Threesology Research Journal

Threesology Research Journal Tripartite Aspects of Various Subjects 2

Aspects 1

Aspects 2

Aspects 3

Aspects 4

Visitors as of Sept. 3rd, 2025

On this page in order of appearance:

Irrational Aspects of 3: [1] (Mathematics)
Psychologically Irrational Aspects of 3: [2]
Mental illness Aspects of 3: [3]
Anatomical Aspects of 3: [4]
Archetectural Aspects of 3: [5] (Misspelling)
Metaphysical Aspects of 3: [6]

[1] Internet query: "Irrational Aspects of 3". Note: It pulled up a math-related perspective and not irrationality in terms of mental illness. I will have to rephrase the query in order to achieve a relevant response, because the AI can't read my mind.

AI (overview) response: The integer 3 is a rational number, but it is associated with several irrational numbers and concepts. A number is irrational if it cannot be expressed as a simple fraction, resulting in a decimal that is non-terminating and non-repeating.

Here are the irrational aspects related to the number 3:

√3 (Theodorus' Constant)

The most direct "irrational aspect of 3" is its square root, √3.
It is an irrational number, which means its decimal representation (1.7320508075...) continues infinitely without repeating.
The irrationality of √3 is proven by the method of contradiction, showing it cannot be written as a fraction of two integers.
It is also known as Theodorus' constant, named after the ancient Greek mathematician Theodorus of Cyrene, who proved its irrationality.

Relationships with other irrational numbers

The number 3 is involved in the formation of other irrational numbers through mathematical operations:

Sums and products: When you add or multiply the integer 3 by an irrational number, the result is also irrational. For example:
- 3 + π ≈ 6.14159... (irrational)
- √2 ≈ 4.24264... (irrational)
Powers: The log₂3 is an irrational number. If it were a rational number ^m⁄_n, then 2^{^m⁄_n} = 3, which leads to 2^m = 3ⁿ. This is a contradiction, as a power of 2 is always even and a power of 3 is always odd.

Geometric connections

The number 3 is used to describe dimensions and shapes, which have irrational properties:

Pythagorean theorem: In a right triangle with legs of length 1 and √2, the hypotenuse is √3. This is an example of an irrational length derived from whole numbers.
Height of an equilateral triangle: For an equilateral triangle with side length 2, the height is √3.

Non-mathematical contexts

While not strictly mathematical, the word "irrational" can also refer to concepts outside of logic or reason. In some spiritual, cultural, and psychological contexts, the number 3 holds mystical or symbolic significance that can be interpreted as transcending pure reason. This is a different, non-mathematical use of the term.

[2] Internet query: "Psychologically Irrational Aspects of 3"

AI (overview) response: The psychological preference for the number three, known as the "Rule of Three," is a cognitive shortcut that can lead to irrational conclusions. The human mind perceives groups of three as more satisfying, complete, and effective than other numbers. This bias is not a product of logic but rather a deeply ingrained mental pattern that can be manipulated in rhetoric, marketing, and decision-making.

Why the mind prefers groups of three

The psychological bias toward the number three is tied to pattern recognition and cognitive fluency.

Pattern-seeking: Three is the minimum number of elements needed to create a discernible pattern. Our brains are wired to find patterns to make sense of complex information, and a triad provides just enough structure to be memorable without being overwhelming.
Completeness: Three-part structures—like a beginning, middle, and end—create a sense of wholeness or narrative completion that feels satisfying. Two elements can seem incomplete, while four or more can feel excessive.
Enhanced recall: The brain can easily hold three to four items in its short-term memory, making information presented in threes easier to process and remember. This is a form of cognitive fluency, where things that are easier to process are also perceived as more truthful or reliable.

Irrational applications of the Rule of Three

Because our brains process trios more effectively, we are more likely to accept information presented in a three-part structure, even when it is not the most logical conclusion.

Forced consensus: In meetings or negotiations, an individual may present three arguments to appear more credible or to force a consensus, even if their three points are not equally strong.
Marketing and persuasion: Advertisers use the "power of three" to create more persuasive messaging, whether through slogans ("Just Do It"), brand aesthetics (the three stripes of Adidas), or a list of three product benefits. This framing makes the message more memorable and believable, even if a single, more impactful benefit is diluted.
Superstition and confirmation bias: The saying "bad luck comes in threes" is a cognitive shortcut that leads us to see patterns in random events. After one or two misfortunes, we are primed to notice a third, reinforcing a superstitious belief that is not based on rational probability.
Problem-solving: Faced with too many options, people can feel overwhelmed. Restricting choices to three can provide clarity but can also lead to premature simplification of a complex problem. The irrationality lies in believing that reducing options is always the optimal path.
The framing effect: A person is more likely to be convinced by three "reasons" to do something, simply because a list of three feels more complete and trustworthy than one or two. This is an irrational response that prioritizes the delivery method over the content's actual value.

[3] Internet query: "Mental illness Aspects of 3"

AI (overview) response: The "3 Ds" (dysfunction, distress, and deviance) are used to define abnormal behavior in mental health, while the three interconnected components of mental health are cognitive, emotional, and behavioral health, all of which impact one another and overall well-being. Mental illness itself involves a health condition affecting thinking, feeling, or behaving, causing distress and functional impairment.

The "3 Ds" of Mental Disorders

These criteria are often used to identify a mental disorder:

Dysfunction: The disorder causes a significant impairment or dysfunction in functioning.
Distress: The condition causes psychological pain or suffering for the individual.
Deviance: The thoughts, feelings, or behaviors are considered unusual or statistically deviant from the norm.

Three Components of Mental Health

Mental health is complex and can be understood through three main, interconnected areas:

Cognitive health: This refers to your ability to think, reason, and process information clearly.
Emotional health: This involves the ability to understand and manage your emotions effectively.
Behavioral health: This relates to your actions, habits, and overall conduct.

How They Relate

A disturbance in one of these areas can affect the others, and all are essential for maintaining good overall mental well-being.
For example, a disruption in cognitive health could lead to an inability to regulate emotions, which in turn could manifest as problematic behaviors.
When one of these aspects is significantly impaired, it can become a mental illness.

Note: My intent for this selection on anatomy, was to see if the AI would reference the List of threes in anatomy put together by Dr. McNulty and associates. It didn't, but it did provide some distinctions.

[4] Internet query: "Anatomical Aspects of 3":

AI (overview) response: The most prominent anatomical reference for "3" is the trigeminal nerve (cranial nerve V), which has three major divisions: the ophthalmic (V1), maxillary (V2), and mandibular (V3) nerves. It is the largest and most complex of the cranial nerves.

Gross anatomy

The trigeminal nerve is a paired nerve, with one nerve located on each side of the head. It has both sensory and motor components.

The nerve originates in the brainstem from four nuclei: three sensory and one motor.
A large sensory root and a smaller motor root emerge from the lateral aspect of the pons.
The roots extend toward the temporal bone and converge at the trigeminal ganglion (also called the Gasserian ganglion), which sits in Meckel's cave.
The trigeminal ganglion then divides into its three major branches.

The three divisions of the trigeminal nerve

1) Ophthalmic nerve (V1)

The smallest and purely sensory division, the ophthalmic nerve exits the skull through the superior orbital fissure. It is responsible for sensation in the upper part of the face and head.

Sensory territories:
- Scalp and forehead
- Upper eyelid and its conjunctiva
- Cornea and lacrimal gland
- Bridge of the nose
- Frontal sinus
Branches: Divides into the lacrimal, frontal, and nasociliary nerves.

2) Maxillary nerve (V2)

This is the second purely sensory division of the trigeminal nerve. It travels through the foramen rotundum to the pterygopalatine fossa.

Sensory territories:
- Middle part of the face, including the cheek and upper lip
- Lower eyelid and its conjunctiva
- Upper teeth and gums
- Nasal cavity and maxillary sinuses
- Roof of the mouth (palate)

3) Mandibular nerve (V3)

The largest division, the mandibular nerve is a mixed nerve with both sensory and motor functions. It exits the skull through the foramen ovale.

Sensory territories:
- Lower part of the face, chin, and jaw
- Lower teeth and gums
- Anterior two-thirds of the tongue (general sensation, not taste)
- Floor of the mouth and the mucous membranes of the cheek
- Parts of the external ear and temple
Motor functions: Controls the muscles of mastication (chewing), including the masseter, temporalis, and pterygoid muscles, as well as the tensor tympani, tensor veli palatini, mylohyoid, and anterior belly of the digastric.

Clinical significance

Anatomical knowledge of the trigeminal nerve is crucial for diagnosing several conditions, including:

Trigeminal neuralgia: A chronic pain condition often caused by a blood vessel compressing the nerve root, typically presenting as intense, sharp, electrical, or shock-like facial pain.
Trigeminal neuropathy: Damage to the trigeminal nerve that can cause symptoms like numbness, pain, or tingling in the face.
Herpes zoster ophthalmicus (shingles): Reactivation of the varicella-zoster virus in the trigeminal ganglion can cause a painful rash in the V1 dermatome. This can lead to eye inflammation and vision loss.
Lateral medullary syndrome (Wallenberg syndrome): A stroke in the brainstem can affect the spinal trigeminal nucleus, leading to an ipsilateral loss of facial sensation.

[5] Internet query: "Archetectural Aspects of 3" (The following is what I got by misspelling "Architectural". After which I supply the results for spelling it correctly.):

AI (overview) response: The architectural aspects related to the number 3 include the Rule of Three in visual design, which uses groupings of three to create balance and interest; the tripartite division of a building's façade into base, shaft, and capital; the three classical orders of architecture (Doric, Ionic, Corinthian); and the three fundamental principles of architecture: durability, utility, and beauty. Another interpretation is the three core aspects of an architectural business: business development, project management, and business management.

The Rule of Three in Design

Visual Harmony:
- Grouping elements in threes (e.g., windows, columns, dormers) creates complexity and variety that is more pleasing than binary groupings, leading to a more harmonious and balanced composition.
Natural Eye Movement:
- The human eye naturally gravitates toward the intersections and lines of the "rule of thirds" grid, making it a useful guideline for arranging elements in a design.

Tripartite Division in Architecture

Façade Design:
- This principle divides a building's façade or elevation into three distinct horizontal sections: the base, the shaft, and the capital (or crown).
Example:
- In Chicago's Marquette Building, the base has large arched windows, the shaft is the main vertical section, and the capital is the upper part, creating a strong, coherent structure.

The Three Classical Orders

Foundation of Western Architecture:
- The ancient Greeks developed three distinct orders for their architecture: Doric, Ionic, and Corinthian.
Architectural Elements:
- Each order features unique stylistic characteristics, particularly in the design of their columns, influencing the appearance of public buildings for centuries.
Vitruvian Principles
- Durability, Utility, Beauty: The Roman architect Vitruvius established three fundamental principles for good architecture: firmitas (firmness/durability), utilitas (utility/usefulness), and venustas (delight/beauty).

Three Aspects of an Architectural Business

Business Development:
- Marketing, sales, and maintaining a consistent message to attract new clients.
Project Management:
- Delivering construction documents accurately and on time, requiring technical knowledge and well-honed processes.
Business Management:
- Establishing and maintaining effective processes to control complexity, especially when adding people, ensuring efficient delivery of projects.

The following is when I spelled "Architecture" correctly:

AI response: The architectural aspects related to the number '3' include Vitruvian principles of firmness, commodity, and delight; the three Greek orders (Doric, Ionic, Corinthian); the tripartite division of a building's facade into base, shaft, and capital; the rule of thirds in composition and the use of the "rule of three" for visual balance; and the three fundamental aspects of architectural business management.

Fundamental Principles & Concepts

Vitruvian Principles:
- Roman architect Vitruvius established three core principles for good buildings: firmness (durability), commodity (utility), and delight (beauty).
Three Greek Orders:
- Ancient Greek architecture developed the Doric, Ionic, and Corinthian orders, which are distinct styles for column design and have influenced architecture for centuries.
Tripartite Division:
- This is a design principle where a building's facade is divided into three horizontal sections: the base, the shaft, and the capital or crown.
Rule of Thirds:
- A compositional guideline, particularly useful in asymmetrical designs, that involves dividing space into a grid of nine boxes to establish hierarchy and balance.
The Rule of Three:
- A design principle suggesting that elements grouped in threes create balance, harmony, and visual interest, whether in interior design or landscape architecture.

Architectural Business

Three Aspects of Architectural Business: To make a living and grow an architectural firm, architects must master business management, attract work through marketing and sales (business development), and successfully deliver projects on time and within budget through project management.

Examples of "Three" in Design

Windows, columns, or dormers:
- Grouping elements like three windows can create visual complexity and variety compared to a simple binary.
Tiered structures:
- The layering of architectural features, such as setbacks in a facade or tiered structures, can be seen as an application of the rule of three.

[6] Internet query: "Mythological Aspects of 3"

AI (overview) response: The number 3 is a powerful and ubiquitous symbol in world mythologies, representing concepts such as divine completeness, harmony, and the cycles of life. It frequently appears in the form of triads, trinities, and repeated actions that mark significant events.

Divine trinities and triads

Many mythologies feature powerful groupings of three deities or a single deity with three aspects.

Hinduism: The Trimurti consists of the deities Brahma (the creator), Vishnu (the preserver), and Shiva (the destroyer), who personify the cosmic functions of the universe. The goddesses Saraswati, Lakshmi, and Parvati form the Tridevi, the consorts of the Trimurti.
Christianity: The Holy Trinity consists of God the Father, God the Son, and God the Holy Spirit, three persons in one divine being.
Ancient Egypt: Deities were often grouped in family-based triads, such as the trio of Osiris, Isis, and their son Horus.
Greek Mythology: The three most powerful Olympian gods are the brothers Zeus (sky), Poseidon (sea), and Hades (underworld), who divided the universe among themselves.
Norse Mythology: The creation of the world was carried out by the three brothers Odin, Vili, and Vé.
Celtic Mythology: Ancient Celts honored tripartite deities, like the triple mother goddess known as the Matres or Matronae.

The cycle of destiny

In many myths, the number 3 symbolizes the stages of life, fate, and the passing of time.

Life stages and deities:
- Greek: The Fates (Moirai)—Clotho, Lachesis, and Atropos—were three sisters who controlled the destiny of mortals by spinning, measuring, and cutting the thread of life.
- Norse: The Norns—Urd (past), Verdandi (present), and Skuld (future)—similarly wove the destinies of all beings.
- Greco-Roman: The goddess Hecate was known as a triple deity who represented the cycle of maiden, mother, and crone.
Cycles of time and creation: The number 3 can signify the past, present, and future. In Norse myth, the World Tree Yggdrasil has three roots, each extending into a different realm.

Mythological events and structure

The number 3 frequently appears as a structural element in stories, signifying a magical or decisive turning point.

Repeated trials: A hero often faces three challenges or receives three opportunities.
- In a Norse myth, Odin took three sips from the Mead of Poetry to gain immense wisdom.
- In the Christian narrative, Satan tempted Jesus three times in the desert.
- Fairy tales often follow this "rule of three" with events or objects like the three little pigs, three wishes, or three attempts to overcome an obstacle.
Cosmological divisions: Many mythologies divide the world into three parts. The Sumerians, for example, believed the universe was made of the heavens, the earth, and the waters.

Associated concepts

Beyond deities and narratives, the number 3 is linked to several symbolic and philosophical ideas.

Harmony and balance: For the ancient Greek Pythagoreans, 3 represented harmony, as it is the sum of unity (1) and duality (2).
Completeness and wholeness: In Christian theology, the number 3 represents divine completeness and fulfillment.
Power and magic: The ubiquity of the number 3 in mythological contexts across cultures has led to its association with magical power.

H.O.B.. Note: the last item in the foregoing selection expresses an opinion that multiple people use as a means of understanding the (assumed) wide-spread prevalence of patterns-of-three as having some sort of inexplicable "power" linked to some sort of grand Cosmological theme. Yet the people who are inclined to make such an assumption frequently omit including examples-of-three from subjects other than mythology, religion, and fairy-tales. This is particularly biased. It is astonishing how many people to not also list such everyday examples from science, even though they are widely known, such as:

Life existing on the 3rd planet from the Sun.
3 basic atomic particles (protons- neutrons- electrons).
3 fingers used to hold a pen, pencil, toothbrush, paintbrush, etc...
Triplet code in DNA
etc...

For whatever reason, many people encounter multiple examples of "threes" in religion and either become dismissive and disparaging, or engage in a cult-like orientation that excludes other considerations that can be derived by an inclusion of other examples from multiple other subjects, whereby they develop some personalized metaphysical interpretation such as the following, which is viewed in terms of someone's interest in attempting to identify some especial trait or characteristic of uniqueness like some self-possessed adolescent engaged in a life-long pursuit of providing themselves with a label whose rune-like characterization may or may not incorporate a permission of adaptability of reassessment and redefinition as a type of life-changing recyclability involving a life-staging ressurectability:

[7] Internet query: "Metaphysical Aspects of 3"

AI (overview) response: Metaphysically, the number 3 represents completeness, creation, and balance, embodying the union of mind, body, and spirit and the dynamic interplay of past, present, and future. It is a universal symbol in spiritual traditions, seen in the Holy Trinity of Christianity, the Hindu Trimurti, and the Buddhist Triple Gem, signifying the divine and the inter-connectedness of all existence. In numerology, 3 is associated with creativity, communication, and self-expression, fostering optimism and joy.

Symbolism of Completeness and Unity

Triadic Structure:
- The number 3 often represents a complete cycle or a union of opposing forces, such as the birth, life, and death cycle.
Union of Elements:
- It symbolizes the connection between the mind, body, and spirit, or the past, present, and future, creating a dynamic whole.
Divine Triads:
- Many spiritual traditions recognize the Trinity, such as the Father, Son, and Holy Spirit in Christianity, or Brahma, Vishnu, and Shiva in Hinduism.

Role in Creation and Manifestation

Creative Force:
- The number 3 embodies the power of creativity and manifestation, encouraging individuals to express their unique talents.
Cosmic Balance:
- It reflects a fundamental order in the universe, such as the three realms of existence (sky, earth, underworld) in some Native American traditions, representing essential balance.
Geometric Significance:
- The triangle, a three-sided figure, is the first geometrical shape, symbolizing the foundational nature of number 3.

Spiritual and Personal Growth

Path to Enlightenment:
- In Buddhism, the Triple Gem (Buddha, Dharma, Sangha) guides practitioners toward enlightenment.
Spiritual Wisdom:
- Number 3 is often seen as a number of wisdom and understanding, facilitating spiritual growth and connection to a higher purpose.
Personal Qualities:
- Individuals influenced by the number 3 are often characterized by optimism, clear communication, and an ability to inspire others.

Page initially created: Wednesday, Sept. 2nd, 2025.... 5:49 AM
Initial posting: Wednesday, Sept. 3rd, 2025... 2:38 AM
Update:Thursday, Sept. 4th, 2025... 1:45 PM