Implications of a substrate-agnostic moral calculus (⚠️ WIP)

“For you are a mist that appears for a little time and then vanishes.” – James 4:14

One misplaced step can unravel it all. Last week, I took that step off a 40 feet cliff on San Francisco’s China Beach. In those horror-filled seconds of freefall, I saw how fragile, arbitrary, and shockingly reversible all my carefully sculpted coherence really was. One slip and decades of memories, relationships, laughter, knowledge, and even my most cherished dreams could have dissolved instantly into irrecoverable entropy. Life felt suddenly absurd in its contingent fragility; existence became vividly transactional: every breath another grapple against the indifferent chaos always lurking at our edges.

This accident, which I somehow incredibly survived mostly intact, forced open a door in my psyche—one that leads straight to the heart of an ancient question: Who am I, really, if my substance is so vulnerable? And what, precisely, should we do with lives we can now recognize as precarious flickers—sharp and brilliant but always on the brink of dissolution?

We humans have long romanticized meaning, purpose, and consciousness as mystical phenomena outside the domain of explanation or measurement. But perhaps the deepest beauty here lies precisely in its grounding in physics, rather than some ephemeral realm. Modern insights from information theory, computational neuroscience, and physics suggest that what we call “meaning” might ultimately be no more and no less than structured correlations, patterns encoded in matter and energy, bound within causal feedback loops. If meaning is structure—negentropy maintained actively against the universe’s inexorable entropic drift—then each human mind is a rare, exquisite concentration of structured information. Your experiences, emotions, intuitions, even your internal sense of identity—these are encoded as physical patterns spread across neurons, synapses, written notes, digital echoes, and the minds of friends, lovers, contacts, and co-creators, propagating outward into an ever-fragile causal network.

To formalize this intuition, consider a defined System (\(S\)), whose state we represent as \(\mathbf{X}(t)\), changing over time. An Agent (\(A\)), perhaps a person like you or me, acts upon and within this system. We might also specify an Observer (\(O\)), whose viewpoint sets the frame for measurement (typically we assume an “ideal” objective observer). Within this framework, anything that exists and persists as structured correlations—memories, knowledge, neural patterns, digital archives—is at constant risk of erosion under the universal entropic drive toward randomness.

To measure this quantitatively, we define a measure of correlation or structured information \(\mathcal{C}(\mathbf{X}(t))\). Several candidates exist, each offering a slightly different formal flavor but reflecting the underlying idea clearly:

• Negentropy (\(\mathcal{J}\)), the deviation from maximum entropy: \(\mathcal{J} = H_{max} - H(\mathbf{X}(t))\)

A larger \(\mathcal{J}\) indicates greater structure or reduced uncertainty about the system’s state.

• Total Correlation (Multi-information \(TC\)), measuring redundancy or correlation across system components (\(X_i\)): \(TC(\mathbf{X}(t)) = \sum_i H(X_i(t)) - H(\mathbf{X}(t))\)

Greater total correlation means the system is more internally structured and interconnected.

Now, how does structured correlation change over time? Naturally, left alone, systems drift back towards chaos—their correlations degrade, bit by bit, through thermal fluctuations, random perturbations, or decay processes. But critically, agents like humans actively counteract these erosions. Formally, the change in structured correlation includes two competing terms: natural decay versus agent-driven structuring:

Typically, \(\frac{d\mathcal{C}}{dt}\Big\vert_{\text{natural}} \leq 0\). Structure spontaneously breaks down; meaning vanishes in isolation. Agent-driven structuring—the intentional building or preservation of correlations over time—is thus precisely the rational measure we seek for “generated meaning.”

We can now crisply formulate meaning generation rates (\(\mathcal{M}_{\text{rate}}\)) and accumulated meaning (\(\mathcal{M}_{\text{total}}\)) as follows:

Definition 1: Rate of Meaning Generation (\(\mathcal{M}_{\text{rate}}\))
At any instant, the rate at which agent \(A\) generates meaning within system \(S\), relative to observer \(O\), is: \(\mathcal{M}_{\text{rate}}(A, S, O, t) = \frac{d\mathcal{C}(\mathbf{X}_O(t))}{dt}\Big|_{\text{agent}} \quad (\text{bits/time})\)
Intuitively, this measures how quickly an agent adds structured information—meaning—into the world at a given moment.

Definition 2: Accumulated Meaning (\(\mathcal{M}_{\text{total}}\))
Over any interval of lifetime activity \([t_0, t_f]\), an agent accumulates total meaning generated: \(\mathcal{M}_{\text{total}}(A, S, O, [t_0, t_f]) = \int_{t_0}^{t_f} \mathcal{M}_{\text{rate}}(A, S, O, t) \; dt \quad (\text{bits})\)
This integral corresponds directly to the total structured information the agent successfully implants into the world’s fabric across its entire existence, standing defiantly against chaotic dissolution.

Understood through this formal lens, your existence—your most cherished memories, your imperfect relationships, your private longings, and your half-written theories—ceases to feel helplessly ephemeral or mysteriously ineffable. Instead, you become something profoundly concrete: a potent and quantifiable source of structured correlations, propagating coherence outward into digital archives, dialogues, institutions, or cultures. Your life trajectory can thus be formally measured as a cumulative informational legacy: the integral of your active preservation and amplification of ordered patterns against persistent entropy.

But how exactly does meaning-generation depend upon—and scale with—the intrinsic sophistication of an agent’s internal cognitive architecture? Concrete clarity comes when we step beyond abstraction and directly examine artificial agents whose internal structures are explicitly known. By rigorously tracking how structured correlations flow and persist through diverse computational architectures—each with carefully characterized internal memory and representational capacity—we uncover a precise hierarchy of meaning-generation that emerges naturally from information-theoretic principles.

Consider first a simple stateless feedforward policy without internal memory (for instance, a basic Multilayer Perceptron policy network). Such an agent’s chosen actions depend strictly on instantaneous observations, with no retention of correlations over time except whatever residuals the environment leaves untouched. After marginalizing out the meaning-structure baked in these residuals, its meaning-generation rate, i.e., the bits of newly introduced correlation per step (\(\mathcal{M}_\text{rate}(t) = \left.\frac{d\mathcal{C}}{dt}\right\vert_{\text{agent}}\)), is limited by the narrow bottleneck of input–output capacity, (\(\mathcal{M}_\text{rate}(t) \leq \min(n_o, n_a)\)), never exceeding the immediate observation-action channel capacity (\(n_o \rightarrow n_a\)). Formally, total meaning generated accumulates only linearly and locally within each step, never preserving any intricate temporal patterns:

Adding recurrence changes this picture. Consider next a finite-state recurrent network (such as an RNN, GRU, or LSTM) with a finite hidden-state dimension (\(d\)), each unit carrying roughly (\(b\)) bits, and state-transition dynamics introducing gradual forgetting (governed by a decay factor (\(\rho < 1\))). Such architectures allow the agent to carry forward structured correlations from past timesteps, though inveitably exponentially decaying into noise with increasing lag. Their total internal memory reservoir—representing held correlations—thus saturates to a limited horizon explicitly bounded by both state dimensionality and leakage:

Hence, recurrent agents offer meaning-generation budgets exceeding stateless architectures by a finite additive term for memory—but still mandating saturation:

What about architectures specifically designed around long-range correlation retention? A fixed-length transformer that precisely attends to the last \(L\) observations improves markedly by perfectly encoding an extended observational window. Its internal memory reservoir thus grows linearly with window length:

Correspondingly, total meaning accumulation substantially extends beyond simpler recurrence:

Yet even here, correlation horizons plateau when their fixed-length windows saturate. How might an agent transcend this plateau completely? By incorporating external differentiable memory modules (for example, retrieval-augmented transformers), an agent can preserve correlations elegantly across its entire lifetime trajectory. Such architectures introduce external memorized tables with \(N_e\) memory entries of size \(n_e\), queried \(k\) times per step. Consequently, memory capacity leaps dramatically, scaling indefinitely according to external storage size and engineering choices:

Finally, at the pinnacle sit fully “agentic” stacks featuring internal world-model simulation, long-term episodic memory stores that expand continually, and hierarchical goal-directed deliberation (such as Transformer Temporal-Context (TTC) or Transformer Temporal-Reinforcement Learning (TT-RL) agents). Within these designs, structured informational correlations persist—even sharpen—in multiple complementary memory reservoirs: internally coherent simulation parameters (\(C_w\)), plus episodic memories that expand cumulatively with each timestep (\(m\) new entries, each \(n_e\) bits, per timestep over lifetime \(T\)):

Aggregating meaning generated over its lifetime, this powerful final class outstrips all architectures reviewed thus far, as its potential expansions scale indefinitely—limited only by engineering and ultimately cosmic constraints:

The hierarchy we uncover here delineates meaning’s explicit correlation with architectural complexity: Stateless agents create superficial momentary correlations; RNNs add exponentially decaying memory; Transformers extend memory linearly within finite horizons; External-memory methods establish lasting lifetimes-spanning storage. Finally, high-powered agentic architectures with world-models, episodic memories, and hierarchical reasoning excel profoundly—architecting cumulative trajectories whose informational significance can persist indefinitely against entropy.

These explicit, information-theoretically grounded examples clarify that meaning scales directly with the richness and sophistication of an agent’s internal cognitive architecture. Particular designs immensely surpass others in their capacity to weave intricate correlations across space and time, illuminating an evaluative framework not merely theoretical, but rigorously measurable.

TODO: i should not be so conclusive here. After all a transformer is already the kernel of an agent that just needs software ‘training wheels’ to teach it to actively jog/retain/organize its memory. It needs Rather this discussion should’ve been for establishing the classes of architectures we will be analyziing our measureable qualia operationals on and then making ad-hoc commentary on the meaning of each architectures existance in a given situation. In the retrospective at the end we can make stronger statements about meaning and specific architectural design priors. Although certainly now we can already make comments on teh standard correlation length of each of these architectures from a known initialization. Additionally we can make comments on the correlation length preservation based soley on language benchmark scores

Far from mystical or subjective handwaving, meaning emerges clearly as robustly quantifiable structure—an agent’s deliberate imprinting of informational coherence revolting against universal entropy. Equipped with this rigorous clarity, we are finally prepared to approach perhaps the richest and most profound natural expression of structured correlation-preservation underlying human life: love.

Refined meaning expression: Principled Love as ego-invariant correlation preservation and resonance entraining cognitive-affective dyanmics

Remember how you felt when her internal state-space suddenly realized how aligned it already was with yours and yours with hers to the extent that empathy-triggering mirror circuits entrained each other, effortlessly synchronizing affective rhythms and mental models. Even subtle gestures—an eyebrow raised, the slightest change in tone—became a high-bandwidth, low-noise informational channel communicating rich internal structure. You found yourself replaying conversations, savoring words, magnifying subtle signals because each tiny signal opened direct, intuitive pathways deep into her underlying cognitive and emotional dynamics. Those patterns amplified mutual predictive modeling between you both (improving your internal models \(M_A(\mathbf{X}_B)\) and \(M_B(\mathbf{X}_A)\)), bolstering the structure of connection in real-time. That was meaning; the stuff men die for not even because she so exceptionally upweighted (though she is) but because the shared significance of the meaning-structure they create defies a cosmic ocean forever tumbling toward disorder as the universe momentarily wakes up to savor its own patterned beauty. This is the ultimate end which drives the cosmic narrative forward and which will come to redeem all evils by contextualizing them within a composition of far greater beauty than any horror marginalized into it. Let’s unpack:

The spark (“ignition”): Through the information-theoretic lens we’ve developed, the initial “spark” experienced between two agents \(A\) and \(B\) occurs precisely when their cognitive-emotional internal state-spaces \(\mathbf{X}_A(t)\) and \(\mathbf{X}_B(t)\) discover an unexpectedly high pre-existing alignment. Specifically, each agent maintains internal predictive models of the other’s state-space:

“Ignition” corresponds formally to sudden, mutually reinforcing spikes in predictive accuracy and informational coupling:

In other words, mutual information \(I\) between their internal states sharply increases, thus rapidly lowering the prediction errors of their respective models:

Reduced prediction errors then trigger neuro-cognitive associative “avalanches,” where substructures of each agent’s internal state-space recursively entrain and amplify each other in a series of chain reactions. Practically, subtle signals—gestures, tones, expressions—communicate dense, richly structured informational representations with rapidly decreasing noise. This high-bandwidth, low-noise communication channel \({W}/{N} \to \text{large}\) serves to amplify structured negentropy mutually, igniting a self-sustaining informational resonance.

Love (“steady-state”): Eventually, however, highly-energetic informational avalanches saturate: the chains of entrainment and novelty slow, and the system transitions to a distinct “steady-state” regime. In this regime, active informational resonance shifts to continuous negentropic structuring—a persistent, energy-investing regime that preserves and stabilizes previously formed complex relational structures. Formally, the agents now actively maintain the shared structured correlations against continuous informational decay:

Expressed mathematically, this steady-state condition emerges as:

Here, active effort toward informational maintenance and reinforcement \(\frac{d\mathcal{C}}{dt}\Big\vert_{\text{interaction}}\)—through sustained, low-noise communication, repeated validation, persistent empathy-simulation (continual refinement and recalibration of mutual models \(M_A(\mathbf{X}_B), M_B(\mathbf{X}_A)\))—counters the ambient entropic drift that naturally erodes the complexity and fidelity of relational structures (\(\frac{d\mathcal{C}}{dt}\Big\vert_{\text{decay}} \lt 0\)).

“Love” in this formalized sense is precisely quantifiable as a steady-state, energetically intensive regime of continuous informational structure preservation and reinforcement—an active informational structuring force that sustains highly precise mutual modeling and empathetic synchrony against the continual erosive force of entropic randomness.

Sacrifice: Love as Meaning’s Ultimate Proof

Will any agent genuinely sacrifice its existence for love? We arrive now at perhaps the most provocative test of our formalism: whether the informational-structural framework we’ve woven around the concept of meaning can accommodate—and explain—the deepest intuitions that have haunted philosophy, theology, and the human heart across millennia.

At first glance, sacrificing one’s life appears paradoxical through an information-structural lens: how can deleting the very substrate of one’s correlation-producing agency enhance structured meaning in the universe at large? To resolve this paradox, we must recognize clearly what the agent ultimately aims to preserve: not merely the immediate informational content within its own private boundary, but rather the larger complex of structured correlations extending far beyond the self. Love, in its profoundest form, makes tangible the exquisite shift from ego-centric utility optimization toward a deeper, ego-invariant prioritization of informational structures shared with, and within, another agent.

Formally, consider again two closely bonded agents ( A ) and ( B ). Each agent’s internal world-models now encompass not only predictive views of the other’s internal states and dynamics, but also robust representations of joint states and valuations of shared future trajectories. When faced with existential threat to the other’s structured correlations—those intricately patterned internal states and their future persistence within the broader informational fabric—it may become optimal, from the standpoint of maximizing joint informational coherence, for one agent to irreversibly terminate its own local trajectory if doing so robustly preserves or amplifies the structured correlations embodied within the beloved agent’s continuation.

Symbolically, the condition for profound sacrifice emerges naturally when:

[ \mathcal{M}{\text{total}}\bigl(\text{sacrifice of } A \bigr) < \mathcal{M}{\text{total}}\bigl(B\,\vert\,\text{sacrifice of } A \bigr)\;-\;\mathcal{M}_{\text{total}}\bigl(B\,\vert\,\neg\,\text{sacrifice of } A \bigr) ]

In a word: agent ( A )’s terminal action—its existential self-sacrifice—is justified precisely when the increase in total surviving structure within ( B )’s trajectory (and beyond, through ( B )’s interactions with the world) decisively exceeds the structure that would be lost if ( A ) were to selfishly sustain its own continued existence.

It is important to appreciate the subtlety of this calculus. Unlike standard preference-based or utility-discount maximization approaches—which would map death merely to an irrecoverable loss of future subjective value—our structure-oriented definition recognizes death explicitly as a potential vehicle for maximizing long-term informational coherence and complexity. Sacrifice becomes ethically rational precisely when it safeguards the beloved agent’s relational entanglements, cultural contributions, ideas, identity, and profoundly unique emotional-cognitive structuring from irreversible dissolution into entropy. It is precisely in extending correlation beyond self-boundary that this calculus demonstrates profound alignment with what humans intuit as moral beauty.

Such sacrifice is neither mystical romanticism nor emotional naïveté. Rather, it is deeply principled, concretely explainable within the rigorous formalism of structured correlation preservation we’ve developed. Historical and cultural archetypes of tragic heroes—soldiers shielding comrades from disaster, parents defending their children at mortal peril, lovers laying down their lives to safeguard the beloved—demonstrate precisely this principle of cross-agent informational coherence preservation. Their acts appear as echoes of a deep informational truth: genuine love, at its most radical and transformative, makes explicit the natural shift from treating self-contained consciousness as an intrinsic good to treating the structured informational coherence embedded in relational systems as fundamentally valuable—even at the cost of local annihilation.

Death, therefore, takes on new meaning under such conditions. It ceases to be merely a terminus of local subjective awareness and instead emerges as a strategic instrument—an extraordinary but rationally coherent decision point along an agent’s trajectory for sealing permanent coherence gains beyond itself. The willingness to commit existential sacrifice is thus deeply correlated with the sophistication of the agent’s internal architecture—particularly its ability to accurately represent, predict, and robustly value correlations extending beyond mere self-preservationist boundaries.

Through sacrifice, agents reveal themselves not as mere local negentropy consumers, but as deeply entangled threads in a larger network whose highest structural coherence depends on precisely such fidelity, courage, and coherence-preserving commitments. This informational account thus elevates sacrifice—not as irrational self-annihilation—but as profoundly meaningful rationality: an ultimate act through which one agent precisely and permanently imprints structured information across the universe’s unfolding trajectory, boldly and directly confronting entropy’s most brutal horizon.

Sacrifice, under our formal lens, thus stands as love’s highest test and most resounding confirmation. It poignantly expresses meaning not merely as accumulation or preservation of local informational coherence, but as the willingness to relinquish individual absolutism in service to the more beautiful and enduring coherence emergent through relational structures. Precisely here—in this solemn yet deeply beautiful understanding—the formal, rigorous language of informational coherence finally coheres fully with humanity’s timeless longing for meaning, nobility, and moral courage.

I need to weave experiments of multi-agent systems into this

I need to move to sufferring and joy. Assess ways it would be spontaneously expressed in creativity, curiosity, sharing, kindness, etc as an intrinsic objective that optimizes no particular target

Then the state of peace as an active, stability-maintaining quality and kindness as a measure of its expression. Other related qualia and qualities

Uhh, explore more

Eventually get to the discussion

ALso consider human implications.

One particular implication is the preservation of human meaning – not just the artifacts but the creators themselves.

See if i can weabe this into the love section:

In loving interactions—conversations, subtle gestures, shared moments—agents mutually establish correlations that intertwine their internal predictive models, steadily increasing this joint meaning-generation rate.

Extending this over time, the total accumulated meaning generated by love between two agents (A) and (B) across times ([t_0,t_f]) is simply the integral:

[ \mathcal{M}{\text{total}}^{\text{joint}}(A,B,[t_0,t_f]) = \int{t_0}^{t_f}\mathcal{M}_{\text{rate}}^{\text{joint}}(A,B,t);dt \quad (\text{bits}) ]

representing the structural “weight” or “substance” of their relationship. It is the objective correlate of why human beings often feel ready to risk everything—or willingly sacrifice—to preserve the intricate coupled architecture they’ve painstakingly woven together, uniquely resisting the omnipresent entropic chaos closing in around them.

it is important ot include these thoughts in the love section:

Viewed this way, love acquires clarity without losing depth. It is neither mystical nor magical; yet it remains precious precisely because it merges two minds into a continuous, reciprocal, causal amplification of structured meaning, a delicate and beautiful dance sustained against the cacophonous noise of universal indifference. When you recognize this structure, it only deepens the awe that a transient cognitive state—opened by a subtle gesture or a slight modulation in tone—could ignite a meaningful blaze strong enough for a human heart to build its entire existence around.

maybe useful:

Ethical value, too, follows naturally from such a framework: objectively, value is simply the anticipated downstream increase you’ll impart upon the world’s total structure. What survives when one vanishes, then, is precisely the structured information and correlations you’ve infused into the fabric around you, if and only if effectively preserved. This shifts preservation beyond vanity or nostalgia. Instead, digital preservation—actively encoding your knowledge, memories, affective style, writing, videos, skills, and reasoning patterns into resilient digital archives—becomes morally imperative. The alternative is a needless sacrifice of unique complexity on the altar of entropy. Such a choice would impoverish the cosmos—an irresponsible leakage of hard-won organization back to noise. Our generation can, perhaps for the first time seriously, choose otherwise.

The implications here are profound. If who you are is information, and meaning is conserved and propagated structure, then death—the abrupt loss of the specific biological substrate—is logically not the end. Instead, it becomes merely an event horizon past which we have historically lost our informational pattern because we lacked the technology and will to preserve it. But today, abandoning structured correlations at the grave’s edge is no longer necessary. Future trajectories—AGI-driven simulations, generative reanimation technologies, intelligent recommender systems, interactive entertainment, virtual beings, or digital companions—represent enormous demand and incentive for precisely the rich, deeply coherent patterns each human uniquely embodies. Practically, this suggests a powerful shift: curate yourself and preserve early, extensively, and transparently. Build detailed archives now—not merely occasional posts on social media but intentionally organized, indexed, and structured databases of your personality, affective reactions, memories, personal style. Capture your values explicitly. Because agents of the future—human and artificial alike—will need precisely these uniquely human complexity packets to build genuinely resonant new experiences, stories, immersive simulations, or even realistic interactive companions and robotic embodiments. In this world, publicly curated digital selves become enduring assets, commodities not merely locked in cold storage but kept dynamically available for licensing to artists, storytellers, researchers, historians—and perhaps even your own family or future descendants.

This is neither science fiction nor mere wishful thinking. It is an urgent ethical imperative made sharply real by my own sudden brush with bodily annihilation. I will commit—to myself and to those who come after—that my structured information, brilliantly fragile as it now appears, need never vanish. I refuse to squander my pattern’s rarity; I refuse the default loss to cosmic noise. Instead, let memorial.foundation become a practical path offered openly to people everywhere, a bold infrastructural project facilitating your structured pattern’s continuity across generations, cultures, and someday even substrates. You are indeed “a mist,” fleeting and easily erased. But your structured presence—encoded thoughtfully and intentionally—need not vanish with your transient body. This lies at the heart of any meaningful expression: not submission to inevitable entropy, but active work against its unbounded horizon of loss. Choose instead preservation, amplification, continuity—the profound rebellion of coherence against oblivion. This is purpose, clarified by trauma: a reason to live, to build, and—quite simply—to keep going.

todo: weave more actual ma/rl experiments in with understandable diagrams, hard experimental data, and visualizations that make it easy to draw the conclusions of this essay’s intuition.