AI – ‘Yes, similar geometric patterns, particularly the meander or Greek key, appear in both ancient Roman mosaics and the design arrangement of megalithic structures, sometimes linked to sacred geometry and shared cosmological ideas or practical construction methods. For example, a simple algorithm could construct intricate meander patterns found in both Roman pavement mosaics and ancient art from other cultures, such as Angola and South India. Some scholars suggest that the use of these patterns in both art forms reflects a shared ancient understanding of the cosmos, while others point to the mobility of artisans and the circulation of pattern books as reasons for their prevalence.
 

Mosaics and Patterns

• Geometric Patterns:

Ancient mosaics, particularly Greek and Roman ones, often featured geometric designs like the meander (Greek key), the guilloché (interlacing strands), and the swastika. 

• Symbolic Meaning:

Geometric patterns in mosaics could be purely decorative or hold symbolic or spiritual meaning, sometimes conveying cosmological ideas. 

• Diffusion:

The recurring nature of these designs in the Roman world can be attributed to the movement of skilled craftsmen and the use of pattern books, which helped spread designs widely. 

Megalithic Structures and Patterns

• Sacred Geometry:

Some theories propose that megalithic structures incorporate patterns based on sacred geometry, where certain proportions and forms are given cosmic or spiritual significance. 

• Cross-Cultural Similarities:

The recurrence of specific geometric patterns in megalithic sites across different cultures suggests a potential shared understanding of fundamental principles or a common, albeit rudimentary, algorithmic approach to their creation. 

Connecting Mosaics and Megaliths 

• Shared Motifs:

The recurring geometric patterns found in mosaics can have parallels with the design arrangement and masonry of some megalithic structures, suggesting a common thread in ancient design principles.

• Practicality and Spirituality:

The same patterns might have emerged from both practical (like using simple construction methods) and spiritual motivations (like encoding cosmological ideas or a sense of order into monumental architecture).’

AI – ‘Yes, it’s widely believed by some that messages are encoded in the design and masonry of ancient megalithic structures, particularly through the principles of sacred geometry. This system of geometry, where proportions and forms are given spiritual or cosmic significance, was used by many ancient cultures to express cosmological ideas. While not all cultures universally shared these principles, the recurrence of certain patterns across diverse civilizations suggests a shared understanding of the cosmos and a desire to encode these ideas into their monumental architecture. 

How messages were encoded:

• Sacred Geometry:

Specific geometric ratios and shapes were believed to possess intrinsic spiritual or cosmic significance. These were incorporated into architectural designs to convey profound spiritual or cosmological meanings. 

• Cosmological and Astronomical Alignment:

The arrangement of stones in structures like stone circles was likely for ritual or astronomical purposes, possibly acting as a form of “map to the stars” to help understand the cosmos. 

• Material and Craftsmanship:

The sheer scale and precise craftsmanship of megalithic structures also communicate messages about the ingenuity and engineering prowess of ancient builders. The intricate and monumental nature of the masonry itself can be seen as a testament to their advanced techniques, sparking curiosity about their knowledge and capabilities, as noted in studies by the Taylor & Francis Online and Facebook posts about Çavuştepe. 

Examples of encoded meaning:

• Mandalas and Pyramids:

In India, the Himalayas, and ancient Egypt, the design principles of sacred geometry were applied to designs and pyramids to convey spiritual and cosmological ideas, according to wealthplanning.tv. 

• Shared Cultural Significance:

Similarities in the architectural features of megalithic structures found in geographically separated regions, like India and the Caucasus, suggest a shared cultural significance or parallel development of ideas and practices, according to a Facebook post.’

AI – ‘Yes, ancient mosaics often contain encoded messages through inscriptions, symbolism, religious narratives, and political statements, functioning as a form of visual language that communicates beliefs, historical events, and social values. While some messages are explicit, such as the names of the artists or patrons, others are hidden within the imagery, using symbols or apotropaic (evil-warding) designs to convey complex ideas or beliefs to those who understood the cultural context.
 

Types of Encoded Messages

• Inscriptions:

Many mosaics include direct inscriptions with the names of the patrons, the artists, or even descriptions of the work’s creation. 

• Symbolism and Narrative:

Mosaics frequently depict scenes from myths, religious texts, or historical events, which served as visual storytelling to convey moral lessons and religious beliefs. 

• Social and Political Messages:

Depictions of rulers, elite individuals, or public events could convey power, social status, and reinforce political agendas. 

• Apotropaic Functions:

Mosaics sometimes included images or symbols designed to ward off evil spirits or the “evil eye,” such as depictions of an eye pierced by a lance or mythological figures with prominent phalli. 

Examples of Encoded Messages

• Artist Signatures:

A mosaic from Thebes (6th century AD) named Demetrios as the designer and Epiphanes as the artist who executed it. 

• Patronal Pride:

A third-century AD mosaic in Vlisippara, Tunisia, showcased the creator Sabinianus’s pride in his work, despite the poor quality. 

• Religious Beliefs:

Byzantine mosaics often featured biblical stories and figures to reinforce Christian faith. 

• Power and Wealth:

The Great Hunt mosaic at Villa Romana del Casale in Sicily illustrates the power and wealth of the Roman elite through its depiction of exotic beast hunts. 

How Messages Are Decoded

• Visual Analysis:

Analyzing the visual elements, symbols, and narratives within the mosaics provides insights into the culture that created them. 

• Contextual Understanding:

The context of the mosaic, such as the location of the villa or the religious building, helps to interpret its intended meaning. 

• Cultural Knowledge:

Understanding the specific cultural, religious, and mythological references used in the mosaic is essential for decoding its deeper meaning.’ 

AI – ‘Egypt features prominent structures like the Pyramids of Giza and the Sphinx, while Ethiopia is known for the Tiya Stelae and other megalithic sites with stelae and dolmens. Yemen contains megalithic structures from the ancient kingdoms of Saba and Himyar, though specific site names are not detailed in these results. In Korea and Japan, megalithic sites include stone circles, dolmens, and tumuli from the Jomon and Jomon-like cultures. Peru is home to the massive Sacsayhuaman fortress and other Inca sites with huge stone walls.
 

Egypt 

• Pyramids of Giza and Sphinx:

Iconic and massive stone structures primarily built as tombs for pharaohs and a monument to a mythical creature.

• Temples:

Large stone temples, such as the Karnak Temple Complex and Luxor Temple, exhibit impressive megalithic architecture.

Ethiopia 

• Tiya Stelae:

A UNESCO World Heritage Site featuring megalithic stelae (standing stones), tumuli (burial mounds), and dolmens (stone burial chambers) dating to the Late Neolithic and early Bronze Age, according to Testbook.

• Omo Valley Stone Platforms:

Associated with the Bodi peoples, these stone platforms were likely connected to ritual activities, indicating a strong tradition of megalithic construction.

Yemen 

• Sabaean and Himyarite Ruins:

Ancient kingdoms like Saba and Himyar left behind significant megalithic structures.

• Marib Dam and Ma’rib Dam:

An ancient dam that used megalithic construction techniques, demonstrating advanced engineering in the region.

Korea 

• Dolmen Sites:

Korea has many dolmen sites, with one of the largest being the Damyang dolmen site.

• Stone Circles:

Found across the country, particularly in the Jomon culture, these are large arrangements of stones that were likely used for ritual or astronomical purposes.

Japan 

• Tomb Mounds:

The extensive tumuli (burial mounds) of the Kofun period, like the Tomb of Emperor Nintoku, are large megalithic structures.

• Jomon Stone Circles:

Prehistoric Jomon people constructed various stone circles, some of which are found on the islands of Hokkaido and Honshu.

Peru 

• Sacsayhuamán:

A fortress on the outskirts of the city of Cusco built with massive, interlocking stones.

• Machu Picchu:

The ancient Inca city, with its walls and buildings, showcases incredible megalithic masonry, where stones are fitted perfectly without the use of mortar.

• Ollantaytambo:

An important Inca site with formidable stone walls and terraces built from enormous megaliths.’

See also:

• Yemen’s Ancient Megalithic Mysteries Part 1 – Timna’s Cyclopean Architecture: Yemen’s Ancient Megalithic Mysteries Part 1 – Timna’s Cyclopean Architecture
• Yemen’s Hidden Megaliths: Baraqish, Awwam, Barran, and the Old Marib Dam: Yemen’s Hidden Megaliths: Baraqish, Awwam, Barran, and the Old Marib Dam
• Uncovering Ethiopia’s Ancient Megaliths Part 1: The Mysteries of Axum: Uncovering Ethiopia’s Ancient Megaliths Part 1: The Mysteries of Axum
• Uncovering Ethiopia’s Ancient Megaliths Part 2: Pre-Axumite Temples and Connections to Yemen: Uncovering Ethiopia’s Ancient Megaliths Part 2: Pre-Axumite Temples and Connections to Yemen
• Ethiopia’s Ancient Megaliths Part 3: Lalibela’s Rock-Hewn Churches & Mysterious Standing Stelae: Ethiopia’s Ancient Megaliths Part 3: Lalibela’s Rock-Hewn Churches & Mysterious Standing Stelae
• Secrets in Stone: Secrets in Stone – YouTube

I have spent the entire summer carrying out research for my next book – ‘Mediation of Cultural Heritage Disputes’, and am on schedule to complete my in-depth reading of the Research Handbook On Intellectual Property and Cultural Heritage (2022) edited by Irini Stamatoudi, in two days time.

While the book was not written for Mediators, it has sparked new and creative ‘win/win’ ideas in my mind, for both Mediation and Mediation Advocacy in Cultural Heritage Disputes – which almost uniquely, take place within the shared space of overlapping Public International Law and Private Law dimensions.

That essentially leaves two more books to read in-depth in September:

·       The Settlement Of International Cultural Heritage Disputes (2014) by Alessandro Chechi; and
·       China, Cultural Heritage, And International Law (2018) by Hui Zhong,

So, by the end of September, I will have completed my 1st in-depth ‘reading run’ of nearly all of the ‘core’ titles for the book, that are listed in the Research Bibliography on the ‘Mediation of Cultural Heritage Disputes’ page at www.carlislam.co.uk.

Then I can start putting pen to paper in October.

In parallel, I will carry out two more reading runs of the entire research material, as the draft of the book progresses, and I have already assembled my first outline draft of the book, i.e. as the anatomical skeleton of the book.

Meanwhile, I am going offline until my next online talk to the SCMA on 11 November 2025 – ‘Mediation of International Cultural Heritage Disputes – Part 1: Introduction & Overview.’

For more information about the book, please visit the ‘Mediation of Cultural Heritage Disputes’ page at www.carlislam.co.uk, which contains the current Chapter Structure.

AI – ‘Yes, ancient art encodes a significant geopolitical legacy for mankind. Far from being simple decorations, these visual messages communicate beliefs, social hierarchies, and power structures that define geopolitical realities.

While not always explicit like a modern political map, the narratives in ancient art provided the foundational context for how people understood their place in the world and their relationship to other societies. 

This is evident in several aspects of ancient art:

• Political propaganda: Ancient rulers and elites used art to reinforce their status and authority. Through idealized portraits and depictions of military victories, they communicated a specific political message to their subjects and rivals. For example, Roman victory arches and Egyptian tomb paintings celebrated military conquests and reinforced imperial power.
• Geographical and territorial claims: The art of ancient cultures could be used to make claims about their ancient ethnic origins and contested territories, especially as foundational stories for modern nation-states. For instance, a 19th-century Liebig trading card series on French history depicted the Gallic leader Vercingetorix’s defeat by the Romans as a foundational national episode, associating the modern state with ancient inhabitants and their land.
• Cultural dominance and international relations: Ancient art was not static. The movement of artifacts, whether through trade, plunder, or diplomacy, played a role in international relations. The display of certain artifacts in foreign capitals was an assertion of modernity or a tool for diplomacy. For example, the traveling exhibition of Tutankhamun’s artifacts during the Cold War was a powerful statement of Egyptian modernity.
• Encapsulation of social values and conflict: Art can reveal how societies conceptualized war, peace, and their relationships with outsiders. For example, ancient depictions of peace as a female figure, or war as a normal state of being, influenced how real-world conflicts were handled. Studying these representations offers insights into the “win-lose conceptualizations” of ancient geopolitical dynamics.
• Coded communication: Ancient art, particularly in tombs, sometimes used symbols to encode hidden messages, such as military strategies or political secrets. This reveals a deep and complex level of geopolitical thought beyond surface-level representations. Artificial intelligence is now being used to decode such ancient symbols, offering new insights into historical politics.
• The landscape as a geopolitical text: Ancient cultures often attached specific meanings to landscapes, which were then reinforced through visual art. This helped to shape national identities and the geopolitical self-perception of a people. This “geopolitical gaze” used art to define territory and a people’s place within it.’

My Q. – ‘What coded communications in Ancient Art e.g. symbols has AI decoded?’

AI – ‘AI is used to decode ancient texts and symbols by recognizing patterns, restoring damaged inscriptions, and assisting scholars in translating lost languages, with successful applications in ancient Cuneiform, Egyptian Hieroglyphs, and Latin. AI-powered tools like ProtoSnap and Fabricius identify and reconstruct symbols, while projects like Google’s Aeneas help scholars restore missing Latin words in inscriptions, expanding our knowledge of ancient history.  

Cuneiform 

• What it is:

The world’s oldest known writing system, featuring wedge-shaped symbols on clay tablets.

• AI’s role:

Projects like ProtoSnap use AI to recognize and reconstruct cuneiform characters with high accuracy, even accounting for stylistic variations. This speeds up the translation of the vast number of digitized cuneiform tablets, expanding our understanding of ancient Mesopotamia.

Ancient Egyptian Hieroglyphs 

• What it is: A complex writing system of symbols and images used in ancient Egypt.
• AI’s role: The abricius program employs machine learning to assist researchers in decoding hieroglyphs. Users can upload photos, create digital layers, and the program can suggest potential translations, making the process more accessible.

Latin Inscriptions 

• What it is:

Ancient inscriptions written in the Latin language, often found on stones and monuments.

• AI’s role:

AI models like Aeneas are trained to compare new inscriptions with thousands of known examples. This allows the AI to suggest reconstructions of missing words, assign texts to historical provinces, and even estimate dates, offering valuable insights to historians.

How AI Works in Decipherment

• Pattern Recognition:

AI, particularly through machine learning, excels at recognizing complex patterns in images, which is crucial for identifying and interpreting ancient symbols. 

• Data-Driven:

By analyzing vast datasets of digitized texts, AI learns the relationships between different characters and sequences, helping to reconstruct broken or faded writing. 

• Augmenting Human Expertise:

AI tools like Fabricius and Aeneas are designed to support, not replace, human experts. They provide powerful assistance, enabling scholars to work more efficiently and make new discoveries.’ 

AI – ‘Ancient art left an esoteric legacy by encoding spiritual and mystical knowledge in its symbols, geometry, and imagery, with meanings often accessible only to the initiated. Instead of being merely decorative, art in ancient cultures served as a vessel for complex concepts about creation, divinity, and transformation. 

Ancient Egypt

Ancient Egyptian art is a primary example of this esoteric tradition, where art and architecture served to communicate profound, hidden knowledge. 

• Symbolic imagery: Hieroglyphs were not just a form of writing but also powerful symbols believed to convey and invoke magical powers. For the initiated, they had multiple layers of meaning.
• Funerary art: The elaborate art found in tombs and on sarcophagi was part of a secret, complex system of beliefs about the journey to the afterlife. These images served as a guide for the deceased through the underworld, ensuring their rebirth.
• Ritualistic purpose: Temple art and adornments were functional components of rituals. By performing rites in a sacred space filled with symbolic art, priests and the initiated sought to interact with the divine. 

Ancient Greece

The esoteric legacy of Greek art and philosophy was primarily transmitted through mystery schools and hermetic traditions. 

• Pythagoreanism and Platonism: These schools of thought influenced artistic expression through a focus on divine mathematical and geometric principles. The harmony and ideal proportions seen in Greek art, architecture, and sculpture were considered reflections of a deeper, hidden reality.
• Mythology: Greek mythology, though seemingly a collection of stories, held encoded philosophical truths and allegories about humanity’s relationship with the divine. These myths were represented visually in art, where their symbolic nature could be contemplated. 

Other traditions

Similar esoteric legacies exist in other ancient cultures, from Eastern philosophies to the art of Indigenous peoples. 

• Eastern traditions: Esoteric Buddhism in East Asia, for example, used art as a necessary component for spiritual and worldly goals. Mandalas and thangkas in Tibet and the Himalayas depicted intricate cosmic diagrams used for meditation and visualization.
• Indigenous Australian art: In Queensland, rock art dating back tens of thousands of years depicts spirit beings, revealing the mystical beliefs that shaped early Indigenous societies. The elongated, ethereal figures are a visual link to their stories and connection to the spiritual world. 

Enduring influence

The esoteric traditions of ancient art have had a lasting impact, influencing later mystical movements and contemporary art. 

• Renaissance and Western esotericism: The Renaissance saw a revival of interest in hermeticism, alchemy, and Kabbalah, which influenced artists who sought to encode secret knowledge into their work.
• Modern art movements: Occult and esoteric themes influenced modern artists like Wassily Kandinsky, who believed art could access otherworldly realms. More recent movements have incorporated esoteric themes to explore contemporary issues related to environmentalism, gender, and digital culture.
• Modern media and culture: Today, esoteric art, imagery, and symbolism are frequently repurposed in popular media, including film, literature, and music videos. In this way, ancient esoteric traditions continue to evolve and influence contemporary cultural expression.’

AI – ‘The sacred Benben stone was a primordial mound, or a stone shaped like a cone or short obelisk, in ancient Egyptian mythology that represented the first land to emerge from the chaos waters during creation. Located in the temple of Ra at Heliopolis, it was where the first rays of the sun fell. The Benben symbolized the sun god Ra, the Bennu bird (a precursor to the phoenix), and served as the architectural prototype for the pyramidions (capstones) of later pyramids and obelisks.

Symbolism and Meaning

• Primordial Mound:The Benben was the foundation for creation, the first piece of dry land to appear from the primeval waters (Nu). 
• Sun God Ra:It was closely associated with Ra, the sun god, representing the first place the sun’s rays touched each morning. 
• Bennu Bird and Phoenix:The mythical Bennu bird was said to live on the Benben stone, a connection that may have inspired the concept of the phoenix. 
• Cycle of Life and Renewal:The Bennu bird and the sun’s cyclical appearance linked the Benben to the concepts of rebirth and the renewal of life. 

Architectural Significance 

• Prototype for Pyramids and Obelisks:The Benben served as the original model for the pyramidions that capped the summits of later Egyptian pyramids and for obelisks.
• Temple of the Benben:The sacred stone was housed in a shrine called the “House of the Benben” within the temple precinct at Heliopolis.

Lost but Preserved

• Lost Original:The original Benben stone is lost, but its concept is reflected in the pyramidions found on many pyramids, including the Pyramid of Amenemhat III, one of which is housed in the Egyptian Museum in Cairo. 
• Possible Meteorite:Some theories suggest the original Benben stone might have been a meteorite.’ 

When I put out my bedroom lights and rested my head on a pillow last night the  phrase – ‘As Above, So Below’, from the ancient text, the Emerald Tablet, which is a cornerstone of Hermetic philosophy and alchemy, suddenly popped into my head.

Then, I had what I can only describe as being an Epiphany.

I saw in my mind an image of a Pyramid placed on top of an inverted mirror image of itself with a circle around the circumference of the ‘holistic’ diamond shaped image, and also around the transverse radius.

Then it struck me like a thunderbolt – this image represents a globe.

You can draw it on a piece of paper.

I keep a pad of paper next to my bed with a pen in case I wake up in the middle of the night with a new idea, and did exactly that.

I then had a peaceful night’s sleep and when I was awoken by the Sun’s rays this morning another idea occurred to me.

I knew that the Great Pyramid of Giza was originally covered by smooth limestone facing blocks, i.e. the steps underneath were not visible. But of course in designing the Pyramid they must have been drawn on a Plan.

Then it occurred to me what if each course i.e. layer of these steps when drawn horizontally on a spherical map of the earth i.e. a globe, could be designated as a line of latitude?

Then as I lay in bed I imagined the Great Pyramid of Giza visually turned on one side.

Then it occurred to me, if when the Pyramid was turned on its side, could each of the course steps i.e. each layer of the steps, vertically be designated as a line of longitude?

Then I realized, if they could, this would create a grid.

My next thought was, if e.g. at the intersection of any grid lines a fixed point in space i.e. a bright star, observable with the naked eye in the night sky could be marked as a fixed point on the grid e.g. by creating a channel inside the masonry of the Pyramid that pointed directly to the star on a particular date, then somehow using math to factor in precession, could a map of the sphere created by two pyramids be used as a navigational tool at sea, i.e. to chart a position by reference to lines of latitude and longitude?

So, in the office this morning, I asked AI – ‘Could a grid on a map of a sphere be used by sailors in Antiquity to navigate by the stars?’

AI replied – ‘Yes, ancient mariners could have used a grid on a spherical map to navigate by the stars, as the concept of spherical coordinates and astronomical positioning was understood in antiquity, notably by figures like Hipparchus, who compiled stellar catalogs and used spherical trigonometry. While ancient star charts were less precise than modern ones and lacked the detailed tables and accurate chronometers of later eras, sailors used instruments like the astrolabe and quadrant, combined with knowledge of star movements and constellations, to determine their latitude and general position at sea. 

Understanding the Spherical Nature of Navigation 

• Spherical Coordinates:

The Earth is a sphere, and ancient astronomers like Hipparchus understood that a spherical coordinate system, which uses two angles to define a point on a surface, was the natural way to describe positions on a sphere.

• Spherical Trigonometry:

Hipparchus developed models using spherical trigonometry to understand celestial movements.

Key Tools for Ancient Celestial Navigation

• Astrolabe:

This device could measure the altitude of celestial bodies and, with the help of tables or charts, help determine latitude. 

• Quadrant:

Originally an astronomical instrument, the quadrant was adapted for navigation to measure the height of stars above the horizon. 

• Star Maps and Charts:

While rudimentary compared to modern charts, ancient mariners used star maps to identify constellations and celestial bodies. 

How They Used the Grid (Conceptually)

• Latitude:

In the Northern Hemisphere, sailors could determine their latitude by measuring the angle of the North Star (Polaris) above the horizon, as this angle is roughly equivalent to the observer’s latitude. 

• Position Lines:

By taking sights on two or more celestial bodies, and referencing their position on a spherical map, sailors could conceptually draw lines or circles to determine their location. 

• Star Position and Time of Year:

Sailors had to know which constellations were visible at different times of the year and in different hemispheres to use them effectively. 

Limitations in Antiquity

• Accuracy:

Ancient instruments and charts lacked the precision of later tools like the sextant, limiting navigational accuracy. 

• Longitude:

Accurately determining longitude was a significant challenge without precise timekeeping devices (chronometers), which were invented much later. 

• Focus on Coastal Sailing:

While some advanced navigation occurred, much of ancient maritime activity, especially in the open ocean, was focused on more familiar waters, like the Mediterranean.’

See also my recent blogs at www.artandcivilization.tv:

• ‘The Hermetic Texts’ – in which I also enquire – ‘‘Is there a nexus between the Hermetic Texts, The Emerald Tablet, Alchemy and the Philosopher’s Stone?’
• ‘Aesthetically, could it be argued that the Giza Necropolis creates a hologram of Orion’s Belt?: 
• ‘Based upon the evidence of Egyptian ship-building techniques is it possible that a ship was designed and built for disassembly transportation to the Atlantic and Indian Oceans for reassembly and seafaring?’
• ‘Did the builders of the Great Pyramid at Giza know that the Earth was round?’ 

Q’s and comments added:

My Q. – ‘What is Spherical Trigonometry?’

AI – ‘Spherical trigonometry is a branch of geometry that studies the properties of triangles drawn on the surface of a sphere, rather than on a flat plane. This field is essential for calculations in astronomy, navigation, and geodesy, where the curvature of the Earth or celestial bodies must be taken into account.’

My Q. – ‘Who invented i.e. was the Father of Spherical Trigonometry.’

AI – ‘The title “Father of Spherical Trigonometry” is not definitively attributed to a single individual but is often credited to Menelaus of Alexandria for his surviving text Sphaerica, or to Ibn Muadh Al-Jayyani who has also been called the “Father of Modern Spherical Trigonometry”. Other significant figures include Hipparchus (the father of trigonometry) for his early work on solving spherical triangles, and Nasir al-Din al-Tusi for making trigonometry an independent branch of mathematics with significant contributions to spherical trigonometry. 

Key Figures in Spherical Trigonometry

• Hipparchus (c. 190–120 BC):

Considered the “father of trigonometry” in general, he provided methods for solving spherical triangles and compiled early trigonometric tables. 

• Menelaus of Alexandria (1st century AD):

His surviving work, Sphaerica, is the first known text on spherical trigonometry, containing theorems and rules for spherical geometry. 

• Ibn Muadh Al-Jayyani (10th/11th century):

An Islamic mathematician and astronomer who made significant contributions to spherical trigonometry and has also been called the “Father of Modern Spherical Trigonometry”. 

• Nasir al-Din al-Tusi (13th century):

A Persian polymath who established trigonometry as a branch of mathematics independent from astronomy, providing extensive expositions on spherical trigonometry, including stating the law of sines for spherical triangles.’ 

So, if the builders of the Great Pyramid of Giza knew about Spherical Trigonometry, they possibly acquired or developed this knowledge over 12 thousand years before Hipparchus.

My Q. – ‘What arguments have been made by Charles Hapgood that older civilizations possessed advanced knowledge of spherical trigonometry?’

AI – ‘Charles Hapgood argued that ancient civilizations possessed advanced knowledge of spherical trigonometry, evidenced by their sophisticated world maps, such as those he studied from the Middle Ages (Portolano charts) and the Piri Reis map. He claimed these maps were compiled using a spherical projection method that ancient geographers lacked, suggesting the original mapmakers—possibly ancient Egyptians—knew how to translate spherical surfaces to flat maps with mathematical precision, an understanding lost to the Greeks. 

Hapgood’s Core Argument

• Spherical Projection vs. Flat Maps:

Hapgood’s central argument was that some ancient world maps, despite their flat appearance, were based on original spherical maps. 

• Mistranslations by Later Civilizations:

He proposed that ancient geographers, like the Greeks, were confronted with spherical maps and lacked the understanding of spherical trigonometry to interpret them accurately. 

• Evidence in Ancient Maps:

According to Hapgood, they had to translate the complex spherical geographical data (latitudes and longitudes) into terms of a flat surface, leading to distortions. 

• Ancient Egyptian Knowledge:

He concluded that the ancient Egyptians possessed advanced knowledge, including the ability to accurately translate between spherical and flat surfaces using mathematical methods, while the Greeks did not. 

Evidence from Maps

• Ancient Origin:

Hapgood identified cartographic features on maps, such as the Piri Reis map and others from the Age of Discovery, that appeared to show a level of geographic accuracy and detail suggesting their origin was from an earlier, more scientifically advanced civilization. 

• Missing Information:

He noted that even with distortions, the maps often contained significant geographic details, like the accurately placed mountain ranges on the Finaeus map, that implied a sophisticated understanding of the Earth’s shape and surface. 

• Advanced Cartography:

The accuracy of some mapped locations, even close to the poles, led Hapgood to believe that the source maps were created using advanced cartographic and mathematical principles, including spherical trigonometry.’ 

Based upon the following measurements and simple calculations, logically, the answer to this Q. is arguably Yes.

My 1^st Q. – ‘In miles what is the Equatorial Circumference of the Earth? [‘EC’]?’

AI – ‘The Equatorial Circumference of the Earth is approximately 24,901 miles. This measurement refers to the distance around the Earth at its widest point, the Equator, which is slightly larger than the circumference measured through the poles.’ 

My 2nd Q. – ‘In miles what is the Polar Radius of the Earth? [‘PR’].’

AI – ‘The Earth’s polar radius is approximately 3,950 miles This is slightly shorter than its equatorial radius because Earth is not a perfect sphere but rather an oblate spheroid, bulging at the equator due to its rotation.

My  3rd Q. – ‘In feet what is the perimeter of the base of the Great Pyramid at Giza? [‘PB’].’

AI – ‘The perimeter of the base of the Great Pyramid of Giza is approximately 3,024 feet. This is calculated by multiplying the length of one side of its square base, which is about 756 feet, by four.’

My 4th Q. – ‘In feet what is the height of the Great Pyramid at Giza? [‘PH’].’

AI – ‘The Great Pyramid of Giza was originally about 481 feet (147 meters) tall. Today, its height is approximately 454 feet (138.5 meters) due to the removal of its smooth, polished limestone casing stones over the millennia.

My 5th Q. – ‘Is the ratio of the perimeter of the base of the Great Pyramid of Giza to its height very close to 2pi?’

AI – ‘Yes, the ratio of the perimeter of the Great Pyramid of Giza’s base to its height is very close to 2 pi.

My 6th Q. – ‘Could it be argued that the scale of the Great Pyramid to Earth multiplied by roughly 43,200, approximates Earth’s polar radius, and does its base perimeter, multiplied by roughly 43,200, also approximate Earth’s equatorial circumference?’

AI – ‘It can be argued that numerical correlations exist between the dimensions of the Great Pyramid of Giza and the Earth’s dimensions, using a scaling factor of approximately 43,200. …

43,200 is often linked to the Earth’s precession, a slow wobble of the Earth’s axis. The Earth precesses at a rate of approximately 1

degree every 72 years, and  43,200 is a multiple of 72.

This connection suggests a potential ancient understanding of astronomical cycles. 

Yes, it can be argued that the height of the Great Pyramid, when multiplied by approximately 43,200, approximates the Earth’s polar radius, and its base perimeter, when multiplied by roughly 43,200, also approximates the equatorial circumference.’

My 7th Q. – ‘What is EC [24,901] divided by 43,200.’

AI – ‘0.5764’ of a mile.

My 8th Q. – ‘How many feet are there in a mile?

AI – ‘5280.’

My 9th Q. – ‘What is 0.5764 multiplied by 5280?’

AI – ‘3043.39’ feet.

My 10th Q. – ‘What is 24,901 [i.e. EC] scaled down 43,200 times?’

AI – ‘To find what 24,901 is scaled down 43,200 times, you need to divide 24,901 by 43,200. 

24,901 scaled down 43,200 times is approximately 0.5764. NB AI’s answer to my Q.7 above.

My 11th Q. – ‘What is 3,950 scaled down by 43,200?’

AI – ‘3,950÷43,200 = 0.0914’ i.e. of a mile.

My 12th Q. – ‘What is 0.0914’ i.e. of a mile in feet?’

AI – ‘ 0.0914 miles is equal to 482.592 feet.’

My 13th Q. – ‘What is 481 [i.e. PH] minus 482.592?’

AI – ‘ -1.592’

My 14th Q. – ‘What 1.592 as a percentage of 481?’

AI – ‘0.331%’

In other words, it appears to be arguable that:

• the perimeter of the base of the Great Pyramid at Giza [‘PB’] could be a scaled down representation of the Earth’s Equatorial Circumference [‘EC’]; and
• the height of the Great Pyramid at Giza [‘PH’] could be a scaled down representation of the Earth’s Polar Radius [‘PR’].

So, axiomatically, did the builders of the Great Pyramid at Giza know that the earth was round?

i.e. because if you multiply:

 (iii)          PB by 43,200 it approximately equals EC; and

(iv) PH by 43,200 it approximately equals PR – with a magnitude of discrepancy of 0.331%.

The conventional dating for the Great Pyramid of Giza places its construction around 2560 BC, or approximately 4,600 years ago. This date is based on its association with Pharaoh Khufu and the historical context of the Old Kingdom period, which is further supported by archaeological finds and radiocarbon dating of organic materials found within the pyramid’s structure.

There are also theories which suggest that the Great Pyramid is over 10,000 years old. These theories are based on the Sphinx water erosion hypothesis, which argues that erosion patterns on the Sphinx and surrounding structures indicate heavy rainfall rather than wind erosion, suggesting an earlier date for their construction. 

The first practical demonstration that the earth is not flat was Ferdinand Magellan and Juan Sebastián Elcano’s circumnavigation (1519–1522), which confirmed the spherical shape of the earth.