The Partiality of Wholeness

By: Dr. Sam Vaknin

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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 yet permeated by it.

But what is the relationship between the parts and the whole?

It could be either formal (a word in a sentence, for instance) or physical (a neuron in our brain, for instance).

I. Formal Systems

In a formal relationship, the removal of one (or more) of the parts leads to a corresponding change in the truth value of a sentence / proposition / theorem / syllogism (the whole). This change is prescribed by the formalism itself. Thus, a part could be made to fit into a whole providing we know the formal relationships between them (and the truth values derived thereof).

Things are pretty much the same in the physical realm. The removal of a part renders the whole - NOT whole (in the functional sense, in the structural sense, or in both senses). The part is always smaller (in 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 within the whole to qualify as a part - but it must possess the potential to be active.

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.

The parts define the whole, but they are also defined by their context, by the whole. It is by observing their place in the larger structure, their interactions with other parts, and the general functioning of the whole that we realize that they are its "parts". There are no parts without a whole.

It, therefore, would seem that "parts" and "whole" are nothing but conventions of language, merely the way we choose to describe the world - a way compatible with our evolutionary and survival goals and with our sensory input. If this is so, then, being defined by each other, parts and whole are inefficient, cyclical, recursive, and, in short: tautological modes of relating to the world.

This problem is not merely confined to philosophical and linguistic theories. It plays an important part in the definition of physical systems.

II. Physical Systems

A physical system is an assemblage of parts. Yet, parts remain correlated (at least, this is the assumption in post-Einsteinean 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 slow for the purposes of keeping a functioning system) - the correlation rests solely on retained "memories" (i.e., past data).

Memories, however, present two problems. First, they are subject to the second law of thermodynamics and deteriorate through entropy. Second, as time passes, the likelihood grows that the retained memories will no longer reflect the true state of the system.

It would, therefore, seem that a physical system is dependent upon proper and timely communication between its parts and cannot rely on "memory" to maintain its "system-hood" (coherence)

This demand, however, conflicts with some interpretations of the formalism of Quantum Mechanics which fail to uphold locality and causality. The fact that a whole is defined by its parts which, in turn, define the whole - contradicts our current worldview in physics.

III. Biological Systems

Can we say, in any rigorous sense, that the essence of a whole (=its wholeness, its holistic attributes and actions) can be learned from its parts? If we were to observe the parts long enough, using potent measurement instruments - would we then have been able to predict how the whole should look like, what will its traits and qualities be, and how it will react and function under changing circumstances?

Can we glean everything about an organism from a cell, for instance? If we were extraterrestrial aliens and were to come to possess a human cell - having never set eyes on a human before - would we have been able to reconstruct one? Probably yes, if we were also the outcomes of DNA-based genetics. And what if we were not?

Granted: if we were to place the DNA in the right biochemical "context" and inject the right chemical and electric "stimuli" into the brew - a human, possibly, might have emerged. But is this tantamount to learning about the whole from its parts? Is elaborate reconstruction of the whole from its parts - the equivalent of learning about the whole by observing and measuring said parts? This is counter-intuitive.

DNA (the part) includes all the information needed to construct an organism (a whole). Yet, this feat is dependent on the existence of a carefully regulated environment, which includes 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. But we cannot say that this information about the whole can be extracted (or decoded) merely by observing the DNA. More vigorous actions are necessary.

IV. Holograms and Fractals

This is not the case with a fractal. It is a mathematical construct - but it appears abundantly in nature. Each part of the fractal is a perfectly identical fractal, though on a smaller scale. Is DNA a fractal? It is not. The observable form of the fractal is totally preserved in every part of the fractal. Studying any part of the fractal - observing and measuring it - is actually studying the whole of it. No other actions are needed: just observation and measurement.

Still, the fractal is a mere structure, a form. Is this, its form, the essence of the whole? Moreover, given that the fractal, on every level, is the exact and perfect copy of the whole - can we safely predict that each of its parts will function as the whole does, or that it will possess the same attributes as the whole?

In other words: are observations of the fractal's form sufficient to establish a functional identity between the whole and the part - or do we need to apply additional tests: physical and metaphysical? The answer seems obvious: form is not a determinant. We cannot base our learning (predictions) on form alone. We need additional data: how do the parts function, what are their other properties. Even then, we can never be sure that each part is identical to the whole without applying the very same battery of experiments to the latter.

Consider emergent phenomena (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 or derived from a complete knowledge of the properties of the constituent parts (single gas molecules or the elements hydrogen and oxygen). Can thought be derived from the study of single neurons?

We can never be sure that the essence of the whole is, indeed, completely resident in the part.

Holograms and fractals are idiosyncratic cases: the shape of the whole is absolutely discernible in the tiniest part. Still shape is only one characteristic of the whole - and hardly the most important, pertinent, or interesting one.

DNA is another (and more convincing) case. Admittedly, in studying DNA, we have to resort to very complex procedures (which go beyond  non-intrusive observation). Still, the entire information about the whole (i.e., the organism) is clearly 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 on the whole (i.e., the organism), of the whole's evolution and its history, and of the interactions between its components. The whole still remains unpredictable - no matter how intimate and detailed our knowledge of its DNA (i.e., its part) becomes.

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, or more intrusive methods). This, at least, is true in the physical world.

Abstractions may be a different matter altogether. A particle can be construed to constitute 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 materialistic approach, consciousness IS the brain. Moreover, consciousness is really we - and the brain is merely one of our parts! Thus, consciousness would appear to be a part of the brain and to include it at the same time!

Dualism (wave-particle, brain-mind) is a response to the confusing relationships between members of whole-part pairs in which one of the members of the pair is concrete and the other abstract.

V. God as a Watchmaker

Perhaps the most intriguing approach to part versus hole issues is "God as a watchmaker".

God (the whole) is compared to an artist and the world of phenomena - a part of Him - to His art. The art (the part) is supposed to reflect the "nature" of the artist (the whole). A painting tells us a lot about the painter. We know that the painter can see (i.e., reacts to certain electromagnetic frequencies), or that he uses extensions of his body to apply colour to cloth. It is also assumed that a work of art can accurately inform us about the psychology of the artist: his internal world. This is because art emanates from this world, it is part of it, it is influenced by it, and, in turn, it influences it.

The weaknesses of this approach are immediately evident:

  1. A work of art has a life of its own. The artist no longer has a monopoly on the interpretation of his work and his "original intentions" have no privileged status. 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.
  1. 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?
  1. His art influences the artist (presumably his psyche). How can these influences be gauged and monitored? A work of art is often static (snapshot), not dynamic. It tells us nothing about the changing mental state of the artist (which is of real interest to us).
  1. An art work can be substantially and essentially misleading (when it comes to teaching us about the artist). The artist can choose to make it so. Moreover, very important "features" of a 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 of art: the world and its denizens. We, who are His creations (i.e., His works of art), are finite and very far from being either omnipotent or omniscient. In the case of God, His work of art does not have the same properties as the artist and can teach us nothing about Him.

VI. On the Whole...

It is reasonable to hypothesize that our innate ability to distinguish background from foreground is an extension or manifestation of our flight-or-fight response mechanism. Distinguishing friend (non-threatening background) from foe is crucial for survival.

Part and whole are, therefore, PHYSICAL conventions, the results of physical observations. We have demonstrated that whenever an abstract concept is involved (particle, wave, mind), duality results. Part-whole is a duality, akin to the wave-particle duality.

This is also the case with art forms. The relationship between an artist and his work is much more complex than between part and whole. It cannot be reduced to it: a work of art is NOT a part of the artist (the whole). Rather, their interrelatedness is more akin to the one between background and Image. The decision which is which is totally arbitrary and culture-dependent.

Consider a frame carpenter. When confronted with the Mona Lisa - what, for him, would constitute the image and what - the background? Naturally, he is likely to 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 between them is, to a large degree, arbitrary and culture-dependent. The work of art teaches us nothing about the artist that is of enduring value - but it is, irrefutably, part of him and serves to define him (the same way that background and image define each other).

So, there are two ways of being "a part of the whole". The classical, deterministic way (the part is smaller than the whole and included in it) - and through a tautological relationship (the part defines the whole and vice versa). We started our article with this tautology and we end with it. "Part", "Whole", do seem to be language conventions, tautological, dualistic, not very practical, or enlightening, except on the most basic, functional level. The oft-resulting duality is usually a sign of the breakdown of an inadequate conceptual system of thought.

It is also probably a sign that "part" and "whole" do not carry any real information about the world. They are, however, practical (though not empirical) categories (on the basic functional level) and help us in the delicate act of surviving.

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