The Bridge Between the Transfinite and Infinity

"The great act of faith is when man decides that he is not God."
Oliver Wendell Holmes letter to William James 1907

    There have been attempts to bridge the span between observable empirical facts and the present boundaries of  ‘virtual reality’ (See Dr. Frank Luger's "Scientific Theosophy and Ethics”, Telicom Vol. XII No. 35). It has been a remarkable feat of this century to try to extend knowledge beyond these limits to the infiniteness of ‘ultimate reality’. An act of faith…in science?. Is the scaffolding provided by the scientific methodology reliable? Is a “cosmic morality” relevant to a philosophy of human conduct? Should a ‘cosmocentric’  quest for an absolute metaphysical category (God) enjoy a superior hierarchy than the pedestrian, ‘anthropomorphic’ groping of organized religions?, as suggested in Luger's “Summa Theosophica”?

      Scientific methodology is organized common sense, used by all of us daily with varying degrees of rigor and success. It starts with an observation of objects or events as they occur in nature or as simulated in the laboratory. If it is not observable, directly or indirectly, it can NOT be a proper object of a scientific inquiry; this truism represents the great leap forward from the Aristotelian a-priori to the Galilean a-posteriori methodology. Consequently, the scientific evidence thus gathered must be limited to that perceived by the sensorium or instrumental extensions thereof. It becomes immediately self-evident two things:

1.    our conclusions about nature are as reliable as the resolution capacity of the sensory physiological apparatus that made it possible to gather; and perhaps more important,

2.    our conception of the universe thus achieved is essentially subjective, being unable to separate the observer from the observed. The observer is inexorably an integral part of that being observed.

Furthermore, sense perception itself has been the object of numerous scientific studies. If we mix finely granular cane sugar with powdered carbon particles until we can clearly observe a gray hue homogeneous substance being formed. We may well invoke the Heideggerian dilemma of ‘being and existence’ when pondering about the ‘ontological reality’ of such color. A small fire ant from Florida attracted to it may readily ‘sense’ black and white rocks! Which is true? The scale of an observation is an important factor to reckon with in all observations. We can give numerous examples about the trustworthiness of our sensory fitness to build a reliable, ‘scientific’  model of our biosphere, let alone the consciousness, life or cosmos. Can we trust the parallelism of the columns of a building or the ‘disappearance’ of a glass rod when immersed in oil of similar optical density, or the rectilinear path of a bullet or a plane, or the absence of electromagnetic radiation outside the visual spectrum, as evidenced by our senses? That being said, one first suspicion might be whether the absolute truth, or the knowledge of God (or its equivalent 'material' conception), may be beyond the power of resolution provided by our senses?, alone or as extended by appropriate instrumentation. Yet, our author concedes that “..at the present stage of our evolution and turbulent emotional adolescence, we still need God…”, “..religion is a normal by-product of cultural evolution..” Are we thus sentenced to live a life of sensations? Not necessarily, because modern scientific methodology requires that observations be represented graphically and subjected to a statistical analysis, to study their shapes and temporal variations and more important their reliability, a determination of how close is the measurement to its ‘absolute’ value, i.e., what is its probability within the fiducial limits agreed-on regarding that particular observation. Once that data is statistically ‘purified’ we go back to the graphs to see if we can distinguish patterns, tendencies, cycles, etc. Then we describe our results as either displaying a sinusoidal behavior, following elliptical orbits, etc. All of which, of course, reflecting the approximation (best fit) of the observed measurements to the mathematical descriptions of the geometrical patterns they resemble so closely. This forced fitting now makes it possible for the scientist to formulate schemes or conceptual models that make generalizations possible. Because mathematics experienced such a phenomenal growth and development independent of observations made in the laboratory and now they are used so successfully, by ‘classical logic’ and analogical reasoning, they become a powerful tool in science in that they may be useful in predicting nature’s behavior and extending  our world of sensations to a virtual world to be found “..between 0 degrees Kelvin and the speed of light on the one hand, and the Big Bang-Big Crunches on the other…”. 

     Virtual reality is here!  Now we are ready for the next bridge that will  take us across eternity to the ‘Ultimate Reality’!, says Luger. By adding on to our armamentarium “..complex inequalities, abstract algebraic structures, and associated vector spaces in semi-topogeneous orders..” , we will have a ‘trascendental mathematics‘ that will lead the way to crash land the asymptote and end the extrapolation effort to approximate! In that way, Luger suggests, "we will have so matured ethically that global catastrophe and possible self-annihilation will be avoided!" Are you sure sir, here on earth?

       But life existed long before Leibnitz, Newton, Maxwell or the complex number fields. Mathematics neither has an independent life of its own nor can it be animated -like Pulcinella, the doll in Stravinsky’s Petrushka-, for mathematics is an invention of man, product of his mind (brain) activity, suitably adapted to man’s genetic crave to explain to himself the realities of his biospheric ecosystem. It does not have an existence of its own, independent of the species limitation in its brain’s architecture. It is just an useful, but limited, predictive tool to the observer of facts, no more, no less. In fact it would have died into oblivion a long time ago had it not been for its usefulness as a tool to explain the observed facts of Archimides and others during the Alexandrian stage of the Greek civilization. Then and now mathematics has been extremely useful in advancing and extending the boundaries of our virtual reality, as our author has so elegantly accomplished. Here are some historical examples.

      The purity and elegance of abstract mathematics is lost when made to pay its due to real-time society, but now the scientist can make generalizations, inductive (using the isolated observation as a starting point) or deductive (predicting the possible existence of an  individual unknown entity based on the observation of many similar [not identical] entities with same general specifications). The fantastic success of deductive reasoning in Mendeleyeff’s periodic table gave chemistry in particular and science in general, an unprecedented status in the various theories of thought, as we discussed in Ch. 1 above.

From then on, with the powerful use of mathematics as a possible predictive tool, useful conceptual models became possible (atomic theory, photosynthesis, Bohr’s atomic orbits, Darwinian evolution, cell theory, etc.); all based on observable, measurable facts about nature.

 But this was not enough; science was slowly becoming the exclusive reliable tool to understand nature. Once we have succeeded in extending our knowledge outside the constraints imposed by the limited resolution capability of our finite sensory apparatus, we can now reasonably anticipate using the approximations provided by the mathematical / logic models, we are now in the transfinite level of understanding.

Notwithstanding the many documented failures of scientific models in explaining nature’s behavior, many intelligent scientists ignore man’s intellectual limitations inherent in properly managing an infinite number of variables. Heisenberg’s uncertainty principle best illustrates this limitation in trying to have an absolute understanding of anything, as required by our author to reach the ‘Ultimate Reality’. This unbridled optimism has given birth to a materialistic reductionist movement that overwhelms modern western thinking patterns. Everything  can now be explained using a physico-mathematical model / scheme / conceptual structure. In his obsessive preoccupation for understanding, so typical of our species, man has reduced the level of organization of his observation in a relentless effort to understand its most elemental constitution …..and beyond, from the factual sensory data to the virtual reality extended by high technology to the ultimate reality dreamed possible by the methodology of metaphysical logic and mathematics set theory, quantum gravity and the “Theories of Everything”. This behavior many a times brings the best minds to assign cosmocentric, albeit bonafide, concerns a primary, superior hierarchy above ‘anthropomorphic’ religious criteria in dealing with the self-evident, observable real-time entities of our existential millieu. Imagine for a moment an existential chemist concerned with the industrial use of graphite, so he embarks on a macro study of its physical characteristics, then its micro features, then the crystalline arrangement of the tetrahedral disposition of its carbon atoms, then the orbital disposition of electrons around the carbon atoms, then the subatomic organization, and so on. Specialization makes you learn more and more about less and less until you reach the absurd possibility of knowing everything about nothing! Is this the science bridge from virtual reality to ultimate reality or a disguised self righteous “anthropocentric arrogance” of a different kind?

Since we do NOT live “..beyond the limits of the universe..” but with a zip code, man does need love even before he needs knowledge. We don’t need to scorn the efforts of organized religions to bring to your door a glimpse of a palatable, pedagogically viable concept of eternity. After so many years teaching medical and premedical students one learns to teach that which  a human being can learn. The anthropomorphism of organized religions is only a psycho-pedagogical tool to communicate the sophistications of eternity considerations, the catechismal level with its sundry assortment of purgatories, demons and angels. But this is only one level of understanding of organized religions. A different, much more sophisticated philosophical level is also available to St. Thomas, St. Augustine, and our quoted author! Maybe a computer model may, for the sake of argument, bring us close to a glimpse of the infinite reality of the Absolute, but can you read it on the monitor?, can you print it?, and if you could, what would you do with the data? As Dr. Luger correctly said: “..we need God as the common denominator to unite humanity and survive any and all calamity and maybe prosper and thrive in the long run..”  We do not need the use of science to “..purge our thinking of the twin evils of anthropomorphic ignorance and anthropocentric arrogance..”, for they, unfortunately, represent the natural state of affairs dictated by billions of years of  a neocortical evolution, indelible prints etched into our brains, a fact of science itself!

There can not be an Absolute, which is perfectly homogeneous, isotropic and non-material!, as our author proposes. Not anymore than there are planes that fly, submarines that swim or computers that  think!  Only humans do! As a valuable, worthwhile effort to advance our understanding, i.e., extending our sensory-limited view of our cosmos, reaching out for a virtual (not factual!) speculation about reality, we can accept the premises of a scientific theosophy.  However, it is another thing to suggest it as a path to an understanding of an ‘ultimate reality’; this is too pretentious as a real-time solution. Organized religions can do a better job. As to a possible future solution (end of time?), quare! Popeye cannot lead Mr. Magoo along that infinite bridge to eternity.

“General propositions do not decide concrete cases, the decision will depend on a judgement or intuition more subtle than any articulate major premise.”      Oliver Wendell Holmes , 1841-1935

End of Chapter 4