Formalizing Constructed Value

The preceding chapter introduced constructed value theory in intuitive terms. Value is enacted through transactions between embodied organisms and their environments. The transaction is the sufficient statistic. Friction governs whether and how value construction occurs.

This chapter makes these ideas precise. We formalize the core concepts, distinguish related mechanisms that are often conflated, and state the theory in terms that permit empirical testing. The goal is not mathematical elegance for its own sake but conceptual clarity that grounds the framework in measurable reality.

The CTV Sequence

Constructed value theory proposes a causal sequence from internal state to observable trace. We call this the CTV sequence (Constructed-Trace-Value):

\[ \text{Interoception} \rightarrow \text{Motivation} \rightarrow \text{Action} \rightarrow \text{Transaction} \rightarrow \text{Trace} \rightarrow \text{Stratigraphy} \]

Each stage has a precise meaning:

Stage 1: Interoception

Definition. Interoception is the organism’s sensing of its internal physiological state. This includes signals related to hunger, thirst, temperature, fatigue, arousal, pain, and visceral sensation.¹

Formal characterization. Let $S(t)$ denote the organism’s internal state vector at time $t$. This vector includes:

Metabolic variables (blood glucose, hydration, temperature)
Arousal variables (cortisol, adrenaline, heart rate variability)
Affective variables (valence, activation)

The organism does not have direct access to $S(t)$. It perceives a noisy, compressed representation $\hat{S}(t)$ through interoceptive channels. This representation is what drives behavior.

Key insight. Interoception is not merely reactive. The brain continuously generates predictions about future states, comparing predicted $S(t+\Delta)$ against current resources. This predictive interoception is the basis of allostatic motivation (see below).

Stage 2: Motivation

Definition. Motivation is the disposition to act, generated by the relationship between interoceptive state and environmental affordances.

Formal characterization. Let $M(t)$ denote motivational intensity toward a particular action at time $t$. Motivation is a function of:

\[ M(t) = f(\hat{S}(t), A(t), \theta) \]

where:

$\hat{S}(t)$ is the perceived internal state
$A(t)$ is the set of perceived affordances in the environment
$\theta$ represents stable individual parameters (learning history, temperament)

This formulation captures the core insight of alliesthesia: the same environmental affordance $A$ produces different motivation $M$ depending on internal state $\hat{S}$.

Stage 3: Action

Definition. Action is sensory-motor engagement with the environment—reaching, grasping, clicking, signing, speaking. Action is physical movement that potentially modifies the organism-environment coupling.

Formal characterization. Let $a(t)$ denote the action taken at time $t$. Action is selected (not necessarily consciously) based on motivation:

\[ a(t) = \arg\max_{a \in A(t)} \left[ M_a(t) - F_a(t) \right] \]

where $F_a(t)$ is the perceived friction associated with action $a$. The organism acts when motivation exceeds friction for at least one available action.

Stage 4: Transaction

Definition. A transaction is a completed exchange that modifies the state of the economic scaffold. Not all actions become transactions—friction may prevent completion.

Formal characterization. Let $T$ denote the set of completed transactions. A transaction $\tau \in T$ is characterized by:

\[ \tau = (t, \text{parties}, \text{terms}, \text{result}) \]

where $t$ is the timestamp, parties identifies the transacting organisms or addresses, terms specifies what was exchanged, and result indicates success or failure.

The critical point: $\tau$ is observable. We do not need to know the internal states $S$ or motivations $M$ that produced the transaction. We observe the transaction itself.

Stage 5: Trace

Definition. A trace is the physical record of a transaction, persisting in some substrate after the transaction completes.

Formal characterization. Let $\text{Tr}(\tau)$ denote the trace of transaction $\tau$. In traditional systems, traces are heterogeneous:

Memory traces (in brains): high noise, rapid decay
Paper traces (in ledgers): moderate noise, slow decay, local access
Digital traces (in databases): low noise, indefinite persistence, access controlled by custodians

In Bitcoin, traces have specific properties:

\[ \text{Tr}_{\text{BTC}}(\tau) = (\text{txid}, \text{block}, \text{confirmations}, \text{UTXO state}) \]

The trace is globally replicated, cryptographically committed, and thermodynamically secured.

Stage 6: Stratigraphy

Definition. Stratigraphy is the accumulated structure of traces over time, organized by temporal ordering.

Formal characterization. Let $\Sigma(t)$ denote the stratigraphic state at time $t$—the complete history of traces up to $t$. In Bitcoin:

\[ \Sigma(t) = \{\text{Tr}(\tau) : \tau \text{ confirmed before } t\} \]

The stratigraphy has depth (older traces are buried under newer ones) and a surface (the chain tip, reflecting the current state).

Two Modes of Regulation: Homeostasis and Allostasis

A crucial refinement distinguishes two modes of physiological regulation that drive economic behavior differently.

Homeostasis: Reactive Error-Correction

Definition. Homeostasis is regulation by negative feedback, maintaining a variable near a fixed set-point by correcting deviations after they occur.

Formal characterization. In homeostatic regulation:

\[ \text{Response}(t) = k \cdot [S_{\text{set}} - S(t)] \]

where $S_{\text{set}}$ is the defended set-point and $k$ is a gain parameter. The organism detects deviation from set-point and acts to reduce the error.

Example. Body temperature regulation around 37°C. When core temperature drops, shivering generates heat; when it rises, sweating dissipates heat. The response is proportional to the deviation.

Economic analog. Reactive consumption: eating when hungry, drinking when thirsty. The transaction responds to a current deficit.

Allostasis: Predictive Anticipation

Definition. Allostasis is “stability through change”—regulation by predictive adjustment of the set-point itself, in anticipation of future demands.²

Formal characterization. In allostatic regulation:

\[ S_{\text{target}}(t) = g(\mathbb{E}[D(t+\Delta) \mid I(t)]) \]

where $D(t+\Delta)$ is anticipated future demand and $I(t)$ is current information. The organism shifts its operating level before the demand arrives.

Example. Heart rate increases before exercise begins—the brain predicts the demand and pre-adjusts. Blood pressure rises upon waking, anticipating the transition to upright posture.

Economic analog. Anticipatory transactions: buying groceries before hunger, purchasing insurance before loss, saving for retirement decades away. The transaction responds to a predicted deficit, not a current one.

The Dominance of Allostasis in Economic Behavior

Most economic transactions are allostatic, not homeostatic.

Consider the ledger. If transactions were primarily homeostatic, we would see patterns of acute need followed by immediate resolution: hunger → food purchase → satiation. But the ledger shows something different:

Weekly grocery runs (anticipating the week’s needs)
Monthly rent payments (anticipating shelter needs)
Insurance premiums (anticipating low-probability catastrophes)
Retirement savings (anticipating needs decades away)

These are not responses to current deficits. They are anticipatory positioning based on predicted futures. The organism models its future states and transacts now to prepare.

Implication for interpretation. When we observe a transaction on the ledger, we cannot infer whether it was homeostatic (responding to current deficit) or allostatic (preparing for anticipated deficit). The trace does not distinguish. But we can infer that allostatic transactions dominate by volume.

Allostatic Load and Chronic Friction

Allostatic regulation has costs. Allostatic load is the cumulative wear from repeated or sustained adjustment.³ The system pays a price for flexibility.

Economic friction that is chronic produces allostatic load. Poverty is not merely lack of resources—it is the cumulative cost of perpetual allostatic adjustment to scarcity. The organism must continuously recalibrate, prioritize, and cope. This recalibration is exhausting.

Formal characterization. Let $L(t)$ denote allostatic load at time $t$:

\[ L(t) = \int_0^t \lambda(s) \cdot |S(s) - S_{\text{baseline}}| \, ds \]

where $\lambda(s)$ is a time-varying weight reflecting the organism’s capacity to recover. Chronic deviation from baseline accumulates load; recovery time reduces it.

Implication for policy. Interventions that reduce chronic friction also reduce allostatic load. The benefit is not merely the friction avoided but the cumulative damage prevented.

Wanting and Liking: Dissociable Components of Motivation

The motivation stage of the CTV sequence requires further refinement. Motivation is not unitary. It comprises at least two dissociable components: wanting and liking.⁴

The Distinction

Component	Psychological Description	Neural Substrate
Wanting	Incentive salience; motivation to pursue	Mesolimbic dopamine system
Liking	Hedonic impact; pleasure from consumption	Opioid/endocannabinoid hotspots

Wanting is the motivational pull toward a stimulus. It makes things attention-grabbing, approach-inducing, effortful-pursuit-worthy.

Liking is the hedonic pleasure experienced upon consumption. It is the “good feeling” that (in normal circumstances) rewards successful pursuit.

The Dissociation

The crucial discovery: wanting and liking can come apart.⁵

Wanting without liking. Addiction exemplifies this. The addict compulsively seeks the drug (intense wanting) even though it no longer produces pleasure (tolerance has eliminated liking). The dopamine system is sensitized; the hedonic system is blunted.

Liking without wanting. Satiation exemplifies this. After a satisfying meal, food still tastes good if it touches the tongue (liking intact), but there is no motivation to eat more (wanting suppressed).

Neither. Depression often involves anhedonia—neither wanting nor liking. The organism is unmotivated AND finds no pleasure.

Implications for the CTV Sequence

The wanting/liking distinction refines our understanding of what transactions reveal.

Transactions reveal wanting, not liking. A completed transaction shows that the organism was motivated to pursue the good enough to overcome friction. It does not show that the organism derived pleasure from the outcome.

Formally, let $W(\tau)$ denote the wanting that produced transaction $\tau$, and let $L(\tau)$ denote the liking experienced upon completion. The transaction trace $\text{Tr}(\tau)$ is determined by $W$, not by $L$:

\[ \text{Tr}(\tau) = h(W(\tau)) \quad \text{(not a function of } L(\tau) \text{)} \]

This has profound consequences:

Revealed preference is revealed wanting. The traditional economic assumption that transactions reveal preferences implicitly assumes wanting and liking are identical. They are not. Transactions reveal what organisms were motivated to pursue, which may diverge from what they enjoyed.
Post-transaction behavior reveals liking. Returns, complaints, non-repeat purchases, negative reviews—these are traces of liking deficits. The original transaction captured wanting; subsequent behavior captures the wanting-liking gap.
Advertising targets wanting. Marketing that increases incentive salience (wanting) without affecting hedonic value (liking) can drive transactions that produce disappointment. The ledger captures the transactions; subsequent behavior reveals the mismatch.
Addiction patterns are ledger-visible. Compulsive transaction patterns—repeated purchases with diminishing satisfaction—show sensitized wanting with diminished liking. The pattern is visible in the stratigraphy even if the internal dissociation is not.

Wanting, Liking, and Alliesthesia

Alliesthesia modulates both wanting and liking, but potentially differentially:

Alliesthetic wanting: Thirst increases incentive salience of water. The glass becomes more attention-grabbing, more motivating to pursue.
Alliesthetic liking: Thirst increases hedonic impact of water. The water tastes better, feels more satisfying.

In normal circumstances, alliesthesia shifts wanting and liking together. But pathology, drugs, or unusual circumstances can dissociate them. The ledger captures the wanting-driven transactions; the organism experiences the liking (or its absence).

Friction: The Central Variable

Having formalized the internal dynamics, we now formalize the external constraint: friction.

Definition

Friction is any resistance that reduces the probability of an action becoming a transaction, or increases the cost of that completion.

Dimensions of Friction

Friction is multidimensional. We identify six primary dimensions:

1. Transaction friction ($F_{\text{tx}}$): Direct costs of completing an exchange. - Fees, commissions, spreads - Paperwork and bureaucratic requirements - Time spent navigating processes

2. Temporal friction ($F_{\text{time}}$): Delay between action initiation and transaction completion. - Settlement time - Waiting periods - Confirmation requirements

3. Cognitive friction ($F_{\text{cog}}$): Mental effort required to understand and execute. - Complexity of options - Opacity of terms - Expertise required

4. Regulatory friction ($F_{\text{reg}}$): Institutional barriers imposed by authorities. - Licensing requirements - Compliance obligations - Prohibitions

5. Access friction ($F_{\text{access}}$): Barriers to participation. - Geographic availability - Credential requirements - Capital minimums

6. Liquidity friction ($F_{\text{liq}}$): Difficulty of converting assets. - Bid-ask spreads - Market depth - Time to find counterparty

Aggregate Friction

Total friction for a given action is a function of these dimensions:

\[ F_{\text{total}} = \phi(F_{\text{tx}}, F_{\text{time}}, F_{\text{cog}}, F_{\text{reg}}, F_{\text{access}}, F_{\text{liq}}) \]

The function $\phi$ may be additive, multiplicative, or more complex. In general, frictions interact: high cognitive friction amplifies the impact of access friction; regulatory friction compounds transaction friction.

Friction as Design Variable

A key insight: friction is not merely an obstacle to be minimized. It is a design variable that can be optimized.

Productive friction serves functions: - Bitcoin’s proof-of-work is friction that creates security - Settlement delays are friction that permits error correction - Regulatory friction can exclude bad actors

Unproductive friction impedes without benefit: - Bureaucratic complexity that serves no purpose - Rent-seeking intermediation - Information asymmetry exploited by insiders

The goal is not frictionless markets but appropriate friction—enough to provide necessary structure, not so much as to prevent beneficial value construction.

Friction and Value Construction

The fundamental equation of constructed value theory relates motivation, friction, and transaction:

\[ P(\text{Transaction}) = \sigma(M - F) \]

where $M$ is motivation, $F$ is aggregate friction, and $\sigma$ is a sigmoid function mapping the difference to a probability.

When $M > F$, transaction is likely. When $M < F$, transaction is unlikely. The steepness of $\sigma$ determines how sharply the transition occurs.

Value is constructed when $M > F$. The transaction occurs, the trace is created, and the stratigraphy grows. The value that is constructed depends on what the transaction enables—the change in the organism-environment coupling that the transaction produces.

The Sufficient Statistic Claim

We now state precisely what it means to call the transaction a “sufficient statistic.”

Statistical Definition

In statistics, a sufficient statistic $T(X)$ for a parameter $\theta$ is a function of the data $X$ such that the conditional distribution of $X$ given $T(X)$ does not depend on $\theta$. Intuitively, $T$ captures all the information in $X$ that is relevant for inference about $\theta$.

Application to Transactions

Claim. The transaction is a sufficient statistic for valuation in the following sense: conditional on observing the transaction, additional information about the organism’s internal states does not improve prediction of subsequent economic behavior.

Formally, let $B_{t+1}$ denote the organism’s economic behavior after time $t$. Let $\tau_t$ denote their transaction at time $t$. Let $S_t$ denote their internal state at time $t$.

The sufficient statistic claim is:

\[ P(B_{t+1} \mid \tau_t, S_t) = P(B_{t+1} \mid \tau_t) \]

Once we condition on the transaction, the internal state adds no predictive value.

Interpretation

This is a strong claim. It does not say that internal states are causally irrelevant—they cause transactions. It says that for the purpose of predicting future behavior, observing the transaction is as good as observing the internal state.

Why might this hold? Because:

Internal states are transient and context-dependent. The hunger that motivated a food purchase dissipates upon eating.
Transactions modify the organism-environment coupling in durable ways. The purchase changes what the organism has access to.
Future behavior depends on current state, which is shaped by past transactions more than by past internal states.

Caveats

The claim is approximate, not exact. In practice:

Extreme internal states may have persistent effects
Some information in internal states (health conditions, psychological traits) may predict beyond transactions
The claim is about economic behavior, not all behavior

The claim is methodological, not metaphysical. It says: for practical analysis, focus on transactions, not inferred internal states. The ledger is where the action is.

Empirical Predictions

A formalized theory should generate testable predictions. Constructed value theory predicts:

Prediction 1: Alliesthetic Modulation of Transaction Timing

If alliesthesia modulates motivation, then transactions should cluster around states of high alliesthetic sensitivity.

Test: Examine the timing of transactions relative to physiological state (using wearable sensors). Food purchases should cluster before meals (anticipatory) and correlate with hunger signals. Discretionary purchases should correlate with arousal states.

Prediction 2: Allostatic Patterns in Long-Term Transaction Series

If allostasis drives anticipatory transactions, then organisms should show patterns of preparation followed by consumption.

Test: Examine individual transaction histories for allostatic signatures: accumulation phases (saving, stocking) followed by deployment phases (spending, consuming). The ratio of anticipatory to reactive transactions should vary with predictability of environment.

Prediction 3: Wanting-Liking Dissociation in Repeat Purchase Patterns

If wanting and liking can dissociate, then some transaction patterns should show increasing frequency (sensitized wanting) with decreasing satisfaction (diminished liking).

Test: Identify products or services with high repeat-purchase rates but low satisfaction ratings. These represent wanting-liking dissociation. Compare to products with matched wanting and liking (high repeat, high satisfaction).

Prediction 4: Friction Reduction Increases Transaction Volume

If friction constrains value construction, then reducing friction should increase transaction volume.

Test: Natural experiments where friction is reduced (new payment systems, regulatory reform, infrastructure improvement) should show increased transaction rates, controlling for other factors.

Prediction 5: Chronic Friction Produces Allostatic Load Signatures

If chronic friction imposes allostatic load, then populations facing sustained economic friction should show physiological stress markers.

Test: Compare cortisol levels, inflammatory markers, and other stress indicators between populations with high vs. low chronic economic friction, controlling for acute economic status.

Summary

This chapter has formalized the core concepts of constructed value theory:

The CTV sequence traces the causal chain from interoception through transaction to stratigraphy.
Allostasis vs. homeostasis distinguishes anticipatory from reactive regulation; most economic behavior is allostatic.
Wanting vs. liking distinguishes motivation from hedonic impact; transactions reveal wanting, not liking.
Friction is a multidimensional variable that governs whether motivation becomes transaction.
The sufficient statistic claim holds that transactions capture what matters for predicting economic behavior.

These formalizations are not merely academic exercises. They ground the theory in measurable quantities, generate testable predictions, and clarify what the ledger actually records: the traces of embodied organisms, driven by alliesthetic motivation, navigating friction, leaving marks in the stratigraphy.

The next chapter applies this framework to the specific affordances of the Bitcoin scaffold.

A. D. Craig, “How Do You Feel? Interoception: The Sense of the Physiological Condition of the Body,” Nature Reviews Neuroscience 3, no. 8 (2002): 655–66; A. D. Craig, “How Do You Feel — Now? The Anterior Insula and Human Awareness,” Nature Reviews Neuroscience 10, no. 1 (2009): 59–70.↩︎
Peter Sterling and Joseph Eyer, Allostasis: A New Paradigm to Explain Arousal Pathology, (New York, NY), Wiley, 1988, 629–49; Peter Sterling, “Allostasis: A Model of Predictive Regulation,” Physiology & Behavior 106, no. 1 (2012): 5–15.↩︎
Bruce S. McEwen, “Stress, Adaptation, and Disease: Allostasis and Allostatic Load,” Annals of the New York Academy of Sciences 840, no. 1 (1998): 33–44.↩︎
Kent C. Berridge, “The Debate over Dopamine’s Role in Reward: The Case for Incentive Salience,” Psychopharmacology 191, no. 3 (2007): 391–431; Kent C. Berridge and Terry E. Robinson, “Liking, Wanting, and the Incentive-Sensitization Theory of Addiction,” American Psychologist 71, no. 8 (2016): 670–79.↩︎
Kent C. Berridge, “Food Reward: Brain Substrates of Wanting and Liking,” Neuroscience & Biobehavioral Reviews 20, no. 1 (1996): 1–25.↩︎

--- title: "Formalizing Constructed Value" --- The preceding chapter introduced constructed value theory in intuitive terms. Value is enacted through transactions between embodied organisms and their environments. The transaction is the sufficient statistic. Friction governs whether and how value construction occurs. This chapter makes these ideas precise. We formalize the core concepts, distinguish related mechanisms that are often conflated, and state the theory in terms that permit empirical testing. The goal is not mathematical elegance for its own sake but conceptual clarity that grounds the framework in measurable reality. ## The CTV Sequence Constructed value theory proposes a causal sequence from internal state to observable trace. We call this the **CTV sequence** (Constructed-Trace-Value): $$ \text{Interoception} \rightarrow \text{Motivation} \rightarrow \text{Action} \rightarrow \text{Transaction} \rightarrow \text{Trace} \rightarrow \text{Stratigraphy} $$ Each stage has a precise meaning: ### Stage 1: Interoception **Definition.** Interoception is the organism's sensing of its internal physiological state. This includes signals related to hunger, thirst, temperature, fatigue, arousal, pain, and visceral sensation [@craig_interoception; @craig_interoception_2009]. **Formal characterization.** Let $S(t)$ denote the organism's internal state vector at time $t$. This vector includes: - Metabolic variables (blood glucose, hydration, temperature) - Arousal variables (cortisol, adrenaline, heart rate variability) - Affective variables (valence, activation) The organism does not have direct access to $S(t)$. It perceives a noisy, compressed representation $\hat{S}(t)$ through interoceptive channels. This representation is what drives behavior. **Key insight.** Interoception is not merely reactive. The brain continuously generates predictions about future states, comparing predicted $S(t+\Delta)$ against current resources. This predictive interoception is the basis of allostatic motivation (see below). ### Stage 2: Motivation **Definition.** Motivation is the disposition to act, generated by the relationship between interoceptive state and environmental affordances. **Formal characterization.** Let $M(t)$ denote motivational intensity toward a particular action at time $t$. Motivation is a function of: $$ M(t) = f(\hat{S}(t), A(t), \theta) $$ where: - $\hat{S}(t)$ is the perceived internal state - $A(t)$ is the set of perceived affordances in the environment - $\theta$ represents stable individual parameters (learning history, temperament) This formulation captures the core insight of alliesthesia: the same environmental affordance $A$ produces different motivation $M$ depending on internal state $\hat{S}$. ### Stage 3: Action **Definition.** Action is sensory-motor engagement with the environment---reaching, grasping, clicking, signing, speaking. Action is physical movement that potentially modifies the organism-environment coupling. **Formal characterization.** Let $a(t)$ denote the action taken at time $t$. Action is selected (not necessarily consciously) based on motivation: $$ a(t) = \arg\max_{a \in A(t)} \left[ M_a(t) - F_a(t) \right] $$ where $F_a(t)$ is the perceived friction associated with action $a$. The organism acts when motivation exceeds friction for at least one available action. ### Stage 4: Transaction **Definition.** A transaction is a completed exchange that modifies the state of the economic scaffold. Not all actions become transactions---friction may prevent completion. **Formal characterization.** Let $T$ denote the set of completed transactions. A transaction $\tau \in T$ is characterized by: $$ \tau = (t, \text{parties}, \text{terms}, \text{result}) $$ where $t$ is the timestamp, parties identifies the transacting organisms or addresses, terms specifies what was exchanged, and result indicates success or failure. The critical point: $\tau$ is observable. We do not need to know the internal states $S$ or motivations $M$ that produced the transaction. We observe the transaction itself. ### Stage 5: Trace **Definition.** A trace is the physical record of a transaction, persisting in some substrate after the transaction completes. **Formal characterization.** Let $\text{Tr}(\tau)$ denote the trace of transaction $\tau$. In traditional systems, traces are heterogeneous: - Memory traces (in brains): high noise, rapid decay - Paper traces (in ledgers): moderate noise, slow decay, local access - Digital traces (in databases): low noise, indefinite persistence, access controlled by custodians In Bitcoin, traces have specific properties: $$ \text{Tr}_{\text{BTC}}(\tau) = (\text{txid}, \text{block}, \text{confirmations}, \text{UTXO state}) $$ The trace is globally replicated, cryptographically committed, and thermodynamically secured. ### Stage 6: Stratigraphy **Definition.** Stratigraphy is the accumulated structure of traces over time, organized by temporal ordering. **Formal characterization.** Let $\Sigma(t)$ denote the stratigraphic state at time $t$---the complete history of traces up to $t$. In Bitcoin: $$ \Sigma(t) = \{\text{Tr}(\tau) : \tau \text{ confirmed before } t\} $$ The stratigraphy has depth (older traces are buried under newer ones) and a surface (the chain tip, reflecting the current state). ## Two Modes of Regulation: Homeostasis and Allostasis A crucial refinement distinguishes two modes of physiological regulation that drive economic behavior differently. ### Homeostasis: Reactive Error-Correction **Definition.** Homeostasis is regulation by negative feedback, maintaining a variable near a fixed set-point by correcting deviations after they occur. **Formal characterization.** In homeostatic regulation: $$ \text{Response}(t) = k \cdot [S_{\text{set}} - S(t)] $$ where $S_{\text{set}}$ is the defended set-point and $k$ is a gain parameter. The organism detects deviation from set-point and acts to reduce the error. **Example.** Body temperature regulation around 37°C. When core temperature drops, shivering generates heat; when it rises, sweating dissipates heat. The response is proportional to the deviation. **Economic analog.** Reactive consumption: eating when hungry, drinking when thirsty. The transaction responds to a current deficit. ### Allostasis: Predictive Anticipation **Definition.** Allostasis is "stability through change"---regulation by predictive adjustment of the set-point itself, in anticipation of future demands [@sterling_allostasis; @sterling_allostasis_2012]. **Formal characterization.** In allostatic regulation: $$ S_{\text{target}}(t) = g(\mathbb{E}[D(t+\Delta) \mid I(t)]) $$ where $D(t+\Delta)$ is anticipated future demand and $I(t)$ is current information. The organism shifts its operating level *before* the demand arrives. **Example.** Heart rate increases before exercise begins---the brain predicts the demand and pre-adjusts. Blood pressure rises upon waking, anticipating the transition to upright posture. **Economic analog.** Anticipatory transactions: buying groceries before hunger, purchasing insurance before loss, saving for retirement decades away. The transaction responds to a *predicted* deficit, not a current one. ### The Dominance of Allostasis in Economic Behavior Most economic transactions are allostatic, not homeostatic. Consider the ledger. If transactions were primarily homeostatic, we would see patterns of acute need followed by immediate resolution: hunger → food purchase → satiation. But the ledger shows something different: - Weekly grocery runs (anticipating the week's needs) - Monthly rent payments (anticipating shelter needs) - Insurance premiums (anticipating low-probability catastrophes) - Retirement savings (anticipating needs decades away) These are not responses to current deficits. They are anticipatory positioning based on predicted futures. The organism models its future states and transacts now to prepare. **Implication for interpretation.** When we observe a transaction on the ledger, we cannot infer whether it was homeostatic (responding to current deficit) or allostatic (preparing for anticipated deficit). The trace does not distinguish. But we can infer that allostatic transactions dominate by volume. ### Allostatic Load and Chronic Friction Allostatic regulation has costs. **Allostatic load** is the cumulative wear from repeated or sustained adjustment [@mcewan_allostatic_load]. The system pays a price for flexibility. Economic friction that is *chronic* produces allostatic load. Poverty is not merely lack of resources---it is the cumulative cost of perpetual allostatic adjustment to scarcity. The organism must continuously recalibrate, prioritize, and cope. This recalibration is exhausting. **Formal characterization.** Let $L(t)$ denote allostatic load at time $t$: $$ L(t) = \int_0^t \lambda(s) \cdot |S(s) - S_{\text{baseline}}| \, ds $$ where $\lambda(s)$ is a time-varying weight reflecting the organism's capacity to recover. Chronic deviation from baseline accumulates load; recovery time reduces it. **Implication for policy.** Interventions that reduce chronic friction also reduce allostatic load. The benefit is not merely the friction avoided but the cumulative damage prevented. ## Wanting and Liking: Dissociable Components of Motivation The motivation stage of the CTV sequence requires further refinement. Motivation is not unitary. It comprises at least two dissociable components: **wanting** and **liking** [@berridge_wanting_liking_2007; @berridge_robinson_2016]. ### The Distinction | Component | Psychological Description | Neural Substrate | |-----------|--------------------------|------------------| | **Wanting** | Incentive salience; motivation to pursue | Mesolimbic dopamine system | | **Liking** | Hedonic impact; pleasure from consumption | Opioid/endocannabinoid hotspots | **Wanting** is the motivational pull toward a stimulus. It makes things attention-grabbing, approach-inducing, effortful-pursuit-worthy. **Liking** is the hedonic pleasure experienced upon consumption. It is the "good feeling" that (in normal circumstances) rewards successful pursuit. ### The Dissociation The crucial discovery: wanting and liking can come apart [@berridge_food_reward_1996]. **Wanting without liking.** Addiction exemplifies this. The addict compulsively seeks the drug (intense wanting) even though it no longer produces pleasure (tolerance has eliminated liking). The dopamine system is sensitized; the hedonic system is blunted. **Liking without wanting.** Satiation exemplifies this. After a satisfying meal, food still tastes good if it touches the tongue (liking intact), but there is no motivation to eat more (wanting suppressed). **Neither.** Depression often involves anhedonia---neither wanting nor liking. The organism is unmotivated AND finds no pleasure. ### Implications for the CTV Sequence The wanting/liking distinction refines our understanding of what transactions reveal. **Transactions reveal wanting, not liking.** A completed transaction shows that the organism was motivated to pursue the good enough to overcome friction. It does not show that the organism derived pleasure from the outcome. Formally, let $W(\tau)$ denote the wanting that produced transaction $\tau$, and let $L(\tau)$ denote the liking experienced upon completion. The transaction trace $\text{Tr}(\tau)$ is determined by $W$, not by $L$: $$ \text{Tr}(\tau) = h(W(\tau)) \quad \text{(not a function of } L(\tau) \text{)} $$ This has profound consequences: 1. **Revealed preference is revealed wanting.** The traditional economic assumption that transactions reveal preferences implicitly assumes wanting and liking are identical. They are not. Transactions reveal what organisms were motivated to pursue, which may diverge from what they enjoyed. 2. **Post-transaction behavior reveals liking.** Returns, complaints, non-repeat purchases, negative reviews---these are traces of liking deficits. The original transaction captured wanting; subsequent behavior captures the wanting-liking gap. 3. **Advertising targets wanting.** Marketing that increases incentive salience (wanting) without affecting hedonic value (liking) can drive transactions that produce disappointment. The ledger captures the transactions; subsequent behavior reveals the mismatch. 4. **Addiction patterns are ledger-visible.** Compulsive transaction patterns---repeated purchases with diminishing satisfaction---show sensitized wanting with diminished liking. The pattern is visible in the stratigraphy even if the internal dissociation is not. ### Wanting, Liking, and Alliesthesia Alliesthesia modulates both wanting and liking, but potentially differentially: - **Alliesthetic wanting:** Thirst increases incentive salience of water. The glass becomes more attention-grabbing, more motivating to pursue. - **Alliesthetic liking:** Thirst increases hedonic impact of water. The water tastes better, feels more satisfying. In normal circumstances, alliesthesia shifts wanting and liking together. But pathology, drugs, or unusual circumstances can dissociate them. The ledger captures the wanting-driven transactions; the organism experiences the liking (or its absence). ## Friction: The Central Variable Having formalized the internal dynamics, we now formalize the external constraint: friction. ### Definition **Friction** is any resistance that reduces the probability of an action becoming a transaction, or increases the cost of that completion. ### Dimensions of Friction Friction is multidimensional. We identify six primary dimensions: **1. Transaction friction** ($F_{\text{tx}}$): Direct costs of completing an exchange. - Fees, commissions, spreads - Paperwork and bureaucratic requirements - Time spent navigating processes **2. Temporal friction** ($F_{\text{time}}$): Delay between action initiation and transaction completion. - Settlement time - Waiting periods - Confirmation requirements **3. Cognitive friction** ($F_{\text{cog}}$): Mental effort required to understand and execute. - Complexity of options - Opacity of terms - Expertise required **4. Regulatory friction** ($F_{\text{reg}}$): Institutional barriers imposed by authorities. - Licensing requirements - Compliance obligations - Prohibitions **5. Access friction** ($F_{\text{access}}$): Barriers to participation. - Geographic availability - Credential requirements - Capital minimums **6. Liquidity friction** ($F_{\text{liq}}$): Difficulty of converting assets. - Bid-ask spreads - Market depth - Time to find counterparty ### Aggregate Friction Total friction for a given action is a function of these dimensions: $$ F_{\text{total}} = \phi(F_{\text{tx}}, F_{\text{time}}, F_{\text{cog}}, F_{\text{reg}}, F_{\text{access}}, F_{\text{liq}}) $$ The function $\phi$ may be additive, multiplicative, or more complex. In general, frictions interact: high cognitive friction amplifies the impact of access friction; regulatory friction compounds transaction friction. ### Friction as Design Variable A key insight: friction is not merely an obstacle to be minimized. It is a design variable that can be optimized. **Productive friction** serves functions: - Bitcoin's proof-of-work is friction that creates security - Settlement delays are friction that permits error correction - Regulatory friction can exclude bad actors **Unproductive friction** impedes without benefit: - Bureaucratic complexity that serves no purpose - Rent-seeking intermediation - Information asymmetry exploited by insiders The goal is not frictionless markets but *appropriate* friction---enough to provide necessary structure, not so much as to prevent beneficial value construction. ### Friction and Value Construction The fundamental equation of constructed value theory relates motivation, friction, and transaction: $$ P(\text{Transaction}) = \sigma(M - F) $$ where $M$ is motivation, $F$ is aggregate friction, and $\sigma$ is a sigmoid function mapping the difference to a probability. When $M > F$, transaction is likely. When $M < F$, transaction is unlikely. The steepness of $\sigma$ determines how sharply the transition occurs. **Value is constructed when $M > F$.** The transaction occurs, the trace is created, and the stratigraphy grows. The value that is constructed depends on what the transaction enables---the change in the organism-environment coupling that the transaction produces. ## The Sufficient Statistic Claim We now state precisely what it means to call the transaction a "sufficient statistic." ### Statistical Definition In statistics, a sufficient statistic $T(X)$ for a parameter $\theta$ is a function of the data $X$ such that the conditional distribution of $X$ given $T(X)$ does not depend on $\theta$. Intuitively, $T$ captures all the information in $X$ that is relevant for inference about $\theta$. ### Application to Transactions **Claim.** The transaction is a sufficient statistic for valuation in the following sense: conditional on observing the transaction, additional information about the organism's internal states does not improve prediction of subsequent economic behavior. Formally, let $B_{t+1}$ denote the organism's economic behavior after time $t$. Let $\tau_t$ denote their transaction at time $t$. Let $S_t$ denote their internal state at time $t$. The sufficient statistic claim is: $$ P(B_{t+1} \mid \tau_t, S_t) = P(B_{t+1} \mid \tau_t) $$ Once we condition on the transaction, the internal state adds no predictive value. ### Interpretation This is a strong claim. It does *not* say that internal states are causally irrelevant---they cause transactions. It says that for the purpose of predicting future behavior, observing the transaction is as good as observing the internal state. Why might this hold? Because: 1. Internal states are transient and context-dependent. The hunger that motivated a food purchase dissipates upon eating. 2. Transactions modify the organism-environment coupling in durable ways. The purchase changes what the organism has access to. 3. Future behavior depends on current state, which is shaped by past transactions more than by past internal states. ### Caveats The claim is approximate, not exact. In practice: - Extreme internal states may have persistent effects - Some information in internal states (health conditions, psychological traits) may predict beyond transactions - The claim is about *economic* behavior, not all behavior The claim is methodological, not metaphysical. It says: for practical analysis, focus on transactions, not inferred internal states. The ledger is where the action is. ## Empirical Predictions A formalized theory should generate testable predictions. Constructed value theory predicts: ### Prediction 1: Alliesthetic Modulation of Transaction Timing If alliesthesia modulates motivation, then transactions should cluster around states of high alliesthetic sensitivity. **Test:** Examine the timing of transactions relative to physiological state (using wearable sensors). Food purchases should cluster before meals (anticipatory) and correlate with hunger signals. Discretionary purchases should correlate with arousal states. ### Prediction 2: Allostatic Patterns in Long-Term Transaction Series If allostasis drives anticipatory transactions, then organisms should show patterns of preparation followed by consumption. **Test:** Examine individual transaction histories for allostatic signatures: accumulation phases (saving, stocking) followed by deployment phases (spending, consuming). The ratio of anticipatory to reactive transactions should vary with predictability of environment. ### Prediction 3: Wanting-Liking Dissociation in Repeat Purchase Patterns If wanting and liking can dissociate, then some transaction patterns should show increasing frequency (sensitized wanting) with decreasing satisfaction (diminished liking). **Test:** Identify products or services with high repeat-purchase rates but low satisfaction ratings. These represent wanting-liking dissociation. Compare to products with matched wanting and liking (high repeat, high satisfaction). ### Prediction 4: Friction Reduction Increases Transaction Volume If friction constrains value construction, then reducing friction should increase transaction volume. **Test:** Natural experiments where friction is reduced (new payment systems, regulatory reform, infrastructure improvement) should show increased transaction rates, controlling for other factors. ### Prediction 5: Chronic Friction Produces Allostatic Load Signatures If chronic friction imposes allostatic load, then populations facing sustained economic friction should show physiological stress markers. **Test:** Compare cortisol levels, inflammatory markers, and other stress indicators between populations with high vs. low chronic economic friction, controlling for acute economic status. ## Summary This chapter has formalized the core concepts of constructed value theory: 1. **The CTV sequence** traces the causal chain from interoception through transaction to stratigraphy. 2. **Allostasis vs. homeostasis** distinguishes anticipatory from reactive regulation; most economic behavior is allostatic. 3. **Wanting vs. liking** distinguishes motivation from hedonic impact; transactions reveal wanting, not liking. 4. **Friction** is a multidimensional variable that governs whether motivation becomes transaction. 5. **The sufficient statistic claim** holds that transactions capture what matters for predicting economic behavior. These formalizations are not merely academic exercises. They ground the theory in measurable quantities, generate testable predictions, and clarify what the ledger actually records: the traces of embodied organisms, driven by alliesthetic motivation, navigating friction, leaving marks in the stratigraphy. The next chapter applies this framework to the specific affordances of the Bitcoin scaffold.