Podcast Series 2, Episode 5: Triads and Forces – Part 2
Continuing a talk on how three forces were created, and how they may orient themselves in the Universe to produce varying effects of transformation, and additionally, what the Law of Octaves is, and how it operates. Part 2 of 5.
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Hi, I’m Gary
Welcome to a series of podcasts on how to achieve a peaceful and mindful state through mental awareness exercises, and morseo, in gaining understanding into the laws of world creation and world maintenance, specifically as described within the works of George Gurdjieff and the Fourth Way.
Each episode in this series focuses upon a particular element of what we call the dog teachings, insights into and developments upon Gurdjieff’s Fourth Way. It aims to bring simple understanding to what was frequently hidden in plain sight.
PICKING UP FROM WHERE WE LEFT OFF IN OUR LAST PODCAST…
We were talking about Triads and the three forces, as described by the fellow in Texas…
We had a model that said, “The Forces that were all in the same place for God… became separated for us;” and, with the help of THAT model, we deduced that the separation of the three forces was the first change in Creation.
Continuing with that model, here is an interesting thought… if the forces are separated for us, then, where are they?
How would you separate three forces?
As an aside, this is tough for me to say, because it is so contrary to what we have been taught in the Work.
We learned about Affirming, Denying, and Reconciling forces. For seventy years they have been talking to us about them.
So, you better grab on to your seat, because what I am about to tell you may be a little hard to take.
There is no such thing as a denying force.
There is no such thing as a reconciling force.
They are all affirming forces.
All forces are created equal.
All forces are affirming forces. There is no one in the model that says, “I am a denying force.”
Now, as with all things objective, this can be proved.
You get over on that side of the room and run this way; and, I will get over on the other side of the room and run that way. When we meet, it will just be two affirming forces colliding.
But, based on our age and strength and girth, one of us might knock the other one down on his backside. Therefore, for that event, someone might say, hey, that guy knocked that guy on his bum, so… he denied him.
Ok, you might give one guy that label, but in truth, he was not a denying guy before they collided. He was labeled a denying guy after they collided. But, by himself, he was just an affirming force.
There have been some interesting science shows over the years. One was about the jungles of India. Slithering through the jungle was a boa constrictor; and, prowling through the jungle was a tiger. There was an encounter between the boa constrictor and the tiger, and a battle ensued. In one model, the tiger got the boa constrictor behind the head, bit its neck, and killed it. In another encounter, the boa constrictor coiled himself around the tiger, suffocated, and swallowed him.
So, which one is the denying force?
In the event where the tiger killed the boa constrictor… the tiger was the denying force; but, in the event where the boa constrictor coiled around the tiger, suffocated, and swallowed him… the boa constrictor was the denying force.
But, innately, by themselves, neither was a denying force.
All forces are created equal.
I repeat, all forces are created equal!
All forces are affirming forces. Nobody is a denying force. Nobody is a reconciling force.
We label the forces Affirming, Denying, and Reconciling not because they are affirming, denying, and reconciling, but because of how they interact in an event.
Let’s take another event. A boa constrictor and the tiger again meet and battle. The tiger is protecting its cubs which are near. She is a mother defending her children. She fights a little harder to keep the boa constrictor away from her cubs, ultimately causing the boa to flee. We then label the tiger’s cubs as the reconciling force because they helped tiger.
We label things as denying and reconciling forces based on this concept. But forces, by themselves, are neither denying nor reconciling forces… just affirming forces.
You got the picture? Does that make sense to you? I am sorry to kill your belief that there are denying and reconciling forces. But there are not.
A tree has been growing for thirty years. It is surrounded by other forces: bugs, birds, blights, bacteria, and stuff… all trying to eat it. But that tree has its bark and its sap fending them off. However, someday that tree is going to become old and weak, and will stop ascending, when it does, all the other forces that are still trying to ascend, will consume it. They are not denying forces. They are all just affirming forces trying to survive.
OK, Enough about trees. Back to the question. If the forces are separated, where are they?
We begin by remembering that all forces are created equal. All forces are affirming forces. They are not plus, minus, and neutral forces. They are all plus, plus, and plus forces.
So, if we separated three plus forces, where do you think they would go?
I decided that the only way to separate them was to place them at the points of a triangle. An equilateral triangle. I envisioned this equilateral separation in many ways.
One good model is to imagine a magnet that looked like a coin with its north pole on the heads side of the coin and its south pole on the tails side. Then imagine that you glued a toothpick size long stick sticking up from the center of the south pole side of your magnet and hung the other end of the stick on a hook so that the magnet could swing freely. What would it do? If you said it would just hang there, motionless, you are correct. It would just hang there,
Then, if you took a second magnet that was configured in the same way; one that had the same polar strength as the first magnet (equal forces), and hung it down on its stick next to the first magnet, how do you think the two magnets would interact? If you said they would repel each other, you are again correct. They would repel each other.
They would each try to hang straight down… but would keep repelling each other, they would be very unstable, and you would have a very chaotic system… one that is always in motion.
Then, if you took a third, similarly configured magnet, with the same polar strength (equal forces), and hung it down next to the other two, how do you think that the three magnets would interact?
If you said that they would all repel each other, you are again correct… but this time they would take the shape of a perfect equilateral triangle with one magnet at each point of the triangle.
A perfect equilateral triangle.
Each magnet would be trying to fall to the center, but since it was being repelled from two different directions, it would be held in place.
The three magnets would lock into an equilateral separation. A very stable configuration.
The whole system may rotate, but the magnets would be locked in to perfect equilateral separation.
The separation of three equal forces can only be equilateral.
Who would have thought? You make a little model with magnets, and realise, of course!
We also see similar stable configurations in chemistry. If we had a molecule like Methane, which contains four hydrogen atoms, what shape do you think it would take?
If you said a tetrahedron because the four positive protons in the Hydrogen atoms would all repel each other, you are right.
It would be a perfect tetrahedron. Four hydrogens. One at each point.
And the distance and angles to all of them would be identical, 109.5 degrees. Tetrahedral separation. A four-sided triangular, geometric structure called a tetrahedron. Wow.
We see many such precise shapes when we look at the geometry of molecules, which is dictated by how the atoms in those molecules interact. So, it’s not hard to understand how three equal forces will form an equilateral triangle; and, how four equal forces will form a tetrahedron.
Let’s do one more. What about salt?
Salt is a molecule made of sodium and chlorine, called sodium chloride. Its shape is a perfect cube! Like a little dice. Sodium and Chlorine form cubes, that is the only way they can orient. If you have a magnifying glass, shake out some salt and take a look. They are perfect little cubes. Wow!
Things acquire shapes based on their molecular properties. Sodium and chlorine make cubes and Carbon makes diamonds, which you can cut into 50 to 58 facets . Fascinating!
The point is, if we have three forces that are not plus, minus, neutral, but rather, plus, plus, plus they must take the shape of an equilateral triangle, a perfect triangle
All amazing stuff.
We now know something about the separation of forces. They went from all being at the same place, to being at different places. And, when they became separated, they took the shape of an equilateral triangle.
The three forces are now at three-thirds, two-thirds, and one-third of the whole.
We have now successfully understood the changing of the Law of Three.
It went from everything being at one spot, to things becoming separated. And that separation allowed for only one shape, the shape of an equilateral triangle… just like methane is a tetrahedron, and salt is a cube.
The forces that were one in the Holy Sun Absolute were split into three. Thus, creation began.
The forces are at the thirds. That is where they live. The forces were separated and now live at the thirds – at DO, LA, and FA.
So, we now know that the first act of creation was the separation of the three forces. They went from a single place, to being in three places. But, that is just the start.
Now we must talk about the structure of the law of seven, again, as described by the fellow in Texas…
In order to continue our study into the structure of octaves, we will examine the biblical assertion that man is made in the image of God, which is a pretty humbling thought. But what does it mean… that man is made in the image of God?
Well, Scientists have discovered that man’s genes are only 1% different from those of an ape.
Does that mean that the image of God was held out of the Universe for 13.8 billion years and then placed in the last 1% of the genetics of organic life? Does that make sense?
The fellow in Texas postulated that if the image of God was in man, then, it must be in everything. That is, there must be an axiomatic image that permeates the whole Universe, which worked its way into everything… even into man.
And, if that is true… and, if the image of God is everywhere… then, we should be able to find it. In some places it may be obfuscated, but in other places it should be obvious… and, if we look… we will find this “obvious” in music and light.
The spectrum of visible light, Red, Orange, Yellow, Green, Blue, Indigo, and Violet, is proportional to the musical intervals… and the notes of the musical octave, Do, Re, Mi, Fa, So, La, Ti, and Do, are at the transition points between those colors.
It is amazing that these two separate phenomena, music and light, can be found in the same structure.
One is at the notes of the musical octave and the other is in the spaces in between those notes.
Question: “How can music and light be in the same structure?” Answer: “They can be in the same structure if they are both obeying the same axiomatic truth.”
Man has searched for this axiomatic truth in philosophy, in Zen, in religion, in mysticism, etc., and if one of those ways was fortunate enough to find a hint of it, they, unfortunately, attached so many other things to it that, after a while, it became unrecognizable… to where, even their followers had to be bullied into believing it. Believe! You must believe!
Contrarily, Gurdjieff’s model did not start with belief. In fact, it started with “Do not believe.” Gurdjieff said we should verify everything… rather than just blindly believe it.
Which is probably why Gurdjieff tenaciously pursued the following question:
“What is the sense and significance of life on earth, and in particular the aim and purpose of the life of man?”
These podcasts are not offered as a recapitulation of that “Gurdjieff Question”, which it has subsequently come to be called, but rather, as an exposition on what we call the “Gurdjieff Answers.”
ANSWERS SO POWERFUL THAT THEIR KNOWLEDGE CAN NOT ONLY EFFECTUATE A SPIRITUAL EVOLUTION IN MAN, BUT POSSIBLY, A SPIRITUAL REVOLUTION IN MANKIND.
We can find those answers purposefully concealed by Gurdjieff in his writings. John Bennett addressed this idea in the following excerpt:
“He himself [Gurdjieff] used to listen to chapters read aloud and if he found that the key passages were taken too easily–and therefore almost inevitably too superficially–he would rewrite them in order, as he put it, to ‘bury the dog deeper’. When people corrected him and said that he surely meant ‘bury the bone deeper’, he would turn on them and say it is not ‘bones’ but ‘the dog’ that you have to find.”
Ouspensky said something similar:
“There is a certain book of aphorisms which says: To know means to know all. To know a part of something means not to know. It is not difficult to know all, because in order to know all one has to know very little. But in order to know this little one has to know pretty much. So, we have to start with ‘pretty much’, with the idea of coming to this ‘very little’ which is necessary for the knowledge of all.”
Ouspensky further stated that most religions and philosophies do not know the all, because they were looking for truth through a narrow slit; and, therefore, were only able to see a sliver of it.
He said that truth was much bigger than what could be seen through a narrow slit.
Gurdjieff was saying the same thing. That we need to find enough pieces to see the whole; or, in this case, to find the dog… not just a bone.
As a result, many religions and philosophies are incomplete.
In religion, man has four bodies – physical, natural, spiritual, and divine.
In metaphysics, man has four bodies – physical, astral, mental, and causal.
But, in Gurdjieff’s model, man has three bodies – physical, kesdjan, and higher being.
Why are the religious and metaphysical models different from Gurdjieff’s model?
Well, hold up four fingers.
How many spaces do you see between those four fingers?
Eureka! There are three spaces. Bodies are the spaces not the fingers.
However, you need the four fingers to identify three spaces.
Religion and metaphysics labeled the fingers… Gurdjieff labeled the spaces.
Both were talking about the same thing but, since they did not share the same truth, they caused confusion amongst the people.
If they had the same truth, everyone would have realized that the bodies of man were in the spaces.
Man only has three bodies… but needs four points to define them.
Physical, astral, mental, and causal are the points.
Physical, kesdjan, and higher being are the spaces.
I repeat: Things take place in the spaces. The points are only there to designate when something undergoes a change of space.
For example: At some point in your life you were a teenager.
Teenagerness took place in a space… and had a duration.
At 12:01 AM on your 13th birthday you became a teenager. You entered the space of being a teenager. You stayed in that space until your 20th birthday. Then, you became an adult, and you stayed in that space until you became a senior citizen.
All of life happens in the spaces. The points are only needed to designate when there is a change of space… like 10th grade, 11th grade, and high school.
Spaces are durations not moments. High school was a duration not a moment.
Even Eric Clapton once said, “I do not play the notes, I play the spaces in between.” I like that.
So, life is about the spaces, not the notes – unless, of course, you are singing. ????
I repeat, “The notes are only needed to designate a change of space.”
Thus, the confusion of one system, which designated the higher bodies of man by four points, and the other system, which designated them by three spaces, can now be resolved.
OK, now that we know something about music and light. That is, about the inner structure of the Law of Seven, let’s take a look at the definition of an octave, not from Gurdjieff… but from Merriam Webster.
Webster’s New World Dictionary, second college edition, defines the octave thus: “The eighth full tone above a given tone, having twice as many vibrations per second, or below a given tone, having half as many vibrations per second.” Also, “the interval of eight diatonic degrees between a tone and either of its octaves.”
We now have a two-fold definition of the Law of Octaves. One involves the doubling and halving, and the other involves the six additional, what are called, diatonic degrees that occur within the doubling and halving.
This means that octaves have a requisite inherency to double or half. For example, Middle C is at 256 vibrations per second and High C is at 512 vibrations per second – twice Middle C; and, Low C is at 128 vibrations per second – half of Middle C. Also, there are six additional notes between the doubling or halving which occur at very specific vibrations.
The doubling is easy to see in nature – cells double; halving is more difficult.
Here is a scenario that may help you to understand halving. Scientists say that if you had twenty pounds of Uranium 235, put it in a box, and waited 713 million years, when you opened the box you would only have ten pounds left.
Ten pounds! “What happened to the other ten pounds?” Answer: “It decayed.” To a man of mathematics, that is a rate of decay called ten pounds per 713 million years.
That makes sense. We found a constant… or did we?
We like constants. For example: If a cow eats a bushel of hay this week, how much hay would she eat next week? If you answered, “A bushel”, you are correct.
The constant is a bushel per week.
Therefore, if in 713 million years you lose 10 pounds… then, you should lose, in the next 713 million years, another 10 pounds, right?
It sounds like you found a constant, the constant of ten pounds per 713 million years.
But that is not what happens. In the second 713 million years, you only lose 5 pounds… not 10.
Eureka, you have discovered the principle of half-life decay, which is a cool principle.
Many things decay by half-life. Medicine for example. That is why a doctor can tell you how often to take your medicine, because your medicine loses its potency based on half-life.
And, it happens that way because of the law of octaves. Octaves double or half, in this case half. That’s just the way it is, 512 halfs to 256 halfs to 128 halfs to 64, etc.
OK, we found the constant of half-life decay. It is the constant of an octave. In 713 million years, Uranium 235 decays “an octave.” In the next 713 million years it decays “another octave.” It is not our fault that the next octave is only half as big.
I repeat, we now have a constant for half-life decay. Things decay based on octaves.
Now, back to the principle of doubling.
An octave begins at one vibration per second. Double it to two… and you complete the first octave.
Double it again to 4, and you complete the second octave.
Double it to 8, then to 16, then 32, 64, 128, and when you double it for the eighth time and reach 256, you will be at what is called Middle C or, “scientific pitch”.
Many folks, with musical degrees, do not know why 256 is called scientific pitch; they were just told that it was. No one bothered to explain to them that Middle C was the eighth pure doubling of “one” (1, 2, 4, 8, 16, 32, 64, 128, 256). Double it again and you reach High C.
The eighth doubling of “one” also explains why computers have a 256 Character Limitation.
In addition to the doubling of Middle C to High C or the doubling of Low C to Middle C, there are also six additional vibrations, Re, Mi, Fa, So, La, and Ti, that exist within these doublings.
And, those vibrations are at very specific places called “diatonic degrees”.
Let’s find them.
A good way to conceptualize these “diatonic degrees” is on a Monochord.
A monochord is made by stretching a string between two points. And, when the string is plucked, it produces a tone. By placing a movable “fret” under the string, the tone can be altered by changing the position of the fret. You will find that, when the fret is moved to “certain places,” the tone that is produced is resonant to the tone that was produced by the string at its fixed length.
You might not be able to see this on a Monochord, but if you affixed another string, right next to the first string, and tightened it until it sounded the same tone as the first string, you would be able to see the second string vibrate when the first string was plucked; and, vice versa.
In addition, these “certain places” that are resonant to one string, will also cause the other string to vibrate. By doing this, you can identify the what are called diatonic degrees; or, the vibrations of music.
You can also see these resonant vibrations on an oscilloscope.
If you convert the vibration of Middle C into voltage, you would see a sine wave on the oscilloscope.
How cool! You can play a tone on a keyboard and see it on an oscilloscope.
However, you would also see other sine waves on the oscilloscope. Sine waves that have lesser amplitudes and shorter wavelengths, which were also created by the sound of Middle C. That is, tones with a higher pitch… but, at a lower volume.
A chanter can produce these high tones with his voice. You can hear him chanting a low tone and also hear high tones. How can a low tone produce high tones? It can, because the high tones are in the low tone. We know them as overtones. They are at the harmonic places of stability within the whole.
Thus, contained within a vibrating string are all the harmonic tones that can be seen on an oscilloscope. But, to our ear, they become drowned out by the louder sounding C.
All right, let’s take a look at the mathematics of these harmonic places of stability.
They were first documented by Pythagoras, a philosopher and mathematician in the 6th century B.C., and are fittingly called the Pythagorean Harmonies. He discovered what are called the Perfect Fifths. The Perfect Fifths produce all the vibrations on a piano, both the white and the black keys. However, a few vibrations do vary slightly. Those variations were corrected by Ptolemy to produce the diatonic scale we use today.
We can produce Ptolemy’s diatonic scale by taking a tone (DO) and increasing the DO by 1 and ⅛, when we do, it will sound RE. If we increase the DO by 1 and ¼, it will sound MI. If we increase the DO by 1 and ⅓, it will sound FA. If we increase the DO by 1 and ½, it will sound SO. If we increase the DO by 1 and ⅔, it will sound LA. If we increase the DO by 1 and ⅞, it will sound TI. And, if we increase the DO by 2, that is double it, it will sound the higher DO.
In William Braid White’s book, Piano Tuning and Allied Arts, we can find the mathematics of these diatonic ratios. That is, the same ratios as Ptolemy’s diatonic scale:
They are as follows: the bottom C is 1, D is 9/8, E is 5/4, F is 4/3, G is 3/2, A is 5/3, B is 15/8, and top C is 2.
Mr. White says, “These ratios may readily be verified by taking a string of convenient length, say 60 inches, on a monochord, tuning it to C and then successively shortening it in the reciprocals of the figures shown. It will then be found that a speaking length:
of 53.33 inches (60 divided by 9/8) will sound D,
one of 48 inches (60 divided by 5/4) will give E,
one of 45 inches (60 divided by 4/3) will give F; and so on.”
The Rudolph Wurlitzer Company also used these ratios to make pipe organs. They cut pipes into various lengths as indicated by these ratios; and, then, when they blew air through those pipes, they produced the tones DO, RE, MI, FA, SO, LA, TI, and DO.
In addition, the frets on a guitar are fixed according to the math 12√2, which also produces the diatonic ratios (within 1%).
The best way to study this proportionality is the octave of 24. That is, in an octave with a length of 24. So, if you wish, write this down.
We will make the bottom DO, DO-24. If the bottom DO is 24, RE would be 27, MI would be 30, FA would be 32, SO would be 36, LA would be 40, TI would be 45, and the top DO would be double the value of the bottom DO which would make it 48.
Congratulations, you now have an objective model for studying the proportionality of an octave.
The first thing you should write down are the intervals. That is, the length of the spaces between the notes.
They are, from the bottom DO up, 3, 3, 2, 4, 4, 5, 3, which total 24, spanning the entire distance from DO-24 to DO-48.
Earlier, we talked about the spectrum of visible light. Now we can see its proportionality: Red is proportional to 3, Orange is also proportional to 3, Yellow is smaller, it is a 2, Green is twice as big as yellow, it is a 4, and so is Blue, Indigo is the big one, it is a 5, and Violet has the same proportionality as Red and Orange, a 3.
All octaves follow this same proportionality, 3, 3, 2, 4, 4, 5, and 3. Or cumulatively 0, 3, 6, 8, 12, 16, 21, and 24… spanning the entire length of the octave. You can take any octave, say the octave of a person’s life, and mark it off in this proponality and understand volumes.
Any whole phenomenon can be calculated as an octave, as a “something” that runs from its allness to its nothingness, or vice versa, dividing the totality “diatonically” by the ratios: 1/8, 1/4, 1/3, 1/2, 2/3, and 7/8.
IN THE NEXT PODCAST, continuing this talk on Triads and Forces, we will explore the mathematics of the three forces in an octave, and discuss how all phenomena can be represented as a diatonic octave.
Thank you for listening, and, if you’d like to know more about the subjects and exercises we’ve been covering in these podcasts, including the book and guide that underpins all of this, and how we work with it, you can find us at The Dog Pub Dot Com. That’s T H E D O G P U B DOT COM
Goodbye until next time.