The discipline

Every section of the discipline, with its theory map, figures, formulas and tables, as on the home page before r15.

The discipline

Evidence, counterevidence, uncertainty, revision.

How Anavi keeps its claims honest: what it assumes, what would show it wrong, what it leaves open, and how it changes its mind. The theorems, theories, principles, frameworks and patterns below each carry two labels: what kind of source it is, and what kind of claim this page makes with it.

How to read the entries: a theorem is proved under stated assumptions; a theory is an established scientific or mathematical framework; a principle is a law or finding; a framework is a philosophical position; a pattern is a design pattern or standard. Each entry says how this page uses it: as a formal analogue, as a chosen inspiration, or as an operating commitment. Among the five kinds of claim in What kind of claim is this?, these are a structural analogue, a speculative analogy and a design formalization—Anavi’s own way of working, not an external law. One entry (U3) is listed only so that it is kept distinct, and is not used. None is a claim that Anavi runs the algorithm it describes.

How we test: a correction worth keeping

In one recorded development case, a shortened book title produced a confident answer: “not owned.” The repair kept a likely match visible, marked the uncertainty and let the reader inspect the candidate copy. One repair does not establish the whole system’s reliability. It shows why corrections belong in the record.

The discipline

Theories, theorems and principles—connected.

No single theory explains how work takes shape. These do so together: theorems proved under stated assumptions, scientific theories, principles, philosophical frameworks and design patterns—each with a distinct role, each connected to the others. Choose any one to see what it is, what it assumes, and what it touches.

Figure M · The foundations map. Filled circles are theorems; rings are theories; diamonds are principles; squares are frameworks; rounded squares are patterns. Uncertainty sits at the centre; the parts of the movement they inform run around it. Line styles name each connection.

Ground · Heisenberg’s uncertainty principle — a core motivation for Anavi

Sharp here, broad there.

Some limits on knowing are not failures of effort. In physics, a state sharp in position is broad in momentum; the limit is a theorem, not clumsiness. Anavi takes that as a discipline: say what an observation settles and what it leaves open, keep the alternatives, and examine from complementary sides.

Established the physics, and the mathematics of Figure H Speculative analogy how Anavi takes it

The physics (Heisenberg 1927; Kennard 1927; Robertson 1929)

σ_{x} σ_{p} \geq \frac{ℏ}{2}

σ_{A} σ_{B} \geq \frac{1}{2} | ⟨ [A, B] ⟩ |, [x, p] = i ℏ

ψ (x) \propto e^{- x^{2} / 4 s^{2}} \Rightarrow σ_{x} = s, σ_{p} = \frac{ℏ}{2 s}

σ_x and σ_p are the standard deviations of position and momentum in the same quantum state; ħ is the reduced Planck constant (the figure uses units with ħ = 1). The relation limits their simultaneous statistical sharpness. It is a statement about the preparation of states—distinct from error–disturbance relations about measurement (Ozawa 2003; Busch, Lahti & Werner 2013), which are not used interchangeably here. The Gaussian reaches the bound; not every state does (the first excited oscillator state gives 3ħ/2).

What this is not: quantum mechanics governing business, or business measures relabelled as conjugate observables.

How Anavi takes it (a chosen inspiration, not physics): acknowledge what an observation establishes and leaves unresolved; state the frame, variables and assumptions; avoid claiming total knowledge from a partial representation; preserve alternatives and uncertainty rather than suppressing them; use complementary examinations and revisable decisions.

Uncertainty is a condition of inquiry. Anavi’s commitment is to make it explicit, investigate it rigorously, and act without pretending it has disappeared.

Width s 0.80 State

The figure as a table

Figure H · Position density |ψ(x)|² (top) and momentum density |φ(p)|² (bottom). φ is computed here by a numerical Fourier transform of ψ, and σ_x, σ_p are computed from the densities on the full numerical grids, which extend beyond the plotted ranges (ħ = 1; each density has area 1; heights are scaled for display).

Question · Formalize

A question opens a space.

A question is not answered by one idea. It opens a space of candidates—every combination of choices a solution could make. Most of that space is unusable. The work is to learn its shape.

Established the mathematics of constraints and even placement Design formalization the model of a question’s space of candidates

Formal model

x = (x_{1}, \dots, x_{d}) \in Ω = X_{1} \times \dots \times X_{d}

Ω_{C} = {x \in Ω : c_{1} (x) \land \dots \land c_{n} (x)}

Assumptions: a candidate is described by finitely many choices; constraints are known and testable (in practice some are learned); the figure is a two-dimensional slice of a space with many dimensions. Low-discrepancy placement (Halton, bases 2 and 3) typically covers the space more evenly than uniform random placement for the same number of candidates—a typical and asymptotic advantage, not a guarantee for every random draw; in this figure the largest empty gap is 0.075 with Halton placement against 0.089 with random placement. In the Evolve mode, fitness is an imperfect proxy and nothing converges to a guaranteed optimum.

What this is not: a model of any real project, or a claim that the studio enumerates the space.

Our commitment: before choosing, to write down what an answer must honour—access, privacy, evidence, cost—and to let those conditions narrow the possible.

Constraints (illustrative) meets accessibility requirements keeps personal data private supported by evidence affordable to build

Placement Probe, choice 1 Probe, choice 2

The figure as a table

Figure 1 · The possibility field. 400 candidates on a slice through a space of choices; constraints carve the feasible region Ω_C. “Run a generation” evolves a population inside it; variants that fail a constraint stay as grey marks, and the table keeps the reasons recorded when each failed; variants lost to selection are not kept.

Test · choosing what to try

Explore before you exploit.

Where should the next effort go—where the work already looks good, or where too little is known? Too little exploration builds mediocre ideas efficiently; too much never ships. The balance moves as evidence arrives.

Established the theorems, in their stated settings Structural analogue choosing what to try next

Formal model (an analogue)

f \sim GP (m, k), k (x, x^{'}) = σ_{f}^{2} \exp (- \frac{{(x - x^{'})}^{2}}{2 ℓ^{2}})

μ_{t} (x) = m + k_{t} {(x)}^{⊤} {(K_{t} + σ_{n}^{2} I)}^{- 1} (𝐲 - m 𝟏)

σ_{t}^{2} (x) = k (x, x) - k_{t} {(x)}^{⊤} {(K_{t} + σ_{n}^{2} I)}^{- 1} k_{t} (x)

a (x) = μ_{t} (x) + κ σ_{t} (x), x_{t + 1} = \underset{x}{argmax} a (x)

EI (x) = {\begin{matrix} d Φ (z) + σ_{t} (x) φ (z), & σ_{t} (x) > 0 \\ \max (d, 0), & σ_{t} (x) = 0 \end{matrix} d = μ_{t} (x) - f^{+} - ξ, z = d / σ_{t} (x)

Expected improvement is shown for reference: f⁺ is the best value observed, ξ ≥ 0 a small margin, Φ and φ the standard normal cumulative distribution function and density; where the posterior variance is zero the improvement is certain and equals max(d, 0). The figure uses the upper confidence bound a(x). Here x is one-dimensional; k_t(x) = (k(x, x₁), …, k(x, x_t))^⊤, K_t is the t × t matrix [k(x_i, x_j)], 𝐲 holds the t observed values and 𝟏 is a vector of ones. Assumptions: one scalar objective, fixed in time; noisy, costly evaluations (σ_n = 0.01); a Gaussian-process prior with length-scale ℓ = 0.07 and spread σ_f = 0.35; a constant prior mean m, estimated as the mean of the observations and then treated as known; hyperparameters fixed. The length-scale is an assumption about the objective, and here it is deliberately wrong in one place: the hidden objective includes a narrow peak (standard deviation 0.03, less than half of ℓ), so the model is misspecified there and can under-sample that peak—an honest limit of any surrogate whose assumptions do not match the work. The objective is synthetic and hidden until you reveal it. Small κ exploits; large κ explores.

What this is not: the studio does not run Gaussian-process optimisation over its portfolio. The correspondence is structural—uncertainty helps decide what to investigate next.

A deeper connection: annealing

P (accept worse move) = \min (1, e^{- Δ E / T}), T_{k} = T_{0} α^{k}

Assumptions: a synthetic energy landscape; candidate moves drawn uniformly within ±0.08. Convergence is conditional: for a finite state space whose neighbourhoods, together with the energy, are irreducible and weakly reversible (Hajek’s Property WR), with the Metropolis acceptance rule above and a non-increasing schedule with T_k → 0, the probability of occupying a global minimum tends to 1 if and only if Σ_k exp(−d*/T_k) = ∞, where d* is the depth of the deepest non-global local minimum—met, for example, by T_k = c / log(k+1) with c ≥ d* (Hajek 1988). This demonstration does not meet those conditions, and no convergence is claimed for it or for any process at the studio.

Our commitment: to keep early work wide—several designs, several readings—and to give more care to fewer paths as evidence accumulates.

κ 2.0 Position

The figure as a table

Starting temperature T₀ Cooling α

Figure 2 · Where to look next. Top: the surrogate’s mean (line), its ±2σ band, the evaluations (dots) and the acquisition a(x) below, with its maximum marked. Bottom: an annealing walker on a rugged landscape—wide moves while hot, strict selection as it cools.

Test · evidence and counterevidence

Try to break it.

A claim earns trust by surviving honest attempts to break it. Three different ideas meet here, and they are kept distinct: Bayes’ theorem, which updates degrees of belief; Popper’s criticism, which seeks the error; and the psychology of why we must go looking for it.

Established Bayes’ theorem, the data-processing inequality and confirmation bias Structural analogue updating and criticism in Anavi’s work

Bayes’ theorem — updating (a theorem)

P (H | D) = \frac{P (D | H) P (H)}{P (D)}, \frac{P (H_{1} | D)}{P (H_{0} | D)} = \frac{P (H_{1})}{P (H_{0})} \cdot \frac{P (D | H_{1})}{P (D | H_{0})}

Where defined, posterior odds equal prior odds multiplied by the Bayes factor. Evidence matters by how differently the competing hypotheses lead us to expect it. A severe test is one a false claim would probably fail and a true claim would probably pass: passing it multiplies the odds by a large factor; passing an easy test barely moves them. Any probabilities shown belong to a stated illustrative model.

Conjecture and refutation — criticism (a framework)

Popper (1959, 1963; the schema P₁ → TT → EE → P₂ is from Objective Knowledge, 1972): knowledge grows by bold conjecture and error elimination. Popper rejected probabilistic confirmation; Bayes is used above only to show why severe tests inform, not to merge the two. The Duhem–Quine thesis (Duhem 1906; Quine 1951) adds that a claim meets a test together with auxiliary assumptions, so a failure may indict an assumption rather than the claim.

Confirmation bias — the psychology (a principle)

People tend to seek and weigh confirming evidence (Wason 1960, 1966; reviewed by Nickerson 1998)—a general human tendency, which is why disconfirmation has to be designed in.

The data-processing inequality — why provenance is kept (a theorem)

X \to Y \to Z \Rightarrow I (X; Z) \leq I (X; Y)

Processing cannot restore information that was lost. In a deliberately specified toy model, let S say whether a statement was quoted or inferred (equally likely), let both produce the same displayed text T, and let a label P record S. Then I(S;T) = 0 and I(S;T,P) = 1 bit: the words alone cannot reveal the source; the label preserves it.

Our commitment: to look for the evidence that would show a claim wrong, and to keep the record of what failed.

Create · judgment

Many goods, no single best.

Useful, clear, private, affordable—good work serves several ends that pull against one another. Where improving one worsens another, there is no single best: only a frontier of honest trade-offs, and a choice that expresses values.

Established Pareto optimality and its theorems, as stated Design formalization naming the trade-off that settles a choice

Formal model

\max_{x \in Ω_{C}} 𝐅 (x) = (f_{1} (x), \dots, f_{m} (x))

x ≻ y \Leftrightarrow \forall i : f_{i} (x) \geq f_{i} (y) \land \exists j : f_{j} (x) > f_{j} (y)

𝒫 = {x \in Ω_{C} : ∄ y \in Ω_{C}, y ≻ x}

\underset{x}{argmax} \sum_{i} w_{i} f_{i} (x) or \underset{x}{argmin} \max_{i} w_{i} | z_{i}^{*} - f_{i} (x) |

Assumptions: objectives measurable and scaled to [0, 1]; 60 synthetic candidates; dominance is computed on the two objectives shown. With strictly positive weights, every maximiser of a weighted sum is Pareto-optimal (with some weights zero, only weakly Pareto-optimal unless it is unique); conversely, when the set of attainable objective vectors is convex, every Pareto-optimal point maximises some weighted sum with non-negative weights—otherwise, as here, some points cannot be reached that way. With a reference point z* strictly better than the best attainable value of every objective and positive weights, every Pareto-optimal point minimises some weighted Chebyshev distance, and every such minimiser is at least weakly Pareto-optimal (Bowman 1976; Miettinen 1999). In the figure itself, the weights are w and 1 − w for w from 0 to 1, and both endpoints are kept as valid controls. The choice is made only among frontier points, so it is Pareto-optimal for every w. The positive-weight results above apply only for 0 < w < 1; at w = 0 or 1 one weight is zero, and they are not applied there. The Chebyshev form uses the ideal point—the best value of each objective—not a strictly better one, so that theorem’s conditions are not met as implemented; in this figure every frontier point is still reached by some setting of the slider, which was checked for all twelve pairs of objectives. Choosing among frontier points is a value judgment, not the calculation of an optimum.

What this is not: a claim that any studio decision is optimal.

Our commitment: when goods conflict—beauty and speed, openness and privacy—to name the trade-off and the value that settles it, rather than claim an optimum.

Horizontal Vertical Weight on horizontal 0.50

How the choice is made weighted sum Chebyshev

The frontier as a table

Figure 4 · The frontier and the choice. Dominated candidates are dimmed; the frontier is drawn; hollow rings mark frontier points no weighted sum can select. The chosen point follows your weights.

Create · judgment, continued

Keep the option open.

An irreversible commitment gives up the chance to learn first. Real-options reasoning prices that chance; bounded rationality reminds us that deliberation has costs of its own.

Established the arithmetic of the illustration Structural analogue real-options reasoning applied to Anavi’s choices

V_{now} = p a + (1 - p) b - I, V_{wait} = β [p \max (a - I, 0) + (1 - p) \max (b - I, 0)] - c

A one-period, two-state illustration: an irreversible investment I; a payoff of a with probability p, otherwise b (a > b); a discount factor β; a delay cost c. Waiting is worth more when V_wait exceeds max(V_now, 0)—and it can be worth less even while it would still teach something, when its costs exceed that value. Real options is a theory (Myers 1977; Dixit & Pindyck 1994); formal pricing models need assumptions not met here and are not used. Bounded rationality (Simon 1955, 1956) is the reason the page claims stated criteria met, never an optimum.

Our commitment: to weigh what further information could change against the cost of delay and the consequences of commitment.

Revise

Form that corrects itself.

What takes shape is compared with what it was meant to do. Small gaps are corrected in the work; a gap that persists asks whether the assumptions—or the method that produced them—were right.

Established requisite variety in Ashby’s setting; the toy’s condition Structural analogue their use here Design formalization double-loop review of our own work

e_{k} = r - y_{k}, y_{k + 1} = y_{k} + K e_{k} \Rightarrow e_{k + 1} = (1 - K) e_{k}

A scalar, linear, first-order toy with no disturbance: the error shrinks if and only if |1 − K| < 1. This is a property of the toy, not a stability claim about any studio process. The good regulator theorem (Conant & Ashby 1970; its formal status is debated) says that a good regulator must be a model of the system it regulates. The internal model principle (Francis & Wonham 1976) says something different: robust regulation requires the controller to contain a model of the exogenous signals—the references to be tracked and the disturbances to be rejected—not of the plant. By analogy, both are one reason records of the work matter: correcting it needs a model of the work and of what pushes it off course.

Requisite variety (a principle, applied here only by analogy)

V_{O} \geq \frac{V_{D}}{V_{R}} (equivalently \log_{2} V_{O} \geq \log_{2} V_{D} - \log_{2} V_{R})

Ashby’s formulation (An Introduction to Cybernetics, 1956, ch. 11): a game table in which D chooses a disturbance, R then chooses a response, and the table fixes the outcome, with the condition that in each response’s column no outcome occurs twice—a response never maps two different disturbances to the same outcome. Under that condition the number of distinct outcomes R can hold the system to is at least V_D/V_R; only variety in R can reduce variety in outcomes. Applied to a studio this is an illustration—different difficulties call for different responses—not a proved property of Anavi, and it fixes no number of people or agents.

Double-loop learning (a theory)

Argyris and Schön (1978): single-loop learning changes actions within the governing assumptions; double-loop learning changes the assumptions themselves.

Our commitment: to compare what we make with what it was meant to do. A release review may revise our assumptions and methods; an approved requirement changes only by explicit decision of whoever approved it.

Across the movement

Memory with reasons, thinking across people and instruments.

The present state of a piece of work is not enough to understand it. Keeping the sequence of decisions that produced it—including corrections—lets others see not only what changed, but why.

Established event sourcing, provenance, CAP and happens-before, in their settings Structural analogue their use for coordinating work

S_{n} = fold (apply, S_{0}, ⟨ E_{1}, \dots, E_{n} ⟩)

Event sourcing (a pattern): state as a fold over an append-only log; deterministic replicas that process the same ordered inputs reach the same state (Schneider 1990). Provenance (W3C PROV-DM) relates entities, activities and agents. The CAP theorem (Brewer 2000; Gilbert & Lynch 2002) concerns replicated data under a network partition, and Lamport’s happens-before relation (1978) orders events in message-passing systems; by analogy, they motivate canonical records, clear ownership and explicit handoffs in distributed work. Distributed cognition (Hutchins 1995) and the extended mind (Clark & Chalmers 1998) describe thinking carried across people, artifacts and representations. These are correspondences, not claims of conformance or measured outcomes.

Our commitment: to keep the reasons and the evidence for consequential decisions, including their corrections, and to hold the same standard of evidence whoever carries the work—a person, an AI model, a document, code or a test.

Further connections

Still being mapped.

Piagetian assimilation and accommodation; Vygotskian scaffolding; enactivism; evolutionary epistemology; path dependence (Arthur 1989); dynamical and complex adaptive systems. Potentially fruitful, and still needing specified mappings before they carry weight here: active inference, autopoiesis, Hebbian learning, category theory and renormalisation.

Speculative analogy each connection listed here, until a specified mapping gives it weight

The discipline

Evidence, counter­evidence, uncertainty, revision.

How we test: a correction worth keeping

Theories, theorems and principles—connected.

Sharp here, broad there.

The physics (Heisenberg 1927; Kennard 1927; Robertson 1929)

A question opens a space.

Formal model

Explore before you exploit.

Formal model (an analogue)

A deeper connection: annealing

Try to break it.

Bayes’ theorem — updating (a theorem)

Conjecture and refutation — criticism (a framework)

Confirmation bias — the psychology (a principle)

The data-processing inequality — why provenance is kept (a theorem)

Many goods, no single best.

Formal model

Keep the option open.

Form that corrects itself.

Requisite variety (a principle, applied here only by analogy)

Double-loop learning (a theory)

Memory with reasons, thinking across people and instruments.

Still being mapped.

Evidence, counterevidence, uncertainty, revision.