March 27, 2013


September 26, 2013, Rhodes Palace Hotel, Rhodes, Greece
Session at the ICNAAM 2013

Christian Corda,
(Italy, Email:;
Thomas Vougiouklis, (Greece) Email and
Richard Anderson,U. S. A., Email

Recall that all living organisms are irreversible over time because they experience birth, life and death. Consequently, quantum mechanics and chemistry are insufficient for a consistent representation of biological structures due to their notorious lack of an "arrow of time," their notorious incompatibility with the theory of deformation (to maintain the basic exact rotational symmetry), and other well known but generally unspoken reasons.

The Italian-American scientist Ruggero Maria Santilli (see his curriculum) has shown that despite their irreversible character and full compatibility with the deformation theory, his Lie-admissible formulations studied in the preceding workshop are insufficient for the representation of biological structures because they are single valued, namely, their ordered product of two generic quantities A, B, produces only one value C, i. e.,A → B = C.

Among a variety of arguments that will be reviewed at the workshop, Santilli's [1] most suggestive analysis is that two correlated atoms in a DNA can produce an entire organ of a living entity with a very large number of atoms. But the correlation of two atoms in a DNA can be mathematically represented with the multiplication. Therefore, a mathematics necessary to represent biological structures should be multi-valued, in the sense that an ordered product between two atoms A and B can yield a very large number of ordered results that can be of the order of 1030 or more,

(1) A → B = {N1, N2, N3, N4, N5, N6, N7, N8, ........, N1030}.

where the brackets evidently represent an ordered set.

This type of multiplication is typically that of hyperstructures. However, to verify its predictions, any theory has to admit experimental verifications that, in turn, are only possible when said theory is formulated over a numeric field here referred to a set of elements verifying the axioms of a numeric field.

To achieve the latter requirement, Santilli proposed in the early 1990s the use of a yet new mathematics, admitting the preceding iso- and geno-mathematics as simple particular cases, today known as Santilli hypermathematics, which is referred to two different and inequivalent multi-valued hyperliftings of the entire 20th century applied mathematics, including numeric fields, functional analysis, differential calculus, algebras, geometries, etc., one hypermathematics with all quantities and operations ordered to the right and admitting for basic unit at all levels of treatment the multivalued, ordered, invertible forward hyperunit characterized by an order set with an arbitrary number of elements

(2) I = {N1, I2, I3, I4, I5, I6, I7, I8, ........, I1030} = 1/S

with ordered forward hyperproduct of the type

(3) A → B = A S B = {AB/N1, AB/I2, AB/I3, AB/I4, AB/I5, AB/I6, I7, AB/I8, ........, AB/I1030}

the second hypermathematics being characterized by quantities are their operations ordered to the left and admitting at all levels of treatment the most general known unit, Santilli multi-valued hyperunit ordered to the right for ireversible motion forward in time or to the left for irreversible motion backward in time.

As one can see, hyper products of type (3) are indeed of the type (1) needed for at least a first mathematical representation of the process according to which a very small DNA can produce a large living organism with an extremely large number of atoms.

There is no point in indicating possible aspects that will be studied at this workshop since they are so many and so deep; to signal indeed the birth of a new theoretical biology. The very notion of DNA as a "molecule" per current beliefs is replaced with that of a forward hypermagnecule with ensuing diagnostic character deeper than current very limited beliefs; we have for the first time a realistic possibility of at least initiating the quantitative understanding of the DNA code via Santilli forward hypernumbers, since its understanding with four thousand year old number has clearly no chance in view of the complexity of a DNA; the attempt for a deeper understanding of our brain synopsis; and other possibilities beyond our imagination at this writing.

All scientists interested in participating in this workshop must apply to one of the organizers with a statement of interest, whether as a speaker or as auditor, and include a CV. No participant will be admitted to this workshop without the written authorization by one of the organizers.

the R. M. Santilli Foundation has allocated financial sup[port for participation to this workshop, including the support of travel, lodging and registration, which funds are available on a first come first serve basis for all qualified speakers or auditors, including graduate students. The Foundation has additionally allocated $1,000 (one thousand U. S. dollars) for the writing of a review or research papers, provided it is based on Lie-admissible formulations and related genomathematics. For all financial support, following and only following written acceptance by one of the organizers, please contact
Richard Anderson
Trustee, the R. M. Santilli Foundation

As shown by R. M. Santilli in the monograph

Foundations of Hadronic Chemistry, with Applications to New Clean Energies and Fuels,
R. M. Santilli, Kluwer Academic Publishers (2001)

the DNA cannot be a "molecule" as conventionally understood in quantum chemistry due to the evident lack of the needed extremely large number of valence electrons. Santilli has also shown the insufficiencies of 20th century methods due to the complexity of the DNA code and the need of the most general known mathematics, the multivalued hypermathematics in its most general Hv form pioneered by T. Vougiouklis, see the outline for this workshop Vougiouklis Hv hyperstructures

Section of a DNA illustrating the insufficiencies of 20th century mathematics, physics and chemistry. The workshop shall study the DNA at the most general conceivable mathematical, physical and chemical levels, such as hyperchemistry whose mathematical structure is that of the most general known mathematics, Vougiouklis Hv hyperstructures in Santilli's multi-valued irreversible realization.

[1] R. M. Santilli, Isotopic, Genotopic and Hyperstructural Methods in Theoretical Biology, Ukrainian Academy of Sciences, Kiev (1996).

[2] R.M. Santilli and T. Vougiouklis, Isotopies, genotopies, hyperstructures and their applications, New frontiers in hyperstructures (Molise, 1995), 1-48, Ser. New Front. Adv. Math. Ist. Ric. Base, Hadronic Press, Palm Harbor, FL, 1996.

[3] B. Davvaza, R. M. Santillib, and T. Vougiouklisc , "Studies of Multi-Valued Hyperstructures for the Characterization of Matter-Antimatter Systems and their Extension," in Proceedings of the 2011 International Conference on Lie-admissible Formulations for Irreversible Processes, C. Corda, editor, Kathmandu University, Nepal, April (2011) pages 45-57