And Hypersonic Flight

We can look at the universe as a continuous manifoldthat creates singularities, a universe whose continuity isredefined by such singularities. We look at the universeitself as a fluid, but from the standpoint of real Riemanniangeometry; singularity formation changes the potential andthe topological characteristics of the space-time manifold.Such transformation is reflected in changes of metric and"changes of state." The Riemannian hydrodynamic approachsolves the apparent discreteness-continuity paradoxby emphasizing the primacy of self-transformation.Historically, this is the only way in which real breakthroughsin technological progress occur. This is the samemethod, although at a lower epistemological level, thatallowed Schrodinger, Heisenberg, and de Broglie to introducenew and correct concepts to fundamental physics atthe beginning of the 20th century. 7 This same approach hasbeen carried forward in the realm of economy by giving adirectionality to the creation of singularities, in order todefine a shift in potential either entropically or negentropically.8This is the only standpoint from which evolving systemscan be represented. 8 The apparently local, entropic effectof the creation of a singularity is not the primary parameter;the issue is to analyze whether that singularity accomplishesa shift in the geometry of the system as a whole, sothat an "entropic" effect on the lower manifold of an existingstage of development is lower than the negentropiceffect for the transformed system as a whole.Energy conservation, then, although an important topologicalcharacteristic, does not become the absolute fixedlimit that it is according to the Kelvin-Helmholtz approach,which would, in effect, prevent the creation of new singularities.Kelvin and Helmholtz superimposed their own ideologicalinterpretation of Leibniz's statement of the conservationof vis viva, in order to prove their mechanistic, Cartesianoutlook. Stability is not synonymous with static, oreven dynamic, equilibrium. Such a notion is an artificialideological construct.'' Energy conservation is a boundarycondition for a given manifold, but it shifts precisely withthe topological shift of the manifold, according to the directionalityimposed by the new, real singularity formed.In that sense, new singularities are not necessarily symptomaticof "more chaos," nor do they necessarily lead to astatistical approach. On the contrary, such singularities moreappropriately approximate a Riemann-Weierstrass type offunction that is everywhere dense with singularities but stillcontinuous. 10The other approach to the same problem is the fake hydrodynamicschool of Cauchy, Kelvin, and Helmholtz, todayrepresented by llya Prigogine." They present themselvesas anti-Newtonian, insofar as Newton emphasizedthe discrete manifold—the hard-ball universe of self-evidentatoms. In reality they, and Maxwell along with them,have the same approach as Newton. The do not allow forthe creation of singularities.For them, a local discontinuity must be accounted for bya rearrangement of a given state. This is the basis for thevortices of the Helmholtz-Kelvin theory, which creates vortex-atoms.For the hard-ball fixed configuration atoms ofNewton, Helmholtz and Kelvin substitute merely more flexible,but still uncreatable vortex-atoms, found in the sameCartesian space Newton envisioned.Both Kelvin and Prigogine are characterized by a strictlymaterialist-mechanist point of view, revealed by their common—andnot accidental—reference to Lucretius and theEpicurean school. This is why they cannot acknowledge theconcept of rotation. Without this concept of real rotation,each "new structure formation," according to Prigogine,has to be explained symbolically and as "local disequilibrium."The formation of these "new structures" then hasno directionality, because the structures are the result oflocal condensation of atom-vortices. Hence there is no wayto measure if and in which direction we have a shift in theoverall topological characteristic of the field. This is theepistemology of an anarchist, which Prigogine tried first toimpose on the "new physics" and now is applying to the"neweconomics," where the notion of directed technologicalprogress has disappeared.Rotation is not a fixed rearrangement of local atoms; it isa general topological property of our visible universe.Therefore, we do not seek to analyze it as "abnormal localbehavior." What is actually abnormal is the absence of rotation.Any action in the physical universe will have to beseen in terms of the "creation of local rotation," becausethat is the only way action can do work in this universe. Wewill see later how vorticity or spiral forms are neither symbolicnor abnormal, but are the normal way action is shapedin our visual manifold. From galaxies to cells, space-timetransformations take the form of spiral action, and it is—we may hypothesize—not a turbulent, chaotic state of matter,but probably the most stable local state because it is aforce-free state.The issue then is not vortices per se, just as dress is notthe essence of human beings. The issue is the creation ornoncreation of action; its effect in terms of potential shiftwill normally take spiral form when it is real action.Kelvin, Helmholtz, and later Prigogine sought to coverup the old Cartesian approach to this basic problem withsome exotic notion of "local vorticity." This is very attractivefor those trained in symbology, but it negates the lawfulcreation of rotational action because that would upset their"conservation law." So the debate between Prandtl andKelvin was not about linear motion or circular motion, butwhether we are able to create action by shifting the geometryof the field. Action will normally take the form of rotation,and there will be an "entropic" effect on the previousfield potential. The stream lines will appear turbulent.The same method of thinking applied to the evolution ofour own civilization has allowed us to rediscover a line ofcreators in science that had been ignored or obscured bythe "official" schools. We are looking for evolution in scientificthinking, but measuring it against a transinvariantprocess of the conservation and expansion of our humanspecies, which defines directionality in human creative activity.Truth is not measured logically. In the same way,evolution cannot be simply considered as "something new";it must instead be measured in terms of its effect on humanprogress, which consequently is invariant with respect touniversal natural laws. This defines the criteria for identifyinga correct method of thinking from a wrong one. 12FUSION January-February 1986 17