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We will now begin a four-part series on the Pentad.  We will then go further into depth on the most important aspect of the Pentad – the Golden Ratio.


The Pentad: 5: The Symbol of Life & Regeneration

The Pentad is a symbol of reproduction and all biological life – single-celled, plant, insect, animal and human.

The four earthly elements (tetrahedron/fire; cube/earth; octahedron/air; icosahedron/water) with the added heavenly element of spirit (dodecahedron) produces ensouled life.


From 4 to 5

The Tetrad (4) precedes the Pentad (5).

1 and 2 are divisors of 4.

4 (The Tetrad) = the earthly elements.

12 + 22  refers to 1 and 2 raised to a “higher power”.

12 + 22  = 5

5 is the symbol of spirit, soul, and the spirit-soul within humanity.



Atomic Number 5 = Boron

Boron is very hard and very resistant to heat.  It is the second hardest of all the elements when in its crystalline form.  Only carbon (diamond) is harder.  Boron has the 12th highest melting point.  It is an essential nutrient for green plants.  Boron is an indispensable element in NIB magnets (Neodymium – Iron – Boron).  NIB magnets are very powerful magnets used in computers, cell phones, medical equipment, and other technology.

In 2008 researchers were on the verge of “unleashing the power of the element boron in a new generation of drugs and therapies, as decades of research begins to bear fruit…The applications in bio sensing, biomaterials, and drug development all spring from the fundamental chemical properties of boron.  All life is derived ultimately from the element carbon, which lies next to boron in the periodic table of elements, their respective atomic numbers being six and five. Boron compounds share some similarities with carbon but also have important differences.  It is the combination of these similarities and differences that give boron its unique potential in medicine.

The important similarity is that boron, like carbon, combines with hydrogen to form stable compounds that can participate in biochemical reactions and syntheses. The key difference is that these compounds have distinctive geometrical shapes and electronic charge distributions with greater 3D complexity than their carbon based equivalents.

As Lesnikowski put it, while organic carbon molecules tend to comprise rings and chains, boron hydrides (compounds comprising mostly boron and hydrogen) are made up of clusters and cages. This 3D structure makes it possible to design molecules with specific charge distributions by varying their internal structure, and this in turn brings the potential to tune how each part of the structure relates to water molecules, and biomolecules present in living organisms – if a component is hydrophobic, meaning it repels water, it is well placed to enter cells by crossing the membrane. If it is hydrophilic, meaning water-loving, it will naturally be soluble in water. The hydrophobic/hydrophilic interactions also affect how a molecule makes contact and communication with target proteins and nucleic acids.”1

This study impresses the importance of the geometry of molecules upon us.  As is seen here, the distinctive geometrical shapes that occur with boron give it more healing potential.  These geometric shapes are clusters and cages…which means they are arranged according to Platonic/Archimedean solid structure.  Once again, geometry is the key!


Atomic Number 50 = Tin

Tin is a silvery-white, soft metal that can be highly polished.  It has a highly crystalline structure.  When a tin bar is bent, a ‘tin cry’ is heard, due to breaking of these crystals.  Tin is used to coat other metals to prevent corrosion such as ‘tin’ cans which are made of tin-coated steel.


Atomic Number 55 = Cesium

Cesium is one of 4 metals that are liquid near room temperature.  Cesium is extremely reactive to metal and the most alkaline of the elements.  It reacts explosively upon contact with water.  Cesium is used in atomic clocks, which are incredibly accurate.  Currently the most accurate cesium atomic clock neither gains nor loses as much as a second in more than 300 million years.



Arithmetic Properties of the Pentad

Five marries 2 (male) + 3 (female) = 5 (life)

12 + 2= 5

Divisors: 1, 5

5 is the:

  • 5th Fibonacci number
  • 2nd pentagonal number


5 is the diagonal of a 3 x 4 rectangle.  This refers to the 3-4-5 triangle.


Five always retains its identity when it reacts with other numbers:  Every number multiplied by 5 will always end in a 5 or a 0.


And as we have repeatedly said, there are Five Platonic solids:



Powers of Five



25 is the smallest square that is also a sum of two non-zero squares (25 = 32 + 42)

25 is the sum of the single-digit odd numbers which are also the first five odd numbers:                            (1 + 3 + 5 + 7 + 9 = 25)

Atomic Number 25 = Manganese

Manganese is an essential element in photosynthesis.  Without it, there would be no free                oxygen on Earth.  Manganese also performs vital metabolic functions in humans yet our                      bodies cannot store it.










Theology of Arithmetic – Iamblichus

As we have been doing, we will now take a look at the meaning of the Pentad as prepared by Neo-Platonist philosopher, biographer of Pythagoras, Greek mystic and mathematician Iamblichus (245-325 AD).


The pentad is the first number to encompass the specific identity of all number, since it encompasses 2, the first even number, and 3, the first odd number.

It is called ‘marriage’ since it is formed of male and female.

It is the mid-point of the decad.


When squared, it always encompasses itself, for 5 x 5 = 25.

When multiplied again, it both encompasses the square as a whole and terminates at itself, for 5 x 25 = 125.


There are five solid figures with equal sides and equal angles – tetrahedron, octahedron, icosahedron, cube and dodecahedron.

Hence, there are five general elements of the universe – earth, water, air, fire, and aether.


Geometric concord is thought to fall under 5.

Whatever you use to add up to 10, 5 will be the arithmetic mean.

For example:  9+1, 8+2, 7+3, and 6+4.  The arithmetic mean is 5 in each case.


The pentad is first to exhibit the best and most natural mediacy.  (2 x 5 = 1 x 10)


The pentad is particularly comprehensive of the natural phenomena of the universe.

The whole universe is manifestly completed and enclosed by the decad, seeded by the monad, gains movement thanks to the dyad, and life thanks to the pentad.


The pentad necessarily entails equivalence, while the dyad entails ambivalence.


There are five parallel circles in the heavens: equator; summer and winter tropics (Tropics of Cancer & Capricorn 23.4 degrees North & South), Arctic and Antarctic circles.

Nature separated each of the extremities of our bodily parts in a five-fold way (fingers and toes).

There are 5 types of internal organ: kidneys, lungs, liver, spleen, heart.

There are five types of parts visible on the surface of the body: head, arms, trunk, genitals, and legs.

There are five genera of creatures: those that live in fire, air, earth, water, and amphibious.

The pentad is called ‘lack of strife’, because it represents the aether, which is set apart on its own, remains unchanging, while there is strife and change among the things under it.

The primary two different and dissimilar kinds of number, even and odd, are reconciled and knitted together by the pentad.

Megillus states in On Numbers, “The pentad is alteration, light, lack of strife: alteration because it changes three-dimensionality into the sameness of the sphere, by moving cyclically and engendering light – hence it is light too; and it is lack of strife because it combines everything which was formerly discordant, and brings together and reconciles the two types of number.”


The pentad is highly expressive of justice, and justice comprehends all other virtues.

Justice also governs equality in the soul.

Where the soul is concerned there will be an equal part and an unequal part.  The equal part will be divine and rational, while the unequal part will be mortal and irrational; and the greater aspect of the unequal part is the passionate soul (for it is a boiling over and a desire to shed excess), while the lesser aspect is the appetitive soul (for it is defective because of its seeking for what is missing).

When these two parts partake of equality, they gain virtue – the passionate part acquires courage, the appetitive part, moderation. (Golden mean: unequal parts that are equal.)

The Pythagorean definition of justice: “The power of repayment of what is equal and appropriate, being encompassed by the mean of a square odd number.”


The pentad has neither excess nor defectiveness and it will turn out to provide this property for the rest of the numbers.


The pentad is also called ‘Nemesis’ because it distributes the heavenly and divine and physical elements by means of five.  It distributes the five forms to the cyclical movements both the moon and of the rest of the bodies – evening setting, evening rising, dawn setting, dawn rising, and simple revolution.


The general structure of plants is five-fold: root, stem, bark, leaf, and fruit.

There are five precipitations: rain, snow, dew, hail, and frost.

There are five exhalations: stream, smoke, fog, mist, and cyclone (whirlwind).


The pentad is called ‘Providence’ because it levels out inequality.

It is also called ‘Aphrodite’ because it binds to each other a male and female number.


It is also called ‘nuptial’, ‘androgyny’ and ‘demigod’.

‘Demigod’ because it is half of ten, which is divine, but also because in its special diagram it is assigned the central place.


It is called ‘twin’ because it divides in two the decad.

It is also called ‘heart-like’ because of the heart being assigned the center in living creatures (as well as 5 being associated with the golden ratio and the heart shape coming from the golden spiral).



More Fives in Nature, Music & Religion:

  • Five animals – scaled, winged, naked, furred, shelled

  • Five fingers on every human hand; five toes on every foot
  • Five extremities of a human body – 2 arms, 2 legs, 1 head


  • Five senses – sight, hearing, touch, smell, taste
  • Five tastes – sour, bitter, sweet, spicy, salty


  • Five directions and colors – east (green), south (red), center (yellow), west (white), north (black)


  • Five Chinese elements – fire, earth, metal, water, wood
  • Five Chinese virtues – benevolence, propriety, good faith, righteousness, knowledge


  • Five Notes of the Pentatonic scale – black keys on the piano – the most universal scale made of 5 tones, grouped into 2 and 3

  • Major Third Interval – 5:4


  • Five orders of Architecture – Tuscan, Doric, Ionic, Corinthian, Composite


  • Five Buddhist elements – void, water, earth, fire, air

  • Five Buddhist poisons – confusion, pride, envy, hatred, desire
  • Five Buddhist precepts – respect for life, respect for property, chastity, sobriety, speaking the truth

  • Five Buddhist virtues – kindness, goodness, respect, economy, altruism


    1. European Science Foundation, Unique Properties Of Boron Harnessed To Develop New Drugs And Diagnostics, Science Daily, 23 October, 2008,

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