Mind Wave Model — Mathematical Simulation of Cognition

Mind Wave Model — Mathematical Simulation of Cognition

Why do human cognition, emotion, and decision-making differ so dramatically between individuals? Why do two people placed in the same situation react in completely different ways?

This research independently incorporates concepts from neuroanatomist Dr. Jill Bolte Taylor's 4-Character Model into the TAP Wave Propagation Theory developed at the Minami Laboratory, Graduate School of Management, Kyoto University, to provide a mathematical framework for these questions. Note that this is not a collaboration with Dr. Taylor; the Minami Laboratory independently modeled the concepts inspired by her published work. By treating information as "waves" rather than "particles" and simulating how they pass through four cognitive filters (kernels), we quantitatively describe how what people perceive as "reality" is reconstructed.

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1. Model Overview

1.1 The Four Cognitive Characters

Neuroanatomist Dr. Jill Bolte Taylor, based on detailed self-observation during her recovery from a stroke, proposed that four cognitive functions (characters) coexist simultaneously in the human brain. This model adopts her classification as its foundation.

Character	Brain Region	Role	Lens Properties
A1 (Drive)	Left brain, thinking	Goal pursuit, analysis	Narrow, sharp focus. Amplifies opportunity, overlooks danger
A2 (Anxiety)	Left brain, emotion	Threat detection, vigilance	Narrow, sharp focus. Amplifies threat, overlooks opportunity
A3 (Curiosity)	Right brain, emotion	Curiosity, creativity	Wide field of view. Sees the whole as it is
A4 (Observer)	Right brain, thinking	Meta-cognition, observation	Widest field of view. Sees reality with minimal distortion

What people experience as "reality" is an image reconstructed through the filters of these four characters. Depending on which character is dominant, the same event is perceived as entirely different "realities."

1.2 Integration with TAP Wave Theory

In this model, external information is treated not as "particles" but as "waves" that pass through four kernels (lenses). Each kernel applies three effects — decay, temporal misalignment, and character-specific bias — and the image reconstructed after passage becomes that person's perceived "reality."

The accuracy of reconstruction is quantified as cognitive quality Q, where $Q = 1$ represents perfect reconstruction of reality and $Q < 0$ means distortion exceeds the actual signal.

1.3 Alpha–Beta Separation

The model cleanly separates universal laws (Beta) from individual differences (Alpha).

• Beta (universal laws): Kernel functional forms, three theorems (Circle of Competence, exponential degradation, lens effect), 90-second natural decay of emotional waves
• Alpha (individual parameters): Each character's center, $\gamma$, $\sigma$, bias, $\tau$, weight

The weights $w_i$ of the four characters are normalized to sum to one:

$$w_1 + w_2 + w_3 + w_4 = 1$$

This normalization condition is the mathematical foundation for many of the findings described below.

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2. Six Findings from Simulation

Finding 1: A wider field of view sees reality more accurately

A right-brain perspective (low $\gamma$, wide field of view) can reconstruct reality roughly twice as accurately as a left-brain perspective (high $\gamma$, narrow focus). Gazing at the whole picture is ultimately more accurate than analyzing details.

Finding 2: Rumination exponentially degrades cognitive quality

For a number of re-processing iterations $N$, the signal-to-noise ratio (SNR) degrades exponentially:

$$\text{SNR} = \frac{1}{e^{N\sigma^2} - 1}$$

1–3 iterations are safe, but beyond 10 the signal collapses rapidly, and at 20 iterations contact with reality is lost. "The more you think, the better your judgment" is mathematically false.

Finding 3: Emotional waves naturally decay in 90 seconds

The chemical reaction underlying an emotional wave disappears naturally in approximately 90 seconds. If you are still suffering after 90 seconds, it is because you thought about the same thing again in your mind, re-exciting the wave.

Finding 4: As anxiety grows, the capacity to observe automatically disappears

Due to the normalization condition $\sum w_i = 1$, when the weight of A2 (anxiety) increases, the weight of A4 (observer) mathematically and automatically decreases. No one is intentionally suppressing it — it is an inevitable consequence of the normalization structure.

Finding 5: Simply "noticing" restores cognitive quality

The act of noticing — "Ah, my anxious self is shouting right now" — is itself an activity of A4. When A4's weight rises, A2's relative proportion falls through normalization. You don't need to eliminate anxiety. Just noticing changes the structure.

Finding 6: Rest means stopping judgment, not stopping the brain

Even during rest, the brain remains active. But the cessation of action-judgment reduces input to A2 to zero, allowing A4 to relatively recover. Short, frequent rest is more effective than long breaks.

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3. Case Study: A New Employee's First-Day Resignation

As an application of this model, we analyze a scenario in which a new employee used a resignation agency to quit on their very first day.

3.1 Background

The following is a simulation based on a scenario in which a new employee used a resignation agency to quit on their first day.

A new employee used a resignation service to quit after just one day. No particular pressure had been applied, and many others in the same cohort stayed. Why does this happen?

From the company's perspective, the situation appears "normal" — but the new employee's experience does not necessarily align with that perception. Below, we use the model to analyze why the same environment can become an entirely different experience depending on the individual.

3.2 Differences in Cognitive Structure: A Three-Type Comparison

The model's simulation shows three cognitive types reacting differently to the same workplace environment.

Type	A1 (Drive)	A2 (Anxiety)	A3 (Curiosity)	A4 (Observer)	Q
A: Adaptive (majority)	27.0%	34.6%	17.9%	20.5%	+0.35
B: High anxiety	10.1%	80.4%	5.4%	4.1%	+0.08
C: Extreme anxiety	3.0%	94.4%	1.4%	1.1%	−0.04

In Type C, A2 occupies 94.4%, and the normalization law causes the other three characters to virtually vanish. A4 (observer) is reduced to just 1.1% — the capacity to objectively view one's own state is nearly gone.

3.3 Timeline of Day One

The simulation traces how Type C's cognition collapses over time.

Time	A2	Q	State
Night before	91.5%	+0.24	Cannot sleep due to tension
30 min after arrival	99.5%	−7.6	Sees environmental uncertainty
60 min	99.5%	−49.8	Some trigger occurs
90 min	99.5%	−383.6	Rumination: "I can't do this"
120 min	99.5%	−2854.9	Contacts resignation agency

Once rumination begins, Q collapses exponentially (Finding 2). With only 0.1% of A4 available to stop it, there is no brake.

3.4 Core Insight: Pressure Is Not Only External

For someone with extremely high A2, the new workplace environment itself is pressure. Unknown people, unknown rules, the gaze of evaluation — even if no one says anything, A2 continues scanning the threat side of the information space. Even when there is no actual threat.

They are viewing the same reality $V(\xi)$ through a different lens.

• A person with A2 at 30% → "A normal new workplace. I'll get used to it"
• A person with A2 at 94% → "A place where my survival is threatened"

What the company provided as "a normal work environment" became an entirely different reality through this person's lens. This is not a question of assigning blame to either side — it is a structural issue where the same reality becomes a different experience when processed through a different cognitive structure. This is precisely why environment design informed by an understanding of cognitive diversity becomes important.

3.5 Why a Resignation Agency?

The act of saying "I quit" directly appears to A2 as "reprimand, persuasion, confrontation." The ensuing rumination causes Q to collapse further (simulation value: $Q = -3462$), reaching a state where the person physically cannot speak.

A resignation agency eliminates direct contact with the threat. With input to A2 reduced to zero, it was the only option that could function for this individual.

3.6 Origins Are Compound

The model distinguishes three possible origins for this state.

Origin	A2 Characteristics	A2 Effective Value
High-stress childhood environment	$\sigma$ (distortion noise) is high → the world itself appears distorted	84.5%
Competitive/evaluative society	$\gamma$ (sensitivity) specialized toward evaluation → extreme reaction to "being watched"	72.1%
Innate sensitivity	$\gamma$ is extremely high → perceives the same stimuli more strongly than others	77.7%
All three combined (reality)	All overlap	93.8%

In reality, these origins are almost always compounded. "This is the cause" cannot be isolated to a single factor — this is the model's answer.

From the model's perspective, the boundary between psychological distress and wellness lies not in "the level of A2" but in "the level of A4." Even with A2 at 80%, if A4 is at 15%, the person can function despite suffering. But when A2 reaches 94% and A4 drops to 1%, "the brake no longer exists." Whether this is called a psychological condition is a matter of clinical diagnosis. In model terms, it is a state where A4 is structurally unable to function. It is not a matter of willpower or effort.

3.7 Possible Interventions

Had the model's insights been available beforehand, the following interventions could have been considered.

Intervention	A2	Q
No intervention (actual)	99.5%	−195
A: Detailed advance explanation of the day's schedule	99.2%	−4.3
B: Explicitly stating "You don't need to memorize anything today, just observe"	94.6%	−1.3
C: First day in a quiet, one-on-one setting	96.1%	−2.0
A+B+C combined	86.6%	+0.07

Combining all three interventions nudges Q just barely into positive territory. The meaning of each:

• A (advance explanation): Prevents A2 from converting uncertainty into "threat." Eliminates room for imagination
• B (removing evaluation): Pre-emptively eliminates the largest input to A2 ("What if I fail?")
• C (reducing the environment): Physically reduces the volume of threat that A2 can detect

Note, however, that A2 remains at 86% even with all interventions combined. The essence of intervention is not "lowering A2" but rather reducing threat-side input to a level where collapse is prevented even with high A2.

Crucially, all of these interventions are things the organization can design. Changing an individual's cognitive structure is difficult, but changing the design of the environment is possible. Designing onboarding processes that account for cognitive diversity is key to preventing attrition.

3.8 The Incubator Group Concept

We simulated the effect of an "incubator group" — a structure where A3 (curiosity) and A4 (observer) are nurtured in an evaluation-free, safe environment before transitioning to core work.

Conventional Path (hired → immediate core work)

Week	A1	A2	A3	A4	Q	Status
0	0.3%	99.5%	0.1%	0.1%	−168	Day one → at limit
2	0.3%	99.5%	0.1%	0.1%	−414	Resignation or leave

Incubator Path (3 months → core work transition)

Week	A1	A2	A3	A4	Q	Phase
0	0.3%	99.5%	0.1%	0.1%	−170	Incubator begins
6	0.5%	97.8%	0.9%	0.7%	−4.9	Incremental change
11	9.6%	52.7%	19.4%	18.4%	+0.47	A3 and A4 bloom
12	9.7%	47.1%	22.4%	20.8%	+0.27	Core work transition
17	6.1%	84.6%	1.6%	7.7%	−0.47	A2 rises again
23	0.5%	97.3%	1.2%	1.0%	−5.1	Returns near original state

A dramatic shift occurs at week 11. In an evaluation-free, safe environment, A3 spontaneously ignites and A2 drops to 52.7%. However, after transitioning to core work, A2 rises again, and the A3/A4 nurtured during incubation are overwhelmed by anxiety from the work environment.

Comparison	Conventional	Incubator
A2 at core work entry	99.5%	74.8%
A4 at core work entry	0.1%	12.6%
Q at core work entry	−168	−0.11

The improvement is substantial. "First-day resignation" transforms into "a self-determined decision after three months."

Four conditions for an incubator group to function:

Condition	Why It Matters
1. No evaluation	Ask only "Was it interesting?" — not "Did you succeed or fail?"
2. No output requirements	No deadlines or quality standards. Rumination naturally settles to 1–2 iterations
3. Seniors act as fellow learners	A senior's A3 propagates to the newcomer's A3
4. Connection to core work revealed only after month 3	Saying "This is for work" from the start re-triggers A2

Honest limitations: What the incubator can provide is transforming "resignation on day one" into "a decision the individual makes after three months" — not a guarantee of continued employment. Yet this represents an entirely different outcome for both the individual and the organization. The true value of the incubator may not be preventing attrition, but rather creating a state where individuals can make decisions of their own volition.

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4. Summary and Future Directions

What the Model Shows

1. Each person sees reality through a different lens (Alpha). The same situation becomes an entirely different experience depending on the individual
2. Rumination exponentially destroys cognitive quality. Thinking itself can make the problem worse
3. Simply "noticing" (activating A4) changes the structure. There is no need to eliminate anxiety
4. Environmental design can prevent collapse even with high anxiety. Controlling input volume is key

Future Research Directions

To empirically validate and broaden the applicability of this model, the following research is needed:

• Development of methods for estimating Alpha parameters in laboratory settings
• Quantitative validation of changes in cognitive quality Q before and after interventions
• Applied research in education, organizational design, and mental wellness
• Theoretical integration with other cognitive science models

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Technical Information

TAP Wave Propagation Theory

TAP (Tomographic Asset Pricing) theory is a mathematical model of information propagation developed at the Minami Laboratory, Graduate School of Management, Kyoto University (Shotaro Minami, Ph.D.). It treats information as "waves" rather than "particles" and derives three theorems based on isomorphism with scattering physics (the paper is currently under journal review). This project applies the theory from financial markets to human internal cognition.

Jill Bolte Taylor's 4-Character Model

A model of the brain's four cognitive functions proposed by neuroanatomist Dr. Jill Bolte Taylor. Based on self-observation during recovery from a stroke, it systematizes four functions: left-brain thinking, left-brain emotion, right-brain emotion, and right-brain thinking. This research is not a collaboration with Dr. Taylor; the Minami Laboratory independently modeled the concepts inspired by her published work.