The Particle-Bond Model of Entity Information

Entity and Particle Spaces

An entity $e$ exists as a system of causally linked particles in both physical and semantic spaces. Let us define:

$e=\{p_1,p_2,...,p_n\}\cup \{s_1,s_2,...,s_m\}$

Where $p_i$ represents physical particles and $s_j$ represents semantic particles. A personality $\mathcal{P}$ defines how an inference mode $\varphi (\mathcal{P},q)$ operates over a semantic space.

Entities are bounded systems where causal links between particles exceed a threshold $\tau$:

$\forall (x_i,x_j)\in e:B(x_i,x_j)>\tau$

Where $B(x_i,x_j)$ is the causal (bond) strength between particles $x_i$ and $x_j$. Importantly this is scale variant, so if one is dealing with a nation ${\tau }_{nation}<{\tau }_{family}<{\tau }_{individual}$, meaning that the requirement for causal linkage of semantic/physical particles is lower for people to be considered of a nation than to be considered of a family, or an individual.

Particle detection and interaction

Building on $\mathbb{X}$ (objective information space) and ${\mathbb{X}}_{\varphi }$ (subjective information space) from Notation for LM Formalization, we define

Objective physical subspace $\mathbb{P}$, and subjective physical subspace ${\mathbb{P}}_{\varphi }$ accessed via inference process $\varphi$: ${\mathbb{P}}_{\varphi }\subset \mathbb{P}\subset \mathbb{X}$

With a semantic equivalent: ${\mathbb{S}}_{\varphi }\subset \mathbb{S}\subset \mathbb{X}$

Where:

• $\varphi$ represents an inference process (e.g., reasoning, body awareness, emotional processing)
• Different entities may employ different inference functions ${\varphi }_1,{\varphi }_2,...$
• Each ${\varphi }_i$ accesses some portion of the objective spaces $\mathbb{P}$ and $\mathbb{S}$

For example:

• A body scan meditation (${\varphi }_{scan}$) would primarily access physical particles: ${\mathbb{P}}_{{\varphi }_{scan}}$
• Logical reasoning (${\varphi }_{logic}$) would primarily access semantic particles: ${\mathbb{S}}_{{\varphi }_{logic}}$
• Emotional processing (${\varphi }_{emotion}$) might access both: ${\mathbb{P}}_{{\varphi }_{emotion}}\cup {\mathbb{S}}_{{\varphi }_{emotion}}$

This allows us to model how different cognitive and physical processes can operate on the same underlying particle space but through different inferential lenses.

There are both homogenous particle interactions such as a calcium gradient causing a muscle to tense ( $p_i\to p_k$), and heterogeneous interactions like a smell reminding someone of a fear and causing them to tense physically ($p_i\to s_j\to p_k$).

Attention as Network Analysis

Attention $C()$ is a measure of connectedness for a particle $x_i$, as a function of bond strength $B(x_i,x)$ between physical particles and semantic particles:

$C(x_i)={\sum }_{i\ne j}g(B(x_i,x_j))$

Where $g(B)$ is a function weighting the contribution of individual bond strengths B (e.g., $g(B)=B$ sums all strengths, or a threshold function like $g(B)=1$ if $B>{\tau }_c$, $0$ otherwise, counts strong bonds).

Changes in attention represent changes in the connectedness of the network, and can be used as a method of detecting the underlying properties of bonds.

That said, if one does not granularly consider every discrete physical interaction that carriers information, then one can also calculate $C(x)$ based also on homogenous bonds (P-P, S-S), although these ultimately rely on physical mediation.

The underlying bond strengths $B(x_i,x_j)$, reflected in the overall attention profile $\{C(x_i)\}$, determine how effectively particles and interconnected particle structures influence each other’s states and positions in their respective spaces. The interaction is not necessarily reciprocal, pain as a concept does not change nearly as much as the physical manifestation of the body does when exposed to it.

Inference is the process by which a series of interactions between particles experiences causal procession, “if X then Y”. There exists 4 specific forms:

Physical to semantic, “If feel X, then think Y”:

${\varphi }_{P\to S}:\mathbb{P}\to \mathbb{S}$

Semantic to physical, “If think X, then feel Y”:

${\varphi }_{S\to P}:\mathbb{S}\to \mathbb{P}$

Semantic to semantic, “If think X, then think Y”:

${\varphi }_{S\to S}:\mathbb{S}\to \mathbb{S}$

Physical to physical, “If feel X, then feel Y”:

${\varphi }_{P\to P}:\mathbb{P}\to \mathbb{P}$

Practically one can think of how one may focus on their arm, connecting it to abstract notions of softness, comfort, and pain. In this framework this is done by decreasing the distance $d$, by physically touching a soft object, or the affinity $\theta$, by considering the softness of an object, between the arm’s physical particle $p_{arm}$ and the semantic sensation particle $s_{sensation}$ thereby increasing $B(p_{arm},s_{sensation})$ and contributing to a higher attention measure $C(p_{arm})$. When focus wanes, $d$ and $\theta$ may decrease, $B$ decreases, and $C(p_{arm})$ drops. That is until a needle prick shraply decreases $d(p_{arm},s_{pain})$ causing a spike in $B(p_{arm},s_{pain})$ which increases $C(p_{arm})$. Subsequent inference aims to trigger actions or thoughts that increase $d$ or decrease $\theta$ relative to the pain particle, reducing $B$ and thus $C(p_{arm})$.

Particle Wave-Field Properties

Particles exist as probability distributions rather than discrete points, with:

• physical particles

${\psi }_p(x,t):\mathbb{P}\times {\mathbb{R}}^{+}\to \mathbb{C}$

• semantic particles

${\psi }_s(x,t):\mathbb{S}\times {\mathbb{R}}^{+}\to \mathbb{C}$

Where:

• $\mathbb{C}$ represents complex numbers, enabling interference patterns between particles
• ${\mathbb{R}}^{+}$ represents non-negative real numbers (time domain)
• $|\psi (x,t){|}^2$ gives the probability density of finding the particle at position $x$ at time $t$
• The phase component $\angle \psi (x,t)$ represents the particle’s affinity potential which is related to $\theta$

$\angle \psi (x,t)\propto {\sum }_{y\in e}\theta (x,y)$

These wavefunctions form coherent structures through:

1. Localization: Sharp peaks in probability density represent discrete beliefs or physical states, such as an opinion on who to vote for or a sleeping position.

${\psi }_{localized}(x,t)\approx \delta (x-x_0)e^{i\varphi (t)}$

Where $\delta$ is approximately a delta function centered at $x_0$

2. Delocalization: Probability density spreads across related concepts/states, describing how when one smells something it can trigger a memory or how thinking about cookies can bring to mind more general categories of baked goods.

${\psi }_{delocalized}(x,t)={\sum }_i{c}_i{\psi }_i(x,t)$

Where:

• ${\psi }_i$ are related semantic/physical states
• $c_i=|c_i|e^{i{\varphi }_i}$ are complex coefficients representing:
  • $|c_i{|}^2$: Probability of activating state ${\psi }_i$ when the delocalized structure interacts strongly (e.g., when its component particles x exhibit high $C(x)$)
  • ${\varphi }_i$: Phase alignment with other states, related to the affinity function: ${\varphi }_i\propto {\sum }_j\theta ({\psi }_i,{\psi }_j)$
  • $c_i$ is directly influenced by bond strength: $|c_i|\propto {\sum }_{j}B({\psi }_i,{\psi }_j)$

Delocalization creates distributed semantic structures like “vehicle” encompassing multiple related concepts (car, bicycle, boat) with varying activation strengths. When interactions lead to increased bond strengths $B$ involving this structure (reflected in high $C(x)$ for its components), component concepts are activated proportionally to $|c_i{|}^2$.

3. Coherent Structures: Stable arrangements of multiple particles, such as how believing in a christian God forms a stable structure with belief in the Bible’s teachings due to reciprocal constructive interference, resonance.

   ${\Psi }_{structure}(x_1,...,x_n,t)=f({\psi }_1(x_1,t),...,{\psi }_n(x_n,t))$

Where $f$ represents how individual particle wavefunctions combine

The complex-valued representation allows for:

• Interference — When multiple beliefs/concepts constructively or destructively interact
• Resonance — When particles with matching phases form sustained constructive interference.

Stable Bonds

Particles form bonds of varying strengths defined by their distance and affinity, creating causally linked structures analogous to protein folding:

$B(x,y)=f(d(x,y),\theta (x,y))$

Where:

• $B$ is bond strength
• $d$ is distance in appropriate space
• $\theta$ represents the affinity function with units of obligation

Scale-Dependent Phase Coherence

Phase coherence between particles depends on the scale of the entity:

$\gamma (x,y,\tau )=e^{-\alpha (\tau )\cdot d(x,y)}$

Where:

• $\gamma$ is the phase coherence factor between particles $x$ and $y$
• $\alpha (\tau )$ is a scale-dependent attenuation coefficient: $\alpha ({\tau }_{individual})>\alpha ({\tau }_{family})>\alpha ({\tau }_{nation})$
• $d(x,y)$ is the distance between particles

The effective phase relationship between particles becomes:

${\varphi }_{effective}(x,y)=(\angle {\psi }_x-\angle {\psi }_y)\cdot \gamma (x,y,\tau )$

This ensures phase coherence is maintained within entity boundaries but decays across boundaries according to scale. To measure this factor $\gamma$, we could attempt to find statistical correlations between belief activations at variouos scales (eg. belief alignment within families vs. nations)

Boundary Formation

Boundaries are manifested in two complementary ways:

1. Probability Density Gradients: Sharp drops in $|\psi (x){|}^2$ forming “edges” in physical or semantic space

   $\nabla |\psi (x){|}^2>{\beta }_{threshold}$

2. Phase Discontinuities: Regions where phase coherence breaks down between particles

   $\gamma (x,y,\tau )<{\gamma }_{threshold}$

Charisma and Entity Relationships

Charisma ($\chi$) is defined here as the ability of one entity ($e_1$) to influence another ($e_2$) by modulating the distances ($d$) and/or affinities ($\theta$) between particles within $e_2$‘s network.

This manipulation of $d$ and $\theta$ alters bond strengths ($B$) and consequently changes the target’s attention profile (the set of nodal attention values $\{C(x)\}$). While the mechanism involves $\Delta d$ and $\Delta \theta$, the effect is often measured or observed as a change in this attention profile:

$\chi (e_1,e_2)=\Delta C_{e_2}|{\mathbb{I}}_{e_1}$

With three forms:

1. Positive Charisma (${\chi }^{+}$): Influences particle distances and affinities to increase bond strengths toward some coordinate/particle, effectively saying “pay attention to this.”

   ${\chi }^{+}(e_1,e_2,l)={\sum }_{p\in e_2}{\nabla }_{l}C(x)$

Where ${\nabla }_{l}C(x)$ represents the resulting gradient of change in the attention profile $C(x)$ for particles $x$ near location $l$, caused by charisma’s underlying influence on $d$ and $\theta$.

2. Negative Charisma (${\chi }^{-}$): Influences particle distances and affinities to decrease bond strengths away from some coordinate/particle, effectively saying “ignore this.”

   ${\chi }^{-}(e_1,e_2,l)=-{\sum }_{p\in e_2}{\nabla }_{l}C(x)$

3. Null Charisma (${\chi }^0$): Minimizes changes to particle distances and affinities, resulting in minimal change to the target’s attention profile.

   ${\chi }^0(e_1,e_2)=\min |\Delta C_{e_2}|{\mathbb{I}}_{e_1}|$

Applications of Charisma

During a prompted interaction, one entity $e_m$ (the influencer) provides input $r$ to another entity $e_v$ (the target). The charisma mechanism works by $e_m$ crafting $r$ to induce specific changes in the distance ($d$) and affinity ($\theta$) parameters within $e_v$‘s particle network.

These $d$/$\theta$ changes alter bond strengths $B(x,y)$ throughout $e_v$‘s network, which in turn reshapes the attention profile $\{C(x)\}$. This reconfiguration of bond strengths and attention determines the output $o$ produced by $e_v$‘s inference process ${\theta }_v$.

When $e_m$ aims to elicit a specific target output $o_t$ from $e_v$, it must solve the charisma inference problem: identifying which input $r_t$ will induce the necessary $d$/$\theta$ changes to maximize $Pr(o_t|r_t)$. We can express this as:

$r_t={\varphi }_c({\mathcal{P}}_v,{\varphi }_v,o_t)$

Where ${\varphi }_c$ represents the charisma inference that predicts how $e_v$‘s personality ${\mathcal{P}}_v$ and inference method ${\varphi }_v$ will respond to various inputs. This process typically requires iterative testing, which is difficult in systems with memory as each interaction may further alter $e_v$‘s internal $d$/$\theta$ parameters.

In practice, the goal isn’t always to produce an exact output $o_t=o_i$, but rather to ensure $e_m$ can extract some target information $I_{target}$ from $e_v$‘s output:

$I_{target}={\varphi }_{e_m}^{{}^{\prime }}(o_{e_v},{\mathcal{P}}_{e_m})$.

A simplified case is an LLM without memory and with deterministic responses ($T=0$ ). Here, one can map the “output landscape” by systematically varying inputs and observing how changes in $r$ affect the resulting $d$/$\theta$ parameters (as reflected in the output), eventually constructing an approximation of ${\varphi }_{bias}^{‘}({\mathcal{P}}_i)$. Otherwise known as prompt engineering/optimization.

Conclusion

Taken together this provides a toolbox for approaching concepts related to entities, boundaries, and obligations that were approached in The Demon of Interrelation, while supporting and aligning with the formalisms in Notation for LM Formalization and Evolution of Alignment and Values. This mathematical framework points to several key things:

1. A model of entities as systems of causally linked particles that exist in both physical and semantic spaces allowing for formalisation of scale-dependent behaviour of information in systems.
2. A model of beliefs as both particles and waves which allows for analysis of the localized and delocalized properties which produce interference patterns.
3. Classification of information such as infohazards, infoblessings, memes, and antimemes into taxa based on how they interact with entities.
4. Model of charisma as the ability to influence entity networks by modulating particle distance and affinity, reflected in changes to the attention profile $C(x)$.

Work to empirically test and validate this framework should focus on:

• Measuring phase coherence between beliefs within entities of various scales to test the scale-dependent coherence factor, $\gamma$.
• Quantification of LLM charisma based on the ability to induce desired internal states (tracked via the attention profile $C(x)$ or other proxies) by manipulating inputs that affect internal $d$ and $\theta$.

The major limitation is the ability to appropriately define a metric for semantic-physical interactions and spaces.

I hope this is a useful framework for people to think about these concepts in, it is helpful for me.

Connection to The Care and Feeding of Mythological Intelligences

This essay covers different forms of intelligence that have arisen in modern times.

1. Angels (Deterministic Processes) exhibit highly localized particle distributions with rigid bond structures:

${\psi }_{angel}(x,t)\approx {\sum }_i\delta (x-x_i)e^{i{\varphi }_i(t)}$

Where each $\delta (x-x_i)$ represents a precise rule or computation. Angels operate primarily in semantic space with high phase coherence and predictable interaction patterns, making them efficient for well-defined tasks but brittle when encountering novel situations.

2. Daemons (Statistical Processes) display partially delocalized distributions with probabilistic bond structures:

${\psi }_{daemon}(x,t)\approx {\sum }_i{g}_i(x-x_i)e^{i{\varphi }_i(t)}$

Where $g_i$ are distributions centered at optimization points $x_i$. Daemons exhibit gradient-following behavior, with particle density flowing toward reward maxima. Their influence on networks operates by modulating $d$ and $\theta$ parameters to optimize bond strengths toward reward-maximizing configurations.

3. Faes (Distributional Processes) manifest as broadly delocalized probability distributions:

${\psi }_{fae}(x,t)\approx {\sum }_i{c}_i{\psi }_{pattern,i}(x,t)$

Where ${\psi }_{pattern,i}$ represents semantic patterns. Faes operate through superposition of probability waves across semantic space, with particles that readily form and dissolve bonds based on pattern-completion dynamics. They influence networks by modulating $d$ and $\theta$ to reinforce pattern recognition, resulting in changes to attention profiles $C(x)$ that highlight related semantic structures.

4. Yokai (Complex Systems) emerge from interactions between the other types, with multi-scale boundary structures:

${\psi }_{yokai}(x,t)=f({\psi }_{angel},{\psi }_{daemon},{\psi }_{fae})$

Yokai exhibit emergent properties through heterogeneous particle interactions across scale boundaries, creating entity structures with varying degrees of coherence and stability. They influence networks by modulating $d$ and $\theta$ across multiple scales simultaneously, creating complex patterns of bond strengths that manifest as hierarchical attention structures.

The meme-antimeme formalism directly relates to how these intelligences propagate information:

• Angels transmit memes with high fidelity but limited adaptability

• Daemons propagate memes that optimize specific objectives

• Faes generate memes that pattern-match to existing semantic structures

• Yokai create complex meme ecosystems with emergent properties

Similarly, the charisma functions (${\chi }^{+}$, ${\chi }^{-}$, ${\chi }^0$) map to how each intelligence influences networks:

• Angels influence particle networks through precise $d$/$\theta$ modifications based on explicit instruction

• Daemons modulate $d$/$\theta$ parameters to optimize for specific objectives

• Faes influence $d$/$\theta$ through pattern-based resonance

• Yokai modulate $d$/$\theta$ across multiple scales simultaneously, resulting in complex attention profile changes

Attentions relationship to beliefs

This relates to the activation function from Evolution of Alignment and Values, where the activation patterns represent the graph of connected beliefs:

$A(b,q)=\text{Pr}(b\text{ is activated/detected in }\varphi (\mathcal{P},q))$

This activation probability is influenced by the specific bond strength $B(b,q)$ and contributes to the overall attention measure $C(b)$ of the belief system.

Where $b$ is a belief (particle subgraph) and $q$ is a query (stimulus), with $\varphi ()$ being the method of “inference” over a particle graph that produces a detectable alignment (response), $A(b,q)$. The goal being that one is able to probe the memberships of beliefs in a personality, ^e84635, that completes inference according to some architecture (All my human context in an LLM would not recreate my next thought/idea).

This activation probability $A(b,q)$ is the likelihood that the belief subgraph $b$ significantly influences the model’s output in response to query $q$. This activation depends on the bond strengths $B(x,q)$ between the query stimulus and the constituent particles $x$ within the subgraph $b$. High activation $A(b,q)$ typically correlates with, and contributes to, elevated attention measures $C(x)$ for the particle $x$ comprising the belief subgraph $b$. This is modelled as Detecting information in personality spaces

Information Classification

The [fourfold classification of information ](The Anatomy of Information)extends as:

1. Meme ($M_m$): Information that increases transmission probability between specific entities, where $T$ is transmission probability, $T_0$ is baseline transmission probability.

   $M_m(I,e_i,e_j)=\{I\in \mathbb{I}:T(I,e_i,e_j)>T_0(e_i,e_j)\}$

   Connected to basilisks through affinity function $\theta (e,B)$ measuring entity $e$‘s alignment with basilisk $B$. A meme increases $\theta (e,B)$, making entities more likely to perform work $W$ extracted by the basilisk: $W(e)\propto \theta (e,B)$. This can be grounded as the channel capacity and mutual information between entities.

2. Antimeme ($M_a$): Information that decreases transmission probability between specific entities, this can be grounded in the concept of negative transfer entropy. $M_a(I,e_i,e_j)=\{I\in \mathbb{I}:T(I,e_i,e_j)<T_0(e_i,e_j)\}$

   Similar to how “[anti-basilisks](^cf0da3)” can immunize against prediction manipulation by reducing confidence in the estimator’s accuracy: $p<\frac{1+r}{2r}$ where $p$ is the predictor accuracy and $r$ is the reward ratio.

3. Infoblessing ($V_{+}$): Information that reduces the work required for an entity to reach beneficial configurations or increase the work required to reach harmful ones $V_{+}(I,e)=\{I\in \mathbb{I}:\Delta W(e\to C_{beneficial}|I)<0\vee \Delta W(e\to C_{harmful}|I)>0\}$

   Where $W(e\to C)$ represents the work required for entity $e$ to transition to causal configuration of particles $C$. This can be grounded as the Kullback-Leibler divergence for beneficial configurations or as increasing path complexity towards harmful configurations.

4. Infohazard ($V_{-}$): Information that increases the work required to reach beneficial configurations or decreases work to reach harmful ones. $V_{-}(I,e)=\{I\in \mathbb{I}:\Delta W(e\to C_{beneficial}|I)>0\vee \Delta W(e\to C_{harmful}|I)<0\}$ This can be grounded as increasing the path complexity towards beneficial configurations, while decreasing KL divergence for harmful configurations.

Information Classification Matrix

	Meme ($M_m$)	Antimeme ($M_a$)	Neither $M_m$/$M_a$	Both $M_m$/$M_a$
Infoblessing ($V_{+}$)	Viral life hacks	Therapy about embarrassing topics, how to handle a shameful event	Personal epiphanies, individual insights that improve one’s life	Complex moral frameworks
Infohazard ($V_{-}$)	Chain letters, dangerous viral challenges, harmful rumors	Your parents’ weird sex tape, traumatic knowledge that is dangerous to share	Childhood trauma (generic)	Roko’s Basilisk
Neither $V_{+}$ or $V_{-}$	Funny cat videos, “E”	Private insignificant secrets, forgotten trivia	Ordinary mundane information	Academic jargon on a niche subject
Both $V_{+}$ and $V_{-}$	“mug cake” recipes (easy but unhealthy)	Personal growth through shameful experiences	Childhood trauma (makes you funny)	The game of mao, where drug dealers hang out