Numerical Archetype 3: Revealing The Simple Triple Polarity

Numerical archetypes tell the true character of number. Knowing the nature of number is useful for doing math intuitively. The numerical archetype 3 is all about transcendence of opposites or integration of opposites.

“Tripartite” means having three corresponding parts. Tripartite visions can help free us from duality. The nature of triad is a telling of a story, a beginning, a middle, and end. Now things become connected in a more complex way than a simple line connecting two opposites.

The three-body problem

In physics, a two-body problem involving momentum or gravitation, can predict the outcome when two initial bodies begin on trajectories and start the clock. Collisions and resulting behaviors from then till infinity is easily determined. However with three bodies, no closed form solutions exist. This means you can find out what happens if you make numerical charts, but you can’t find a set of functions true through infinity.

Two opposites, balanced by a third, relieving the tension of duality. A lever has two ends and a fulcrum balancing the two. In a way, this allows the nature of both extreme to be experienced more. The fulcrum mitigates the rotation from one side to the other. Both sides are then on equal footing, expressing each and co-existing.

Birth of a Triangle for Numerical Archetype 3

One and two are male and female respectively. Together they are the parents of numbers and 3 is the firstborn child. Here is the third step of the vesica picsis, an ancient geometrical construction process for finding numerical archetypes. Drawing the steps helps you to feel the archetypes. See all my numerical archetype posts here.

Vesica Picsis Number 3

The equilateral triangle produced encloses the smallest area for the perimeter. It is a triangle with interior angles all equal to 60 degrees. The three sides of the triangle are all equal. This alone produces the shape to study, but there are more triangles to see in the vesica picsis.

This part reminds me of rattling around a ball in a triangular frame. You can also think of it as a ray of light reflecting the center of each side of the larger triangle.

Making more patterns of stability

Now with this composite of bigger equilateral triangle with an identical yet smaller equilateral triangle nested inside, we not only have triforce but also a regular trapezoid.

In equilateral triangles, the seed ratio is the root of three to one, structurally rigid by geometry alone. The square root of three arises from using Pythagorean theorem on a half-equilateral (30-60-90) triangle. Read about seed ratio with square root of five (golden ratio).

See it can continue to tile over space and fill it with no gaps. The gapless tiling nature of equilateral triangles imparts fantastic stability. No gaps means full contact to transfer strain.

Through the vesica picsis we see the space filling properties and the square root of three arising from equilateral triangle proportions. See any other patterns?

Through-ness in the Company of Three

A swinging pendulum showing how threeness can tell a story. Like a heart beat, or anything going in pulses and waves, there is oscillation between two extremes, passing through one center.

The numerical archetype 3 is that of wholeness, strength, stability, and process. Arches and architectural supports show support in threeness in the overall shape of a triad.

The keystone mediates the two sides which could not stand on their own. the human body has the pelvis mediating the right and left legs. Threeness reconciles problems. Often when you find yourself stuck between two choices, you can reconcile it with a mediating factor. For example, if you don’t know if you want to stay in or go out, you might consider the weather, or events.

Linguistics and History of Third-wheeling

Egyptians said “thrice dark”, “thrice hidden”, to indicate superlative. Similar to the “good, better, and best”, “thrice” was the utmost. In general saying doing something three times to signify completeness, with “thrice great” being an epithet for Thoth.

Egyptian jewelry also frequently had trapezoidal geometry like the regular trapezoid shown above.

According to Micheal Schneider’s “Constructing the Universe”, Native American languages Nez Perce and Shahaptian call three the “center of one.”

The powerful symbol of the trefoil knot is sometimes shown with an interlocking circle or without. It is a representation of threeness, and originally used by non-Christian Celts to symbolize the cycle of birth, life, and death, or any of the threeness themes discussed below.

Logos, icons and symbols

Many of the triangular motifs invoke an arresting feeling of alertness. As such it can bestow an attentive message, and is commonly using in logos and branding.

• wheelbarrow
• bluetooth symbol
• three rings in Lord of the Rings
• Triskelion
• recycling symbol
• Isle of Man/ Siciliy flags
• hazardous waste symbol
• Penrose tribar
• trefoil knots
• Borromean rings
• three legged stool
• prayer hands (forming 120 degrees, central angles of an equilateral triangle)

The trefoil knot is a way of twisting a rope and re-conjoining it with no breaks. The trefoil knot is studied in group theory and knot theory for its interesting properties.

Additionally, threeness appears in braids. Havdalah braided candles of the Jewish tradition show respect to the numerical archetype three. We also have braided sweetgrass in many Native American traditions.

Borromean rings are different than the trefoil knot. The trefoil knot can be made with one string or conjoining one unit of braid. The Borromean rings at first look interconnected, but are actually just lain on top of each other.

Numerical Archetype 3 Examples

• birth, life, death
• past, present, future
• dawn, noon, dusk
• max, min, equilibrium (trig functions)
• plant, harvest, dormant
• ready set go
• green, yellow, red light
• ABC’s & 123’s
• holy trinity
• too hot, too cold, just right (Goldilocks)
• three blind mice
• three wise men
• three kings
• three chances/attempts
• triptychs
• three types of triangle
• three types of angle
• fruits like cucumbers, squash, melons
• flowers like iris, orchid, trillum family, nightshades, daffodils, crocus, tulips, ginger, pawpaw,
• action, reaction, resultant (physics)
• thesis, antithesis, synthesis (philosophy)
• protons, electrons, neutrons
• energy, mass, light
• solid, liquid, gas
• subtractive colors, light: red, green, blue-violet
• additive colors, pigment: red, blue, yellow
• brahma the creator, vishnu the preserver, shiva the destroyer

Do you even tri-force bro

Threeness tessalated shows us the triforce inception, or the triforce within triforce. As a fun doodle, you can make a triangle with all equal sides, and then connect the midpoints of those sides to make a smaller triangle. Continue for as small as you can see.

A few final more ubiquitous manifestations of threeness include fruits of curcubits. this includes cucumbers, melons, and many squashes.

the numerical archetype 3 contains some of the strongest structure and balance. In later numbers this also confers onto the 6 and 9 explored later in the series on numerical archetypes.

Resources:

Constructing the Universe by Micheal S. Schneider;  http://www.constructingtheuniverse.com/