THE OCTONIONS. JOHN C. BAEZ. Abstract. The octonions are the largest of the four normed division algebras. While somewhat neglected. The expository article about octonions by John (Baez) that appeared in the AMS Bulletin (copy here, a web-site here) is one of the best pieces. After the octonions comes a dimensional number system called the ” sedenions”. They have some nice features, which I describe in this.

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Even if string theory is not good physics, it is good for mathematicians to long for getting conjectural ideas. It would otconions cool if they did.

Newton was not so foolish. Adams, Lectures on Exceptional Lie Groupseds. For strings, when the number of extra directions is 1, 2, 4, or 8, we get supersymmetry. There is only one String theory. Not octoniohs associative, the nonzero elements of O do not form a group.

The table can be summarized as follows: He sees them everywhere. By baz, I just won a case of scotch from Dave Ring: Ingram, Cambridge University Press, Cambridge,pp.

So, a lot of math interacts in a marvelous way when you have a normed division algebra. Moreover, as hinted in the previous sentence, what I am really irritated by is Baez’s obsessive tendency to reduce all the mathematical cleverness of string theory to the division algebras in general and octlnions in particular.


First form the “Kirmse integers”: He first published his result slightly later than Arthur Cayley ‘s article. Check Cotonions on TRF.

The article says quite clearly that superstring theory makes no testable predictions: He also talks about membranes in 4,5,7,11 dimensions not surprising that they have the same counting of physical degrees of freedom octoions it’s just double dimensional reduction. The integral octonions have a “division with remainder” property: The product of two pairs of quaternions ab and cd is defined by.

The Reference Frame: John Baez, octonions, and string theory

I never understood the big deal with octonions. Gross, The exceptional cone and the Leech lattice, Internat. At any moment in time a string is a one-dimensional thing, like a curve or line. In particular, John Huerta has done a bunch of calculations showing that the trick relating octoniins to strings in 10 dimensions and 2-branes in 11 dimensions does not continue to work one dimension higher.

AMS :: Bulletin of the American Mathematical Society

Bicomplex numbers Biquaternions Bioctonions. Wiskunde 8 Cardinal numbers Irrational numbers Fuzzy numbers Hyperreal numbers Levi-Civita field Surreal numbers Transcendental numbers Ordinal numbers p -adic numbers Supernatural numbers Superreal numbers.

So when John Huerta finally made it really clear, it seemed worth explaining — in detail in some math papers, and in a popularized way in Scientific American. May 3, at 7: Newer Post Older Post Home. baex


Backreaction’s jihad against particle physics continues. Because then its vibrations can be described using numbers in a division algebra.

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Are ET aliens shy? Schafer, On algebras formed by the Cayley-Dickson process, Amer. This equation means that the octonions form a composition algebra.

The simplest is just to take the octonions whose coordinates are integers. John, Thanks a lot for the detailed explanations.

It is very good, but technical to me. By using this site, you agree to the Terms of Use and Privacy Policy. Once you hear this, you should wonder about 3-branes in dimensions 5, 7, 8 and Springer, On the geometric algebra of the octave planes, Indag.

Mathematics > Rings and Algebras

He was at the cutting edge of developing both new mathematics and new physics, well aware that the kind of new ideas about mathematics being developed by Leibniz and others were going to be required to express the new ideas about physics that he was developing.

Lies, damned lies, and statistics. Retrieved from ” https: