Please feel free to leave questions, comments, concerns, I am always glad to hear what others think. Perhaps there's more to this than I have discovered. There exist a few outliers / questions I would like to solve. One is the difference between [0, 9] and [1, 10] (in this context) and also I believe Modular Arithmetic could have connections to this but I don't understand Modular Arithmetic very well.
Pythagoras' Tetractys
God's Universal Law of Generation
First I would like to show that this principal is found in all [mammalian] reproductive cycles, Webster's 1828 Dictionary and 1913 Dictionary define the word 'Commerce' as "Familiar Intercourse between the sexes." This is because if I "extend" you an offer, and you "receive / accept" the offer, the two of us enter into an endeavor to bring something new into being together.
The Holy Trinity
- God, the Father: The Active principle (MAN-ufacture), traditionally the initiator or provider.
- Jesus Christ, the Son: The Passive principle (Labor / Delivery), the nurturing, receptive force.
- Holy Spirit: God Incarnate in Man (Christ), after the Work of Christ is declared 'finished' at the cross, this gives rise to the Holy Spirit.
- Jerusalem / Zion / The Holy Trinity in and of Itself (Manifest): That's to say that the Trinity is not only 3 individuals, the 4 could be thought of as there's something that happens when they all are together that makes 3-in-1 something in itself.
- Father: The Active principle (MAN-ufacture), traditionally the initiator or provider.
- Mother: The Passive principle (Labor / Delivery), the nurturing, receptive force.
- Child: The Neuter principle (Child could be M or F so we say that it's a 0 / Null / Neutral Charge), the product of the union, balancing the parental energies.
- Family Unit (Manifest): The cohesive unit, a new entity that transcends the individual roles, capable of growth and perpetuation. Many family units make up the whole of a city / town and make city / towns make up a state.
- Proton (+): Represents the Active force, the positive charge driving interaction.
- Electron (-): Embodies the Passive force, the negative charge that balances the proton.
- Neutron (0): Acts as the Neuter force, stabilizing the nucleus without charge.
- Atom (Manifest): The unified result, a stable entity capable of further interactions, manifesting the potential of the triadic components.
- State: The Active force, exerting authority and structure.
- Church: The Passive force, providing moral and spiritual guidance.
- Mob (People): The Neuter force, the collective will that balances power dynamics.
- Society (Manifest): The integrated system, a functioning whole that emerges from the interplay of these forces.
- Sunlight: The Active force, providing energy to initiate the process.
- Water: The Passive force, the receptive medium absorbed by the plant.
- Carbon Dioxide: The Neuter force, a neutral input that balances the reaction.
- Glucose (Manifest): The resulting product, a manifest form of energy that sustains life, with oxygen as a byproduct, enabling further cycles.
-
Fire: The Active force, representing transformative energy. -
Water: The Passive force, embodying adaptability and flow. -
Air: The Neuter force, balancing through movement and connection. -
Earth (Manifest): The stable, manifest result, a tangible foundation that integrates the elemental forces, often associated with the quintessence (aether) in esoteric traditions.
Fire
Water
Air
Earth- Thesis: The Active force, an initial proposition or idea.
- Antithesis: The Passive force, the opposing idea that challenges the thesis.
- Synthesis: The Neuter force, reconciling the opposition into a balanced perspective.
- New Paradigm (Manifest): The emergent understanding, a higher truth that transcends the initial conflict, becoming the basis for further inquiry.
- Root Note: The Active force, establishing the tonal foundation.
- Third Note: The Passive force, adding emotional depth (major or minor).
- Fifth Note: The Neuter force, providing harmonic stability.
- Chord (Manifest): The resulting harmony, a unified sound that resonates as a whole, capable of supporting melody and further composition.
For the mathematical basis for this, we will need to make use of two older operations of number manipulation.
Pythagorean Reduction (Decimal Reduction)
Decimal Reduction simply takes any multiple digit number and "boils / reduces" it down to 1-9 and as such, all numbers can be associated with only the first 10 numbers.
Example: Reducing 16 you simply add 1+ 6 = 7 - so one can say that 16 reduces to 7
Example: If you get another number larger than 10 simply repeat until you have 1 digit. 138 is 1+3+8 = 12 = 1+2 = 3
Triangulation / Decimal Cumulation (Tetractys)
This operation may have significance in a counting system such as marking tallies, or counting before reading was commonly accessible (those are my own theories).
To compute this value to N (The Triangulation of N) you add consecutive numbers
1 + 2 + 3 + 4 + .......+ N
Shorthand Formula: ( N * (N+1) ) / 2
The triangulation of 4 is 4+3+2+1 (The number of dots in a Tetractys of N rows) is 10
The triangulation of 6 is 6+5+4+3+2+1 = 21
Combining the Two
The beauty of this is that the same fourfold pattern I demonstrated is found in many parts of nature can be found in the first four numbers (1, 2, 3, 4) but will continue to hold forever.
Let 1, 2, 3, 4 be the Active (+), Passive (2, -), Neuter (3, Null/0) and 4 the manifestation.
1 = Active
2 = Passive
3 = Neuter
4 = Active Manifest
By first triangulating 4 (4+3+2+1 = 10) and then reducing (1+0 = 1) we can begin the same pattern again but since 4 goes back to 1, let 4 begin the new set.
4 = Active
5 = Passive
6 = Neuter
7 = Active Manifest
Triangulate 7 as 7+6+5+4+3+2+1 = 28 and reduce 2+8 = 10 = 1+0 = 1 and we continue
7 = Active
8 = Passive
9 = Neuter
10 = Active Manifest
(Using shorthand formula) (10*11)/2 is 55, reduce 5+5 = 10 = 1+0 = 1
10, 11, 12, 13
Triangulate (13*14)/2 is 91, reduce 9+1 = 10 = 1+0 = 1
13, 14, 15, 16
(16*17)/2 = 136
1+3+6 = 10 = 1+0 = 1
16, 17, 18, 19
(19*20)/2 = 190
1+9+0 = 10 = 1+0 = 1
(You can continue this forever)
The Perfection of the Number 7
I do believe that we can even see this pattern in the creation week of Genesis. Note that if (1,2,3,4) days God creates the Macrocosm, day 4 God creates the Sun, Moon and Stars + the Luminaries (Lesser Illuminaries) which thus enables the passing of time and in days (5,6) God creates Sea Creatures and Birds in correspondence with Firmament and Waters on day 2 , and Land Animals & Humans on Day 6 in Correspondence with Land / Sea + Vegetation on day 3.
Finally, the Seventh Day, the Sabbath as the most important day as work is completed (7 reduces to 1) and both the Macrocosm and the Microcosm have been created and finished.
