Canonical science is based in the so-called canonical theory. A first version of the canonical theory was pioneered by . The modern version is a unified scientific formulation covering a broad range of multidisciplinary phenomena.
The concept of unification as understood in canonical science goes beyond the traditional meaning in physics, including string and M-theory.
Canonical science contains, as special cases with restricted use, the modern disciplines: physics, chemistry, biology, ecology, economy, and others. For instance, particle physics –quantum field theory– is obtained in the scattering region of fundamental canonical processes; mathematical ecology is derived in some well-defined macroscopic regime; the equations used in NMR chemistry are obtained when ignoring gravitation and non-Markovian contributions; classical thermodynamics is a subset of canonical theory for equilibrium regimes; etcetera.
Whereas some disciplines in modern science are almost unrelated, others are relatively interrelated. Physical chemistry, as something at the border between 'pure' physics and 'pure' chemistry, is a nice example of a multidisciplinary subject in modern science. Still if one explores physical chemistry one discovers that the field is not unified. There is not strong link between formalisms; they are mainly unrelated except by some weak connections. Physical chemistry looks like a truly heterogeneous way of studying phenomena of common interest to physicists and chemists. The 'unification' is in the subject under study rather than in the formalism used.
Canonical science breaks the usual barriers between disciplines. The same theory and formal concepts can be applied to both thermodynamic systems and lions populations, to chemical reactions and quantum mechanics, to gravitation and to electromagnetic phenomena, for instance. Disciplines traditionally unrelated –such as quantum field theory and epidemiology– receive a common framework in canonical science.
The complexity of an organized system involves three basic features: multiplicity, interaction between subunits, and integration of subunits into the whole. Modern formulations of complexity science cannot adequately describe the rich behavior we can observe in complex systems because lacking a truly unified formulation linking the different physical, chemical, and biological aspects. Canonical science embraces both elementary and complex phenomena.
writes:
The novel features that appear at each level of complexity [...] do not and even cannot conceptually exist at the level below [...] Such an attitude is not reductionist, it is not a reduction of a level to the lower one(s) but an integration, connecting a level to the other ones by integrating species and interactions to describe and explain increasing complexity of behavior.
Complex levels of organization of matter contain more information than elementary levels do. Canonical science provides an adequate conceptual and mathematical foundation for brilliant thought more is different
.
Our universe is multi-hierarchical. The canonical theory has the same formal structure for the description of phenomena at each level of description: microscopic, mesoscopic, macroscopic, cosmological.
These features from canonical theory invalidate traditional reductionism, which assumed some microscopic description of nature would be considered true laws of nature
whereas other descriptions would be thought as apparent or approximated laws. In its more radical version, reductionism recognized physics as the only true science! Now we see how classical and quantum physics is derived as one special discipline from the more general canonical science.
The formal structure of the canonical theory is very elegant and based in three main principles.
A vector \(n\) represents the state of the natural system at any instant.
Canonical processes represented as
change the state n according to the stoichometric vector w = n(\sup +) – n(\sup –). The rate of change of state follows from
This equation is very general and describes phenomena cannot be described by the usual laws of physics, chemistry, or biology. For example when all terms on the right-hand-side but S can be neglected and the state of the system is well described like pure quantum state, the above equation reduces to the equation of quantum mechanics
Below a heterogeneous sample of canonical processes. The range of processes selected –since particle physics to cosmology going through chemistry, heat science, biology, astrophysics, or epidemiology– illustrates the broad applicability of the canonical theory.
| 2 H(\sub 2)O (\larr ←)(\rarr →) H(\sub 3)O(\sup +) + OH(\sup –) | autoionization of water |
 (\larr ←)(\rarr →) |
keto-enol tautomerization |
| Zn + Cu(\sup 2+) (\larr ←)(\rarr →) Zn(\sup 2+) + Cu | electron transfer |
| e(\sup +) + e(\sup –) (\larr ←)(\rarr →) 2 γ | electron-positron annihilation |
| (\mi (\de (\sup 235)U\(III\) + (\sup 238)U\(IV\) ) (\de (\larr ←)(\rarr →)) (\de (\sup 238)U\(III\) + (\sup 235)U\(IV\))) | Uranium exchange with nuclear spin effect† |
| ε(\sub S) + ε(\sub B) (\larr ←)(\rarr →) ε'(\sub S) + ε'(\sub B) | system-bath heat transfer |
 (\larr ←)(\rarr →) |
electronic resonance† |
| B–C (\larr ←)(\rarr →) B + C | breaking-formation process |
| (\mi (\de hydrophilic-surface + HMDS) (\de (\larr ←)(\rarr →)) (\de hydrophobic-surface + NH(\sub 3))) | HMDS dip-pen nanolitography writing on semiconductor surface |
| S + I (\larr ←)(\rarr →) 2 I | SIR spread of a disease in epidemiology |
| ρ(\sub A) + ρ(\sub B) (\larr ←)(\rarr →) ρ(\sub C) + ρ(\sub D) | ensemble process |
| M(\sup *) (\larr ←)(\rarr →) M + ћν | emission-absorption of microwaves |
| vacuum (\sub j) (\larr ←)(\rarr →) vacuum (\sub k) + universe | Big Bang†† |
| D(\sup +·) + A(\sup −·) (\larr ←)(\rarr →) D(\sup ··) + A(\sup 0) | 's stabilization of a triplet state |
| C(x) + M(x(\sub m)) (\larr ←)(\rarr →) C(x + x(\sub m)) | homogeneous nucleation by clustering |
| (\mi (\de customer–p€ + business–item) (\de (\larr ←)(\rarr →)) (\de customer–item + business–p€)) | purchase-sale of item by p Eurs†† |
| C + X(inside) (\larr ←)(\rarr →) C + X(outside) | two-state channel biomembrane transport |
| v(\sub 1) + v(\sub 2) (\larr ←)(\rarr →) v(\sub 1) + v(\sub 2) | atomic elastic scattering |
| Prey + Lion (\larr ←)(\rarr →) 2 Lion | L/V predator-prey ecology |
Canonical science has next interesting properties:
Go to the research zone on the index for scientific details on each program or contact with the Center for more information.
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