Buy New
  • List Price: $42.00
  • Save: $4.66 (11%)
In Stock.
Ships from and sold by
Gift-wrap available.
Division Algebras, Lattic... has been added to your Cart
Sell yours for a Gift Card
We'll buy it for $2.00
Learn More
Trade in now
Have one to sell? Sell on Amazon
Flip to back Flip to front
Listen Playing... Paused   You're listening to a sample of the Audible audio edition.
Learn more
See this image

Division Algebras, Lattices, Physics, Windmill Tilting Paperback – August 30, 2011

See all formats and editions Hide other formats and editions
Amazon Price New from Used from
"Please retry"
$33.34 $39.30

Best Books of the Year
See the Best Books of 2014
Looking for something great to read? Browse our editors' picks for 2014's Best Books of the Year in fiction, nonfiction, mysteries, children's books, and much more.


Best Books of the Month
Best Books of the Month
Want to know our Editors' picks for the best books of the month? Browse Best Books of the Month, featuring our favorite new books in more than a dozen categories.

Product Details

  • Paperback: 128 pages
  • Publisher: CreateSpace Independent Publishing Platform (August 30, 2011)
  • Language: English
  • ISBN-10: 1463730802
  • ISBN-13: 978-1463730802
  • Product Dimensions: 8 x 0.3 x 10 inches
  • Shipping Weight: 11.2 ounces (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Best Sellers Rank: #1,989,286 in Books (See Top 100 in Books)

Customer Reviews

5.0 out of 5 stars
5 star
4 star
3 star
2 star
1 star
See all 3 customer reviews
Share your thoughts with other customers

Most Helpful Customer Reviews

5 of 7 people found the following review helpful By John Shuster on January 12, 2012
Format: Paperback
Upon first scan of Geoffrey M. Dixon's "Division Algebra, Lattices, Physics, Windmill Tilting," my eyes settled upon section 9, "Ternary Stuff". Drawn to "C_3: Ternary Version of C," in which he develops a 3D Complex space with ternary product, I recalled Asimov's "The Gods Themselves," where aliens mate in threes! Most importantly, Dixon uses "mathematical resonance," a notion which reflects his belief that "mathematics and physics, at their most profound levels, are unified: they are one science" [p.8]. This resonance seems to guide his pursuit of math-physics, i.e., he pursues only research into what he finds mathematically resonant! (An admirable MOtivation, IMO.)

Chapter after chapter, Dixon reveals amazing results that flow from this resonance and his struggle to be true to it. In his "Multiverse Critique" [pp 44-49] he shows that all the talk about multiverses doesn't mean just any multiverse is possible, but only those which would conform to the math-physics of mathematical reasonance. (Science fiction writers take note!)

I was powerfully struck by his simple parenthetical comment [p 121]: "...QM (quantum mechanics) and GR (general relativity) should not be unified, they should be derived." IMHOpinion, current mathematical physics could benefit immensely from such a philosophical bent.

Not only is this a book for the mathematically inclined, it is for anyone who wishes to be true to his/her inner motivation to "Do it your way!" I can't help but feel that any reader (including the so-inclined graduate students) will find wonderful direction and example from Dixon's long journey and his compelling findings.
-- John Shuster, 1-12-2012
Comment Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback. If this review is inappropriate, please let us know.
Sorry, we failed to record your vote. Please try again
3 of 5 people found the following review helpful By J. Koeplinger on December 29, 2011
Format: Paperback Verified Purchase
If you've heard about quaternions or octonions and their speculated uses in the description of physical law, if you have basic college-level training in math and algebra, if you've ever wondered about finding nature's symmetries from the Standard Model in physics from beautifully simple algebraic constructs, or if you're even familiar with these topics since the 1970's and would like to see personal view on history paired with a compact presentation of 30 years of research and vision, then this your book. I've read Dixon's "Division Algebras: Octonions Quaternions Complex Numbers and the Algebraic Design of Physics" (1994) a little while ago, and left off both inspired and confused. This new book, "Division Algebras, Lattices, Physics, and Windmill Tilting", is not only much cheaper, it is also much more compact and approachable in the mathematical presentation. Dixon's seminal proposal from the 1980's and 1990's has since become a benchmark for octonionic models in physical mathematics when aiming at modeling fundamental particle interactions. It is great to see his T = RxCxHxO spinor introduced in this accessible, concise, and easily quotable format. Next to this, I enjoyed the fascinating personal history on how Dixon's ideas unfolded in academia, his "Multiverse Critique", the discussion on octonion products and lattices, and a section on his more recent work on ternary systems. You may enjoy Dixon's brisk humor and cheek, such as: "Michael Atiyah, a deity of mathematical physics at Oxford, recently gave a talk at Princeton extolling the virtues of applying all the division algebras in physics (he suspected that the octonions would be linked to gravity, which is wrong, but still ...).Read more ›
Comment Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback. If this review is inappropriate, please let us know.
Sorry, we failed to record your vote. Please try again
0 of 1 people found the following review helpful By Benjamin Goertzel on September 16, 2014
Format: Paperback Verified Purchase
A fun read for anyone who loves mathematical physics. Down-to-earth calculations regarding fascinating, beautiful mathematical structures, interspersed with personal anecdotes and speculative comments. The informality and life of a blog, but the rigor and care of an advanced textbook -- great combination!
Comment Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback. If this review is inappropriate, please let us know.
Sorry, we failed to record your vote. Please try again

More About the Author

Discover books, learn about writers, read author blogs, and more.

What Other Items Do Customers Buy After Viewing This Item?