Introduction
Hyperoctonions and hyperquaternions
Number theoretical compactification and M^{8}H duality
Romantic stuff
Notations
Quaternion and octonion structures and their hyper counterparts
Octonions and quaternions
Hyperoctonions and hyperquaternions
Basic constraints
How to define hyperquaternionic and hyperoctonionic structures?
How to end up to quantum TGD from number theory?
pAdic length scale hypothesis and quaternionic and hyperquaternionic primes
Quantum TGD in nutshell
Geometric ideas
The notions of imbedding space, 3surface, and configuration space
The construction of Mmatrix
Number theoretic compactification and M^{8}H duality
Basic idea behind M^{8}M^{4}× CP_{2} duality
Hyperoctonionic Pauli "matrices" and the definition of associativity
Are Kähler and spinor structures necessary in M^{8}?
How could one solve associativity/coassociativity conditions?
Quaternionicity at the level of imbedding space quantum numbers
Questions
Summary
Octotwistors and twistor space
Two manners to twistorialize imbedding space
Octotwistorialization of M^{8}
Octonionicity, SO(1,7), G_{2}, and nonassociative Malcev group
Octonionic spinors in M^{8} and real complexifiedquaternionic spinors in H?
What the replacement of SO(7,1) sigma matrices with octonionic sigma matrices could mean?
About the twistorial description of lightlikeness in 8D sense using octonionic spinors
An attempt to understand preferred extremals of Kähler action
What "preferred" could mean?
Basic ideas about preferred extremals
What could be the construction recipe for the preferred extremals assuming CP_{2}= CP_{2}^{mod}?
In what sense TGD could be an integrable theory?
What integrable theories are?
Why TGD could be integrable theory in some sense?
Questions
Could TGD be an integrable theory?
Could quaternion analyticity make sense for the preferred extremals?
Are Euclidian regions of preferred extremals quaternionKähler manifolds?
