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RECENT ARTICLES
click titles to read articles
Discord in the Quantum World
An alternative quantum resource to entanglement could help physicists in the quest to construct a quantum computer.
A View From the Top
Thinking of causation as a "two-way street"—along which the passage of information can be inverted—could have implications for the origin of life.
Classic Article: Black Holes, Paradox Regained
In 2004, Stephen Hawking famously conceded that black holes do not devour all information when they swallow matter—seemingly resolving the "black hole information paradox" that had perplexed physicists for decades. But some argue that the paradox remains open, and we must abandon our simple picture of spacetime to unravel it.
Quantum Biology: Making Waves in the Natural World
Could quantum effects explain the mechanisms behind smell, photosynthesis and bird navigation?
The Accidental Universe
Have we been fooled into seeing one form of reality, with particular fundamental forces and laws, based on the peculiar way that we have chosen to measure time?
Сергей Белокрылов: "Вот..." in Melting Spacetime
Author Frank Martin DiMeglio: "Importantly, outer space involves FULL inertia due to the impossibility of..." in An Accidental Universe
Author Frank Martin DiMeglio: "We cannot (and do not) experience outer space. Because, do (and can) we..." in An Accidental Universe
Pentcho Valev: "Giving up sanity for constant speed of light III Albert Einstein..." in Faster than Light
Сергей Белокрылов: "Если Вам еще..." in Melting Spacetime
Anonymous: "It is our own consciousness that is the reason of our illusion that is..." in Our Not-So-Special...
Satyavarapu Gupta: "Peter I did not see your post , orelse I would have replied it long..." in Alternative Models of...
Dov Henis: "Graviton's Energy-Mass Dualism Gravity, The Monotheism Of The Universe ..." in Our Not-So-Special...
RECENT ARTICLES
click titles to read articles
Discord in the Quantum World
An alternative quantum resource to entanglement could help physicists in the quest to construct a quantum computer.
A View From the Top
Thinking of causation as a "two-way street"—along which the passage of information can be inverted—could have implications for the origin of life.
Classic Article: Black Holes, Paradox Regained
In 2004, Stephen Hawking famously conceded that black holes do not devour all information when they swallow matter—seemingly resolving the "black hole information paradox" that had perplexed physicists for decades. But some argue that the paradox remains open, and we must abandon our simple picture of spacetime to unravel it.
Quantum Biology: Making Waves in the Natural World
Could quantum effects explain the mechanisms behind smell, photosynthesis and bird navigation?
The Accidental Universe
Have we been fooled into seeing one form of reality, with particular fundamental forces and laws, based on the peculiar way that we have chosen to measure time?
FQXI ARTICLE
May 25, 2013
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!