Category: the beautiful

Cohl Furey – summary – links between the Standard Model of particle physics and the octonions

In mathematics, the octonions are a normed division algebra over the real numbers, usually represented by the capital letter O, using boldface O or blackboard bold {\displaystyle \mathbb {O} } \mathbb {O} . Octonions have eight dimensions; twice the number of dimensions of the quaternions, of which they are an extension. They are noncommutative and nonassociative, but satisfy a weaker form of associativity; namely, they are alternative.

Octonions are not as well known as the quaternions and complex numbers, which are much more widely studied and used. Despite this, they have some interesting properties and are related to a number of exceptional structures in mathematics, among them the exceptional Lie groups. Additionally, octonions have applications in fields such as string theory, special relativity, and quantum logic. [ wikipedia ]

Cohl Furey

Cézanne

 

 

 

 

 

 

 

 

 

 

 

 

 

Paul Cézanne    |    Madame Cézanne (Hortense Fiquet, 1850–1922) in the Conservatory    |    1891
Oil on canvas : 36 1/4 x 28 3/4 in. (92.1 x 73 cm)    |    The Metropolitan Museum of Art

 

Kurt Schwitters

Kurt Schwitters 1887-1948
Inscribed ’39 Westmoreland Road’ on the back, along part of the support
Oil on wood and plaster construction in painted white frame, dimensions without frame, 16 1/4 x 12 3/4 x 4 (41.3 x 32.5 x 10.2), including frame 19 1/2 x 16 1/4 x 4 (49.2 x 41.3 x 10.2)
c.1942-5
Tate

Seated Bodhisattva

Seated Bodhisattva in Meditation, His Hands in Dhyana-mudra Kushan period    |    c.100 BCE-250 CE
Stucco with traces of polychromy    |    Gandharan style, perhaps from Hadda, Afghanistan
H. 51 x W. 30.5 x D. 12 cm ( 20 1/16 x 12 x 4 3/4 in. )
Harvard Art Museums / Arthur M. Sackler Museum