The Immanent Invariant and the Transcendental Transforming Horizon.

Quo Vadis Evolution? The Immanent Invariant and the Transcendental Transforming Horizons.

Lux, Veritas et Vera

Lux, Veritas et Vera

At some point in our lives we all have experienced and enjoyed the immense pleasure of an introspective, self conscious trip into ourselves, a kind of self-induced solitary confinement from the surrounding crowds, trying to ponder on the physically invariant aspects of our individualized existential reality, the what of ‘I’ vis a vis ‘the other’, i.e., trying to explain to yourself why some things do change while others apparently remain the same, wondering how you got where you are and where will you go, if anywhere, when you….and everyone else die, quo vadis? More often than not you feel overwhelmed by the super complexity of the physical sensory phenomena reaching consciousness, not to mention the equally experienced qualia originating from the extrasensory/metaphysical object or event invisible to our direct sensory detection or measurement. Then, in frustration, you conclude that ‘the more things change, the more they remain the same’, “vivir es ver volver” (life is to see same things past come back)? But, if you are afflicted by the ‘sane psychosis’ of curiosity, then you make it a hobby to meditate deep about the why, using whatever information resources, whatever science, technology and metaphysical logic has been placed within your reach. But the conclusions are disappointing when we find out that other subhuman species enjoy lower thresholds to the same sensory information and we discover that our human brain natural combinatorial capacity without the aid of instruments is dismally low.
Yet, we all witness the self-evident truths about the Newtonian apple falling to the ground, rain water streaming down hill, the loss of structure and/or function of complex objects falling from high buildings or contrariwise, the required supply of externally applied energy or effort to make same object move or spontaneously restructure itself when returning to its original locus in the tall building. A closer look will immediately evidence that complexly structured objects or events exhibit either a bilateral or rotational symmetry, the kind of ordered complexity that was never the result of natural spontaneous processes. On the other hand, the loss of order and complexity, as when a tall building naturally collapses, brings all systems to a minimum of free energy and a corresponding increase in entropy. Then we observe, with Pierre Curie, that the symmetry elements of the causes must be found in their effects while the converse is not true, i.e., the effects can be more symmetric than the causes. Is evolution fueled by asymmetry, induced by external forces or spontaneous?
Then we wonder like Leibniz did in his ‘Principle of Sufficient Reason’ (PSR): Why so? Then we also naturally posit the intervention of an efficient causal agency as the driving force behind this transformational change in the direction of a lesser entropy content (negentropy) and increased organizational complexity. If there is no sufficient reason for one thing to happen instead of another, the Leibniz principle says that nothing will happen and the initial situation will not change. What then is the efficient causal agency in defiance of natural laws and why? Where in infinity or transfinity is this agency located? Maybe inside our own human brains? If the latter, since it cannot spontaneously come into being, where –if anywhere- is the external source of inspirational righteousness originating the information being transferred to our decisional human brain lobe?
The simplest way to start digging into this analysis is to postpone the identification of the source and start with the relatively easier chore of characterizing the kind of information being transferred….or settle for the complex structural/functional evolutionary changes resulting therefrom? To differentiate the constituent elements of complexity we notice, prima facie, order in structure and function of either single sensory objects or in situations where interacting sensory objects describe a measurable event. This is the proper domain of the 4-d ontological aspect of the scientific methodology. But much beyond the reaches of this Minkowsky spatio- temporal domain we find the equally relevant epistemological n-1 d metaphysical logic to assist in the explanation of that experienced force which cannot be described experimentally as a physical object or observable event. To follow is a brief exposition of the need for a hybrid epistemontological approach when analyzing existential reality where symmetry considerations play a decisive role in the human brain when processing the information input when ordering the complexities of physical and metaphysical reality.
We notice that most sensory objects have in common a given symmetry, either a bilateral symmetry (e.g., two arms of a human body statue in anatomical position) or a rotational symmetry (e.g., spherical objects) where there is complete equivalence between the existing alternatives (the left hand with respect to the right hand or a full 360 degree axial rotation of a human statue/spherical object, respectively). As in nature, we also notice that, in the absence of an asymmetric transforming cause (externally applied or self-induced force?), the initial invariant state symmetry is preserved, i.e., a breaking of the original symmetry -whether human-induced or in its highest natural entropy state- cannot happen without a reason because an asymmetry cannot originate spontaneously. How then was microscopic and cosmological order ‘created’? A tall order for the scientific community to handle with its methodology, imagine now the level of complexity faced when you consider the invariance under a specified group of transformations and the symmetry concept is now applied not only to ontological spatial statues or spherical objects but also to relevant epistemologically abstract virtual ‘objects’ such as found in metaphysical logic math expressions, e.g., dynamical equations of state.
But the curious mind has to start from the sense-phenomenal physically obvious to the statistically probable, metaphysically inferred and then the theosophically possible explanations model when the effort has exceeded the human brain capacities to epistemontologically hybridize and harmonize all the different elements in the first two as a coherent unit or unitary whole. An extraordinary task when you have to consider the constitutive elements in a single human being made up of trillions of microscopic living cells, the majority of which of different species and each, not only following their individualized trajectories through the Many World universes according to the idiosyncrasies of their many molecules, atoms, subatomic particles, etc., but also tracking the evolutionary path of the unit human life to its ultimate destination. Yet you are able to maintain through life the ‘singularity’ of your unit body and mind as it invariantly persist while changing. In other words, you are simultaneously a statistically invariant, physico-chemical you and a constantly transforming many, while you traverse a world line in one or many universes…. going somewhere.
So, historically we start by a classification of sensory reality according to their varied symmetry, structural macro properties as manifested in harmony, beauty, and unity followed by their inferred micro structural properties after their epistemological translation into irreducible representations of their fundamental physical symmetry groups, e.g., a group-theoretical account of objects or their canonical Hamiltonian representation as dynamic entities. The next step was to harmonize the invariant geometrical abstractions with the dynamic Hamiltonian equations of motion. The complex evolving dynamic theories of nature were made easier to comprehend by Jacobi with the strategy of applying transformations of the dynamic variables that leave the Hamiltonian equations invariant. This way the original formulation became thereby transformed into a new one that is simpler but perfectly equivalent albeit somewhat removed from the existential reality it purports to substitute for. May this be carrying symmetry principles too far, the reason why general relativity and quantum physics cannot be integrated into a unit theory and allow both to reconcile. We briefly analyzed this constrain in a previous chapter.
From both an ontological and epistemological perspective, symmetries in theories represent properties existing in nature that characterize the structure and function of the physical world as illustrated by their methodological success in predicting the existence of new particles in physics, e.g., the prediction of the W and Z particles in the unification of the weak and electromagnetic interactions. Of course some symmetries are observed while others are only inferred and thus validated by their predictive value. It would seem as if symmetries represent natural, minimum free energy states in equilibrium. As such they serve the purpose of being used as constraints on the evolution of new physical theories, a valuable normative role assuring the compatibility of quantities, dimensions and form in their constitutive equations. This is especially important now while we struggle to find a unified description of all the fundamental forces of nature (gravitational, weak, electromagnetic and strong) in terms of underlying local symmetry groups. Hopefully the unification is just as credible at the explicit, measurable, ontological level as it may be at the implicit representational/epistemological levels, i.e., observably invariant global space time symmetry and the inferred locally varying continuous symmetry. In our opinion all symmetry principles are operational transcendental strategies aimed at making our understanding of the world more intelligible with no guarantee of reaching reality ‘in se’. But, there is indeed a natural connection between the invariables and structural realism just like between symmetry and objectivity, the validity of which is predicated on being the same for all observers and do not depend on any particular perspective under which is being considered. Objective realism is that which remains invariant no matter how many transformations it suffered when forced into a convenient reference frame. Can we make the same claim for what seems the human-contrived epistemological explanations of transfinite dynamic invisibilities ‘existing’ beyond the human 4-d spatiotemporal Minkowsky cage?
Why did the human species historically and conveniently choose the invariant features of symmetry to explain his dynamic evolution through space time? Was it unconsciously genetically/biologically determined, subconsciously mimetically/psychosocially imposed by circumstantial/environmental constraints or is it the inevitable consequence of the freely willed, self conscious effort of a few historical prophets inspired by transfinite ‘revelations’ guiding their efforts through the pathways of righteousness to preserve life, psychic comfort and social conviviality, i.e., create and sustain a biopsychosocial (BPS) equilibrium through life? The common denominator found in a BPS equilibrium is ‘symmetry’, whether discovered or invented in the mathematical proportions and harmonies they contain, or the related properties and beauty of their form. A combination of an essential biological, life preserving effort and the convenience of a happy psychosocial environment in guarantee of the survival of human life and self consciousness. The symmetric proportions of material objects not only have an esthetic appeal (beauty, regularity and unity) but, when deliberately designed by the architect or engineer as e.g., the regular polygons, polyhedrals, etc. as the structural foundations of buildings, factories, etc., the geometry is defined in terms of their invariance under specified groups of rotations and reflections, not necessarily esthetic criteria. No wonder the current appeal of differential geometry and topology to theoretical physicists when explaining the invisible domain of relevant sub atomic and cosmological reality. This time symmetry considerations propitiated the development of group-theoretic representations that have been so useful in modern physics to create ‘equivalent groups’ by symmetry transformations easier to exchange with one another without allegedly substantially changing the unit wholeness being considered. In our opinion, this may introduce non-compatible elements into general formulations affecting their claimed invariance under the transformation when equivalent elements are exchanged according to one of the specified mathematical operations, as the case may be. Having perhaps reached the limits of human instrumental resolution in the description of objects or phenomena, we have now emphasized more the application of symmetry principles to natural laws in our attempt to achieve a unity of different and equal elements in our explanations/conceptualizations of reality which has become central to modern physics. There are always serious problems when you hybridize invariant symmetry principles with transforming symmetry arguments into a unit whole theory.
Summary and Conclusions.
Needless to say, the professions of medicine, law and engineering practitioners have been more efficient in doing their ‘thing’ than their academic philosophy equivalents in the same areas because the former are mostly dealing with the ontologically and statistically invariant macro aspects of 4-d space time reality while the latter must conceptually keep simultaneous control of both invariant and transforming aspects of real time existential and virtual universal models of the same reality. The application of symmetry principles has provided ontology and epistemology useful tools to discover the structure and function of absolute reality, all within the known perceptual and conceptual limitations of the human observer to find/identify noumenal reality.
The most successful efforts in that direction have been to control the dynamic Hamiltonian formulations of measurable phenomena by conveniently holding them as invariant by the use of transforming operations of the relevant variables in the dynamic equations (Jacobian transforms). This way the intractable dynamics are transformed into simpler but perfectly equivalent now amenable to to combine, permute, exchange with equivalent representations, etc. Whether this simplification correspond to reality, quare!
We have dramatize the complexity of reality by reminding the reader that the historical, lifetime chronology of a single living human being is a macro statistical description conveniently ignoring the concomitant evolutionary path of trillions of microscopic living entities, mostly of different subhuman species, e.g., bacteria, molds, etc., each cell, molecule, atom, subatomic particle, etc following independent trajectories through the various Multiverse options. Yet the unitary integrity of your physical body and mental idiosyncrasies remain distinguishable whether you traverse a world line in one universe, or many.

Because of the successful influence of symmetry principles in scientific methodology pursuits, as outlined above, we do not appreciate as much its impact on the metaphysical logic of our explanatory models of existential and abstract/virtual reality equivalents. We briefly discussed two outstanding influences, the Leibnizean Principle of Sufficient Reason (PSR) and Pierre Curie’s theory of causality. PSR stresses the correlation between symmetry (bilateral or rotational) and natural stability implied in the complete equivalence between the existing alternatives, as discussed above, e.g., if the alternative positions are equivalent why choose among them (invariance). This means that in the absence of an asymmetric efficient cause there is no reason to change, i.e., a breaking of the initial symmetry cannot happen without a reason, or an asymmetry cannot originate spontaneously without defying laws of nature, yet it happens, as argued.
In a related argument, Pierre Curie, argues that the symmetry elements of the causes must be found in their effects while the converse is not true, i.e., the effects can be more symmetric than the causes. And we ask: is evolution fueled by asymmetry, induced by external forces or spontaneous?

Dr. Angell O. de la Sierra, Esq. Deltona, Florida Spring 2012

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