PRESENT RESEARCH INTERESTS

• Related to the EXPERIMENTAL STUDY OF PULSE within the frame of my last essay ("The left hand of chaos"), I am considering its possible relations with the division algebras, quaternions, bi-quaternions, and particularly OCTONIONS. The problem of functional asymmetry within bilateral symmetry, and the problem of the apparent experimental duality between arterial and venous pulse (look paragraph 40), besides its relation with time in general and with cognitive sciences, lead naturally to algebraic questions. On the other hand, we have unsuspected group symmetries within the continous evolution of pulse related with chinese meridians and the evolving sections of the gunas. But, until nowadays, there is no known application of octonions to biology issues, and they remain as an object of pure mathematics and theoretical physics. We can put these abstract algebras much closer to our jugular vein -and to complex systems in general. What could mean some types of equilibrium in terms of time for octonions? And biological equilibrium? Some people relate nonassociativity with irreversibility, but this is not well sound. These algebras are useful, but still have considerable ambiguity in its applications. The next topic is related with this.
  Any idea about this topic is welcome.

• I find very interesting and promising the "Perfect Symmetry Number Theory" created by Derek Nalls. Conventional number system arises itself as broken symmetry. Unlike many other attempts of this area, this new system is not a mere curiosity or an artifact, but applicable, elegant, useful and informative. This system precludes the existence of complex and hypercomplex numbers. But the main aim is not to avoid them, but to put the operation of multiplication in the desirable order. Many modern problems in mathematics arise from this. Think that we operate everyday with the multiplication operation rules arbitrarily created by Brahmagupta circa 628! Think about the problems that multiplication involves in number theory, the Riemann zeta, for example. Think about the ambiguities of hypercomplex algebras when we try to apply them and to understand what they are and what they could possibly mean. All this is related at a very fundamental level. We need this new approach, at least in comparative terms. Brahmagupta's utilitarian criterion not only has implications for algebra in general, but also deep psychological effects -representational and performative effects. It could be argued that will take a lot of time to master this system. Not at all, for young mathematicians; many students of physics and mathematics spend such a time or longer to master some special algebras that cannot yield something comparable for a general worldview in mathematics. Derek Nalls gives us a great present. Is there anybody out there ready to receive it?
  Any impression or idea about this system is welcome.