Content uploaded by Robert Fuchs
Author content
All content in this area was uploaded by Robert Fuchs on Nov 16, 2024
Content may be subject to copyright.
Content uploaded by Robert Fuchs
Author content
All content in this area was uploaded by Robert Fuchs on Oct 27, 2024
Content may be subject to copyright.
Content uploaded by Robert Fuchs
Author content
All content in this area was uploaded by Robert Fuchs on Oct 27, 2024
Content may be subject to copyright.
1
Pseudomorph: A Quantum-Geometric Model of Consciousness
for Psychotherapy Based on PSL(2,7), Semantic Differentials,
Universal Symmetry Principles, and Connections to
Neuroscience
Robert.Fuchs@HappinesGroup.eu
Abstract:
This paper introduces Pseudomorph, a novel quantum-geometric model of consciousness and
psychotherapy that integrates the symmetry group PSL(2,7), semanc differenals, and principles of
informaon theory. Drawing connecons with modern neuroscience—such as Karl Friston’s acve
inference and free energy principles, as well as holographic brain models—Pseudomorph links
unconscious, subconscious, and conscious states through a unified framework of symmetry. False
beliefs about the self are modeled as deviaons from natural symmetries, measured using the
Kullback-Leibler (KL) divergence. This paper proposes a new theory of mind and offers a structured
approach to psychotherapy based on universal principles.
Keywords: Pseudomorph, quantum cognion, symmetry, group theory, PSL(2,7), cognive
distorons, free energy principle, acve inference, psychotherapy, semanc differenals, Kullback-
Leibler divergence, neuroscience, mental health, cognive realignment, neuropsychiatry, holographic
brain theory, fourth way, Euler-Bernoulli beam equaon, Pilot Wave Theory.
1. Introducon
Background
The study of consciousness, a profound and complex facet of human cognion, spans numerous
disciplines. Tradional cognive models typically conceptualize consciousness as a linear sequence of
cognive processes—percepon, reasoning, and decision-making—that operate in a determinisc
manner. Yet, these classical models oen fall short in explaining the non-linear, dynamic nature of
human thought. Emerging models rooted in quantum cognion have begun to address this limitaon
by drawing on principles from quantum mechanics. These quantum-inspired approaches emphasize
probabilisc and indeterminate elements in decision-making, especially under ambiguous
circumstances, thus enabling more nuanced models of memory and choice. However, despite these
advancements, a robust integraon with neurobiological processes remains elusive.
Quantum cognive models suggest that human thought, akin to quantum systems, exists in a
superposion of possibilies, resolving into a parcular state upon decision or acon. These models
excel in capturing the intrinsic uncertainty and probabilisc aspects of cognion but lack a cohesive
framework linking cognive phenomena to underlying mathemacal structures or universal natural
principles.
Advances in neuroscience, parcularly through Karl Friston’s work on acve inference and the free
energy principle, have introduced compelling models that view the brain as a predicve mechanism.
This framework proposes that the brain connuously refines its internal models to minimize “free
2
energy” or predicon error by aligning sensory inputs with prior expectaons. Such a predicve
architecture resonates with cognive processes, wherein symmetry-breaking distorons in thought
may reflect the brain’s efforts to minimize predicon errors. In addion, holographic models of brain
funcon suggest that cognive operaons are distributed and holisc, implying that any part of the
brain can represent the whole, reflecng the deeply interconnected nature of human cognion.
Introducon to Group Theory and PSL(2,7)
Group theory, parcularly through the finite simple group PSL(2,7), provides an abstract
mathemacal framework for describing symmetries. PSL(2,7), a group with 168 elements, is notable
for its structured and finite nature, allowing it to define symmetrical properes and transformaons.
This makes it a promising candidate for modeling cognive processes, as its symmetry principles may
serve as analogies for mental states that maintain coherence or balance over me. In cognion,
symmetry reflects states of equilibrium in thought or emoon, while symmetry violaons—cognive
distorons—can manifest as false beliefs, irraonal fears, or inconsistent emoonal responses.
The Intersecon of Cognive Science, Neuroscience, and Group Theory
A growing area of research seeks to integrate cognive science, neuroscience, and mathemacal
principles to advance a unified theory of mind. The proposed model, termed "Pseudomorph,"
combines the geometric structure of group theory, parcularly PSL(2,7), with neuroscienfic
principles, such as acve inference and holography. This model posits that cognive distorons
represent deviaons from natural symmetries, which can be quantavely idenfied and adjusted.
Such a framework not only provides a theorecal basis for understanding cognive distorons but
also offers a pathway for therapeuc intervenon, enabling the correcon of false beliefs and
alleviaon of cognive dissonance.
Objecve of the Paper
To introduce Pseudomorph as a comprehensive model: This paper presents Pseudomorph, a model
that synthesizes quantum cognion, group theory, and neuroscience to advance a unified framework
for consciousness. By leveraging the symmetry group PSL(2,7), Pseudomorph offers a geometric and
algebraic structure for understanding consciousness. The model incorporates semanc differenals—
scales that assess how individuals ascribe meaning to their experiences and emoons—thereby
linking beliefs, emoons, and cognive processes to fundamental principles of symmetry.
Furthermore, informaon-theorec measures, such as Kullback-Leibler (KL) divergence, are employed
to quanfy deviaons from an idealized “true self.” Such deviaons are conceptualized as symmetry
violaons, reflecng the brain’s tendency toward balance and coherence, as described by Friston’s
free energy principle.
To propose Pseudomorph as a structured framework for psychotherapy: This paper also posits
Pseudomorph as a praccal framework for psychotherapy. By idenfying and addressing cognive
distorons—interpreted here as disrupons in cognive symmetry—the model provides a structured
approach to diagnosing and treang psychological disorders. Grounded in universal principles that
transcend individual differences, this approach moves beyond subjecve assessment, offering
therapists a systemac and objecve model for intervenon. Pseudomorph aligns with the brain’s
innate drive for symmetry and order, integrang the symmetry structures from group theory with the
free energy minimizaon observed in neuroscienfic models. This integraon allows for a disncve
approach to understanding the architecture of the mind and implemenng therapeuc strategies to
correct distorted paerns of thought.
3
2. Theorecal Foundaons
Symmetry and Group Theory in Cognion
Explanaon of the Symmetry Group PSL(2,7) and Its Finite Structure in Cognion
The projecve special linear group, PSL(2,7), is a highly structured mathemacal group comprising
168 elements, each represenng transformaons on a two-dimensional vector space over a finite
field with seven elements. This group is notable for its finite nature and inherent symmetry, making it
an ideal framework for modeling bounded cognive structures. The finite structure of PSL(2,7) aligns
with the limited yet complex nature of human cognion, allowing for a closed and comprehensible
model of cognive operaons.
In the context of cognion, the elements of PSL(2,7) can be interpreted as fundamental cognive
transformaons or shis in mental states. These transformaons resemble how the mind updates
beliefs, emoons, and percepons, paralleling how symmetry transformaons in physics describe
invariances or structured changes within physical systems. The 168 elements serve as disnct
cognive "states" or operaons that collecvely guide the evoluon of beliefs and mental processes,
forming the foundaonal units of cognive transformaons. When cognive processes align with
these symmetrical transformaons, the mind operates in a state of harmony, promong psychological
well-being. However, deviaons from these symmetries—when cognive processes fail to match
symmetrical operaons—manifest as cognive distorons or false beliefs, oen resulng in
psychological distress or emoonal imbalance.
The finite nature of PSL(2,7) is crucial for modeling cognion as it provides a complete and bounded
set of transformaons. This finiteness mirrors the brain’s inherent limitaons, including memory
capacity and finite neural resources, much like the constraints seen in bounded systems. Such
symmetry structures are thus not only reflecve of the brain’s cognive framework but also capture
the limited yet ordered structure within which the mind operates, parcularly over defined intervals.
Symmetry as a Universal Principle in Cognive Transformaons, Emoonal States, and Beliefs
Symmetry, a foundaonal concept across sciences such as physics and biology, serves as a powerful
metaphor and operaonal principle in understanding cognive processes. In cognive science,
symmetry manifests as the mind’s tendency to seek coherence and balance in beliefs, percepons,
and emoonal states. Just as natural systems strive for equilibrium, the mind operates by aiming for
symmetry across cognive transformaons.
Cognive transions, including belief updates and emoonal adjustments, can be viewed as shis
between symmetrical states. When beliefs align with reality, they occupy a symmetrical state of
coherence and stability, whereas misalignments with reality lead to symmetry violaons—
manifesng as cognive distorons and psychological discomfort. In Pseudomorph, the symmetry
group PSL(2,7) provides a precise framework to model these cognive transformaons, suggesng
that the mind’s natural state is one of symmetry. Deviaons from this symmetry correspond to
cognive errors or distorons, implying that restoring symmetry can lead to mental clarity, emoonal
stability, and alignment with one’s “true self.”
4
Figure 1: The road to reality
Integraon with Neuroscience
Connecon to Friston’s Acve Inference and Free Energy Principle
Karl Friston’s principles of acve inference and free energy minimizaon offer a compelling
neuroscienfic model that integrates well with Pseudomorph. According to Friston’s framework, the
brain funcons as a predicve system, constantly updang its internal models to minimize predicon
error or “free energy.” The brain generates predicons about sensory input and refines these
predicons to match the actual inputs it receives from the environment. This minimizaon of free
energy aligns predicons with reality, creang a state of cognive harmony. Conversely, mismatches
between expectaons and reality elevate free energy, signaling cognive dissonance or error.
The Pseudomorph model parallels Friston’s concept of free energy with cognive symmetry.
Symmetry violaons in Pseudomorph represent elevated free energy states, where cognive beliefs
or emoons diverge from reality. False beliefs can thus be viewed as predicve errors within the
brain’s internal model, leading to misalignments with reality. Using Kullback-Leibler (KL) divergence as
a metric, Pseudomorph quanfies these deviaons from the “true self” as instances of increased free
energy. The greater the KL divergence, the more pronounced the cognive distoron, highlighng a
disconnect between beliefs and reality. Reducing this divergence aligns with reducing free energy,
fostering cognive and emoonal stability by minimizing dissonance and promong equilibrium.
Symmetry within PSL(2,7) as a “Low Free Energy” State
The elements of PSL(2,7) can be understood as cognive states associated with low free energy, or
states where predicon error is minimized. When an individual’s cognive and emoonal processes
align with these symmetrical states, they experience coherence and stability, indicave of
psychological well-being. In this low free energy state, the brain’s internal models are congruent with
reality, achieving cognive harmony.
5
Just as the brain minimizes free energy to opmize cognive funcon, Pseudomorph posits that the
mind naturally strives for symmetry. False beliefs, cognive distorons, and emoonal dysregulaon
can all be conceptualized as high free energy states, where symmetry is disrupted. By mapping
cognive processes onto the symmetrical structure of PSL(2,7), Pseudomorph provides a framework
for idenfying areas of cognive dissonance and working to restore symmetry, thereby reducing
predicon error and fostering mental balance.
Holographic Brain Models and Symmetry
The holographic brain model suggests that cognion is distributed, with each part of the brain
containing informaon about the whole. This model implies that cognive funcons are not localized
but instead interconnected, with each process reflecng part of an integrated cognive system, much
like a hologram. In Pseudomorph, the elements of PSL(2,7) represent individual cognive
transformaons, yet each transformaon contributes to a comprehensive, interconnected mental
structure.
This holographic nature of thought aligns with the symmetrical structure of PSL(2,7), where each
cognive element not only represents a specific transformaon but also reflects the relaonships
between transformaons. By treang cognion as a holisc system governed by symmetrical
operaons, Pseudomorph suggests that even small cognive distorons can affect the overall
structure of thought. Thus, therapeuc intervenon can focus on restoring global cognive symmetry
by addressing local distorons.
Cognive Layers in Pseudomorph
Unconscious, Subconscious, and Conscious States
In Pseudomorph, consciousness is modeled as a mul-layered system encompassing unconscious,
subconscious, and conscious states, each interconnected through symmetrical transformaons.
Cognive processes within these layers operate under the constraints of the symmetry group
PSL(2,7), which provides structure to the transions between these states.
The unconscious mind contains fundamental drives, insncts, and movaons, oen operang
automacally. The subconscious layer bridges unconscious impulses and conscious thought,
processing learned behaviors and semi-conscious responses. The conscious mind acvely engages
with surroundings, forms beliefs, and makes decisions, encapsulang self-reflecve thought.
Pseudomorph suggests that transions between these layers are guided by symmetrical
transformaons within PSL(2,7), where each transformaon represents a shi in mental state. This
structured progression supports balanced cognion across the layers of consciousness.
Progression from Unconscious to Consciousness, with Symmetry Violaons Leading to Cognive
Distorons
In Pseudomorph, consciousness progresses naturally from unconscious to subconscious and then to
conscious thought, forming a coherent self-percepon. This progression relies on symmetrical
transformaons, which allow unconscious impulses to integrate seamlessly into conscious reflecon.
When symmetrical transions are disrupted, cognive distorons arise, manifesng as false beliefs or
inaccurate percepons.
Symmetry violaons can impede the integraon of unconscious impulses, resulng in distorted self-
percepons that prevent personal growth. For example, unresolved unconscious conflicts may bias
subconscious processing, leading to inaccurate conscious beliefs. By mapping these cognive
6
distorons geometrically using the group-theorec structure of PSL(2,7), therapists can idenfy
disrupons in the cognive process and work to restore symmetry and coherence.
False Beliefs as Geometric Deviaons from Symmetry
False beliefs arise when the natural cognive symmetry within Pseudomorph is broken. These beliefs
represent asymmetrical deviaons from the “true self,” a balanced state where cognion aligns with
reality. In Pseudomorph, false beliefs can be mapped as deviaons from symmetry within PSL(2,7),
where misaligned elements or transformaons indicate cognive distorons. This geometric mapping
offers a precise way to idenfy distorons and provides therapeuc pathways to restore cognive
balance.
Figure 2: The three aspects of life and change, decision making and error dynamics
KL Divergence as a Measure of False Beliefs
Kullback-Leibler (KL) Divergence and Symmetry
Kullback-Leibler (KL) divergence measures the difference between two probability distribuons,
offering a way to quanfy deviaons from an individual’s “true self”—an ideal cognive state where
symmetry is preserved. The “true self” represents cognive harmony, with beliefs, emoons, and
thought processes aligned with reality. In Pseudomorph, KL divergence quanfies the misalignment
between an individual’s current state and this symmetrical baseline. High KL divergence indicates
cognive distorons, while low divergence suggests cognive balance and coherence.
False Beliefs as Symmetry Deviaons
In Pseudomorph, false beliefs represent deviaons from cognive symmetry, comparable to
predicve errors in Friston’s free energy model. These deviaons, measured as KL divergence,
indicate misalignments between an individual’s beliefs and their symmetrical “true self.” The greater
7
the divergence, the more distorted the beliefs, leading to psychological discomfort. Reducing KL
divergence, like minimizing free energy, restores cognive equilibrium.
Therapeuc Recalibraon through KL Divergence Reducon
Therapeuc recalibraon in Pseudomorph focuses on reducing KL divergence to realign an
individual’s beliefs with their natural symmetrical state. This process involves idenfying and
restructuring distorted beliefs to restore cognive symmetry. By using semanc differenals and
challenging cognive distorons, therapy aims to guide individuals toward coherence, reducing KL
divergence and restoring mental balance. This recalibraon aligns with Friston’s minimizaon of
predicon error, promong psychological well-being by aligning cognion with a state of equilibrium.
Conclusion
Pseudomorph offers a comprehensive framework that integrates unconscious, subconscious, and
conscious states through the principle of cognive symmetry. By employing KL divergence as a
measure of deviaons from the “true self,” Pseudomorph provides both a theorecal basis for
understanding cognive distorons and praccal therapeuc strategies for achieving cognive and
emoonal balance.
3. Semanc Differenals and Value Pairs
Introducon to Semanc Differenals
Overview of Semanc Differenals
Semanc differenals are a psychological tool developed by Charles Osgood to measure an
individual’s percepon of meaning and emoonal responses using bipolar value pairs. These pairs
consist of opposing qualies—such as good-bad, strong-weak, or acve-passive—that capture
subjecve connotaons associated with words, experiences, or beliefs. Semanc differenals provide
a way to quanfy how individuals evaluate or emoonally respond to various concepts along these
bipolar dimensions, offering insight into their cognive and emoonal landscapes.
In the Pseudomorph model, semanc differenals are instrumental in understanding an individual’s
cognive and emoonal structure. They allow for a structured analysis of how experiences, emoons,
and beliefs are interpreted by mapping these interpretaons onto specific value pairs. This approach
transforms complex psychological states into measurable dimensions, enabling precise evaluaon of
whether thoughts and emoons are aligned or misaligned.
Using Semanc Differenals to Decode Value Pairs in Psychological States
Semanc differenal scales break down cognive and emoonal states into core value pairs, offering
a detailed picture of how meaning and emoon are processed. For instance, a person may interpret a
scenario as both “good” and “acve” or “bad” and “weak.” These bipolar pairs reflect the
foundaonal structure of thought and emoon, granng insight into an individual’s underlying mental
framework.
In therapeuc contexts, these value pairs serve as diagnosc tools to assess alignment within an
individual’s thoughts and emoons. When a person persistently interprets neutral experiences as
negave, for example, it signals a potenal cognive distoron. Semanc differenals allow for these
imbalances to be mapped and addressed, providing a framework to realign misinterpretaons and
restore a more symmetrical state of mind.
8
Connecon to PSL(2,7) and Value Pairs
Mapping the 168 Elements of PSL(2,7) onto Semanc Differenal Value Pairs
The finite group PSL(2,7) encompasses 168 elements, each represenng transformaons that can be
mapped to semanc differenal value pairs. Each element of PSL(2,7) is associated with a specific
transformaon or operaon that corresponds to a bipolar pair, such as good-bad, strong-weak, or
asserve-passive. These pairs characterize the individual’s cognive and emoonal interpretaons of
the world.
These value pairs are fundamental units of cognive operaons, each represenng disnct aspects of
human cognion—such as evaluang risk (safe-dangerous), emoonal involvement (distant-close), or
moral judgment (right-wrong). The 168 elements of PSL(2,7) span the range of potenal cognive and
emoonal transformaons, providing a framework to represent shis in belief or emoonal
response. By mapping changes in these states onto PSL(2,7) transformaons, Pseudomorph links
cognive and emoonal states to the symmetrical structure of the group.
Value Pairs as Fundamental Units of Cognive Operaons
Alignment or misalignment of value pairs is key to idenfying cognive symmetry or asymmetry. In a
state of cognive symmetry, bipolar value pairs align with the individual’s true percepon and
emoonal understanding. However, when distorons arise—such as when neutral experiences are
consistently interpreted negavely or weakly—these asymmetries indicate cognive distorons.
Within the Pseudomorph model, false beliefs and emoonal misalignments are represented as
symmetry violaons, where cognive processes diverge from the natural, balanced structure
encoded by PSL(2,7). Therapy in this model focuses on realigning these value pairs with
corresponding symmetrical transformaons to restore cognive balance.
Connecon to Friston’s Acve Inference
Semanc differenals also connect with Friston’s acve inference framework, where each value pair
is viewed as part of the brain’s effort to minimize predicon error. According to acve inference, the
brain generates predicons about sensory input and adjusts beliefs to match incoming informaon,
reducing predicon error and achieving cognive harmony.
Within semanc differenals, each bipolar pair contributes to this predicon process. The brain
assigns a meaning to an event or belief along a dimension such as good-bad and updates this
evaluaon as new informaon arrives. Proper alignment of these value pairs minimizes free energy,
allowing cognive processes to funcon smoothly. When a mismatch occurs between an individual’s
evaluaon and reality, this misalignment heightens free energy and introduces cognive dissonance.
In Pseudomorph, aligning these bipolar dimensions within the framework of PSL(2,7) mirrors the
reducon of free energy, promong cognive symmetry and emoonal stability.
Building a New Theory of Mind
The Mind as a Dynamic System Striving for Symmetry
The Pseudomorph model proposes that the mind operates as a dynamic system constantly striving
for symmetry and balance. This symmetry is reflected in the alignment of value pairs, which organize
the mind’s interpretaons of meaning, emoon, and percepon. When the mind maintains
symmetry, cognive processes align with reality, resulng in balanced and well-regulated emoons.
9
Disturbances to this symmetry—whether through misaligned value pairs, false beliefs, or emoonal
dysregulaon—result in cognive distorons and psychological discomfort.
These distorons oen emerge from asymmetric thought processes, where value pairs become
skewed or misaligned. In therapy, idenfying and correcng these asymmetries is essenal for
restoring balance and allowing the mind to return to a natural state of symmetry.
The Pseudomorph Model’s Integraon of Value Pairs with PSL(2,7)
The 168 elements of PSL(2,7) serve as the mathemacal foundaon for Pseudomorph’s theory of
mind. These elements encompass possible transformaons of value pairs, ensuring cognive
processes and emoonal states remain within a structured and balanced framework. By integrang
value pairs into this symmetrical structure, Pseudomorph provides a model for understanding the
evoluon of thoughts and emoons.
When cognive processes deviate from the symmetrical structure of PSL(2,7), false beliefs and
emoonal imbalances arise. These deviaons can be mapped to specific transformaons within
PSL(2,7), offering a geometric and algebraic representaon of cognive distorons. In therapy,
symmetry is restored by idenfying misaligned value pairs and using PSL(2,7) principles to guide
realignment.
Symmetry-Based Cognion in Line with Acve Inference
Pseudomorph suggests that the mind naturally strives for states of minimal divergence—or low KL
divergence—from its true symmetrical self. Analogous to Friston’s acve inference model, in which
the brain minimizes predicon error to align with reality, Pseudomorph proposes that the mind seeks
symmetry-based cognion, reducing cognive and emoonal divergence from balance.
Aligned value pairs and minimal free energy result in cognive harmony, creang a balanced state
where beliefs, percepons, and emoons harmonize. Therapy within the Pseudomorph model aims
to reduce KL divergence, helping individuals align thoughts, emoons, and beliefs with their authenc
state of mind.
Summary
Pseudomorph offers a novel framework for understanding mind and cognion by integrang
semanc differenals and value pairs with the symmetrical structure of PSL(2,7). This approach
supports a new theory of mind grounded in symmetry-based cognion, connecng cognive and
emoonal processes with Friston’s principles of acve inference and free energy minimizaon.
Through the alignment of cognive processes with symmetrical operaons, Pseudomorph provides a
structured path for understanding and treang cognive distorons.
4. A New Psychotherapy Based on Universal Principles
Symmetry Violaons and Psychological Disorders
Common Psychological Disorders as Symmetry Violaons in Value Pairs
In the Pseudomorph model, psychological disorders like anxiety, depression, and obsessive-
compulsive disorder (OCD) are understood as manifestaons of symmetry violaons in cognive and
emoonal processing. These disorders indicate disrupons in the mind’s natural balance, leading to
10
misalignments between an individual’s internal beliefs, emoonal responses, and the reality of their
"true self."
Anxiety may arise from an overesmaon of threats or dangers, reflecng an imbalance in
the value pair (safe-dangerous). A cognive skew toward “dangerous” triggers excessive
worry and fear.
Depression oen stems from distorted evaluaons of self-worth or the future, where value
pairs such as (good-bad) or (hopeful-hopeless) become imbalanced, promong negave or
despairing outlooks.
OCD can be seen as a form of cognive rigidity, where certain value pairs (clean-dirty, order-
chaos) become fixated in an exaggerated or distorted manner, resulng in compulsive
behaviors that aempt to restore a sense of control or symmetry.
In each case, the cognive distorons reflect asymmetries in the value pairs that govern thoughts and
emoons. These imbalances lead to emoonal distress and maladapve behaviors, as individuals
strive—oen unsuccessfully—to restore a sense of order to their cognive world.
Integraon with Neuroscience: Psychological Distress as States of High Free Energy
According to Friston’s free energy principle, psychological distress is conceptualized as a state of high
free energy, where the brain’s predicons about the self and environment are misaligned with
sensory input and reality. This discrepancy generates predicon errors, leading to emoonal and
cognive discomfort.
In Pseudomorph, these high free energy states correspond to symmetry violaons in cognive
processing. A balanced mind minimizes predicon errors by aligning beliefs with reality, but when
predicons fail due to skewed value pairs, cognive dissonance and emoonal distress arise,
manifesng as psychological disorders.
Therapeuc Intervenons to Restore Symmetry and Reduce Predicon Error
Therapeuc intervenons within the Pseudomorph framework target the restoraon of symmetry in
cognive and emoonal processing. By idenfying misaligned value pairs, therapists can help
individuals realign their beliefs and emoonal responses, reducing predicon errors and restoring the
brain’s internal models to a more accurate reflecon of reality. This reducon in free energy fosters
cognive harmony and emoonal well-being, as the mind returns to a symmetrical state that reflects
the individual’s true nature.
Therapeuc Applicaons of Pseudomorph
Diagnosc Tool
Using Semanc Differenals and KL Divergence to Idenfy Cognive Distorons:
Pseudomorph provides a diagnosc approach for therapists to pinpoint cognive distorons
using semanc differenals and Kullback-Leibler (KL) divergence. Semanc differenals allow
therapists to assess how individuals interpret their experiences and beliefs by rang bipolar
value pairs. Consistent imbalances—such as rang neutral situaons as negave or
threatening—suggest cognive distoron.
KL Divergence as a Quantave Measure: KL divergence quanfies discrepancies between
an individual’s current belief system and their ideal, symmetrical state. High KL divergence
11
indicates significant cognive misalignment, while low divergence suggests alignment with
the true self. This diagnosc process enables therapists to track the deviaons in an
individual’s beliefs and emoons from their natural cognive symmetry.
Example: In depression, semanc differenals might reveal a skewed good-bad value pair, with the
individual perceiving neutral or even posive events negavely. Calculang KL divergence allows
therapists to measure the extent of this distoron, guiding the therapeuc process toward
realignment.
Therapeuc Intervenon: Cognive Realignment through Symmetry Restoraon
Therapy in the Pseudomorph model centers on cognive realignment by restoring the natural
symmetry that underpins healthy thought and emoonal processes. By targeng specific misaligned
value pairs—such as overesmaons of threat or underesmaons of self-worth—therapists assist
individuals in restructuring their beliefs to achieve a more balanced and truthful perspecve.
Specific Techniques Based on Pseudomorph’s Principles
1. Idenfy Asymmetries in Value Pairs: Semanc differenals help reveal areas of cognive
imbalance, such as overesmang danger or underesmang one’s abilies.
2. Map Distorons Using PSL(2,7): By mapping these distorons onto the symmetrical structure
of PSL(2,7), therapists gain a geometric and algebraic understanding of how cognive
processes deviate from symmetry.
3. Guide Cognive Restructuring: Intervenons then focus on correcng these asymmetries,
helping individuals develop balanced, realisc percepons of themselves and their
environment.
Alignment with Acve Inference
These intervenons align with Friston’s acve inference model, as therapy reduces predicon error
and cognive dissonance by bringing beliefs and emoonal responses closer to reality. As predicon
errors decrease, free energy is minimized, guiding the mind toward symmetry. This low-free-energy
state promotes cognive harmony, where thoughts and emoons align with the individual’s authenc
self.
Case Studies and Praccal Implementaon
Hypothecal Case Study: Social Anxiety
To demonstrate the Pseudomorph model in therapy, consider a hypothecal case of social anxiety:
1. Imbalance in Safe-Dangerous Value Pair: The individual consistently interprets social
situaons as dangerous, even when neutral or posive.
2. Semanc Differenals Reveal Overesmaon of Threat: Semanc differenal assessments
show that the individual overesmates threat in social sengs.
3. High KL Divergence: Calculang KL divergence shows a high degree of cognive distoron,
indicang significant misalignment with the individual’s true self.
12
In therapy, the therapist assists the individual in recalibrang percepons using symmetry restoraon
techniques based on PSL(2,7). As the individual’s percepons realign, their beliefs about social
situaons become more balanced, leading to reduced KL divergence and alleviated anxiety.
Implemenng the Model in Therapy Sessions: A Praccal Guide for Clinicians
1. Step 1: Use semanc differenal scales to assess value pairs across various cognive and
emoonal dimensions (e.g., good-bad, safe-dangerous, strong-weak).
2. Step 2: Measure KL divergence to quanfy cognive distoron and idenfy specific areas of
misalignment between beliefs, emoons, and reality.
3. Step 3: Apply PSL(2,7) principles to map cognive distorons onto symmetry violaons,
offering a geometric framework to understand cognive deviaons.
4. Step 4: Employ cognive restructuring techniques to help the individual realign beliefs and
emoonal responses, reducing predicon error and restoring cognive symmetry.
Conclusion
Pseudomorph offers a structured approach to psychotherapy, rooted in universal principles of
symmetry and closely integrated with neuroscienfic insights, such as Friston’s acve inference and
free energy minimizaon. By diagnosing and addressing cognive distorons as symmetry violaons,
Pseudomorph provides therapists and clients with a precise, objecve path toward mental and
emoonal well-being. Through the structured analysis of value pairs and the applicaon of PSL(2,7)
transformaons, this model represents a novel framework for restoring cognive harmony and
aligning individuals with their true selves.
5. Implicaons and Future Research
Theorecal Implicaons for the Science of Mind
Pseudomorph as a Groundbreaking Model Integrang Group Theory, Informaon Theory, and
Neuroscience
The Pseudomorph model marks a significant leap in the science of mind by synthesizing group theory,
informaon theory, and neuroscienfic principles, such as Friston’s acve inference and the free
energy principle. It introduces a cohesive, mathemacally grounded theory of consciousness,
modeling mental processes as symmetry transformaons within the group PSL(2,7). This structure
provides a formal, objecve framework for understanding the evoluon and interacon of cognive
processes, emoons, and beliefs.
By employing Kullback-Leibler (KL) divergence as a measure of cognive deviaon from the “true
self,” the model aligns with informaon theory’s emphasis on minimizing uncertainty, adding a
quantave dimension to consciousness studies. This interdisciplinary integraon—mathemacs,
neuroscience, and psychology—creates a robust framework for idenfying and modeling cognive
distorons, pushing the boundaries of tradional cognive science.
Contribuons to and Expansion on Holographic Brain Theory
Pseudomorph also builds on holographic brain models, which propose that cognive funcons are
distributed across the brain, with each part encoding informaon about the whole. The
13
Pseudomorph model expands on this concept by proposing that cognion operates through
symmetrical, holisc paerns that can be mathemacally captured using PSL(2,7). Each mental
transformaon is viewed as part of an interconnected system, with the 168 elements of PSL(2,7)
represenng the complete set of cognive transformaons. This approach adds a precise,
mathemacal representaon of cognive funcons, suggesng that symmetry serves as a guiding
principle for maintaining coherence and self-awareness in cognion.
Praccal Implicaons for Psychotherapy
Transformave Potenal for Therapeuc Pracces
The Pseudomorph model offers a universal framework that could revoluonize therapeuc pracces
by focusing on the symmetry or asymmetry within an individual’s thought and emoonal processes.
By pinpoinng specific symmetry violaons (cognive distorons like false beliefs or irraonal fears),
therapists can more accurately diagnose and address cognive misalignments. The model’s
structured approach provides a way to objecvely map and quanfy these distorons, enhancing the
effecveness and precision of therapeuc intervenons.
Semanc differenals and KL divergence offer therapists tools to idenfy imbalances in value pairs
and to measure cognive distoron severity. This facilitates more personalized treatment plans,
where specific distorons can be mapped to PSL(2,7)’s symmetry structure and systemacally
corrected, leading to targeted, effecve therapy.
Alignment with Cung-Edge Neuroscience
The alignment of Pseudomorph with Friston’s acve inference and the free energy principle further
enhances its relevance in both psychology and neuropsychiatry. Conceptualizing cognive distorons
as predicon errors or high free energy states situates Pseudomorph within current neuroscienfic
frameworks focused on reducing cognive dissonance. This makes the model applicable to not only
psychotherapy but also neuropsychiatry, supporng a deeper understanding and treatment of
cognive misalignments at the neurological level.
Applicaons in Neuropsychiatry, Trauma Recovery, and Group Therapy
Pseudomorph’s structured nature and precision make it highly suitable for neuropsychiatric contexts,
where accurate diagnosis and treatment are crucial. The focus on symmetry restoraon provides a
clear therapeuc path for addressing disorders like depression, anxiety, PTSD, and OCD, in which
cognive distorons are prevalent.
In trauma recovery, Pseudomorph offers a framework to analyze trauma-induced symmetry
violaons, idenfying disrupons in beliefs and emoonal responses that result from traumac
experiences. Restoring cognive symmetry helps individuals process and integrate traumac
memories, fostering emoonal healing. The model is also adaptable for group therapy, where
symmetry violaons can be examined in both individuals and group dynamics, promong balanced,
harmonious interacons that enhance therapeuc outcomes for all parcipants.
Future Research Direcons
Empirical Validaon of Pseudomorph’s Predicons and Therapeuc Effecveness
An essenal direcon for future research involves empirical validaon of Pseudomorph’s theorecal
predicons and its therapeuc effecveness. Clinical trials could assess the model’s capacity to
diagnose and treat cognive distorons in diverse psychological disorders. Measuring symmetry
restoraon’s impact on KL divergence and free energy levels in paents would provide quantave
14
data on the model’s efficacy. Addionally, studies should invesgate Pseudomorph’s integraon into
exisng therapeuc frameworks, evaluang its outcomes compared to tradional methods.
Exploring Other Finite Groups Beyond PSL(2,7) for Cognive Applicaons
While PSL(2,7) provides a robust structure for modeling cognion, other finite groups may offer
valuable insights into different aspects of mental processing or specific types of cognive distorons.
Future research could explore connecons between other finite groups and cognive funcons,
potenally leading to further refinement of the Pseudomorph model or the development of
complementary frameworks for understanding consciousness and psychological treatment.
Expanding the Model Through Neuroimaging Studies
Future studies could also incorporate neuroimaging techniques, such as fMRI or EEG, to observe
changes in free energy, symmetry restoraon, and KL divergence during therapeuc intervenons. By
tracking the neurological correlates of symmetry violaons and their resoluon, researchers can gain
insight into how cognive transformaons are represented in brain acvity. Such studies would
deepen the understanding of how neurological changes correspond to reducons in psychological
distress, supporng the development of therapies that address cognive and neurobiological
processes simultaneously.
Conclusion
The Pseudomorph model presents a significant advancement in both theorecal and praccal
applicaons, providing a comprehensive theory of consciousness grounded in symmetry and a
universal framework for psychotherapy. Its potenal to reshape therapeuc pracces, combined with
its alignment with cung-edge neuroscience, establishes its relevance across psychological and
neurological disciplines. Future research focused on validang and expanding Pseudomorph promises
to unlock new insights into cognive distorons, offering a more structured and objecve approach
to the science of mind.
6. Conclusion
In summary, Pseudomorph introduces an integrave quantum-geometric model of consciousness
that unites the mathemacal precision of group theory—specifically through the finite group
PSL(2,7)—with leading neuroscienfic principles, such as Friston’s acve inference and the free
energy principle. By conceptualizing the mind as a system that naturally seeks symmetry,
Pseudomorph provides a cohesive and innovave framework for understanding cognive processes,
emoonal dynamics, and the development of false beliefs. Symmetry violaons within this
framework, modeled through the lens of group theory, offer a structured, objecve foundaon for
diagnosing and recfying cognive distorons.
Pseudomorph presents a promising avenue for transforming psychotherapy by introducing a
symmetry-based approach to idenfying and treang false beliefs and cognive misalignments. The
integraon of semanc differenals, KL divergence, and symmetry restoraon provides therapists
with a comprehensive toolkit to detect and recalibrate imbalanced cognive and emoonal states. By
mapping cognive distorons onto specific symmetry violaons and outlining a structured path to
realignment, Pseudomorph offers a universal therapeuc framework that is applicable to a broad
range of psychological condions, including anxiety, depression, OCD, and trauma.
15
To harness Pseudomorph’s full potenal, interdisciplinary research and clinical applicaons are crucial
to test and refine the model’s efficacy across diverse psychological and neurological domains.
Empirical validaon through clinical trials and neuroimaging studies will be essenal to assess the
model’s effecveness in real-world therapeuc sengs. Drawing on experse from psychology,
neuroscience, mathemacs, and informaon theory, Pseudomorph has the potenal to become a
transformave tool for advancing our understanding of consciousness and improving mental health
outcomes.
References
1. Friston, K. (2010). The free-energy principle: a unified brain theory? Nature Reviews
Neuroscience, 11(2), 127-138. hps://doi.org/10.1038/nrn2787
o Provides the foundaonal framework for the free energy principle, which is central
to the Pseudomorph model’s integraon of cognive processes with symmetry and
predicve coding.
2. Friston, K., & Stephan, K. E. (2007). Free-energy and the brain. Synthese, 159(3), 417-458.
hps://doi.org/10.1007/s11229-007-9237-y
o Further elaborates on the relaonship between free energy and cognion, which
parallels the concept of symmetry in Pseudomorph as a balance-seeking mechanism
in the brain.
3. Osgood, C. E., Suci, G. J., & Tannenbaum, P. H. (1957). The Measurement of Meaning.
University of Illinois Press.
o The seminal work on semanc differenals, which plays a key role in the
Pseudomorph model’s method of decoding cognive and emoonal value pairs.
4. Papo, D. (2013). Why should cognive neurosciensts study the brain’s resng state?
Froners in Human Neuroscience, 7, 45. hps://doi.org/10.3389/fnhum.2013.00045
o Discusses resng-state brain acvity, which is relevant to understanding how
symmetry in mental processes can break down or be restored during states of
psychological distress.
5. MacKay, D. J. C. (2003). Informaon Theory, Inference, and Learning Algorithms. Cambridge
University Press.
o Key text for understanding informaon theory and the use of Kullback-Leibler (KL)
divergence, a crical concept in the Pseudomorph model for measuring cognive
distorons.
6. Pearl, J. (2009). Causality: Models, Reasoning, and Inference (2nd ed.). Cambridge University
Press.
o A key text on causal inference which complements the use of acve inference in
Pseudomorph for explaining how the brain updates its beliefs based on sensory input
and symmetry restoraon.
7. Pribram, K. H. (1991). Brain and Percepon: Holonomy and Structure in Figural Processing.
Lawrence Erlbaum Associates.
16
o Provides a detailed account of the holographic brain theory, supporng the idea that
cognion is a distributed, holisc system, aligning with the Pseudomorph model’s
view of cognive symmetry.
8. Varela, F. J., Thompson, E., & Rosch, E. (1991). The Embodied Mind: Cognive Science and
Human Experience. MIT Press.
o Explores the concept of embodied cognion, which relates to how Pseudomorph views
the interplay between mental, emoonal, and physical states as part of a unified system
seeking symmetry.
11. Roth, G., & Dicke, U. (2005). Evoluon of the brain and intelligence. Trends in Cognive
Sciences, 9(5), 250-257. hps://doi.org/10.1016/j.cs.2005.03.005
o Discusses the evoluonary basis of intelligence, providing context for the Pseudomorph
model’s idea that cognive symmetry and error reducon are deeply rooted in brain
evoluon.
12. Maturana, H. R., & Varela, F. J. (1980). Autopoiesis and Cognion: The Realizaon of the
Living. D. Reidel Publishing.
o Introduces the concept of autopoiesis, relevant to the self-regulang nature of cognion
in the Pseudomorph model, where the mind constantly strives for symmetry and balance.
13. Fuchs, R. (2023). Harmonic holography with the Pseudomorph spaceme crystal: A natural
language translaon of a Shor-like post quantum error correcon code, to measure smallest
purposeful conscious informaon. Abstracts of The Science of Consciousness Conference,
Taormina, Sicily.
o Introduces the concepts of mecrystals and semanc differenals to model
transformaons in spaceme.
14. Rudrauf, D., Bennequin, D., & Williford, K. (2023). The projecve consciousness model:
Projecve geometry at the core of consciousness and the integraon of percepon,
imaginaon, movaon, emoon, social cognion, and acon. Brain Sciences, 13(10), 1435.
hps://doi.org/10.3390/brainsci13101435
o Proposal of the Projecve Consciousness Model, using projecve geometry to unify
consciousness processes like percepon, imaginaon, and emoon, suggesng geometric
principles as foundaonal to mental organizaon.
