J.KonstapelLeiden, ,14-10-2026
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The birth of a shared word is modeled as a Hopf bifurcation; the theory’s coefficients place this birth in the subcritical regime, where lived practice and the fixed word coexist as two stable states separated by an unstable boundary, with history rather than logic deciding which state a group occupies.
Six further correspondences are drawn: readiness-to-hand as “closure is zero force,” source–target fit as natural selection, agentless grammar as an external measure, the loom as the true image of computing, placing people in a room as the reading of addresses, and group life as having two kinds of coherence.
Used Blogs
1 Het Hopf Principe (constable.blog, 2-9-2025)
2 Vacuum.Net Theory: hoe massa, energie en ruimte één net vormen
3 Beyond Synchrony / Closure Is Zero Force
Carried Across
J. Konstapel, Constable Research, Leiden — 14 October 2026
© 2026 J. Konstapel, Constable Research, Leiden. Quotation with attribution is permitted; reproduction of the whole requires written permission. Version 1.1 (readable edition).
Abstract
“Metaphor” and “translation” share the same root meaning: carried across. This essay applies that idea to the Vacuum.Net theory — a model of reality as a single net made of one strand, closed windings, knots and meshes.
The central claim is a match between layers. A metaphor as the body lives it belongs to the theory’s tension layer, where change happens. A metaphor as a community fixes it in a shared word belongs to the address layer, which is frozen topology. The birth of a shared word behaves like a Hopf bifurcation — the moment a system at rest starts to move in a repeating cycle. The theory’s own coefficients place this birth in the subcritical regime, in which the lived practice and the fixed word coexist as two stable states, separated by an unstable boundary. History, not logic, decides which state a group occupies.
Six further correspondences follow: readiness-to-hand as “closure is zero force”; the fit between source and target as natural selection by fit; agentless grammar as an external measure; the loom as the true image of computing; placing people in a room as the reading of addresses; and group life as having two kinds of coherence rather than one. The essay states plainly which claims are proved, which are correspondences, and which remain open.
1. One strand, carried across
The Greek meta-pherein and the Latin trans-latus describe the same action: carrying something across. A metaphor takes structure from a domain the body knows — weight, distance, balance — and uses it to think about a domain one cannot touch, such as time, markets or organisations. Linguists call these the source and the target.
The Vacuum.Net theory describes reality as one net built on five axioms:
- N1 — there is one strand.
- N2 — a state persists only if it closes on itself.
- N3 — the net keeps the orientation in which it was laid.
- N4 — properties depend on the local state.
- N5 — the same pattern returns at every scale.
From these follow four forms: a strand (the net itself), a winding (a strand that returns to itself), a knot (windings that hold each other in three directions) and a mesh (the opening between strands).
Axiom N5 already contains the structure of metaphor. If the same winding appears at every scale, then a pattern found at one depth can legitimately be read at another. Carrying across is then not a figure of speech but identity over scale. This essay follows that thread through the body, the word, grammar, the machine, and the room where people meet.
2. Two layers: the lived metaphor and the fixed word
A hand discovers the use of a stone before any word for it exists. The grip fits; the throw works. Something is treated as something else, entirely in the body. Call this layer metaphor-in-use.
Later, a group settles on a word for that use. The word is shared, taught and policed; using it correctly becomes a condition of belonging. Call this layer the espoused metaphor. The pair follows Argyris and Schön’s classic distinction between theory-in-use and espoused theory. (“Espouse” comes from Latin spondere, to pledge — to espouse a theory is to wed it in public.)
The two layers behave differently:
- The lived metaphor is present tense and resists being named.
- The fixed word arrives late; “a thought” is grammatically a finished thing, like a past participle.
- Articulation creates order, and order is not a property of the present.
The Vacuum.Net theory has the same split, called the two-layer law. The address layer holds frozen topology: which windings exist and how they are linked. The tension layer is the only layer in which anything happens. Exhaustive computation supports the frozen character of the address layer: every admissible local rule on a ring of five sites (1,594,323 sign-symmetric rules and 144 conserving flux-form rules) turned out to be either the identity or a shift. In the address layer there is only passage; change lives in the tension layer.
The correspondence is direct: metaphor-in-use ↔ tension layer; espoused metaphor ↔ address layer. The gap that organisational science observes between what people do and what they profess is the gap between the two layers. Nobody has to lie for it to open.
3. A word is the birth of a winding
When does lived use become a word? When the use repeats and is shared. A one-time grip leaves no trace; a grip that returns, and that others recognise as the same grip, becomes a thing with a name. In net terms: a thing is a turn that keeps coming back.
Dynamical systems theory has a precise description of the birth of a repeating cycle: the Hopf bifurcation. Its normal form, in polar coordinates, is
ṙ = μr − ar³, θ̇ = ω
where r is the amplitude, θ the phase, μ the control parameter and a > 0.
- Step 1. For μ < 0 the only equilibrium is r = 0: rest, or address 0 in the net.
- Step 2. For μ > 0 the rest point loses stability and a closed orbit appears with radius √(μ/a). A phase that returns after one full turn is, by definition, a winding.
- Step 3. The winding number around the rest point jumps from undefined to 1. It cannot change gradually. So μ belongs to the tension layer and the winding number to the address layer; the Hopf point is where the two layers meet.
Exactly at μ = 0, the equation becomes ṙ = −ar³, whose solution is r(t) = r₀/√(1 + 2ar₀²t). With r₀ = 1, a = 1 and t = 100, the amplitude falls to 1/√201 ≈ 0.071. A system sitting precisely on the threshold does not gain a living rhythm; it fades slowly. This matters for the attractive idea of a “permanent Hopf bifurcation”: sitting exactly on the point gives slow decay, not life.
The subcritical form. The net’s coefficients point elsewhere. Its free-energy functional F(A) = αA² + βA⁴ + γA⁶, combined with the tension relation γ = 2π, forces the quartic coefficient negative — a cancellation of (2π − 1)/2π = 5.2832/6.2832 = 84.1%. Under gradient dynamics, a negative quartic term in F yields a positive cubic term in the amplitude equation:
ṙ = μr + ℓr³ − cr⁵, ℓ > 0, c > 0
This is the subcritical Hopf bifurcation, sitting near the Bautin point where ℓ changes sign. Its equilibria are r = 0 plus the solutions of r² = (ℓ ± √(ℓ² + 4μc))/2c, real for μ ≥ −ℓ²/4c.
Worked example. Take ℓ = 1, c = 1, μ = −0.1 (inside the window −0.25 < μ < 0):
- √(1 − 0.4) = 0.775, giving r² = 0.887 (r = 0.942) and r² = 0.113 (r = 0.336).
- Stability follows from f′(r) = μ + 3ℓr² − 5cr⁴:
- r = 0: f′ = −0.1 — stable.
- r² = 0.113: f′ = +0.175 — unstable.
- r² = 0.887: f′ = −1.373 — stable.
Rest and a finite winding are both stable at the same μ, separated by an unstable cycle. This is the dynamical form of the gap between lived use and fixed word: a group can sit in either state under identical conditions, and which one it occupies depends on its history — hysteresis. Note that the window has width ℓ²/4c. It is a range, not a point; the net need not hit an exact threshold to stay in it.
4. Selection by fit
Not every source fits every target. A metaphor for time built from the taste of lemons carries nothing, because taste lacks what time requires: direction, sequence, distance. The body limits which carryings are available, and only a source whose structure fits the target survives. This is selection by fit: what returns in phase stays; what does not fit does not close. No mechanism is needed — nothing pushes the right metaphor into place; the ill-fitting ones simply fail to close.
The limit does not fix a single answer. Speakers of Aymara place the future behind and the past in front, for a bodily reason: one sees what lies ahead, and only the past is known. English uses the opposite map. Both are coherent; both close. In the net’s balanced-ternary register this is the mirror pair: +1 and −1 sit symmetrically around 0, each a full closure with the opposite orientation. Axiom N3 keeps orientation as memory — a culture’s choice of map is such an orientation, laid once and kept.
5. Readiness-to-hand is zero force
Heidegger observed that a tool in use does not appear as an object: a hammer while hammering is invisible, and shows up as a separate thing only when the use breaks down.
The net has a proved counterpart. Its phase register uses three values (−1, 0, +1); a local window holds three consecutive crossings and is closed when its sum is 0 modulo 3. Two kinds of closure exist: homogeneous (all three values equal, e.g. (1,1,1)) and heterogeneous (all three different, e.g. (−1,0,1)). The closure test is the discrete Laplacian tᵢ₋₁ − 2tᵢ + tᵢ₊₁ (mod 3) — the same operator that appears in linearised coupling between neighbouring oscillators. Restricting the phases to the three trit values, the coupling force on the centre of the window is zero exactly when the window is closed. Closure is zero force; an open window carries residual tension.
The correspondence with Heidegger is then exact in form:
- A tool in use is a closed window: no force, no visibility.
- A broken tool is an open window: residual tension makes it appear.
The object is the open window.
6. Condition and the unconditioned
The Latin condicio comes from con-dicere, to speak together. A condition is the residue of a conversation; it exists because it circulates between parties. In net terms, a condition is a closure between people.
Grammar, however, requires a subject, and “It rains” supplies one from nowhere — nothing in the sky does the raining. The same habit hides human choices: “The market moved.” “It had to happen.” “The system won’t let us.” The sentence has no actor, so an objection has no addressee. The same applies to founding speech that fixes a state of affairs with no second party present: nothing was spoken together, and the cause stands outside every conversation that follows.
This is what the Vacuum.Net work calls the external measure. An inventory of 58 silent assumptions in modern science finds that 32 trace back to it; agentless grammar (“one subject per event”) is a second terminal assumption in the same inventory. Rosen’s analysis of living systems offers the alternative: when the chain of production closes on itself, an external driver is no longer needed — the system is its own fixed point. Bayesian reasoning is the formal version of the same stance: every cause stays provisional, today’s estimate being tomorrow’s prior, with no first cause at which the process stops.
A practical consequence follows for anyone who works with groups. The question “why” asks for a cause and lands as a demand for defence. Questions about what happened, what changed and what would need to differ keep the condition open: they stay inside the closure instead of reaching for a driver outside it.
7. “Is” and “is like”
“The market is difficult” asserts an identity between two domains. “The market is like a difficult negotiation” restores the comparison. The second sentence reopens what the first closed.
Vaihinger built a philosophy on this: causation, the unified self and scientific laws work as if — as useful fictions — and the danger begins when the fiction is taken as literal and unconditioned. The Vacuum.Net foundational paper makes the same discipline operational: every claim carries one of five statuses (assumed, conditionally proved, corresponded, predicted, open). “Corresponded” is the status of “is like”; “conditionally proved” is the status of “is”, under named hypotheses. Keeping the two apart is Vaihinger’s warning made routine.
8. The loom and the net
Text, textile, texture and context all come from Latin texere, to weave. A text is a woven thing; making sense and making cloth share a root.
Computing had a weaving origin too. Jacquard’s loom of 1804 ran on punched cards; Babbage adapted the cards for his Analytical Engine; Lovelace wrote in 1843 that the Engine weaves algebraic patterns as the loom weaves flowers and leaves. Later the calculator became the governing image and the loom was buried.
The net is a loom in the strict sense. Its first theorem identifies the elementary mark with a crossing, and the smallest stable knot — the trefoil — holds by its crossings alone and needs exactly three (any diagram with fewer crossings can be undone). Strength in a fishing net does not come from any single thread but from how the threads cross; the same holds for a text, a group and the vacuum.
The difference between calculator and loom is the difference between an external measure and a relation. A calculator returns one correct number against a fixed scale. A loom holds a pattern made of crossings — and in a loom, the weaver is also a thread.
9. Placing people: reading addresses
One method in group work places people silently in a room, each standing for a party in a real case. They know nothing of the case and receive only a stance: left or right, near or far, facing or turned away. Reports are consistent: people placed this way soon speak the situation, often using the same words as the real parties — words they never heard.
The net needs no mechanism to read this. A position in the room is an address; the pull a person feels at that position is the tension at that address. Whoever stands on the same address meets the same tension. This is correspondence and identity over scale, not transmission. The sequence of the method matches the two layers: first the stance, then the feeling, then the words. Tension comes before address; the lived layer before the fixed one. The same holds for objects placed in a circle: a group that has just placed its own objects cannot easily say “it just happened” about the pattern — it saw its own hands make it.
10. Two closures in the room
Conventional coherence is measured by the order parameter R: represent each participant’s phase as an arrow on a circle and average the arrows. Arrows pointing the same way give R near 1; arrows spread out give R near 0, which is usually read as disorder.
The trit register shows why that reading fails. Map the three trit values to the cube roots of unity: 1, e^(2πi/3), e^(4πi/3).
- Homogeneous closure: three equal arrows, R = 1.
- Heterogeneous closure: three arrows at 120°, whose sum is 1 + (−½ + i√3/2) + (−½ − i√3/2) = 0. So R = 0.
Both are exact closures — one is alignment, the other structured difference. Their stability differs. For a ring of N oscillators with coupling K and phase step Δ, perturbation modes grow at λₘ = −4K cos(Δ) sin²(πm/N). For homogeneous closure Δ = 0, so cos Δ = 1 and the state is stable for positive coupling. For heterogeneous closure Δ = 2π/3, so cos Δ = −½ and λₘ = 2K sin²(πm/N): the state is stable only for K < 0. Heterogeneous closure needs the differences to be maintained, not pulled together.
The meaning for groups is plain. A team in which everyone thinks alike shows high coherence. A team in which three people hold three different, mutually necessary roles shows R = 0 — and is no less closed. Measured by alignment alone, the second team looks broken. It is not. The paradoxes of group life — belonging versus individuality, trust versus disclosure, closeness versus distance — do not resolve, and do not need to. They are heterogeneous closures. The work is to keep the window closed while the parts stay different; forcing them into alignment would destroy the closure.
Older contemplative traditions name the same pair: Sufi metaphysics distinguishes jam’ (gathering into unity) from farq (separation into multiplicity), described as simultaneous rather than sequential. In the trit register, jam’ is homogeneous closure and farq is heterogeneous closure, and the subcritical window of section 3 is the dynamical form in which both can hold at once.
11. Three closures and the edge
The net’s ladder runs strand → winding → knot, a knot being closed in three directions. Dynamical systems have a parallel ladder:
- a rest point becomes a cycle (the first Hopf bifurcation);
- the cycle becomes a 2-torus (the Neimark–Sacker bifurcation);
- the 2-torus becomes a 3-torus.
A 3-torus is motion closed in three independent directions. Newhouse, Ruelle and Takens proved in 1978 that quasi-periodic flow on a torus of dimension three or more is fragile: arbitrarily small perturbations can turn it into a strange attractor. Read against the net, three closures are the last stable rung before the edge of chaos — and the knot sits on that edge, at the level the net identifies with mass. This fits the trefoil (three crossings, the minimum for a knot) and the trit register (three values, the minimum for a heterogeneous closure). The number three returns at each depth.
12. Two Hopfs
The name Hopf belongs to two mathematicians. Eberhard Hopf described the bifurcation in 1942; Heinz Hopf described the fibration in 1931. Their work is unrelated in origin, but in the net it meets. The net’s state is a rotor represented by a unit quaternion; unit quaternions form the 3-sphere S³, and the Hopf fibration maps S³ onto the 2-sphere S² with a circle S¹ above each point. Any two such circles are linked exactly once — the Hopf invariant, which the net uses as its conserved topological charge Q ∈ π₃(S²) = ℤ.
Read together: the 2-sphere carries direction and the circle above it carries phase. The cycle born in Eberhard Hopf’s bifurcation is a fibre of Heinz Hopf’s fibration. Every winding is linked to every other winding exactly once — every lived use is threaded through every other one. No word stands alone.
13. Language models: address without tension
A large language model learns the conditional probability of the next token given all previous tokens, over a corpus that others have already argued over. Its words arrive pre-negotiated. In the terms of this essay, the corpus is a frozen address layer: the model reproduces the espoused metaphor with great fluency, but has no tension layer of its own — no hand that found a fit, no stake in being wrong, no group that had to reach agreement.
Two consequences follow for people. The first is practice: fluent, correct language becomes cheap, and the capacity to feel a new fit before it has a name is exercised less; capacities that are not exercised weaken. The second is visibility: a weakening of the lived layer would not appear on any measure, because formal fluency is what institutions are built to count and the lived layer does not announce itself.
Roles that work with people in a room become the place where this layer is kept in practice. The concrete work is simple: let people write before they speak; use their own words back to them; bring an object instead of a question; leave silence after a concrete question. The first answer after a pause usually comes from the lived layer.
14. Status of the claims
Proved or computed in the text
- the decay r(t) = r₀/√(1 + 2ar₀²t) at the Hopf point;
- the subcritical window −ℓ²/4c < μ < 0, with the worked example;
- the cancellation (2π − 1)/2π = 84.1%;
- the link between a negative quartic term and a subcritical bifurcation;
- R = 0 for heterogeneous closure;
- the stability condition K < 0 for heterogeneous closure;
- closure as zero force within the trit model;
- passage-only dynamics in the address layer (on rings of five, nearest-neighbour rules).
Correspondences
- metaphor-in-use and espoused metaphor as the tension and address layers;
- the birth of a shared word as a Hopf bifurcation;
- readiness-to-hand as zero force;
- the fit of source to target as selection by fit;
- the Aymara map as the mirror pair;
- agentless grammar as the external measure;
- placing people as reading addresses;
- jam’ and farq as homogeneous and heterogeneous closure;
- three Hopf steps as the knot;
- the Hopf cycle as a fibre of the Hopf fibration.
Open
- The subcritical regime rests on γ = 2π, which is a correspondence in the theory, not a derivation; a finite lattice computation showed it does not follow from 2π-periodicity alone.
- The coefficient ℓ has not yet been derived from the trit rule directly; that derivation would settle whether the window exists without γ = 2π.
- Hysteresis in language adoption has not been measured: a group adopting a new word should show a different threshold on the way in than on the way out.
- The R = 0 closure as a marker of a well-held group has not been measured; the triplet (R, C_hom, C_het) makes it measurable.
Annotated References
Argyris, C. & Schön, D. A. (1974). Theory in Practice: Increasing Professional Effectiveness. Jossey-Bass, San Francisco.
Source of the distinction between theory-in-use and espoused theory, on which section 2 builds its pair of metaphor layers. Read the first three chapters: they define both terms and show how the gap stays hidden.
Argyris, C. (1990). Overcoming Organizational Defenses. Allyn and Bacon, Boston.
Shows how organisations defend the gap between what they profess and what they do — the organisational face of the two-layer law. The chapters on defensive routines are the core; read them with section 6 in mind.
Bateson, G. (1972). Steps to an Ecology of Mind. Chandler, San Francisco.
Contains the double bind and the definition of information as “a difference that makes a difference”; both bear on agentless grammar. Start with “Toward a Theory of Schizophrenia” and “Form, Substance and Difference”.
Bautin, N. N. (1949). The Behaviour of Dynamical Systems near the Boundaries of the Stability Region. Gostekhizdat, Moscow (in Russian).
Origin of the analysis of the degenerate Hopf point where the cubic coefficient changes sign; section 3 places the net near this point. For most readers Kuznetsov (2004) gives the same result in accessible form.
Geary, J. (2011). I Is an Other: The Secret Life of Metaphor and How It Shapes the Way We See the World. Harper, New York.
A broad survey of metaphor across thought, money, science and politics; estimates about six metaphors a minute in ordinary speech. Read the chapters on etymology and on the body — they supply the material for sections 1 and 2.
Heidegger, M. (1927). Sein und Zeit. Niemeyer, Halle. English: Being and Time, transl. Macquarrie & Robinson, Harper & Row, 1962.
Introduces readiness-to-hand: a tool in use does not appear as an object; section 5 matches this to zero force. Paragraphs 15 and 16 are enough — they contain the hammer example.
Hong, H. & Strogatz, S. H. (2011). “Kuramoto Model of Coupled Oscillators with Positive and Negative Coupling Parameters.” Physical Review Letters 106, 054102.
Shows that negative coupling stabilises non-aligned states — the established mathematics behind the K < 0 result in section 10. Short and self-contained; read the whole paper.
Hopf, E. (1942). “Abzweigung einer periodischen Lösung von einer stationären Lösung eines Differentialsystems.” Berichte der Mathematisch-Physischen Klasse der Sächsischen Akademie der Wissenschaften zu Leipzig 94, 1–22.
The original proof of the bifurcation that bears his name; section 3 rests on it. An English translation with commentary appears in Marsden & McCracken (1976).
Hopf, H. (1931). “Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche.” Mathematische Annalen 104, 637–665.
Introduces the Hopf fibration and the Hopf invariant; section 12 uses both. Demanding; a modern algebraic-topology textbook gives the same content in current notation.
Konstapel, J. (2025). “Het Hopf Principe: Een Principe op het Snijvlak van Wetenschap en Mystiek.” constable.blog, 2 September 2025.
Proposes that reality sits permanently on the Hopf threshold and links this to contemplative traditions; section 3 sharpens that claim. Read the sections on walking as near-falling and on jam’ and farq.
Konstapel, J. (2026a). “Closure Is Zero Force: The Oscillator Framework Read as the Phase Register of the Vacuum.Net Theory.” Constable Research, Leiden.
Proves within the trit model that closure is zero coupling force and introduces homogeneous and heterogeneous closure; sections 5 and 10 rest on it. The proofs are short; read the stability section with a pen.
Konstapel, J. (2026b). “The Vacuum.Net Theory: Foundational Paper.” Constable Research, Leiden.
States the axioms N1–N5, the theorems, the five epistemic statuses and the open computations; every net term in this essay is defined there. Read the axioms and the status section first; the theorems can follow later.
Konstapel, J. (2026c). “The Assumptions Nobody Declares.” constable.blog, 26 July 2026.
An inventory of 58 silent assumptions in modern science, five of them terminal; section 6 uses the external measure and the one-subject-per-event assumption. Read the five terminal assumptions; the rest serves as reference.
Kuznetsov, Y. A. (2004). Elements of Applied Bifurcation Theory, 3rd ed. Springer, New York.
The standard reference for Hopf and Bautin normal forms and their coefficients; all formulas in section 3 can be checked here. Chapter 3 for Hopf, chapter 8 for the Bautin point.
Lakoff, G. & Johnson, M. (1980). Metaphors We Live By. University of Chicago Press, Chicago.
Shows that abstract thought borrows its structure from bodily experience; “argument as war” and “time as space” come from here. Short; read it whole. It is the basis for sections 1 and 4.
Lovelace, A. A. (1843). “Notes by the Translator.” In: L. F. Menabrea, “Sketch of the Analytical Engine Invented by Charles Babbage.” Scientific Memoirs 3, 666–731.
Contains the comparison of the Analytical Engine with the Jacquard loom — computing’s first and buried founding image. Note A contains the loom passage; Note G contains the first program.
Marsden, J. E. & McCracken, M. (1976). The Hopf Bifurcation and Its Applications. Springer, New York.
Gives the full theorem, an English translation of Hopf’s 1942 paper and many applications. Section 1 and the translation are enough for this essay.
Newhouse, S., Ruelle, D. & Takens, F. (1978). “Occurrence of Strange Axiom A Attractors near Quasi Periodic Flows on Tᵐ, m ≥ 3.” Communications in Mathematical Physics 64, 35–40.
Proves that motion closed in three independent directions is fragile; section 11 places the knot on that edge. Six pages; the theorem statement and the introduction carry the point.
Núñez, R. E. & Sweetser, E. (2006). “With the Future Behind Them.” Cognitive Science 30, 401–450.
Documents the Aymara construal of time, with the future behind; section 4 reads it as the mirror pair. Read the gesture data: they show that the map lives in the body before it lives in words.
Reddy, M. J. (1979). “The Conduit Metaphor.” In: A. Ortony (ed.), Metaphor and Thought, 284–324. Cambridge University Press, Cambridge.
Shows that English talk about communication itself runs on a metaphor (ideas as objects, words as containers): there is no metaphor-free place from which to describe metaphor. Read the first half and the appendix of examples.
Rosen, R. (1991). Life Itself. Columbia University Press, New York.
Argues that living systems are closed to efficient causation, making an external driver unnecessary; section 6 uses this. Chapters 10 and 11 hold the argument; the earlier chapters prepare the notation.
Smith, K. K. & Berg, D. N. (1987). Paradoxes of Group Life. Jossey-Bass, San Francisco.
Shows that the tensions of group life are structural and do not resolve; section 10 reads them as heterogeneous closures. Read the chapters on belonging and engaging.
*Vaihinger, H. (1911). Die Philosophie des Als Ob. Reuther & Reichard, Berlin. English: The Philosophy of ‘As If’, transl. C. K. Ogden, 1924.*
Treats causation, the self and scientific laws as useful fictions, warning that the danger begins when the fiction is taken as literal and unconditioned; section 7 uses this. The introduction and Part I are sufficient.
Watzlawick, P., Beavin Bavelas, J. & Jackson, D. D. (1967). Pragmatics of Human Communication. Norton, New York.
States the axiom that one cannot not communicate: behaviour carries message before words do, matching the order tension before address. Chapter 2 holds the axioms.