Search FQXi


Steve Dufourny: "In reading the paper of Maudlin quietly, I have ideas , The aim is to..." in The Noise of Gravitons

Steve Dufourny: "The equation that I have writen here is intuitive and needs probably some..." in The Noise of Gravitons

Steve Dufourny: "A kind of strategy is necessary to create all these solutions.FQXi could..." in Global Collaboration

Steve Dufourny: "This project Global collaboration here on FQXi is possible, we could name..." in Global Collaboration

Steve Dufourny: "stop this please, FQXi is well moderated , so don t insist" in George Ellis - How can...

Martin Gray: "What are the different skin conditions that people often face? Every skin..." in George Ellis - How can...

Steve Dufourny: "Jonathan Dickau ,hope you are well, always cool to have your points of vue,..." in 16th Marcel Grossmann...

Steve Dufourny: "This platform is about theoretical physics, it is irritating to have these..." in 16th Marcel Grossmann...

click titles to read articles

The Math of Consciousness: Q&A with Kobi Kremnitzer
A meditating mathematician is developing a theory of conscious experience to help understand the boundary between the quantum and classical world.

Can We Feel What It’s Like to Be Quantum?
Underground experiments in the heart of the Italian mountains are testing the links between consciousness and collapse theories of quantum physics.

The Thermodynamic Limits of Intelligence: Q&A with David Wolpert
Calculating the energy needed to acquire and compute information could help explain the (in)efficiency of human brains and guide the search for extra-terrestrial intelligence.

Gambling Against the Second Law
Using precision thermometry to make mini heat engines, that might, momentarily, bust through the thermodynamic limit.

Mind and Machine: What Does It Mean to Be Sentient?
Using neural networks to test definitions of 'autonomy.'

July 7, 2022

The Crazy Old Uncle of Algebra
by Anil Ananthaswamy
September 13, 2009
Bookmark and Share

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).

John Baez at the University of California, Riverside, has written that, "The real numbers are the dependable breadwinner of the family, the complete ordered field we all rely on. The complex numbers are a slightly flashier but still respectable younger brother: not ordered, but algebraically complete."

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. "he octonions are the crazy old uncle nobody lets out of the attic," says Baez.

Return to the main article: "Taking on String Theory’s 10-D Universe with 8-D Math."

Comment on this Article

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!
  • Please enter the text of your post, then click the "Submit New Post" button below. You may also optionally add file attachments below before submitting your edits.

  • HTML tags are not permitted in posts, and will automatically be stripped out. Links to other web sites are permitted. For instructions on how to add links, please read the link help page.

  • You may use superscript (10100) and subscript (A2) using [sup]...[/sup] and [sub]...[/sub] tags.

  • You may use bold (important) and italics (emphasize) using [b]...[/b] and [i]...[/i] tags.

  • You may also include LateX equations into your post.

Insert LaTeX Equation [hide]

LaTeX equations may be displayed in FQXi Forum posts by including them within [equation]...[/equation] tags. You may type your equation directly into your post, or use the LaTeX Equation Preview feature below to see how your equation will render (this is recommended).

For more help on LaTeX, please see the LaTeX Project Home Page.

LaTeX Equation Preview

preview equation
clear equation
insert equation into post at cursor

Your name: (optional)

Please enter your e-mail address:
Note: Joining the FQXi mailing list does not give you a login account or constitute membership in the organization.