The Partiality of Wholeness
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Religious people believe in the existence of a supreme being. It has many attributes but two of the most striking are that it seems to both encompass and to pervade everything. Judaic sources are in the habit of saying that we all have a "share of the upper divine soul". Put more formally, we can say that we are both part of a Whole and permeated by it.
But what are the relationships between the parts and the Whole?
They could be either formal (a word in a sentence, for instance) or physical (a neurone in our brain, for instance).
A formal relationship entails an impairment of the truth value of a sentence / proposition / theorem / syllogism with the removal of one or more of its parts. As a result, a part could be reconstructed to fit into an impaired Whole once the formal relationships (and the derivative truth value) are known.
Things are pretty much the same in the physical realm: the removal of the part renders the Whole - NOT Whole (in the functional sense, in the structural sense, or in both senses). A part is immediately discernible: it is always smaller (size, mass, weight) than the Whole and it always possesses the potential to contribute to the functioning / role of the Whole. The part need not be active to qualify as a part - yet, it requires the potential to be active to do so.
In other words : the Whole is defined by its parts - their sum, their synergy, their structure, their functions. Even where epiphenomena occur - it is inconceivable to deal with them without resorting to some discussion of the parts in their relationships with the Whole.
But the parts are also defined by their context, by the Whole. It is by observing their place in the hyperstructure, interactions with other parts and general function of the Whole that we can assign the title ("parts") to them. There are no parts without a Whole.
In this sense, it seems that parts and Wholes are nothing but language conventions, a way that we chose to describe the world that was compatible with our evolutionary and survival goals and with our sensory input. If this is so, then, being defined by each other, parts and Wholes are inefficient, cyclical, recursive, in short: tautological modes of relating to the world.
The problem is not merely confined to philosophical and linguistic theories. It plays an important part in trying to define physical systems.
A physical system is an assemblage of parts. Yet, the parts remain correlated (at least, this is the assumption in post-Einstein physics) only if they can maintain contact (=exchange information about their states) at a maximum speed equal to the speed of light. When such communication is impossible (or too delayed for the purposes of keeping a functioning system) - the correlation rests solely on memories. Memories, however, present two problems : first, they are subject to the second law of thermodynamics and are atrophied through entropy. Second, as time passes, the likelihood that the memories will no longer reflect the true state of the system increases.
It would, therefore, seem that a system in physics is dependent upon the proper and timely communication between its parts. This, however, clashes, head on, with some interpretations of the formalism of Quantum Mechanics which fail to uphold locality and causality (see: "The Many World Interpretation of Quantum Mechanics and the Demise of Science" to be published). The fact that a Whole is defined by its parts which, in turn, define the Whole - contradicts our current worldview in physics.
Moreover, can we say, in any rigorous sense, that the essence of the Whole (=its Wholeness and holistic attributes and actions) can be learned from the part? If we observe the part long enough and are equipped with omnipotent measurement instruments - can we then tell how the Whole will look like, what will be its traits and qualities and how it will react and function under changing and different circumstances?
Can we glean all that from a strand of DNA? If we were aliens living a galaxy away and were to come to possess a strand of DNA - having never set eyes on a human before - would we have been able to reconstruct one? Yes, if we were also the results of DNA genetics. And what if not?
Granted: if we were to place the DNA in the right biochemical "context" and inject the right chemical and electric "urges" into the brew - a human, possibly, might have still emerged. But is this the equal of learning about the Whole from its part? Is elaborate reconstruction the equivalent of observation and measurement? This is counter-intuitive.
DNA is the embodiment of all the information needed to construct a Whole (with protein building blocks). Yet, it is dependent on the existence of a carefully regulated environment, which should include the raw materials and catalysts from which the Whole is to be constructed. In a (strong) sense, it is safe to say that the DNA includes the essence of the Whole (and is part thereof). But we cannot say that this information can be extracted (or decoded) by mere observational methods. More vigorous actions are necessary.
This is not the case with a fractal. The latter is a mathematical construct - but it appears abundantly in nature. Each part of the Whole is a perfect and complete Whole, on a smaller scale. Is DNA a fractal? No. The form of the Whole is totally preserved in the fractal part. By studying the fractal - by observing and measuring it - we actually end up studying the Whole in a rather direct (though only visual) manner. No other actions are needed: just observation and measurement. Still, the fractal is a mere structure, form - is this the essence of the Whole? Moreover, given that the fractal is the exact and perfect copy of the Whole - can we safely predict that it will function as the Whole will do, or that it will possess the same attributes? In other words: are shape-related observations sufficient to establish identity of the Whole and the part in the fractal case - or do we need to apply additional tests: physical and metaphysical? The answer seems obvious: shape is not a determinant. We cannot base our learning (predictions) on it alone. We need additional data: how does the part function, what are its other properties. Even then, we can never be sure that it is identical to the Whole without applying the very same battery of experiments to the latter. Think about epiphenomena: there is information in the Whole (temperature and pressure in the case of gas molecules or wetness in the case of water) - which cannot be predicted from a complete knowledge of the constituent parts (single gas molecules or hydrogen and oxygen). Can the thinking process be surmised from the study of a single neurone - or is the Whole brain under observation the precondition?
We can never be sure that the essence of the Whole is, indeed, resident in the part. Holograms and fractals are one case: the shape of the Whole is absolutely discernible in the tiniest part. Still shape is only one parameter - and hardly the most important, pertinent or interesting one. DNA is a second (more convincing) case. Admittedly, we have to use very complex procedures (which far exceed our intuitive definitions of non-intrusive observation). Still, the whole information is absolutely there. Yet, even in this case we Cannot say that the Whole is in the part. To say so would be to ignore the impact of the environment, of the Whole's evolution and its history, the interactions between its components. The Whole would still remain unpredictable - no matter how intimate and minute our knowledge of its DNA will become.
It would seem that Essence is indivisible. The essence of the Whole is not be found in its parts, no matter what is the procedure employed (observation, measurement, more intrusive procedures). This, at least, is true in the physical world. Abstractions may be a different matter altogether. A particle could be construed to be a part of a wave in Quantum Mechanics - yet, both are really the same thing, two facets of the same natural phenomenon. Consciousness arises in the brain and, therefore, by definition is a part of it. But if we adopt the materialist approach, consciousness IS the brain. Moreover, consciousness is we that include the brain as one of our parts. Dualism (wave-particle, brain-mind) is a response to this confusing admixtures of relationships between Whole-part pairs wherein one or more of the terms is abstract.
Perhaps the most intriguing variant is "God as a Clockmaker". God is compared to an artist and the world of phenomena to His art. The art is supposed to reflect the "nature" of the artist. A painting tells us a lot about the painter: for instance, that it can see (reacts to certain wavelengths), or that it has a limited set of ways of applying colour to cloth (using extensions of his body, for instance). It is also assumed that it can accurately inform us about the psychology of the artist: his internal world. This is because art emanates from this world, is part of it, is influenced by it and influences it in numerous ways.
The weaknesses of this approach are immediately evident:
(1) The art work has a life of its own. The death of the author has been decreed long ago in the sense that the artist no longer has a monopoly on the interpretation of his work and his "original intentions" have no privileged status in this context. In other words, we never look at an art work "objectively", "without prejudice" (see Bakhtin's work on the discourse in the novel). A work of art tells us a lot both about the artist and about ourselves as well.
(2) There is no way to prove or refute any assertion related to the private language of the artist. How can we know for sure that the artist's psyche is indeed expressed in his art?
(3) The art influences the artist (presumably his psyche). How can these influences be gauged and monitored? The work of art may have a snapshot (static) quality - but not a video (dynamic) one. It tells us nothing about the permanent state of the artist (which is of real interest to us).
(4) An art work can be substantially and essentially misleading (when it comes to edifying us concerning the artist). The artist can choose to make it so. Moreover, very important "features" of the work of art can be different from those of the artist. God, to take one notable artist, is described as omnipotent, omnipresent, eternal - yet none of these attributes is manifest in his work. We, who are His creations, are finite and very far from omniscient, to mention but two shortcomings.
In the delicate case of God, there are classical questions, the result of His highly idiosyncratic nature. Can a finite mind grasp any attribute of an infinite one, can an attribute of an infinite, all encompassing, omnipotent and omniscient entity be finite, partial, with limited power and knowledge and so on.
Part and Whole are PHYSICAL definitions, the results of physical observations. We have demonstrated that whenever an abstract concept intervenes (particle, wave, mind), duality results. This is also the case with art forms. The relationships between an artist and his work are much more complex than those prevailing between a part and a Whole and cannot be reduced to it. In the most important aspects, a work of art is not a part of the artist, at least not in the classical sense. Rather, their interrelatedness is more akin to the one between background and Image. The decision which is which is totally arbitrary and culture-dependent. Different people, coming from different cultures and having different vocations and avocations will reassign the roles. Think about a frame carpenter. When confronted with the Mona Lisa - what, for him, would constitute the image and what - the background? Naturally, he will pay much more attention to the exquisite wooden frame than to the glorious painting. The wooden frame would be his image, the mysterious lady - the background. This is largely true in art: artist and art get so entangled that the distinction is, to a large degree, arbitrary and depends on the predominant culture. The work of art teaches us nothing about the artist that is of enduring value - but it is, irrefutably, part of his definition (the same way that background and image define each other).
So, there are two ways of being "a part of": in the classical, deterministic way (the part is smaller than the Whole, etc.) - and by way of definitional relationship (the part defines the Whole and vice versa). We started our article with this tautology and we end it with it. "Part", "Whole" do seem to be language conventions, tautological, dualistic, not very practical, except on the most basic, functional level. Wherever and whenever abstracts are introduced, concepts (wave, particle, mind) - duality results. This is a sure sign of the breakdown of a conceptual system of thought.
It is also probably a sign that "part" and "whole" are
no more than language conventions and do not carry any real information
about the world. They are, however, practical distinctions (on the basic
functional level) and help us in the delicate act of surviving.