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In this article we will continue our discussion of the geometry of the molecular and mineral world.  We will discuss the geometry of soil, rocks and minerals in this article.  We will move onto discuss the geometry of crystals in the next two articles.

“Life is squeezed into a seed, which is a soul.  Everything has soul, including minerals, plants, lakes, mountains, rocks.  Everything is sentient, even at the lowest stage of consciousness.  Once this fact is grasped there can be no more despair.”  ~ Henry Miller, Tropic of Capricorn



Geometry in the Mineral World



As we all should know, soil is important for many reasons.  It is the basis for plant growth that provides food, fuel, animal feed, medicine and raw materials for clothing, household goods and other essentials.  It supports the forests, wetlands, jungles, prairies and grasslands of the world which in turn help to prevent soil erosion.

Soil supports animal biodiversity, both above and below ground.  Soil is teeming with micro-organisms that are essential for maintaining soil quality, decomposition of matter, providing nutrients, breaking down toxic elements, and interacting with air and water to maintain a healthy environment.

Soil is necessary to maintain an adequate water supply and healthy water quality.  Water absorption properties of soil play a role in reducing pollution from chemicals in pesticides and other compounds.

Soil also provides the foundation and base materials for buildings, roads and other infrastructure.


Soil also holds the key to history – preserving artifacts of the past that can help us find a deeper understanding of Earth’s ancient history.


Symbolically speaking the soil is a medium for growth.  If your thoughts, dreams and intentions are seeds, your beliefs are the soil.  Your deepest belief systems are the medium of your growth as a human being.  Your beliefs prepare the ground and offer the nutrients that you will need to rise to your highest potential for the greatest good.

Unhealthy belief systems that revolve around powerlessness, victimization, apathy, hatred, violence, manipulation, elitism, narcissism, and so forth will not allow healthy seeds to grow.

Healthy belief systems that revolve around unity, peace, compassion, empathy, courage, strong will, and self-responsibility will allow healthy seeds to grow.

As Derek Rydall states, “It doesn’t matter what external conditions you’re planted in, your soul is your soil, and if you generate the right inner conditions – mentally, emotionally, and spiritually – your seed will have the right nutrients to thrive.”



There are many parts to soil.  Healthy soils that allow abundant growth have balanced proportions of their constituents.


Constituents of Soil: Minerals, Organic Matter, Air & Water


Symbolism of Soil

Symbolically speaking these constituents reflect different aspects of our consciousness.


Organic Matter represents the physical sustenance we take in including the foods and beverages we imbibe.  Healthy foods in balanced proportions lead to healthy bodies and healthy digestion.


Water represents our emotions.  “Like water, emotions take the form of their container.  They are shaped by our worldview, traditions, beliefs, opinions and thoughts.”  Emotions always follow beliefs and not the other way around.


Air represents our thoughts.  “Like clouds and wind, they are a pollinating source, spreading ideas over our inner landscape.”


Minerals represent the process of our spiritual transformation.  Minerals can be very dense, opaque and irregular or they can be ordered, transparent and crystallized – able to reflect and radiate the light of the Sun.  These different states mirror the transformation of our spirit from someone obsessed or distracted by material possessions, selfishness and materialism to someone who transforms into a compassionate, caring, wise individual able to radiate the light of Unity to all they meet.

The dense opaque minerals represent our material nature and the crystal represents our cosmic nature.  Together these represent the marriage of our intuition with rational thinking; wisdom with compassion; and our human nature with our divine cosmic nature.


  1. “If you can think so deeply that you can rediscover the spiritual roots of thought, if you can recognize thoughts as living, spiritual beings …(Thoughts)
  2. If you can develop a strong enough sense of your own individuality that you can become aware of your interaction with the Thought-Beings that weave in and out of yourself, yet not be overwhelmed by this reality …(Emotions)
  3. If you can recreate the ancient sense of wonder and use this sense of wonder to help awaken the willpower that lies sleeping in your deep, dark recesses …(Will Power)
  4. If the fire of love for your fellow human beings rises from your heart and causes you to weep tears of compassion …(Love/Compassion)

… Then you have been working on the Four Elements. You have begun the process of their transformation.”1



Physical Aspects of Soil (Minerals, Organic Matter, Water, Air)


Minerals ~ 45%

Minerals are naturally occurring inorganic solids.

They have an ordered internal molecular structure and a definite chemical composition.

All minerals are natural chemicals, formed by and found in nature.

Minerals are the main component of rocks and soil.

Minerals are approximately 45% of soil composition.

Over 2000 natural minerals have been identified.


Organic matter ~ 5%

Organic matter in soil makes up approximately 5%.

These include small microorganisms (microbes) responsible for decomposition, larger organisms, soil detritus, and humus.


We will discuss the particulars of the geometry of microorganisms in Articles 188-189.  Small microorganisms responsible for decomposition include:

  • Bacteria
    • Nitrogenfixation is defined as “the chemical processes by which atmospheric nitrogen is assimilated into organic compounds especially by certain microorganisms as part of the nitrogen cycle. Nitrogen in the Earth’s atmosphere is converted into ammonia (NH3 – tetrahedral) or other molecules available to living organisms.”


  • Actinomycetes
    • These are a type of bacteria that share some characteristics with fungi.
    • They form aerial mycelium – fractal-branching of filamentous growth.
    • They also produce antibiotics.


  • Fungi
    • Fungi are a food source for larger organisms.
    • They have a symbiotic relationship with plants and other organisms.


  • Algae
    • Algae make their own nutrients through photosynthesis.
    • They are also involved in nitrogen fixation.


  • Protozoa
    • Protozoa are single-celled organisms including:
      • flagellates – distinguished by flagella which are their means of movement
      • amoebae – slug-like properties; move by a “false foot” or pseudopodia
      • ciliates – largest protozoa; they move by short, numerous cilia that produce beating movements


  • Nematodes – roundworms
    • There are over 25,000 known species
    • Over half are parasitic.


  • Larger organisms (earthworms, insects, ants, mites…etc.)
  • Soil organic matter (detritus) – decomposing plant, insect and animal matter
  • Humus – stable fraction of soil organic matter formed from decomposed plant and animal tissue. Humus is highly nutritious for plant growth.


  • Water ~ 25%


  • Air pockets (gases) ~ 25%



Soil as a Representation of the Element Earth

When we think of the Four Elements Earth, Water, Air, and Fire, soil (and associated plant growth) correspond most strongly to the element Earth.

Soil represents the Earth, ‘The World Mother’ and Nature, or ‘Mother Nature’.

The Earth is associated with the square and cube.

The square and cube symbolize solid ground, matter and mass as well as the four cardinal directions (north, south, east, west), the four steps of becoming (point, line, plane, solid), the four states of matter (solid, liquid, gas, plasma or Aether), the four traditional winds, the four seasons (spring, summer, autumn, winter), the four corners of the Earth, the four blood types (A, B, AB, O), earthbound animals that walk on four legs, and the four stages of transformation in the scarab beetle and butterfly (egg, larva, pupa, adult).


The square represents the nourishing aspects of Mother Nature: She gives birth, clothes her creation with material substance and encourages their growth equally and unconditionally.


The four-cornered cross in the circle is an ancient astronomical symbol for planet Earth.

Crosses symbolize the meeting of two planes of consciousness – human and Divine.

The top arm represents the Infinite Divine.

The other three arms represent the qualities that must be balanced to achieve union with the Infinite Divine:

The lower arm represents power and courage (3rd chakra).

The right arm represents love/compassion (4th chakra).

The left arm represents wisdom/truth/honesty (5th chakra).

The 6th chakra is activated and balanced when power, love and wisdom are balanced in the individual and the individual is able to work for the greatest good and is no longer living in fear and selfishness.



The Crossroads

Black Elk said, “You have set the powers of the four quarters to cross each other.  The good road and the road of difficulties you have made to cross; and where they cross, the place is holy.”

Here we have yet another level of symbolism of the cross that represents the Crossroads.  This takes us back to the idea of “The Choice”.  The Choice hinges around the concept of learning to focus the Will so the choice can be made and continually honored.  This Choice is the choice of walking the road of unity, compassion and peace (acceptance and forgiveness); or choosing to walk the road of separation, selfishness and violence (control and manipulation).

This all-important choice does not occur only once in a single lifetime, but every single day, at every moment where options are present to move us forward in the world.

It is not a choice made once, but a choice made at all times.



Soil Chemistry

Soil contains water soluble weathering products such as calcium, magnesium, sodium and potassium.

It also contains more relatively insoluble elements such as iron and aluminum.


Cation Exchange Capacity:

A cation is a positively charged ion.

Cation Exchange Capacity is the number of exchangeable cations per dry weight that a soil is capable of holding at a given pH value.

It is used to measure soil fertility, nutrient retention capacity, and the capacity to protect groundwater from cation contamination.


Some plant nutrients and metals exist as positively charged ions (cations) in the soil:

  • hydrogen (H+)
  • aluminum (Al+3)
  • calcium (Ca+2)
  • magnesium (Mg+2)
  • potassium (K+)



Types of Soil: Sand, Clay, Silt & Loam

  • Sand
    • Sand is the largest soil particle (2.0 to 0.05 mm).
    • Sand is composed of silicon dioxide (SiO2)
    • Silicon dioxide’s most common form is in quartz.
    • SiO2 has a tetrahedral structure with four oxygen atoms surrounding a central Si atom.

    • These molecules form a hexagonal lattice.


  • Clay
    • Clay is the smallest soil particle (less than .002 mm).
    • It is composed of an octahedral sheet sandwiched between two tetrahedral sheets.
    • These are the layers of tetrahedrally arranged silicate and octahedrally arranged aluminate groups.

    • Clay and humus are the only types of soil particles that have electrostatic surface charges that attract and hold ions.


  • Silt
    • Silt is composed of fine sand, clay or other material carried by running water and deposited as a sediment.
    • Its size is between fine clay and larger sand (0.05 to 0.002 mm).


  • Loam
    • A loam soil is composed of roughly equal concentration of sand, silt and clay.

Soil Composition Chart



12 Soil Classes

  • Clay
  • Sandy Clay
  • Silty Clay
  • Sandy Clay Loam
  • Clay Loam
  • Silty Clay Loam
  • Sandy Loam
  • Loam
  • Silt Loam
  • Silt
  • Loamy Sand
  • Sand

Soil Profile


Geometric Soil structure – Peds

Soil peds are natural, relatively permanent aggregates, separated from each other by voids or natural surfaces of weakness.  They are geometric in structure and mirror crystal forms, although with far less regularity and permanence.  However they are relatively permanent and maintain their structure through cycles of wetting and drying.


These structures are as follows:

  • Platy
    • flat and plate-like
    • oriented horizontally


  • Prismatic
    • bounded by flat to rounded vertical faces


  • Columnar
    • similar to prisms but bounded by flat or slightly rounded vertical faces


  • Angular and subangular (Blocky)
    • block-like or polyhedral


  • Granular and Crumb
    • spherical or polyhedral; bounded by curved or irregular faces



Geometric Cracking and Polygonal Terrain: Hexagonal Y-junctions and Convection Cells

Coequal molecular bonds tear apart and break into three-way 120-degree joints.

This is seen in more elastic materials that crack relatively rapidly over hours, days, or months.

Examples are: concrete and rocks; drying mud; coffee grounds in the filter and bullets piercing an egg.


Hexagonal cells are the result of natural convection as well.  Rayleigh-Benard convection “is a type of natural convection, occurring in a plane horizontal layer of fluid heated from below, in which the fluid develops a regular pattern of convection cells known as Benard cells (pictured below).

Wikipedia tells us “Convection cells can form in any fluid, including the Earth’s atmosphere, boiling water, soup, the ocean, or the surface of the sun.  The size of convection cells is largely determined by the fluid’s properties.  Convection cells can even occur when the heating of a fluid is uniform.”

These hexagonal cells can easily be creating in a lab.  Here a frying pan containing a mixture of silicone oil and fine aluminum powder is heated.  These hexagonal cells spontaneously form.

Each convection cell has an upward moving center that carries hot fluid up from the bottom of the pan.  Once the hot fluid has reached the surface of the cell it flows outward to the edge of the cell where it descends and cools.2

The movement is the upswelling of warmer liquid from the heated bottom layer.  This upswelling spontaneously organizes into a regular pattern of hexagonal cells.

This continual movement of the particles (in this case aluminum powder) is reminiscent of the movement of the colloids in Cymatics.  In both cases the particles are attracted to the invisible geometric framework and flow along edges and corners of the geometry.

The process of Voronoi tessellations and Delaunay triangulation (seen below and Article 180) can clearly be seen in these images.  This same process is used to form hexagonal cellular structures in plants, animals and insects (such as insect wings).


This fascinating process of fluid dynamics shows how the same hexagonal structures can form in a universe filled with fluid-like Aether.

We see this with the formation of large-scale structures on a galactic scale as well as the formation of cellular structures of smaller living organisms.



Polygonal Terrain – Hexagonal Y-Junctions

Hexagonal Y-junctions are seen naturally in:

Giant’s Causeway – Northern Ireland


Fingal’s Cave – Isle of Staffa – Scotland


Devil’s Postpile – California


Devil’s Tower – Wyoming


Reynisfjara Black Sand Beach – Iceland

Credit: Arjen Toet


Svartifoss Waterfall – Vatnajokull National Park – Iceland

Credit: Andreas Tille


Hexagon Pool – Yehudiya Forest Nature Reserve – Golan Heights, Israel

Credit: Leonid Rogachevsky


Los Prismas Basalticos – Hidalgo, Mexico

Credit: Diego Delso


Cape Stolbchaty – Kunashir Island, Kuril Islands – Russia


Basalt Jusangjeolli Cliffs – Jeju Island – South Korea

Credit: Joycekim77


Columns of Ghenh Da Dia – Phu Yen, Vietnam

Credit: Prince Roy


Los Organos – La Gomera, Canary Islands

Credit: Rainer Haessner


Salar de Atacama salt flats – Chile

Credit: Pedro Szekely


“We identified the special ratio of speed, column size and diffusion rate that is the same for all cases, finding that the slower the cooling process, the larger the resulting columns would be.”3


They also enable the prediction of the shapes of other fracture networks such as drying mud, cracking paint or the patterns of fracture in permafrost.

In all cases the cracking is geometric.  This reflects the concept that Nature uses forms that are a reflection of the minimum energy that a system can arrange itself in to provide the most stable state.



Rectilinear (T-junctions)

T-junctions form when a homogeneous slurry is dried or cooled uniformly.

The vertices of these patterns typically contain one crack path intersecting another straight crack at right angles.

Longer times, like years, decades, or centuries result in a four-cornered pattern.

Examples are: old paint; tree bark; porcelain; tiles and glazed ceramic mugs.



Rocks & Stones

Rocks and stones are associated with solidity, stability and being grounded.  The longevity of structures made of rock and stone often means that they are associated with the divine and eternal.  Stone formations often symbolize the passage from one life to the next.

Rocks can also symbolize strength of will, passion and determination.


Stones are essentially rocks that have been worn smooth by the passage of wind or water.  Symbolically our thoughts and emotions are the spiritual water that polishes the rough rock into a smooth, beautiful and shining stone.

Rough ashlars and perfect ashlars are associated with humanity’s moral and spiritual life.  In Freemasonry the ‘rough ashlar’ is a stone taken directly from the quarry which represents the uninitiated soul.  A smooth ashlar (‘perfect ashlar’) represents the initiate who, through education and diligence, has learned the spiritual lessons and lives an upstanding life in which wisdom is fully balanced with compassion and enlightenment for the greatest good is the goal of existence.


Rocks are solid substances that occur naturally because of the effects of three basic geological processes:

  • Magma solidification (This symbolically represents the spiritual fire (magma) condensing into the physical material reality.)
  • Sedimentation of weathered rock debris (This represents the digestion (contemplation) of physical experiences, breaking them down and releasing that which is not needed so that they can come together in a more fluid way to nurture new growth.)
  • Metamorphism (This represents the transformation of the physical material self into a spiritual divine being through the use of the consciousness.)


These three processes together represent the full-circle transformation of the metaphysical to the physical and back to the metaphysical again, yet on a higher level.  It is the completion of a journey and a return to the origin after a purifying transformational experience.

These three processes also reflect the trilogy of the Hero’s Journey: Separation, Initiation and Return.  (See Article 28).

As Keith Critchlow writes, “Three…represents the essential tendencies inherent in the universal spirit:  this is expressed in triangular form as the descending movement away from the first principle, the horizontal expansion and finally the returning ascent back to the first principle.”



Three Main Types of Rocks

Igneous – produced by solidification of molten magma from the Earth’s mantle. (Metaphysical to physical)


Sedimentary – formed by burial, compression and chemical modification of deposited weathered rock debris or sediments at the Earth’s surface. (Horizontal expansion and growth)

Metamorphic – created when existing rock is chemically or physically modified by intense heat or pressure. (Physical back to metaphysical)


As Jakob Bernoulli wrote, “Although changed, I arise again the same.”



Common Elements Found in Earth Rocks

Element & Atomic Number Chemical Symbol Percent Weight in Earth’s Crust
Oxygen (8) O 46.6
Silicon (14) Si 27.72
Aluminum (13) Al 8.13
Iron (26) Fe 5
Calcium (20) Ca 3.63
Sodium (11) Na 2.83
Potassium (19) K 2.59
Magnesium (12) Mg 2.09



Nine Classes of Minerals



There are over 100 known minerals.

Many are composed of only 1 element.

These include metals and nonmetals.

Some metals include: Gold, Silver, and Copper.

Some nonmetals include: sulfur, diamonds, and graphite.

Diamond – naturally occurs as octahedra


Sulfide Group

The sulfide group is economically important.

Many consist of metallic elements with sulfur.

Most ores of important metals such as mercury, iron and lead are extracted from sulfides.  These are used in all kinds of manufacturing processes and products.

Some of these include:

  • Cinnabar – HgS – Mercury
  • Pyrite – FeS2 – Iron
  • Galena – PbS – Lead

Dodecahedron shaped crystals of pyrite from Italy



The principle chemical constituents of halides are fluorine, chlorine, iodine, and bromine.

Many are very soluble in water.

They tend to have a highly ordered molecular structure and high degree of symmetry.

The most well-known is halite – NaCl – cubic rock salt.

A macro shot of salt crystals taken in the Natural History Museum of Vienna.  Credit: wlodi



Oxides are compounds of one or more metallic elements combined with oxygen, water or hydroxyl (OH).

These minerals show the greatest variations of physical properties.

They can be hard or soft.  They can have a metallic luster or be clear and transparent.

Examples include:

  • corundum
  • cuprite
  • hematite

Dodecahedral Hematite.  Credit: Rob Lavinsky,



Carbonates contain one or more metallic elements chemically associated with CO3.

Most are lightly colored.

They are transparent when relatively pure.

All are soft and brittle.

All effervesce when exposed to warm hydrochloric acid.

Examples include:

  • calcite
  • dolomite
  • malachite




Sulfates contain one or more metallic element in combination with the sulfate compound SO4.

All are transparent and soft.

Most are heavy.

Some are soluble in water.

Examples include:

  • anhydrite
  • gypsum




Phosphates are one or more metallic elements chemically associated with the phosphate compound PO4.

Most are heavy but soft.

They are usually brittle and occur in small crystals of compact aggregates.

One example is apatite.

Hexagonal apatite.  Credit: Kevin Walsh



Silicates are the largest group of minerals.

They contain varying amounts of silicon and oxygen.

None are completely opaque.

Most are light in weight.

The construction component of all silicates is the tetrahedron.

A silicon atom is joined by four oxygen atoms (SiO4).


Some examples include:

  • albite
  • augite
  • beryl
  • biotite
  • hornblende
  • microcline
  • muscovite
  • olivine
  • othoclase
  • quartz

Hexagonal quartz



The organics are a rare group containing hydrocarbons.

The mineral definition excludes organic substances, yet some organic substances are found naturally on Earth and exist as crystals that resemble and act like true minerals.

These include:

  • amber (C10H16O) – fossilized tree resin
  • Petrified wood – tree or tree-like plants completely transitioned to stone by the process of permineralization. All the organic materials have been replaced with minerals (mostly a silicate such as quartz.)
  • Jet (lignite) – a precursor to coal, a gemstone, and a mineraloid with an organic origin – derived from decaying wood under extreme pressure.

An ant inside Baltic amber.  Credit: Anders L. Damgaard



In this article we have touched upon the symbolism and compositional parts of soil, including the molecular composition and their aggregate composition.

Note how the soil breaks up into geometrical aggregates on a small scale.  Then note how soil and rock structures and terrain form geometrical structures on a large scale.

We also briefly discussed the types of rocks and the nine classes of minerals, noting the geometric components of each.


In the next article we will delve deeper into the world of crystals – the part of the mineral world where the Platonic solid geometry can most easily be ascertained.


Before we do that, let us take a short journey around the world noticing some incredible geometric structures found in nature.



Geometric Structures in Nature4

Abraham Lake, Alberta Canada – underwater bubbles

Credit: Fred Dunn


Salt Mine, Yekaterinburg, Russia – layered colors

Credit: Mikhail Mishainik


Tsingy de Bemaraha National Park, Madagascar – jagged fractal structures


Perito Moreno, Santa Cruz province, Argentina – fractal glaciers


Quebrada de Humahuaca, Jujuy, Argentina – layered colored hills


Kiama, New South Wales, Australia – hexagonal Bombo Quarry

Credit: Dietmar Down Under


Chocolate Hills, Bohol, Philippines – mound hills


Moeraki Boulders, Otago, South Island, New Zealand


Lencois Maranhenses National Park, Maranhao, Brazil – fractal wave sand bars


Wave Rock, Hyden, Western Australia


Glen Canyon National Recreation Area, Powell Lake


Zabriskie Point, Death Valley, California – fractal mountain structures


Etretat, Normandie, France – layered white cliffs


Cappadocia, Turkey – Rose Valley & Fairy Chimneys


The Danxia Landform, China – striped colored hills


The Wave, Arizona – Coyote Buttes


The Great Blue Hole, Belize


Grand Canyon from the International Space Station – resembles a Lichtenberg Formation


“We [see throughout Cosmic Core] that sharing as a basic pattern-forming process shapes harmonious relationships in animal and human life the same way it shapes proportional harmonies in animal anatomy, in music and in the other arts.  There is indeed a ‘mana of sharing’ throughout nature.  If one looks at a view of the ocean shore, say in California, placing beside it a picture of rock formations, for instance in Colorado, it is hard to tell where the rocks end and clouds or ocean begin, because the folds of the rocks and the clouds share the wavelines of water…

The experience of mana is a strong feeling that ‘life is unity, in which not only gods, but also things, which to us are lifeless have a part.’  Mana is thus a direct experience of ‘the sacred force that permeates existence’.”5  This can be seen in outer space, humanity, animals, plants and even the gloriously diverse mineral world.


  1. Booth, Mark, The Secret History of the World, The Overlook Press, 2010
  2. Solar Surface Convection,
  3. Goehring, Lucas, Evolving fracture patterns: columnar joints, mud cracks, and polygonal terrain, University of Toronto
  5. Doczi, Gyorgy, The Power of Limits, Shambhala Publications, 1981

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