by Milton Dawes

We usually think of “metaphor” as “a figure of speech” and the language of poetry. I think that this specification represents an unfortunate limitation. I would like to propose that metaphor not only qualifies as a figure of speech but more importantly, metaphors and a metaphoric principle go beyond grammar and poetry. Metaphors play an extremely valuable part in all areas of our lives – in our speaking, writing, myths, perception, meanings we give, beliefs, knowledge, communication, learning, and so on.

In our speaking and writing, we often forget that things are not what we think, feel, imagine and say they are. Statements we make are usually not what we are seeing or hearing – they are statements about what we are seeing and hearing.

Picture this, if you will: Metaphor is not only fundamental to language, but since – apart from some philosophic explorations – our words are usually not about other words, but are about the world of non-words; all languages – as means of representing our thoughts, ideas, feelings, and also what our thoughts, ideas, feelings, etc. are about – can be considered as metaphoric.

Metaphor can be considered a subset of the more inclusive general semantics principle of “relative invariance under transformation”. To paraphrase Korzybski, the founder of general semantics:

In a world of diversity and change, when we discover something that seems to remain relatively invariant, (relatively unchanged), then we are unto something of great significance and importance to us in understanding ourselves-in-our-world. (See Chapter X1X of Science and Sanity.)

“Relative invariance under transformation” represents a general semantics generalization that we can use in everyday situations. It reflects the important scientific and mathematical principle related to “Invariance of principles and laws under transformation of frames of reference”.

In the case of special relativity, the equivalence principle – an invariance principle – states that “the laws of physics must be invariant under a transformation from one inertial system to another”.

The invariance principle of general relativity states that “the laws of motion are invariant for all observers, whether accelerated or not”. (Van Nostrand’s Scientific Encyclopedia.)

Wouldn’t it be nice if we had a law of argumentation? It might go something like this: The standards of interpretation must be invariant for all disputants, no matter how angry, disturbed, fed up or frustrated they feel. (By the way. In the discipline of general semantics, we can find proposals for such a standard). So let’s now explore the relative invariance principle.

You could think of relative invariance under transformation as a fancy way of saying some thing-process or happening “A” is structurally similar to, or is like, some other thing-process or happening “B”. Put in other words, we could say: “Although “A” has changed, broadly speaking, there are some features we can abstract from “A” that have remained relatively unchanged.

In brief we are saying “a this” – whatever this happens to be, is like “a that“- some other thing or happening at some other place and time. We are talking relative invariance when we say “Like father, like son.” “The heart of the matter.” “Love is blind.” If we observe our own thinking and speaking we will discover how much we depend on metaphors.

And in terms of the relative invariance principle, we might review our tendency to smirk when in listening to conversations we hear “It’s like….you know?” We might be better off thinking, if not speaking that way.

Laws, rules, constitutions, regulations, policies, mission statements, customs, habits, attitudes, sense of self, myths, labels, names, classifications, analogies, metaphors, simile, examples, explanation, theories, fractals, maps, scale models, taboos, photographs, portraits, plays, and so on, can all be considered as examples of the relative invariance principle.

For example: A law, a regulation, or a theory, is formulated to remain applicable (invariantly useful, applicable, relevant, etc.) at different places-times-situations. When, for instance, we give an explanation, or formulate a theory, we are in effect indicating that there are some similarities, some resemblance, between what we have imagined, between what we are proposing, and the actual situation we are attempting to explain. And when we make a prediction, we are in a sense saying that things will be observed to be like how we imagine them to be.

In addition to the various ways we have written and thought about objects, and our perception of objects, we can apply the relative invariance principle to increase our understanding of this process. Here is an example of an application of the relative invariance principle, incorporating analogy, example, explanation, hypothesis, structural similarity, and so on.

Suppose we ask “How is our perception of objects (a this) like a swarm of bees?” (a that) To facilitate this approach, I invite you to imagine you are observing, from a distance, a very densely packed swarm of bees. Imagine that you don’t know, and cannot see that there is an invisible barrier (let’s say, a Star Trek-like force field) that surrounds and move with this swarm. This creates a boundary that is not easily crossed by a bee. And also imagine that you don’t know that you are looking at bees. Now visualize what you might observe watching this swarm from a distance far enough away that you are unable to see individual bees darting here and there, in all directions within the confines of the swarm.

Now imagine a very large number of densely packed interacting and interrelating subatomic particles, vibrating at varying frequencies. Also imagine some kind of force field accompanying this ‘swarm of particles’ and minimizing the dissipation of the swarm. This force field prevents most of the particles from flying off in all directions as our bees would without their surrounding force field. In terms of “relative invariance ” this eventful subatomic activity, this ‘swarm’ of particles, can be likened to that swarm of bees.

We could now consider an object as “A structure that remains and appears to us relatively unchanged through all the various changes of directions and movements of its constituent sub-atomic structures: A structure that remains topologically relatively invariant through all the tremendous activities and energetic interactions of its constituents.”

In music we might find one of the best examples of the principle. In key changes, musical notes are transformed to other notes. But the relationships between notes, the order, duration, the period between notes and other factors, remain relatively invariant.

“Relative invariance” is very much involved in the communication process. Communication works well when what I think-feel is well represented by what I say or write. And what I intend, say and write is accurately received, and well represented by a listener’s interpretations and meanings. In other words, we could say that there is good communication when this what-a-speaker-or-writer-is-expressing is like that what-a-listener-or-reader has understood.

The principle is also useful in helping us to improve our general understanding of various, seemingly unrelated features, of our world. If for instance, we know that some thing-process “A”, is like some other thing-process “B” with which we are acquainted, then knowing something about the structure, functioning, and relationships of “B” can help us to understand, expect, and sometimes even make predictions about “A”.

A mathematical expression of this can be seen in the statement 2/4 =x/8. As a party game, participants could be invited to come up with some labels – players would say how some other thing is like the object represented by a label. For example, how is an organization like a society? How is a society like an individual? How are ‘minds’ like societies? (I have assumed here, that since ‘minds’ create societies, there might be some relationship between ‘mind’s and their creations. This is like making inferences about what goes on in a factory by observing what it produces.)

Professional translators, to minimize misrepresentations, seek to keep relatively invariant, the ideas, message, referents, etc. when they transform words from one language to another. Unfortunately not many of us, professionals or not, realize that we all do translations when we speak, read, hear, see and so on. Professionals do a double translation. They translate when they interpret an original piece, and they translate when they represent their interpretation of a piece with the words of another of another language. We can attribute a great deal of many conflicts, disagreements and disagreeableness, to our lack of awareness that we all translate. And so what we understand, the meanings we give, often do not well represent what a speaker or writer intended.

The principle of relative invariance under transformation constitutes a fundamental characteristic of scientific activities. Scientific theories as – statements and explanations about what we can expect regarding the behavior of physical systems at different times and different places – would not make much sense, and would not be very useful, without an underlying principle of relative invariance. Living and non-living systems (fads, organizations, business enterprises, etc) exhibit the relative invariant cycle of coming into being, growing, and eventually declining and/or decaying.

We often, to our distress, ignore this relative invariant process when we expect a partner, a friend, a situation, ‘a good thing’ to last or remain unchanged. And we often distress ourselves when we forget that a ‘bad situation’ is also subject to the relatively invariant principle of change. We could better manage ourselves in many stressful situations by remembering one of the most important invariant principle applying to our lives and world, the invariant principle that both ourselves and situations change.

We could define “culture” in terms of relative invariant behavior of a ‘people’ or group in terms of beliefs, customs, values, speech patterns, practices, taboos, music, dance, and so on. The dynamics of societies could be understood, as ways we have found through institutions, laws, rules, regulations, roles, functions, etc., to organize and regulate (keep relatively invariant) to some degree, the diverse interests and activities of large numbers of interacting individuals. Without such regularization, not only would societies not last, but no organization, no functionally active group of humans, no business, no school, etc, no human endeavor would last. In international affairs, we can expect some intransigence, some resentment, and sometimes disasters, when representatives (note representatives) of one culture or society ignore this invariant principle: the values, customs, ways and speed of doing things etc., are not the same, are not invariant from one culture to another.

Businesses, organizations, institutions, etc., whether large or small, will not prosper if attitudes, approaches, policies, rules, etc., are not updated. They must be changed as ‘times’, location, personnel, demands, social norms and values, political variables, significant international factors, etc., change. In problem-solving, whether in our personal, social, or professional lives, invoking the metaphoric principle and asking ourselves “In what ways is this problem like those others I have faced before?” could provide helpful clues toward solving the current problem.

In the technological field, there are cameras that produce sharp pictures, despite shaky hands. Although I know little about the technology involved, I would take a bet that the invariance principle has been applied. The recording industry would not exist without some application of the relative invariance principle. There are transformations involving patterns of air movement from voice or instrument – to voltage and current changes in microphones – to voltage and current changes in magnetic heads and lasers – to magnetic and structural changes in tapes and compact discs – to vibrations in speakers – to patterns of air movement which we respond to as sounds. Without some analogue of relative invariance incorporated in the technological systems, the pitch, timbre, rhythmic patterns, words, etc, of the origin voice or instruments would not be maintained. And a song, a musical piece, a lecture would be unrecognizable when compared with the original.

Our own visual processes would not work well without some underlying biological activities, based on the relative invariant principle, enabling us to see things clearly and sharply, while we were moving our heads around, walking, running, jumping up and down, and so on. We would be in constant danger if what we were seeing – the product of our neural processes – were not in many ways like what was actually there.

We can very easily translate our notion of “wisdom” in terms of the relative invariant principle. In this respect we could propose that the ‘wise’ person is one who has accumulated a wide range of knowledge (relative invariant factors) of our world; and has developed an ability to consistently (relatively unvarying) respond to a wide variety of situations (a diversity of changes-transformations) with a high level of appropriateness (relatively invariant degree of effectiveness).

Another area where the relative invariance principle can be useful has to do with our notion of “self”. In terms of the principle, a “self” can be considered as

“Those characteristics (beliefs, attitudes, interests, values, etc.) of our psycho-logical operations that we recognize as remaining relatively unchanged in a period of ‘time’; and through a diversity of changes and transformations in other areas of our living”.

Each one of us can determine for ourselves what we have discovered in our own thinking-feeling-behavior-attitudes-beliefs-values-needs-fears-pleasures-and so on, that have remained relatively unchanged over a period of ‘time’. (The hyphens serve to emphasize the functional interrelatedness of these factors). In terms of the calculus, the more increments of information we have based on close observation of ourselves in these modes of being, the more accurate our sense of self.

In many instances of disagreements and conflicts, disappointments, frustration, and so on, individuals and groups unknowingly speak and act in terms of “This, that I believe, read, heard on the news, saw on television, and so on, is no different from that, which is going on”.

In such situations, it’s like the actors have forgotten that “Our verbal and perceptual maps are not the territories they represent.” And that “Things are not what we say they are”. But we shouldn’t be surprised. Our culturally established ways of thinking (or, CEWT) and our individual evaluating habits, as relatively invariant ways of behaving, are not easily recognized. They are even more difficult to change.

Thinking in terms of metaphor and relative invariance could help us avoid, minimize, and resolve many conflicts. An attitude expressed in terms of “This, is like that” might sound less authoritative, less dogmatic, less conflict provoking, less challenging, than one expressed in terms of “This is that”. Thinking in terms of “This is like that” rather than “This is that” could make a great deal of difference in the ways we relate with each other, and with ourselves.

Let’s hope that your understanding of this piece bears some correspondence with, is somewhat like, what I intended to convey. In any case, take some responsibility for the meanings you give. And remember: It’s not like I have said all about anything here.

The following serves as an example of an application of the relative invariance principle.

A Metaphorical Approach. This, is like that: something “a” is like some other thing ” b”. Understanding some aspects of the structures and functions of “a”, helps us to understand some aspects of the structures and functions of “b”. As birds build nests in trees, and beavers build dams in waters: The following outline is based on a premise that the human mind-brain-nervous system (mbns) creates the kind of structures it understands and can deal with. And that organizations, institutions, companies, etc., as creations of human ‘mbns’, reflect some characteristics of ‘mbns’ operations.

A premise: If we study the operations and relationships of our human creations, we might get some insights into the operations of our ‘mbns’. In the outline below, let’s remind ourselves of the “organism-as-a-whole-in- environments” principle in terms of interconnections, inter-activities, feedback, etc. between various ‘mbns’ ‘departments’, and their relationship with outside environments.

Let’s take an organization in its day to day activities to represent “consciousness” or “The Department of Consciousness”.

Dept. Of Consciousness in organizations day to day activities include: Inter and intra-departmental communication and transactions … Meetings … Training … Planning … Decision making … Problem-solving … Setting goals … Hiring and firing … Record keeping .. Communication and transactions with the public…etc. ( Interdepartmental communication is sometimes poor and conflicting. Feedback between Dept. Of Con. and Dept. Of Self-Con. might also be poor.)

Dept. of Self-consciousness activities include. Meetings discussing inter and intra-departmental problems … Performance revues … Reports to managers … Internal audits … Retreats, etc. ( The Dept. of Self-con. is usually active in some areas, at some times, and inactive at other times.)

Dept. of The Unconscious include. Board of Trustees… Constitution … Mission statements … Policies … Laws … Rules … Regulations … Values … Traditions. etc. (Note the seemingly ‘static’ and usually “behind the scenes” character of this department compared to the more active and visible operations of the other departments.)

The Dept. Of Unconscious through policies, regulations, etc., provides behind the scenes guidelines for the operations of the Dept. of Con. These are sometimes resisted and not always followed. (We do not always act in respect to our values or resolves.) This can result in confusion, unsureness, conflicts, and tensions. There is usually a time difference between the Dept. of The Unconscious and the Dept. Of Consciousness. Constitutions, trustees, regulations established in earlier times, and based on cultural values of those times, might not be appropriate for new, different, present conditions. This can result in more internal and external conflicts and tensions. Communication between the three departments, and between the departments and outside if poor, usually results in varying degrees of conflicts, tensions, and poor management, and so on.

A game to play: See how many of the above organizational activities and others, you can relate to some of our own operations. For instance “hiring and firing” could be related to ideas, suggestions, advice, etc., we accept, reject, put on hold (probation) etc. We could think of interdepartmental memos as similar to interconnections between neural circuits. Note how many of the organizational, institutional, etc., operations are described by terms also used to describe our own psychic operations ( problem-solving, making decisions , planning, etc.)