In the May 2011 issue of Scientific American mathematician John Baez co-authors "The Strangest Numbers in String Theory," an article about the octonions, an eight-dimensional number system that was discovered in the mid–19th century but that has been largely ignored until quite recently. As the name of the article implies, interest in the octonions has been rekindled by their surprising relationship to recent developments in theoretical physics, including supersymmetry, string theory and M-theory. Baez and his co-author John Huerta wrote, "If string theory is right, the octonions are not a useless curiosity; on the contrary, they provide the deep reason why the universe must have 10 dimensions: in 10 dimensions, matter and force particles are embodied in the same type of numbers—the octonions."

The eight dimensions of the octonions aren't the only interesting thing about the number eight, however. Baez highlights the number eight as one of his three favorite numbers. (The other two? Five and 24.) In 2008 Baez gave a series of lectures explaining what makes five, eight and 24 such unique and mysterious entities. The lectures, which are intended for a general interest audience, live on the Internet as both pdfs of the slides he used and video recordings. Watching them, you can learn not only a lot more about what makes octonions special, but also sphere stacking, the golden ratio, Islamic tiles, and why the sum of all integers equals –1/12.

11 Comments

1. 1. tharriss 08:09 AM 5/4/11

   Well I like the fact that while we may not have all the answers, we are certainly closer to them now than 100 or 50 or even 10 years ago...
   
   It seems to me that the struggle and continuing progress to understand things is pretty central to humanity's purpose, assuming we want to conceive of or generate a purpose for ourselves.

   Reply | Report Abuse | Link to this

2. 2. rsharak 07:18 AM 5/5/11

   Personally, I think the strangest numbers are 7, 13 and 28 because 7x13=28.
   
   http://www.youtube.com/watch?v=Lo4NCXOX0p8
   
   

   Reply | Report Abuse | Link to this

3. 3. Wilhelmus de Wilde 11:08 AM 5/5/11

   Numbers are symbols in our consciousness, symbols of our possibillities to be aware of more then our 4-d causal deterministic universe, we have a symbol for infinity, and the square root of minus one, but are they existing entities in our world or just outcomes of our brains, that is why I doubt the reality of string theory.
   
   Wilhelmus

   Reply | Report Abuse | Link to this

4. 4. HowardB 12:13 PM 5/7/11

   Unfortunately the links in the article to video recordings are broken .... :(

   Reply | Report Abuse | Link to this

5. 5. rdba28 in reply to eofd8s9a 11:10 AM 5/14/11

   Get off this site. You are an irritant.

   Reply | Report Abuse | Link to this

6. 6. Klintus Fang in reply to Wilhelmus de Wilde 01:24 PM 5/14/11

   @Wilhelmus: the behavior of modern electronics are explained by the theory of electromagnetism, in which complex numbers and hence, the square root of -1, are used frequently in the equations.
   
   This is why I doubt electromagnetism and also why I believe everything that I see in this computer screen, including Wilhelmus, do not exist.
   
   :p

   Reply | Report Abuse | Link to this

7. 7. billlee42 in reply to HowardB 01:57 AM 5/15/11

   Look at this web page: http://math.ucr.edu/home/baez/numbers/, as it contains links to the videos that works.

   Reply | Report Abuse | Link to this

8. 8. atreus 11:19 AM 5/15/11

   Hi guys,
   I like your article but it is about all Natural numbers not all Integers... or am I wrong? http://en.wikipedia.org/wiki/Ramanujan_summation
   Thanks

   Reply | Report Abuse | Link to this

9. 9. Dr_Zinj 09:43 AM 6/8/11

   Interesting. Extended Heim Theory, by Walter Dröscher, is currently using an 8 dimension system.

   Reply | Report Abuse | Link to this

10. 10. BruceWMorlan 10:29 AM 5/16/12

    The unfortunate use of dimensionality in two senses may be misleading (I am curious about this). Specifically, if I need seven numbers to describe something (say, temperature, spin, charge, x, y, z and t) then that is a 7-dimensional object even though only 3 (or 4, we won't go there) of the dimensions have a spatial interpretation which is that it is a dimension I could measure with a ruler. And volume could be computed as d.temp*d.x*d.y but there is not much use in that calculation.

    Reply | Report Abuse | Link to this

11. 11. mkilburn 05:08 PM 8/24/12

    5 and 8 are also important numbers in nuclear physics. There are no stable isotopes with mass 5 or 8.

    Reply | Report Abuse | Link to this