families of three—and maybe even how spacetime emerges in 4-dimensions.
Video Article: Evolving Time's Arrow
Why do we perceive time marching in one direction? In this classic article with new video, Craig Callender combines general relativity, evolutionary biology and cognitive science to bring the physics of time in line with everyday experience.
Eckard Blumschein: "Pentcho and Peter, To what degree do you agree on: "the crucial assumption..." in Some-When
Tommy Gilbertson: "Locomoting Whilst Minimizing Cost OxyMorons, Koans & Locomotion..." in The Secret History of...
Edwin Klingman: "Well this certainly stimulated some interesting comments. I'll take a while..." in The Secret History of...
Jason Wolfe: "Dear Sridattadev, If you are looking for Universal spiritual bliss, you..." in The Whole and Nothing But
Jason Wolfe: "Dear Paul, You said, "It is one thing to have a theoretical explanation,..." in Hanny's Voorwerp, and...
James Putnam: "Paul, Before you score any points with me about avoiding derogatory..." in Hanny's Voorwerp, and...
Lawrence B. Crowell: "I just can’t let this slide by! It was proven by Euler nearly 300 years..." in The Whole and Nothing But
John Merryman: "Paul, "Physical reality can only be that which is potentially sensorily..." in On the Origins of Quantum...
RECENT ARTICLES
click titles to read articles
The Cosmic Family Tree
Mapping the ancestral history of spacetime in an effort to unite quantum mechanics and general relativity.
Behind the Shadows
Imagining Schrödinger’s cat peering out from behind a black hole could lead to a theory of quantum gravity.
Why Did Nature Choose Quantum Theory?
Schrödinger’s cat may help reveal while some physical theories are better at describing reality than others.
Video Article: Through a Glass Darkly
Eight-dimensional numbers could be needed to handle string-theory’s 10-dimensional physics. This classic article, with new video content, also tackles the mystery of why elementary particles come in families of three—and maybe even how spacetime emerges in 4-dimensions.
Video Article: Evolving Time's Arrow
Why do we perceive time marching in one direction? In this classic article with new video, Craig Callender combines general relativity, evolutionary biology and cognitive science to bring the physics of time in line with everyday experience.
FQXI ARTICLE
February 9, 2012
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!