Series 2, Episode 21 “The Harmonic Nature of the Universe Part 1 – Dualities”
Published July 2nd 2020
An exploration of the Harmonic Nature of the Universe, a multi-part discussion that begins by discovering Dualities, and follows on to defining Oscillations, creating a third scale of inner octaves, and finally revealing an exquisite model of the Transfer RNA Molecule, mathematically and provably created from music. This episode will discuss specific models, and thus requires access to several diagrams which can be found on this page.
Listen to the podcast
Click to show the diagrams referenced in the episode
The Mathematics of Inner Octaves
The Mathematics of the Duality
SO’s Range of Existence
MI’s Range of Existence
Duality and Oscillations
Major and Minor Oscillations
Click to view Podcast transcript
This is a series of talks about objective consciousness, an objective universe, and an objective way to wake up.
It is primarily based on the works of George I. Gurdjieff and Russell A. Smith, and aims to cut through the swathes of subjectivity that cloud our evolution and journey through life.
Each episode in this series focuses upon a particular element of their teachings and aims to bring simple understanding to what was frequently hidden in plain sight within the various subject areas of the Fourth Way.
In the last talk we discussed the Ray of Creation.
In the next several podcasts, Mr. Smith will explore the Harmonic Nature of the Universe. It will begin by discovering Dualities, next we will define Oscillations, following that, we will create the third scale of inner octaves, and finally reveal an exquisite model of the Transfer RNA Molecule. For these podcasts, diagrams will also be necessary. As such, you can find them on our website thedogteachings.com, by clicking on the link shown in the description of each podcast. So, pause, find the diagrams, print them off if you would like, and let’s begin.
OK. Where are we?
We started series two with this premise… Truth Conquers All Things, which put us on a search to find the truth. The first truth we found was the religious idea that man was made in the image of God. But, since we knew that an ape had 99% the exact same genes as a man, we decided that for man to be made in the image of God… everything had to be made in the image of God, because it made no sense that the image of God would only be in that last 1%.
So, we started looking for an axiomatic image. We postulated, if it was everywhere and in everything, then in some places it should be obvious and therefore easy to find… and it was, we found it in the structure of music and light, in the pattern 3-3-2-4-4-5-3.
It is unlikely that light and sound acquired the same pattern randomly. It is more likely they acquired it because they are both obeying the same set of rules, rules of a diatonic Universe. That is, the colors of the rainbow are in the intervals, and the tones of music are at the notes. Amazing stuff.
Discovering that light and sound had the same pattern, prompted us to ask, “How did it become a diatonic Universe?” To answer this question we had to uncreate the Law of Three and the Law of Seven. So, we returned the three forces to one place… and configured the notes of an octave as even sevenths.
What is next? We had to recreate them…. So, beginning with the Law of Three, we separated the three forces, which dangled like magnets on strings and ended up at thirds. Then, we compared these separated forces with the structure of the Law of Seven, which was still at even sevenths, and saw that the thirds and the sevenths did not have common alignment.
In order to achieve common alignment, the structure of one of these laws would have to be changed. However, since three separated forces can only be equilateral, it will have to be the sevenths. Thus, we were compelled to make a greater change in the Law of Seven. A change that involved the lengthening of one stopinder and the shortening of another. Miraculously, when we did this, the Law of Seven became Diatonic, lined up with the separated forces, and out came the Universe.
At that moment, inner halving’s began… the whole, halved to a half; the half, halved to a quarter; and, the quarter, halved to an eighth. There were now three octaves of radiations, and inside them, there were three more, and so on, etc.… Creating a progression of scales that clearly showed the structure of man, his centers, his parts, and his parts-of-parts.
Most importantly, it revealed that man’s Higher Centers were created from the unification of his lower centers. If a man could just get his lower centers working together and unified, he would remember himself and awake.
Looking back at your moments of self-remembering, you may now be able to recall the event that caused them. Unfortunately, some of your moments of unification may have been caused by physical trauma. Perhaps, somebody whacked you upside the head with a stick and made you conscious. In that moment you were unified. All of you was experiencing the pain in your head… and you were probably cursing at him. Right? It was not an “I am looking forward to this happening again” moment. However, it did cause you to remember yourself, and it did bring you to an awakened state.
Moments like that often happen in life, and, sadly, they can happen in esoteric schools; and, if they do, a few months down the road some student shows up carrying his own stick… requesting that he be humiliated, abused, or whacked upside the head again because the previous whacking woke him up.
To make matters even worse, if someone does awaken due to some artificial shock, then tries to recreate it, they usually find that the next shock has little or no effect.
We must find a better way to remember ourselves… one that does not require a stick.
OK. We saw how life evolved; we saw how man emerged; we saw how man fell asleep; and, we saw how man can awaken… which brings us to the creation of oscillations.
However, before exposing why things oscillate, we will begin by finding what Mr. Smith calls the Duality.
In episode 11, we learned that the notes DO, SO, MI, and RE, in Scale-0, were called Fundamental Points because they existed at natural positions of halving within that octave, and, thereby, became the DO’s of the three Scale-1 inner octaves.
Mr. Smith likes to call this truth, an Axiom, because it applies to all Fundamental Points.
We will now learn how two of those Fundamental Points become oscillating DO’s. And, as we do, we might discover even more Axioms.
So, it is time for some mathematics.
Since we know that the four fundamental points create three inner octaves, let’s calculate them.
We will begin with the All to Nothing octave from 192 to 0, because it is the smallest octave that allows us to calculate Scale-0 and Scale-1 at whole numbers. We will label the octave from 192 to 0, Scale-0, and the three octaves from 192 to 96, 96 to 48, and 48 to 24, Scale-1.
We now have two scales: Scale-0, an all to nothing octave, and Scale-1, musical octaves, where the vibrations of all the like-notes doubles or halves… For example: RE-27, RE-54 and RE-108; or LA-40, LA-80, and LA-160, etc.
Now, let us look at what Mr. Smith calls the “Fate of the Notes.”
Let’s go down the list, note by note, to see if we can find the two oscillating DO’s, as well as, some more Axioms.
The first vibration in Scale-0 is 192, at DO-192. It is the descending DO of that scale, which is often referred to as the Top DO. It is a fundamental point and, as such, it becomes a DO in Scale-1. Hey look, it is also a descending DO in that scale. Ah ha, we have found another Axiom, Axiom #2, “Descending DO’s stay descending DO’s.”
Do you see that?
The next vibration in Scale-0 is 168, at TI-168. 168 does not appear in the next scale. Thus, we do not yet know its fate.
Next is 128. LA-128 in Scale-0 becomes FA-128 in Scale-1. And, another Axiom appears. Axiom #3, “The vibration at LA becomes a FA in the next scale;” or, “LA’s become FA’s.”
Now, technically, LA does not become a FA, 128 does. That is, 128, which was a LA in Scale-0, becomes a FA in Scale-1.
Likewise, if we look at the LA in Scale-1 and ask, “What will LA-160 become in Scale-2?” That’s easy, “A FA-160.”
Next, following 128 is 96. SO-96, which, as a fundamental point, becomes a DO in the next scale. But, it is a special kind of DO. It’s a DO that can either ascend or descend. Because of this, we shall give it a new name, and call it, “an oscillating DO.”
We shall explore what that means in a moment, but first let’s finish looking for more axioms.
OK, moving on. Next, we have FA-64. Notice that FA-64 in Scale-0 is also a FA-64 in Scale-1. Yee-Haw, another Axiom. Axiom #4, “The vibration at FA becomes a FA in the next scale;” or, “FA’s stay FA’s.” Now, technically, like LA, the FA does not become a FA, 64 does… and what, in the next scale, will that FA-64 become? You got it, a FA-64. And, in the next scale? Yep, again, a FA-64.
Gurdjieff once said something very telling about the three forces, which may refer to what we have just discovered. He said that the three forces, Do, Fa, and La, represent the Father, the Son, and the Holy Ghost. He then went on to say that God was always sending the Father. (Behold, the top DO is always a top DO), that God was always sending the Son (Behold, the FA is always a FA), and once he sent the Holy Ghost (Behold, the LA is only a LA once, then it becomes a FA.
It is not clear if that was what Gurdjieff was talking about, but it sure fits well.
OK, 48 is next. MI-48, which, like all fundamental points, becomes a DO in Scale-1. It too is a special kind of DO. One that can either ascend or descend. And, as such, we call DO’s with this kind of behavior, an
Following this is RE-24, which as a fundamental point also becomes a DO in Scale-1. But notice that, in Scale-1, it is an ascending DO. We, therefore, call it an ascending DO, and, sometimes, refer to it as the Bottom DO. Wow, I think that should be another Axiom. OK, Axiom #5, “RE’s become ascending DO’sWe now have four DO’s in Scale-1. The top DO is a descending DO, the two middle DO’s are oscillating DO’s, and the bottom DO is an ascending DO.
Lastly, DO-0 in Scale-0, the ascending DO of Scale-0, does not appear in Scale-1. Interesting, that should be an Axiom, too. Axiom #6, “Ascending DO’s disappear.
Therefore, RE-24 in Scale-0, and RE-27 in Scale- 1, which both become ascending DO’s in the next scale, will also disappear.
OK. We should add one more Axiom. Axiom #7, “SO’s and MI’s become oscillating DO’s.”
We now know the “Fate of the Notes”… and, many axioms, too: Descending DO’s stay descending DO’s, the vibration at TI we do not yet know about, LA’s become FA’s, SO’s become oscillating DO’s, FA’s stay FA’s, MI’s become oscillating DO’s, RE’s become ascending DO’s, and ascending DO’s disappear.
So now, we have two scales, Scale-0 and Scale-1.
In these two scales we have a total of four octaves: one octave in Scale-0; and, three octaves in Scale-1. The four octaves each have a different length, one has a length of 192, one has a length of 96, one has a length of 48, and one has a length of 24.
In Scale-0: if we count all the vibrations, we get 8; if we count the stopinders, we get 7; and, if we count only the vibrations between the DO’s, we get 6.
In Scale-1: if we count all the vibrations, we get 22; if we count the stopinders, we get 21; and, if we count only the vibrations between the top and bottom DO’s, we get 20.
If we count the different vibrations in both scales (not the notes) we get 24.
When Gurdjieff said, “There are 21 gradations of reason, from that of the ordinary man to that of our Endlessness….” OK, that is probably a reflection of the 21 stopinders of Scale-1. That is pretty cool.
Other depictions or manifestations in nature that have the numbers (8, 7, 6) (22, 21, 20) or (24) may also be a reflection of this incredible structure. A very interesting study.
If we continue with the understanding that the four fundamental points in Scale-0 create three octaves in Scale-1, then, the twelve fundamental points in Scale-1 will create nine octaves in Scale-2, etc. Someday, we may calculate them, but for now, we must get back to the theme of this podcast, which is the discovery of the Harmonic Universe. A Universe filled with oscillations.
Now that we know the fate of the notes, and some Axioms, that should be easily accomplished.
To begin, let’s take a look at the Scale-0 octave and the three octaves of Scale-1.
The vibration TI-45 is only found in one octave, and the vibration LA-40 is only found in one octave. In fact, all the vibrations in Scale-1 are only found in one octave… except for these two middle DO’s (DO 48 and DO 96): In Scale-1, DO-48 is the top of one octave and the bottom of the next octave; and, DO-96 is the same. This creates two points of existence, two places of stability in Scale-1.
It is often said that in order to define something, you need to know what came before it and what came after it?
When we look at DO-48, we see that DO-24 came before it and DO-96 comes after it; thus, we can fix its place of existence, DO-48 exists between DO-24 and DO-96. That is, between the DO which came before it and the DO which comes after it. Right?
This same thing happens to DO-96. When we look at DO-96, we see that DO-48 came before it and DO-192 comes after it; thus, we can also fix its place of existence. DO-96 exists between DO-48 and DO-192. That is, between the DO which came before it and the DO which comes after it.
Or, if Middle C was the MI or the SO… then, when it descended to the DO below it, it would be called Low C; and, when it ascended to the DO above it, it would be called High C. Therefore, everywhere between Low C and High C is the range of existence of Middle C.
The ascension and descension of the DO’s, at SO and MI, reveal their range of existence.
OK, back to the journey.
Recapping: We started off with one octave; the octave had four fundamental points, which existed at natural places of halving within the structure of the octave, itself, at DO, SO, MI, and RE; there were three octaves of radiation created between the four fundamental points; and two points of harmonic stability created within them.
Thus, there is a duality created within every octave. Two places where things can exist.
If we take a good look at the world around us, we will see that it is packaged in groups of two: Man and woman, day and night, angiosperms and gymnosperms, the left-hand rail of DNA and the right-hand rail of DNA, dominant genes and recessive genes, trees that keep their leaves and trees that lose their leaves, and plants versus animals. Even molecules, like Oxygen, and many others, are not found as single atoms. Oxygen is O2, two atoms of Oxygen. Why? Because there is even a duality in the process of photosynthesis; a plant must go through the process of photosynthesis twice, and make two atoms of Oxygen, before the Oxygen can be released… again, a packaging of the world in models of two; in pairs.
Now, we can finally look at the structure and see what emerges. In the Scale-0 octave, from 192 to 0, we have two notes, MI and SO, which both become DO’s in scale-1 that can ascend or descend.
First, let’s analyze what happens to SO. SO-96 becomes DO-96. It can either double to 192 or half to 48. Creating a range of existence of 144. Two-thirds of that range is its ascending octave (96) and one-third of that range is its descending octave (48). Mr. Smith labeled them ‘plus two-thirds’ and ‘minus one-third.’
MI experiences the same model. MI-48 becomes DO-48, it can either double to 96 or half to 24. Creating a range of existence of 72. Two-thirds of that range is its ascending octave (48) and one-third of that range is its descending octave (24).
Next, we notice that MI and SO share a common area, the area between 48 and 96.
In MI’s range of existence, when we look at that common area, we see a line coming from SO.
In SO’s range of existence, when we again look at that common area, we see a line coming from MI.
Mr. Smith calls this common area, between MI and SO, “The MI-SO area of coincidence.”
MATHEMATICS OF THE DUALITY
SO has a possibility of 96 in its ascension and 48 in its descension, or a total range of existence of 144 (96 + 48). 2/3 is an ascending octave (plus) and 1/3 is a descending octave (minus).
MI has an ascension of 48 and a descension of 24, or a total range of existence of 72 (48 + 24). Within this range of existence, 2/3 is ascension (plus) and 1/3 is descension (minus).
We have designated the octave’s line of ascension with an “up arrow” and its line of descension with a “down arrow”. Up arrows represent +2/3 of the “something” and down arrows represent -1/3 of the “something”.
In addition, SO and MI have a unique mutual relationship. SO and MI coexist in the octave where “their ranges of existence overlap” ((refer to the diagrams labeled SO’s Range of Existence and MI’s Range of Existence), that is, SO’s -1/3 down arrow and MI’s +2/3 up arrow both exist in the same place; thus, You cannot isolate SO without getting a part of MI–and vice versa.
OK. Let’s look at MI and SO separately.
We will start with SO. The DO that enters at 96 can either ascend to 192 or descend to 48. It has a plus two-thirds ascending force going up to 192, and a minus one-third descending force going down to 48. However, we now see that it experiences a third line of force as well; it feels the plus two-thirds ascending force coming from MI.
What do the three lines of force add up to: plus two-thirds, minus one-third, and plus two-thirds?
If you said +1 you are correct. Wow, that is the electrical charge of a proton!
What if we isolate MI’s existence? The DO that enters at 48 can either ascend to 96 or descend to 24. It has a plus two-thirds ascending force going up to 96, and a minus one-third descending force going down to 24. However, we now see that it experiences a third line of force as well; it feels the minus one-thirds descending force coming from SO.
What do its three lines of force add up to: plus two-thirds, minus one-third, and minus one-third?
If you said zero, you are correct. Wow, that is the electrical charge of a neutron!
Is it possible that we are looking at the structure of an atom? That is, by themselves, the proton and the neutron do not have a charge… but rather, it is the structure, itself, which gives them their charge.
Interesting; and, it makes sense. Where, in the Universe, does a positive force attract a neutral force? Where, in the Universe, does a magnet stick to a piece of wood?
There is no reason for the proton and the neutron to join up; unless they are simply obeying the structure. Simply occupying one of the two available places of existence, becoming a duality, coexisting in a common home, and acquiring the positive and neutral properties of their place of residence. Perhaps without the structure, they would have no charge at all.
Thus, wherever two things exist together as a duality, one will stand in the position of being +1, and the other will stand in the position of being zero….
I think that will get your head swimming, so it is a good place for us to end this podcast.
In the next podcast, we will continue our discussion on the two points of existence and reveal how stable oscillations occur.
Thank you for listening.
If you would like to know more about the subjects and exercises we’ve been covering in these talks, including the book and guide that underpins it all, which is available for PDF download, and also gives you access to an ultimate exercise that is able to objectively wake people up, you can find us at the website thedogteachings.com.
That’s T H E D O G teachings DOT COM.
There, you can also obtain Mr. Smith’s diagrams of the structure, listen to other talks, as well as learn all the mathematics that supports them, and much, much more.
And, you will have real time access to the materials we discuss.
That’s at thedogteachings.com
Goodbye until next time.
All Podcast Episodes
Series 2 – Talks on Gurdjieff: Cosmic Secrets The TEACHING GUIDE
- S2/E21: The Harmonic Nature of the Universe Part 1 – Dualities
- S2/EP20: The Ray of Creation
- S2/EP19: Four Common-Sense Ideas
- S2/EP18: The taste of the notes in an octave
- S2/EP17: There are no such things as descending octaves
- S2/EP16: Mr Smith
- S2/EP15: Outer Octaves
- S2/EP14: How the “shocks” from assisting octaves make ascension possible
- S2/EP13: Why we fell asleep and how we can begin to awaken – Part 3 of 3
- S2/EP12: Why we fell asleep and how we can begin to awaken – Part 2 of 3
- S2/EP11: Why we fell asleep and how we can begin to awaken – Part 1 of 3
- S2/EP10: The changing of the Law of Seven – a working model
- S2/EP9: The Law of Seven and the Enneagram of the Justice System
- S2/EP8: Triads and Forces – Part 5
- S2/EP7: Triads and Forces – Part 4
- S2/EP6: Triads and Forces – Part 3
- S2/EP5: Triads and Forces – Part 2
- S2/EP4: Triads and Forces – Part 1
- S2/EP3: Blending and the Laws of Three and Seven
- S2/EP2: The Five Strivings
- S2/EP1: The Enneagram of Feeding the Community
Series 1 – Exercises
- S1/EP11: Opposite Postures Exercise
- S1/EP10: Active Reasoning Exercise
- S1/EP9: Lying Still for an Hour
- S1/EP8: Unconscious Muscle Movements
- S1/EP7: Where Am I on a Scale from 1 to 10 Exercise
- S1/EP6: Objective Prayer Exercise
- S1/EP5: Viewing Without Verbalizing Exercise
- S1/EP4: Insulate Yourself Exercise
- S1/EP3: Two Ends of the Stick Exercise
- S1/EP2: The “I Am” Exercise
- S1/EP1: Threefold Attention Exercise