counting and account

preface

In this paper, I explore the deep connection between painting and writing, focusing on how both mediums function as forms of accounting (narrating or reporting) and the principle of counting (measuring, reckoning, or organizing). Both painting and writing serve as powerful tools for communication, capable of evoking mental imagery - what we can term “mind-pictures.” These mind-pictures transcend the medium itself, drawing the viewer or reader into a world of ideas, emotions, and symbolic representation.

By examining the parallels between these two art forms - such as their shared ability to translate abstract thoughts into visual or written form, the creation of vivid mental images, reliance on composition and structure, use of symbolism, and their storytelling power - we reveal how painting and writing are deeply interconnected. In the act of accounting, both the painter and the writer recount a narrative or convey an experience, guiding the audience through the representation of external and internal worlds. Just as a painting tells a story through its visual elements, writing communicates through words, each sentence forming brushstrokes on the canvas of the reader’s mind.

Counting plays an equally significant role. In painting, this is seen through the deliberate organization of elements - proportion, perspective, and balance - that work to convey meaning. Similarly, in writing, the structure - whether through meter, rhythm, or narrative pacing - guides the reader, creating an ordered progression of ideas. Both art forms rely on a calculated system of organization that shapes the viewer’s or reader’s experience, underscoring how counting is inherent to the artistic process.

Thus, we find that painting is like writing, and writing is like painting, as both engage the observer’s imagination, offering a dialogue between the artist’s intent and the audience’s interpretation. Ultimately, both are forms of storytelling and emotional expression, where the acts of accounting and counting blend to shape the mental and emotional landscapes they evoke.

why dozen(12) based counting systems historically where preferred over metric(10) ones

Dozen-based counting systems (base-12 or duodecimal) have been historically preferred in certain contexts over base-10 (metric) systems for several practical reasons:

1. Divisibility:

The number 12 is divisible by more factors than 10. Specifically, 12 can be divided evenly by 1, 2, 3, 4, and 6, whereas 10 can only be divided by 1, 2, and 5. This makes it easier to work with fractions. For example, dividing something into thirds (1/3) in a base-12 system results in 4 (1/3 of 12), while in base-10, it leads to a repeating decimal (0.333…).

2. Convenience for Trade and Measurement:

Before the metric system, many cultures and civilizations relied on systems that were better suited for everyday tasks like trade and measurement. Base-12 was especially useful for splitting goods into common fractions like halves, thirds, and quarters. For instance, if you wanted to divide a dozen eggs or a dozen loaves of bread, it was easier to make practical divisions with 12 than with 10.

3. Cultural and Historical Precedents:

Ancient systems, including those used by the Sumerians and Babylonians, frequently relied on base-12 or base-60 counting systems. These systems had long-lasting influences on calendars, timekeeping, and measurement. For example, we still use base-12 in time (12 hours in a day) and in measurements (12 inches in a foot). This historical inertia kept base-12 systems in use for centuries.

4. Dozen as a Natural Unit:

The dozen was a convenient unit for grouping items, especially in commerce. A dozen allows for easy bulk trading, packaging, and pricing. Even today, items like eggs, baked goods, and other goods are commonly sold in dozens, showing the continued relevance of this system.

5. Fingers and Counting:

There’s a theory that base-12 may have been favoured because it is easy to count on fingers. You can count each segment of four fingers (excluding the thumb) on one hand, reaching up to 12, while using the other hand to keep track of the number of dozens. This contrasts with the base-10 system, which typically uses all ten fingers.

While the metric system’s base-10 system was introduced for standardization and ease of calculation in modern times, these historical and practical reasons explain why dozen-based systems persisted for so long and are still used in some contexts today.

base 12 being the higher order aka ‘GODS’ vs. base 10 being natural human

The symbolic distinction between 12 and 10 in various cultures has deeper mythological, religious, and philosophical meanings, reflecting higher-order concepts (12) versus human or natural order (10).

1. 12 as a Symbol of Higher Order (Gods, Divine, or Cosmic)

• Mythology and Religion: The number 12 is often associated with divine order, cosmic balance, and the heavens. Many ancient cultures revered the number 12 as a number of completion or perfection. Examples include:
  • 12 Olympian gods in Greek mythology.
  • 12 apostles in Christianity.
  • 12 tribes of Israel in Judaism.
  • 12 zodiac signs in astrology, symbolizing the cosmos and the heavens.
  • 12 months in a year, representing the natural division of time.

  These symbolic uses of 12 often evoke the sense of completeness, higher wisdom, or divinity. In religious or mythological contexts, 12 frequently represents something beyond the earthly, signifying order and structure in the universe that is governed by higher powers.

• Cosmic Time and Structure: The 12-based system of time, such as the 12 hours in a day and the 12 months in a year, reflects a cyclical view of time and cosmic order. It connects human existence with larger, celestial rhythms.

2. 10 as the Symbol of Natural or Human Order

• Human Limitation: The number 10 is often associated with human physicality and the natural world. It corresponds to the most basic way humans naturally count - on their 10 fingers (base-10 system). This makes 10 a number symbolizing human ability and the physical world.

• Practical Use: In contrast to the divine associations of 12, the number 10 is more tied to practicality and mundane human needs. It is often considered the number of completeness on a more human level. For instance, the Ten Commandments in the Bible symbolize divine laws meant to govern human behaviour, while also being neatly suited to human understanding and behaviour.

• Decimal Systems Reflect Human Nature: The decimal (base-10) system is intuitive to humans because of our anatomy (10 fingers and 10 toes), which makes it the default counting system in most cultures for practical, day-to-day use. It embodies simplicity and a reflection of human experience, in contrast to the more abstract or cosmically significant base-12 systems.

3. Contrast between 12 and 10 in Symbolism

• 12 as Transcendence: The number 12 often symbolizes an elevated, transcendent order - something that surpasses human understanding or control. It’s the number of the gods, the cosmos, or spiritual enlightenment. It exists beyond immediate human grasp, representing the divine or cosmic law that humans aspire to understand.

• 10 as Human Completeness: The number 10, on the other hand, represents human completeness in a more earthly or natural sense. It reflects the limit of human capability and the structure within which human life operates. In this way, base-10 systems are more tied to the physical, material world, while base-12 systems relate more to divine or universal order.

4. Cultural Perceptions

• Ancient Civilizations: Many ancient civilizations, such as the Egyptians, Sumerians, and Babylonians, used base-12 or base-60 systems because they were tied to both practical measurements and the symbolic importance of cosmic or divine cycles. These societies were deeply influenced by religious cosmology, in which numbers like 12 were linked to gods and universal cycles.

• Modern Systems: With the rise of rationalism and science, particularly with the French Revolution’s push for standardization, the base-10 (metric) system became favoured because of its simplicity and alignment with human anatomy. However, the base-12 system persisted in more symbolic or culturally significant areas.

Conclusion

The symbolic difference between 12 and 10 reflects broader philosophical and cultural concepts: 12 as a representation of divine, cosmic, or higher-order realms, and 10 as a symbol of human nature and the material world. This contrast permeates mythology, religion, and even the way systems of measurement and counting evolved over time. The preference for base-12 systems in certain contexts can be seen as a reflection of striving toward the divine or universal order, while base-10 systems remain grounded in human experience.

how does this reflect in the broader concept of counting and accounts

The distinction between 12 (cosmic/divine order) and 10 (human/natural order) also influences broader concepts of counting, accounting, and numerical systems. This duality can be seen in how societies organize systems of measurement, commerce, and governance, reflecting deeper philosophical and symbolic meanings. Here’s how this division plays out in counting and accounts:

1. Base-12 and the Divine or Higher Order in Accounting

In ancient times, the use of base-12 counting systems often reflected a desire to align human activities - such as trade, measurement, and governance - with cosmic or divine principles. This gave a deeper, spiritual significance to practical tasks like accounting and commerce.

• Cosmic Cycles and Trade: Since ancient societies relied heavily on natural cycles (e.g., the movement of celestial bodies, agricultural seasons), base-12 systems often guided their accounting of time, resources, and trade. By aligning accounting with cycles of the heavens, people saw commerce not just as a human activity but as something that harmonized with universal or divine laws. For instance:
  • 12 months in a year: Organizing agricultural and financial activities around the 12-month cycle linked human activities to celestial events, ensuring that commerce was in tune with cosmic rhythms.
  • Zodiac and Divisions of Time: In some societies, business decisions, resource management, and even governance were tied to astrological systems based on 12 zodiac signs. This created an overlap between economic systems and divine or cosmic forces.

• Base-12 in Measurement: Measurements like feet and inches (12 inches in a foot) reflect the practical usefulness of base-12 systems in commerce. The divisibility of 12 allows for easier partitioning, making it efficient for trade, construction, and craftsmanship. This reinforced the idea that base-12 was a system both of divine order and practical utility, blending higher principles with everyday human activities.

• Higher Accounting: In some philosophical or religious traditions, numbers like 12 were used in higher forms of accounting - those connected to governance, celestial calendars, and religious rituals. For example, religious offerings, tributes, and tithes might be structured around the number 12 as a reflection of cosmic order.

2. Base-10 and Human Accounting

In contrast, base-10 counting systems emerged more naturally from human experience, particularly the use of fingers for counting. This base-10 system reflects a more human-centric approach to accounting, grounded in practicality, simplicity, and daily life.

• Decimal System in Modern Accounting: The widespread adoption of the base-10 system in modern accounting and finance aligns with its inherent simplicity. It’s easy to calculate and manage, making it the dominant system for currency, taxes, and financial records. Decimal systems are built around the natural counting experience of humans (10 fingers), so they are practical for everyday tasks.

• Human-centred Economies: The decimal system, particularly since the rise of modern economies, is well-suited for managing large-scale trade, commerce, and taxation systems. Its simplicity allows for greater standardization, ensuring that economies are accessible and manageable by the majority of people.

• Taxation and Base-10: Systems of taxation often use base-10 principles (e.g., percentage-based taxation). This is rooted in the fact that base-10 is efficient for calculating income, sales, and profit margins, making it ideal for systems where precision and ease of calculation are necessary.

3. Base-12 vs. Base-10 in Historical Commerce and Accounts

The tension between base-12 and base-10 systems has manifested in the evolution of commerce and financial systems. Historically, many cultures relied on base-12 (or related systems like base-60), but as societies evolved, particularly during the Enlightenment and Industrial Revolution, base-10 became more dominant.

• Ancient Trade Systems: In ancient Mesopotamia, base-12 and base-60 systems were used in trade and accounting, largely because of their divisibility and connection to cosmic cycles. These systems allowed for complex transactions, such as dividing large amounts of grain, silver, or other commodities into manageable parts. The symbolism of divine order in commerce was reflected in how these societies structured their economy.

• Transition to Base-10: As societies became more secular and focused on rationalism, base-10 gained prominence due to its simplicity and universality. The metric system, introduced during the French Revolution, aimed to create a rational, standardized system for all measurements and accounts, stripping away the mystical or symbolic aspects of base-12 systems.

4. Symbolism in Modern Accounting and Financial Systems

Even in modern accounting, traces of this symbolic division between base-12 (higher order) and base-10 (human order) can be found. While most financial systems today rely on base-10, the persistence of base-12 in certain areas reflects a continued blending of the practical with the symbolic.

• Stock Markets and Time-Based Accounting: Time, still governed by a base-12 system (12 hours, 12 months), is critical in accounting and financial systems. Market cycles, quarterly reports, and financial forecasts are structured around this cosmic division of time, symbolizing a connection between human activity and a larger order.

• Divisibility and Financial Instruments: Even in modern finance, base-12 is occasionally useful in calculating shares, dividends, and portions. The divisibility of 12 into multiple factors (2, 3, 4, 6) allows for practical partitioning of resources, much like it did in ancient commerce.

5. Broader Implications in Governance and Law

The division between base-12 and base-10 also extends into governance, law, and societal structures:

• Divine Law vs. Human Law: Systems of governance or law that are considered divinely inspired or cosmic in nature often feature base-12 structures. For example, the 12 apostles in Christianity or the 12 elders in some traditional societies represent a divine or cosmic order guiding human affairs.
• Human Governance and Decimal Systems: Modern systems of law and governance, built around secular and humanistic principles, often adopt base-10 structures because they align with the human experience and rational calculation. This is evident in modern legal and governmental systems, which prioritize clarity and ease of use.

Conclusion

In broader concepts of counting and accounting, base-12 reflects divine or cosmic order, with connections to higher realms, religion, and ancient systems of commerce and governance, while base-10 represents human-centred practicality and natural order. Both systems have shaped how societies count, measure, and account for resources, and their symbolic meanings continue to influence the way we structure time, financial systems, and governance today.

a synopsis over the three questions so far

1. Why were dozen-based (12) counting systems preferred over metric (10) systems?

Dozen-based systems (base-12) were historically favoured because 12 is more divisible than 10, allowing easier partitioning into common fractions like halves, thirds, and quarters. This was practical for trade and commerce, especially in ancient societies. Base-12 also has cultural and historical roots, with connections to timekeeping and measurement systems, such as the 12 hours in a day or 12 inches in a foot. These systems persisted due to their practicality in daily life and trade, while the base-10 (metric) system gained popularity for its simplicity in modern, standardized accounting.

2. Symbolic meaning of 12 (higher order) vs. 10 (human/natural order)

In various cultures, the number 12 is often linked to divine or cosmic order, representing higher realms, completeness, and spiritual systems, as seen in 12 Olympian gods, 12 apostles, and 12 zodiac signs. Meanwhile, 10 is associated with human experience, being the number of fingers used for counting and reflecting practical, human-centred systems like the decimal system. The number 10 signifies human completeness in a natural or material sense, while 12 represents a transcendent or divine structure governing the cosmos.

3. How does this reflect in broader concepts of counting and accounting?

The distinction between base-12 (divine order) and base-10 (human order) influences broader accounting and numerical systems. Historically, base-12 systems connected trade, governance, and timekeeping to cosmic cycles and divine principles. Base-10, being grounded in human anatomy and practicality, became dominant in modern accounting and finance for its simplicity and ease of use. However, traces of base-12 persist in time-based systems (12 months, 12 hours) and certain financial structures due to its superior divisibility and symbolic ties to higher, cosmic order.

Relevance to time, flow and storytelling by the example of Meander

The concept of Meander - a winding, non-linear flow - can serve as a powerful metaphor for understanding the relationship between time, flow, and storytelling, especially when viewed through the symbolic lens of base-12 (higher order) vs. base-10 (human order).

1. Meander as a Metaphor for Time

The Meander pattern, named after the winding Meander River in ancient Greece, represents a path that is non-linear, fluid, and cyclical. This is significant in storytelling and timekeeping because it contrasts with the linear, rigid structure of time often seen in base-10 or modern systems.

• Cyclical Nature of Time (Base-12): In ancient cultures, time was often viewed as cyclical, much like the flow of the Meander River. Base-12 systems - used for dividing the day into 12 hours or the year into 12 months - reflect this cyclical understanding of time. This view is more fluid, allowing for a sense of eternal return, where time is not strictly linear but loops and flows like a river, often seen in myths and cosmic cycles.

• Linear Time (Base-10): Modern systems of timekeeping, influenced by base-10, emphasize progression and precision. The decimal system promotes a linear, measured understanding of time, focusing on human experience and practicality. Time becomes a sequence of units - hours, minutes, seconds - designed for efficiency, not the fluid, cosmic flow seen in earlier symbolic systems.

2. Meander and Storytelling: Non-Linear Narratives

In storytelling, the Meander pattern can represent a non-linear narrative, where the flow of events isn’t strictly bound by a rigid structure but meanders through time, space, and meaning, much like ancient myths or epics. This mirrors the base-12 concept of higher order storytelling, where stories align with the rhythms of the cosmos, cyclical time, or divine order.

• Non-Linear (Meander) Storytelling: Stories that unfold in a meandering fashion - like epics or myths - often mimic the flow of the Meander. They may not follow a strict sequence of cause and effect but instead weave through various arcs, side stories, and recurring motifs. Examples include Homer’s Odyssey, where the hero’s journey is full of detours, reflecting the winding nature of fate and divine intervention. This type of storytelling connects to a base-12 philosophy, where narratives are cyclical, reflecting cosmic or divine order rather than human linearity.

• Linear Storytelling (Base-10): In contrast, modern storytelling, often influenced by base-10 logic, tends to be linear and goal-oriented. Stories are structured with a clear beginning, middle, and end, progressing toward resolution in a straight line. This approach reflects the practical, human-centred base-10 worldview, where time is linear, and narratives move forward in a measurable, predictable fashion.

3. Flow and the Meander in Time and Accounts

The flow of time and resources in both storytelling and accounting systems can be understood through the Meander metaphor.

• Flow in Base-12 (Meandering Order): Just as the Meander flows naturally and unpredictably, base-12 systems allow for more natural, fluid partitioning in counting and time. In ancient accounting, the base-12 system allowed for easy division into parts (1/2, 1/3, 1/4), making it flexible and adaptable to changing circumstances, much like the winding flow of a river. This flexibility is akin to how a meandering story can adapt and evolve, touching on different themes, characters, and events without a rigid structure.

• Flow in Base-10 (Linear Precision): Base-10 systems, which focus on efficiency and standardization, reflect a more linear, precise flow of time and accounting. Here, time is measured in predictable, equal segments, and resources are divided into neat decimal fractions, emphasizing control, predictability, and human-centred logic. This is ideal for modern financial systems and linear storytelling, where clarity and progression are paramount.

4. Relevance to Storytelling and Human Experience

The Meander’s symbolic winding path offers insight into the way humans experience time, memory, and narrative:

• Non-linear human experience: Human memory and experience often don’t follow a straight line. Much like the Meander, memories resurface, repeat, and intertwine, creating a narrative flow that is cyclical and complex. Storytelling that embraces this meandering structure often feels more reflective of real life, where events are interconnected in ways that a strictly linear structure can’t capture.

• Myth and Cosmic Storytelling: Ancient myths and cosmologies, which often followed base-12 systems, reflect the meandering flow of cosmic time. These stories are deeply intertwined with the movement of celestial bodies and natural cycles, mirroring how time itself seems to loop and repeat in cycles. This is echoed in the winding structure of the Meander, where paths often seem to return to earlier points, much like recurring themes in mythic storytelling.

5. Broader Implications: Meander as a Bridge Between Systems

The Meander can be seen as a bridge between base-12 (cyclical, divine order) and base-10 (linear, human order). In storytelling, accounting, and timekeeping, it represents a synthesis of both worlds:

• Meander as Higher and Human Order: Just as the river’s winding flow combines unpredictability with an underlying sense of direction, human narratives and systems blend the fluidity of divine order (base-12) with the practical needs of human life (base-10).

• Hybrid Systems: Some systems of storytelling, accounting, and timekeeping today reflect both principles. For example, while modern accounting is mostly base-10, the flow of time is still organized around base-12 systems (e.g., 12 months, 12-hour clocks). Similarly, while most modern narratives are linear, many also incorporate non-linear, meandering elements, as seen in movies with flashbacks, looping timelines, or multiple perspectives.

Meander a profound metaphor

The concept of the Meander offers a profound metaphor for how time, flow, and storytelling operate across different symbolic systems. In base-12, time and storytelling reflect a higher, divine order, cyclical and cosmic, much like the winding flow of the river. Base-10 represents human-centred logic, linear progression, and predictability. The Meander allows for the coexistence of both: fluidity within structure, where divine and human systems of time, accounting, and narrative flow together.

other concepts than base-12 and base-10, numeric and non-numeric ones

Many other numeric and non-numeric systems of organizing and understanding the world exists that go beyond the familiar base-10 and base-12 systems. These systems have been used throughout history and in different cultures, often reflecting unique worldviews, practical needs, and symbolic understandings. Below are some examples of both numeric and non-numeric concepts used for counting, organizing, and interpreting the world.

Numeric Systems Beyond Base-10 and Base-12

1. Base-60 (Sexagesimal System)

• Origin: Used by the ancient Babylonians, this system divides numbers by 60, rather than 10 or 12. It was widely used in astronomy, geometry, and early mathematics.
• Applications:
  • We still use base-60 in timekeeping (60 seconds in a minute, 60 minutes in an hour).
  • Degrees in a circle are measured in 360°, a multiple of 60, which comes from this tradition.
• Symbolic Meaning: Base-60 combines the practicality of both 12 and 10, as 60 is divisible by many numbers (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30).

2. Base-2 (Binary System)

• Origin: Binary (base-2) is a mathematical system using only two digits: 0 and 1. It’s the foundational system for modern computing and digital technology.
• Applications:
  • Binary systems represent data in computers (bits and bytes).
  • Logic gates and modern algorithms rely heavily on binary thinking, where everything is reduced to choices or oppositions (yes/no, true/false).
• Symbolic Meaning: Binary reflects the concept of duality, a key principle in many philosophical systems (light/dark, good/evil, order/chaos).

3. Base-5 (Quinary System)

• Origin: Base-5 systems, using five as the foundation, have been used by various indigenous cultures. This system is thought to derive from counting on one hand.
• Applications:
  • Found in ancient Mayan numbering systems and other early cultures for practical counting.
  • Some financial or commodity systems (such as tally marks) are built around groups of five.
• Symbolic Meaning: This system connects to basic human anatomy (five fingers), making it deeply human-centred and practical for small-scale transactions.

4. Base-20 (Vigesimal System)

• Origin: Used by the Mayan civilization and certain Celtic languages, base-20 systems count in units of 20.
• Applications:
  • The Maya used base-20 for calendars, astronomy, and architecture.
  • French language still retains traces of this system (e.g., the word for 80 is “quatre-vingts,” meaning “four twenties”).
• Symbolic Meaning: This system likely evolved from counting on both hands and feet (10 fingers, 10 toes), symbolizing completeness in a different way than base-10.

5. Base-8 (Octal System)

• Origin: Octal (base-8) is used in some computing systems, especially in earlier technologies and in fields like electronics and networking.
• Applications:
  • Often used in digital circuits where 8-bit systems are common.
  • Cultural significance: Certain cultures, such as the Yuki of California, used an octal system based on counting the spaces between fingers rather than the fingers themselves.
• Symbolic Meaning: In cultures that used octal systems, it reflected unique counting methods tied to their worldview and environment.

Non-Numeric Concepts of Organization

Beyond numeric bases, there are non-numeric systems of organization and understanding that provide alternate ways of framing reality, particularly in storytelling, time, philosophy, and culture.

1. Four Elements (Classical Elements)

• Origin: Many ancient cultures, including Greek, Chinese, and Indian traditions, categorized the world into four fundamental elements - earth, water, air, and fire.
• Applications:
  • Used in alchemy, medicine, and early science to explain natural phenomena.
  • In storytelling, many myths and cosmologies incorporate the four elements as archetypal forces that shape the universe.
• Symbolic Meaning: The four elements represent the balance of opposites and natural forces, a way to conceptualize the world through qualitative attributes rather than numerical measures.

2. The Five Phases (Wu Xing)

• Origin: In Chinese philosophy, the Wu Xing represents five phases or elements: wood, fire, earth, metal, and water.
• Applications:
  • This system is used in Chinese medicine, feng shui, martial arts, and philosophy to understand natural cycles and relationships.
  • It describes cyclical processes of creation and destruction, rather than fixed categories.
• Symbolic Meaning: The five phases reflect the dynamic and interconnected nature of life, where elements move and interact with each other in cycles, emphasizing balance and harmony rather than linear progression.

3. The Hero’s Journey (Monomyth)

• Origin: Joseph Campbell’s analysis of myth led to the concept of the Hero’s Journey, a non-numeric system describing a universal narrative pattern found in myths across cultures.
• Applications:
  • Widely used in storytelling, particularly in literature and film, where the structure follows stages like the Call to Adventure, Crossing the Threshold, and Return.
  • The journey itself reflects spiritual and personal growth, not bound to numbers but to symbolic phases of transformation.
• Symbolic Meaning: It portrays the cyclical nature of human experience, where the journey out and return is symbolic of growth, challenge, and renewal, much like the Meander metaphor discussed earlier.

4. I Ching (Yijing) Hexagrams

• Origin: The I Ching, or Book of Changes, is an ancient Chinese text that uses 64 hexagrams (combinations of six broken or unbroken lines) to represent different states and transitions.
• Applications:
  • Used for divination, philosophical contemplation, and understanding dynamic change.
  • Each hexagram represents a specific combination of yin and yang, emphasizing balance and continuous flow.
• Symbolic Meaning: The I Ching is a way to interpret the interconnectedness of all things. It reflects the idea that reality is in constant flux, rather than being governed by rigid numeric systems.

5. The Seven Chakras

• Origin: In Hinduism and various esoteric traditions, the chakra system represents seven centres of spiritual energy in the body.
• Applications:
  • Used in yoga, meditation, and spiritual practices to understand physical and spiritual well-being.
  • Each chakra represents a different aspect of life or consciousness (e.g., survival, love, wisdom).
• Symbolic Meaning: The chakras embody a non-numeric way of categorizing human experience, one that’s holistic and interconnected, reflecting different layers of existence from the material to the spiritual.

Concepts of Time Beyond Numbers

1. Cyclical vs. Linear Time

• Cyclical Time: Many ancient cultures, including the Maya, Hindus, and Greeks, viewed time as cyclical. Events and life processes repeat in cycles, reflecting rebirth and renewal.
  • Example: The Mayan Long Count Calendar conceptualized time as vast cycles (e.g., baktuns) rather than the linear progression of years.
• Linear Time: Western modernity often conceptualizes time as a straight line - moving from past to future without returning, in contrast to the cyclical conceptions.
  • Example: Judeo-Christian ideas of time as a path toward an ultimate conclusion (e.g., the apocalypse or end times).

2. Narrative Structures

• Circular Narratives: Some cultures and storytelling traditions use circular or non-linear narratives, where events echo, repeat, or loop back on themselves.
  • Example: The Dreamtime stories of Aboriginal Australians, where time and narrative are not linear but deeply connected to the land, ancestors, and cycles of life.
• Fractal or Modular Narratives: In postmodern storytelling, narratives may be broken into fractals or modular pieces, where the story doesn’t follow a single arc but is fragmented or presented in pieces.
  • Example: Modern literature and film, such as works by David Lynch or Gabriel García Márquez, may use non-linear or fragmented narrative structures to explore the complexity of time and human experience.

Beyond base-12 and base-10 systems

There are numerous numeric and non-numeric ways of organizing time, counting, storytelling, and understanding the world. From base-60 and base-20 systems to non-numeric systems like the chakras or Wu Xing, these alternate concepts offer unique perspectives on human experience, emphasizing cyclical, dynamic, or interconnected realities rather than linear or purely quantitative ones. These systems reflect the diversity of cultural approaches to counting, time, and meaning, where numbers may symbolize much more than just practical measures.

Ilyas 10 Trojan years - war, human, heroic, fight against love
Odyssey 12 travels of Odysseus - divine intervention, exploration, knowledge, travel for love

(https://www2.classics.upenn.edu/myth/php/homer/index.php?page=odymap)

the concept of a Mind-Picture

The concept of a Mind-Picture refers to a mental image or visual representation that forms in the mind, often as a result of thought, memory, or imagination. It’s a way for the mind to organize and visualize abstract concepts, emotions, or memories. Mind-pictures are central to visual thinking, where ideas are processed as images rather than just words or symbols.

Key Aspects of Mind-Pictures:

1. Visualization of Abstract Ideas: Mind-pictures help in visualizing intangible or abstract ideas. For instance, when someone is explaining a concept like “freedom,” a person might form a mental image of an open sky or a bird in flight.

2. Memory and Recall: Mind-pictures are closely tied to how we recall memories. Instead of remembering everything in words, people often remember past events in the form of mental images or scenes, which can sometimes be vivid and detailed.

3. Creative Thinking: Mind-pictures are often used in creative thinking and problem-solving. Artists, designers, and innovators frequently rely on these mental images to guide their work, whether they are visualizing a painting, a product design, or a narrative structure.

4. Mental Simulation: Mind-pictures allow us to mentally simulate future actions or situations. For example, an athlete might visualize their performance before a game, or someone might picture how a conversation might unfold.

5. Emotional Connections: These mental images can evoke strong emotions, either positive or negative. A memory of a beautiful landscape might bring a sense of peace, while the image of a stressful situation might induce anxiety.

6. Metaphorical Mind-Pictures: In storytelling, philosophy, or teaching, mind-pictures are often used metaphorically. Teachers, for instance, might describe complex ideas in visual terms to help students create a mental image and understand the concept better.

Applications of Mind-Pictures:

• Education: Mind-pictures are used to help students understand complex concepts by encouraging them to visualize them. Diagrams, flowcharts, and illustrative examples often serve as external aids to facilitate mind-picture formation.

• Storytelling: Writers and filmmakers use descriptive language or visuals to evoke mind-pictures in the audience, helping to immerse them in the world of the story.

• Therapy: In practices like guided imagery or visualization therapy, individuals use mind-pictures to confront fears, reduce stress, or work through traumatic experiences.

Related Concepts:

• Mental Imagery: Closely related to mind-pictures, mental imagery refers to the phenomenon of seeing images in the mind without direct sensory input.
• Visual Thinking: A cognitive process in which ideas are processed and understood through images, diagrams, and spatial relations rather than verbal descriptions.
• Mind’s Eye: The concept of an inner “eye” that allows individuals to visualize things in their minds, sometimes referred to as the seat of imagination and creative thinking.

Mind-pictures play a crucial role in how we think, remember, imagine, and communicate. They serve as a bridge between abstract thought and sensory experience, allowing us to “see” what we cannot physically observe.

Keeping this in mind, why painting is (like) writing vice versa

The idea that painting is like writing (and vice versa) can be understood through the lens of mind-pictures, where both mediums - painting and writing - are forms of communication that create mental imagery in the audience. Both artists and writers use their respective tools to evoke images, emotions, and ideas in the mind of the viewer or reader, making the two art forms deeply interconnected. Here’s how they parallel each other:

1. Both Translate Abstract Thoughts into Visual Form Painting: Painters transform abstract ideas, emotions, or concepts into a physical, visual representation using colour, shape, and composition. The process of painting is like externalizing the mind-picture onto a canvas, enabling the viewer to see what the artist imagined or perceived.

Writing: Writers do something very similar but with words. Through descriptive language, metaphor, and narrative, writers paint mental pictures in the minds of their readers. A well-written description can evoke vivid images that readers visualize, making writing a form of painting with words.

Both art forms are essentially translating inner experiences, thoughts, or emotions into forms that others can experience. Just as a painting can represent a scene, so can a well-written paragraph create a visual image in the reader’s mind.

1. Creating Mental Images (Mind-Pictures) In Painting: The visual representation is immediate - the colours, shapes, and lines directly stimulate the viewer’s mind-pictures. When looking at a painting, the viewer interprets what they see, often connecting it with their own memories or emotions, forming a unique mental image of the artwork.

In Writing: Though words are abstract symbols, a writer carefully chooses them to evoke specific sensory and visual experiences. For example, when describing “a dark forest with moonlight filtering through the trees,” the reader forms a vivid mental image of that scene, much like viewing a painting of a similar setting.

In both cases, the audience is actively participating in the creation of the mind-picture, interpreting the artist’s or writer’s cues to build a mental image that resonates with their personal experiences or imagination.

1. Both Rely on Composition and Structure Composition in Painting: The painter organizes elements like balance, symmetry, focus, and perspective to guide the viewer’s eye and create an overall aesthetic experience. The composition of a painting directs how the viewer processes the visual information and forms meaning.

Structure in Writing: Writers similarly use narrative structure, sentence rhythm, and literary devices like symbolism and imagery to guide the reader through the text. Just as composition in painting leads the eye, narrative structure leads the mind, helping the reader form a coherent mental picture.

In this sense, a well-structured story or poem is much like a well-composed painting; both create a harmonious experience, moving the audience through different mental states and impressions.

1. Both Communicate Through Symbolism Painting: Artists use visual symbols - colours, objects, or abstract forms - to represent deeper meanings. A single element in a painting, like a red rose or a stormy sky, might carry symbolic meaning beyond its literal depiction, creating layers of interpretation in the viewer’s mind.

Writing: Writers do the same, using words and phrases that carry symbolic weight. Metaphor, simile, and allegory are literary techniques that parallel the symbolic use of imagery in painting. For example, describing someone’s life as “a winding road” evokes a mental picture of a journey filled with twists and turns, symbolizing challenges and life events.

In both cases, the artist or writer asks the audience to look beyond the literal and interpret the underlying meaning, drawing upon their inner world of mental imagery.

1. Both Are Forms of Storytelling Narrative in Painting: Paintings often tell stories, whether in a single image or across a series of works. Historical paintings, mythological depictions, or even abstract art can convey a sense of time, sequence, or narrative. The viewer “reads” the painting by moving their attention across different parts, creating a narrative in their mind.

Narrative in Writing: Writing, especially in prose and poetry, explicitly tells stories, unfolding over time and through language. Readers follow characters, events, and emotions, building a mental narrative as they proceed. The act of storytelling in writing uses imagery and descriptive language to paint scenes, characters, and emotions in the reader’s mind, much like how a painting visually captures moments in time. Both forms invite the audience to engage in a mental journey that unravels over time, whether it’s through the written word or the painted image.

In both mediums, the artist or writer offers a perspective, but it is the observer or reader who completes the story, interpreting and imagining details that may not be explicitly presented. This interplay between creator and audience highlights how painting and writing are both collaborative forms of storytelling, relying on the shared imagination of both parties to fully bring the story to life.

The relationship between painting and writing is rooted in their shared goal of evoking mind-pictures. Through composition, structure, symbolism, and storytelling, both art forms translate abstract thoughts and emotions into forms that others can experience. Whether through a brushstroke on canvas or a carefully crafted sentence, both mediums engage the audience’s imagination, making them powerful tools for creating mental images, narratives, and emotional responses. Painting is like writing, and vice versa, because both allow us to communicate the intangible through a tangible medium, inviting others into our inner world of thoughts and visions.

Count, recount, account systems, which are based on the Fibonacci or Prime numbers taking “painting is like writing” and “mind-pictures” in consideration.

There are systems based on Fibonacci and prime numbers used in both mathematical and artistic contexts, and they can be related to the concept of accounting, recounting, and mind-pictures. While these systems are more frequently found in mathematics, nature, and design, they can be creatively applied to storytelling, writing, and visual art.

Let’s break this down by considering how painting is like writing and how mind-pictures are evoked using these number systems.

Fibonacci-Based Systems in Art and Writing

The Fibonacci sequence (0, 1, 1, 2, 3, 5, 8, 13, …) is closely related to the golden ratio, which has been used for centuries in composition, architecture, and design. Artists and writers use Fibonacci-based structures to create aesthetic balance, rhythm, and harmony in their works, which directly ties into how these mediums are constructed and perceived.

1. In Painting:
   • The Fibonacci sequence is often used to design the composition of paintings. Many classical works, from Leonardo da Vinci’s to Salvador Dalí’s, use the golden ratio to position key elements, ensuring a naturally appealing and balanced layout.
   • Example: Dalí’s “The Sacrament of the Last Supper” is often cited as being structured according to the golden ratio, with proportions and spacing evoking a harmonious image that draws the eye to specific focal points, creating an organized “account” of the scene.
2. In Writing:
   • In literature and storytelling, Fibonacci-like structuring can create a narrative rhythm that mirrors natural patterns of growth and progression, offering a layered and expansive story that slowly builds, much like the expanding Fibonacci sequence.

   • In a novel or poem, chapters or verses can be structured around Fibonacci numbers, starting small and growing in length or complexity. This mirrors the way ideas or tension can “unfold” like in a Fibonacci spiral.

   • For example, a short story could start with a single event (1), followed by two parallel actions (2), three interwoven themes (3), and continue building with five interconnected characters (5), creating a narrative spiral that deepens as the story progresses.

Prime-Based Systems in Art and Writing

Prime numbers (2, 3, 5, 7, 11, …) have unique mathematical properties because they are divisible only by 1 and themselves. These numbers create a sense of irregularity, structure, and mystery, often applied in artistic and literary forms to evoke complexity and patterns hidden beneath the surface.

1. In Painting:
   • Artists might use primes to define spacing, proportions, or repetitions in a composition. Using prime numbers in this way creates non-repeating, organic patterns, which can lend an artwork a sense of unpredictability or uniqueness.
   • Piet Mondrian’s grid paintings and Islamic art’s geometric designs both use systems inspired by primes to create patterns that seem orderly yet non-repetitive, drawing the viewer into deeper contemplation, just like the flow of a narrative account.
2. In Writing:
   • Prime numbers can structure poems, chapters, or acts in a play. Prime-based systems might create unexpected twists, where crucial events or revelations happen at the 2nd, 3rd, 5th, 7th, and 11th points in the narrative, guiding readers to count forward in anticipation while also keeping them off-balance due to the non-linear progression.
   • Experimental poetry or modernist prose, such as James Joyce’s Ulysses, could incorporate prime numbers in paragraph lengths, sentence structures, or chapter divisions, creating a complex, unpredictable rhythm that challenges readers to “decode” the narrative structure.

Relevance to Mind-Pictures and Accounting

The application of Fibonacci or prime systems to both painting and writing creates structured forms that appeal to the mind’s sense of order and aesthetic harmony. These structures help build and reinforce mental images in unique ways:

• Mind-Pictures in Painting:
  • Fibonacci and prime structures direct the eye naturally, allowing the viewer to mentally “account” for the flow and composition of the artwork. The viewer unconsciously organizes the visual information, counting and recounting the elements in the painting, which builds the mental narrative of the piece.
• Mind-Pictures in Writing:

  • When Fibonacci or prime systems are used in writing, they subtly shape how readers mentally structure and account for the unfolding story. Readers, while unaware of the mathematical pattern, still respond to the ebb and flow, creating vivid mental imagery that aligns with these structural cues.

  • For instance, a Fibonacci-structured plot may build momentum, drawing the reader deeper into the story as each new layer is added. Conversely, a prime-structured story may introduce surprises and asymmetry, engaging the reader’s imagination to reconstruct events or ideas in novel ways.

Painting is Like Writing – Using Fibonacci and Primes

Both Fibonacci and prime-based structures are, in essence, accounting systems for how a story or image is constructed and experienced. They help organize complex visual and narrative elements, much like how an accountant organizes numbers to build a financial report.

1. Accounting in Painting:
   • Artists use these number-based systems to structure their visual storytelling. The act of “accounting” in this sense is the careful counting of proportions, patterns, and relationships between elements in the artwork to create a harmonious or dynamic composition.
2. Accounting in Writing:
   • Writers can also “account” for narrative flow using these systems, creating a scaffold on which the counting of words, sentences, or chapters happens according to Fibonacci or prime patterns. This hidden structure adds depth and rhythm, subtly guiding how the reader forms mind-pictures and interprets the unfolding narrative.

powerful tools for organizing

While not traditionally thought of as accounting systems, Fibonacci and prime numbers serve as powerful tools for organizing and counting elements in both visual art and writing. They allow creators to structure complex, organic forms that naturally engage the viewer or reader’s imagination, helping to construct vivid mental images—or mind-pictures—that tell a deeper story. By intertwining these number systems with narrative and visual elements, both painting and writing become forms of accounting, recounting, and creating deeply immersive experiences.

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