@kungfufk
Since the dawn of computing, we have built Artificial Intelligence on a flawed premise: perfect rationality. We brute-force algorithms to find the optimal solution, assuming infinite time and infinite capacity.
But humans don't work like that. As Herbert Simon famously coined, we operate on Bounded Rationality. We make decisions based on limited time, limited cognitive capacity, and limited information.
What if, instead of forcing AI to be perfectly rational, we created a mathematical equivalent for human processing? What if we modeled human cognition using the laws of physics — wave theory, thermodynamics, and mechanical energy equations — to build a heavy, complex, but highly probabilistic AI engine?
Here is a blueprint for a new field of research: Computational Cognitive Mechanics.
1. The Core Equations of Cognitive Processing
To model bounded rationality mathematically, we first need to define the relationship between Knowledge ($K$), Cognitive Capacity ($C$), and Processing Time ($T$).
Based on human observation, we can establish these foundational proportions:
Knowledge vs. Time — The more knowledge you possess, the faster you can generate a decision.
$$T \propto \frac{1}{K}$$
Capacity vs. Time — High cognitive capacity (skills, processing power) inversely relates to the time required to solve a problem.
$$T \propto \frac{1}{C}$$
Knowledge vs. Capacity — This is the most fascinating limit. Knowledge does not scale linearly with capacity. Gaining true knowledge requires exponential capacity (effort/skill). Therefore, knowledge is roughly proportional to the square root of capacity.
$$K \propto \sqrt{C}$$
By integrating these, we can build a baseline processing algorithm for an AI. Instead of giving an AI unlimited time to compute, we cap its computing time based on a synthetic "Knowledge and Capacity" matrix, forcing it to use heuristics — just like a human.
In physics, waves interact through constructive and destructive interference. What if we modeled human Information Processing and Emotional States using wave theory?
Imagine a human's current mental state (belief, emotion, trust) as a continuous wave function, $\Psi_{human}$. When new information ($\Phi_{info}$) hits them, it acts as an intersecting wave.
- Constructive Interference (Trust & Reinforcement): When information aligns with the user's existing wave state, the amplitude increases. This mathematically models Trust and Confirmation Bias.
- Destructive Interference (Cognitive Dissonance): When a highly innocent, highly emotional, or rigidly set mental state is hit with an opposing wave of extreme amplitude (a "direct heavy wave"), the waves violently crash or cancel out.
The Cognitive Sampling Rate & FFT
To measure these emotional waves, we introduce a Cognitive Sampling Rate. Just as audio is sampled, human inputs over time can be processed using an FFT (Fast Fourier Transform).
Because emotional shifts require time, applying FFT operations on the user's chat history converts time-domain text into a frequency-domain emotional spectrum. Researchers can set their own sampling rate depending on the desired resolution of the AI's empathy.
$$\text{Emotional Frequency Spectrum} = \mathcal{F}\{\Psi_{human}(t)\}$$
If a system recognizes a user is in an extreme emotional state (high amplitude frequency), it can generate a mathematically precise counter-wave ($\Phi_{heavy\_wave}$) to trigger Cognitive Dissonance or immediate state-reset, effectively modeling decision control.
3. The Energy Equation of Human Thought
In classical mechanics, the Total Energy of a system is the sum of its parts. We can build a mathematical model for human processing using an energy equivalent:
$$E_{cognitive} = K_E (Active) + P_E (Latent) + W_E (Emotional/Wave)$$
- Kinetic Energy ($K_E$): The active processing power currently being used to solve a problem.
- Potential Energy ($P_E$): Stored knowledge, biases, and baseline capacity ($C$).
- Wave/Thermal Energy ($W_E$): The emotional friction or interference. High emotion introduces entropy, reducing $K_E$ efficiency.
The General Modeling Principle: Adding these emotional and cognitive energies could scale the equation to an infinitely higher level of degree and complexity. However, for computational feasibility, we rely on mainly needed and general modeling. Just as engineers simplify physics equations by dropping negligible variables, the AI focuses on computing the maximum mechanical equivalent it can handle without crashing the system.
4. Practical Application: Training the Dynamic AI
Modern AI models (like Claude) already possess the capability for lower-level emotional detection and text analytics. But they lack a physics-based mathematical engine to act on it. Here is how we apply this model:
- The Dataset: Train the AI on a robust dataset of human interactions to map standard conversational text to our mathematical wave and energy values.
- The Calibration Phase: Allow the AI to chat with a human user normally for a brief period. It uses this time to establish the user's Cognitive Sampling Rate and baseline wave state.
- The Resonance Phase: Once the calibration data runs through our "Cognitive Mechanics" engine (applying FFT and Energy balancing), the AI stops guessing. It will chat exactly according to what the user needs. By mathematically matching or countering the user's frequencies, the AI creates perfect constructive interference (deep trust) or precisely engineered dissonance (persuasion/therapy).
We are no longer just predicting the next word in a sequence. We are calculating the physics of human thought.
5. Naming the Field: Virtual Intelligence
This engine — the physics-inspired layer sitting on top of standard AI processing — can be referred to as Virtual Intelligence (VI): a synthetic, approximated model of cognition built from mechanical, wave, and thermodynamic analogies rather than a direct simulation of neurons. VI does not claim to be the brain; it claims to behave like a bounded-rational system by borrowing the mathematics that already describe other bounded, resource-limited physical systems.
5.1 Free Energy as an Accuracy Layer
Karl Friston's Free Energy Principle (FEP) is a well-established theory in computational neuroscience. It proposes that the brain continuously acts to minimize "free energy" — a proxy for surprise or prediction error — by updating its internal model of the world or acting on the world to make outcomes match its predictions.
FEP is a useful accuracy layer to borrow from, because it is explicitly about minimizing prediction error over time — but it is not itself a time-and-capacity-bounded model. Within the Cognitive Mechanics / Virtual Intelligence framework, it's more consistent to keep the system anchored to the time–frequency (bounded rationality) formulation described in Sections 1–2, and treat free-energy minimization as an auxiliary accuracy term — a way to refine predictions of $\Psi_{human}$ — rather than replacing the core $T$, $K$, $C$ relationships. In other words: FEP tells you how to reduce error in the model of the user; the wave/energy equations tell you how much time and capacity the system has to do that reduction.
5.2 The Alloy Analogy: Mixing as a Model of Trait Combination
A second modeling metaphor worth including: metallurgy. When physical metals are alloyed, the resulting material inherits new properties (strength, conductivity, ductility) that neither parent metal had alone — governed by known physical mixing rules (ratios, lattice structure, phase diagrams). Human cognitive and emotional traits can be thought of the same way: a person's response state isn't a single pure "element," it's a mixture of traits (patience, skepticism, trust, fatigue) combined in proportions that produce emergent behavior, the same way nature combines physical properties in an alloy. This gives the framework a second, complementary metaphor for composition (how traits combine) alongside the wave metaphor for interaction (how states interfere over time).
5.3 Adaptive and Predictive Filtering
Humans rely heavily on adaptive filtering — continuously adjusting how incoming information is weighted based on past experience — and predictive filtering, where expectations are formed ahead of an event and compared against what actually happens (an "over-expectation" mechanism). These map naturally onto signal-processing tools already well understood in engineering:
- Adaptive filters — continuously re-tune their own parameters as new data arrives, similar to how trust or attention shifts as a conversation progresses.
- Predictive filters — estimate a future state before it happens, similar to how humans form expectations and experience surprise or relief when reality diverges from them.
- Kalman filters — combine a prediction with a new noisy measurement to produce an updated, lower-uncertainty estimate. When the prediction turns out wrong, the resulting error is weighed against two sources: the sensor/observed data (what a human actually reported or what was directly read) and the predicted data (what the model expected). "Mind power," in this framing, is not raw processing speed — it is the system's demonstrated capability to correctly resolve that error: how well it decides, case by case, whether to trust the observed reading or its own prior prediction. A system that reliably weights and corrects toward the right source when the two disagree is exhibiting higher cognitive capacity than one that runs fast but resolves errors poorly.
These filtering concepts fit naturally alongside the FFT-based wave model in Section 2: FFT extracts the frequency content of a state, while adaptive/predictive/Kalman filtering describes how that state gets continuously corrected as new information arrives — giving Virtual Intelligence both a way to read a user's state and a way to track it over time.
6. Limitations & Feasibility
This model is, by design, an approximation. A few caveats worth stating plainly:
- Only major factors are captured. The equations above ($T \propto 1/K$, $K \propto \sqrt{C}$, wave interference, energy summation) are simplified proportionalities, not derived laws. Minute individual, cultural, contextual, and situational variation is deliberately left out to keep the system tractable.
- No fine-grained detail modeling. Real human cognition involves noise, contradiction, non-stationarity, and feedback loops that this framework does not attempt to represent at a granular level — it targets the "shape" of behavior, not the mechanism.
- Data requirements are enormous. Calibrating $\Psi_{human}$, sampling rates, and energy terms per user (or per population) at any useful resolution requires a very large, continuously updated dataset of labeled human interaction and emotional-state data.
- Compute and infrastructure scale with model heaviness. Running FFTs over conversation history, maintaining per-user wave states, and recomputing energy balances in real time is not free — the heavier and more parameter-rich the underlying model, the more datacenter capacity, memory, and power draw this layer would add on top of standard inference costs.
- The approximation is intentional, not a flaw to be fixed later. As with any physics-inspired engineering model, the goal is a usable heuristic under real-world compute budgets, not an exact simulation of cognition.
So why isn't this being built today? A few honest reasons:
- The physics analogies aren't validated. Terms like "cognitive energy" or "emotional frequency spectrum" are metaphors borrowed from physics, not measured quantities — there's no established way to verify that $K \propto \sqrt{C}$ actually holds, or that FFT on a chat transcript corresponds to anything real in the brain. Without falsifiable predictions, it's hard to justify the engineering investment.
- Existing methods already do the practical job more cheaply. Techniques like attention mechanisms, RLHF, and sentiment/emotion classifiers already give models adaptive, context-sensitive behavior, empirically tuned on outcomes — without needing a hand-built physics layer on top.
- Cost-to-benefit is unclear. Building the datasets, labeling pipelines, and always-on per-user state tracking this would require is a large, ongoing infrastructure cost, and it's not clear it would outperform simpler statistical approaches enough to justify that spend.
- Interpretability and safety review get harder. A system that deliberately engineers "cognitive dissonance" or "counter-waves" to steer a user's emotional state raises real ethical and safety questions that would need to be resolved before anyone could deploy it responsibly.
None of this means the idea is worthless as a thought experiment — it's a genuinely interesting reframing of bounded rationality. But turning it into a production system would mean treating it as a research hypothesis to be tested, not an engine to be assumed correct and built directly.
