Ark - where are you headed?

[SoCurious]

Have I got this right?

A monad is the simplest structure and comprises of two 'entities', say 0 and 1.

The simplest groupoid has two 'entities', again 0 and 1.

But nothing works unless there's a trinity? We can have the universe flickering on and off but that in itself is useless unless there's a 'binding' agent, something that gives everything coherence.

So a monad or groupoid or anything for that matter has to have a 3rd element, be it consciousness or gravity or nuetron or whatever?

Am I anywhere in the ballpark?

 

[Mountain Crown]

Have I got this right?

A monad is the simplest structure and comprises of two 'entities', say 0 and 1.

The simplest groupoid has two 'entities', again 0 and 1.

But nothing works unless there's a trinity? We can have the universe flickering on and off but that in itself is useless unless there's a 'binding' agent, something that gives everything coherence.

So a monad or groupoid or anything for that matter has to have a 3rd element, be it consciousness or gravity or nuetron or whatever?

Am I anywhere in the ballpark?

Fwiw- I was looking at the transformation as the third principle.

 

[John G]

Have I got this right?

A monad is the simplest structure and comprises of two 'entities', say 0 and 1.

The simplest groupoid has two 'entities', again 0 and 1.

But nothing works unless there's a trinity? We can have the universe flickering on and off but that in itself is useless unless there's a 'binding' agent, something that gives everything coherence.

So a monad or groupoid or anything for that matter has to have a 3rd element, be it consciousness or gravity or nuetron or whatever?

Am I anywhere in the ballpark?

Fwiw- I was looking at the transformation as the third principle.

There are two transformations being described as "do nothing" (law of 3 passive) and "change to the other one" (law of 3 active). The law of 3 neutral third principle is being linked to the central loop being formed by the transformations (a Greek triad egg of sorts). This monad egg perhaps grows into more types of transformations.

 

[kenlee]

But nothing works unless there's a trinity? We can have the universe flickering on and off but that in itself is useless unless there's a 'binding' agent, something that gives everything coherence.

I was thinking that the monad as a totality is a trinity of some kind but it would still be a whole unit. Maybe any whole unit (including the most fundamental ones) are all monads such as a cell, or a human being, a planet, galaxy etc. Maybe even the entire universe itself. Regarding the blinking off and on I was thinking that perhaps it might be more like a kind of oscillation between two points or perhaps a spinning of some kind. Don't know though, just speculating here.

 

[caballero reyes]

Hi, Ark. Are the Leibnitz concepts of monads refered to two classes of atoms: physics and metaphysics? or he considered to ALL atoms are monads.

 

[ark]

Back to the fundamental groupoid - the atom or monad of the Universe:

There are also four arrows. Four has also an esoteric meaning: it is enough to recall Jung’s quaternity. Quoting Karl Gustav Jung (Jung, 1938):

I cannot omit calling attention to the interesting fact that whereas the central Christian symbolism is a Trinity, the formula of the unconscious mind is a quaternity. As a matter of fact even the orthodox Christian formula is not quite complete, because the dogmatic aspect of the evil principle is absent from the Trinity, the former leading a more or less awkward existence as devil. Since a God identical with man is a heretical assumption, the "God within" is also dogmatically difficult. But the quaternity as understood by the modern mind directly suggests not only the God within, but also the identity of God and man. Contrary to the dogma there are not three, but four aspects. It could easily be inferred that the fourth represents the devil.

 

[clearmiddle]

...It could easily be inferred that the fourth represents the devil.[/i]

A good observation, but not a good way to be popular within a church community, generally. I never actually tried to discuss it with anyone, for some reason. I guess it is OK here, though. :)

 

[SoCurious]

It could easily be inferred that the fourth represents the devil.

We could be talking here about a balancing force. Good balanced by evil, positive balanced by negative. But that is already inferred by the 0 and 1 which is the foundation of the monad.

When we have two forces in opposition they would tend to cancel each other out if not kept at a distance from where they could react without destruction. This would cause "side effects". Also they should not be kept so far from each other that they have no influence on each other.

So we need a 'distancing' force and a connective and communicative force. The latter would be gravity, the former I imagine would be energy in the form of movement. Transition would be perpetual.

I'm struggling along here but if a fifth force is introduced I'm going to be swallowing water :)

 

[caballero reyes]

I think Jung was confused about the application here of the concepts trinity and quaternity.
One thing is quaternity derived of four, in this case 3+1: 3 is "good" and 1 become "evil" (accord to Jung) and other thing is the dark side of all things or in others words the dark side of christian trinity: the "good" trinity and the "evil" trinity. and with this, we could have two very importants concepts: the number "zero" meaning the other "side" of the things or better "the non seeing", and the concept of antimateria. By the way the Trinity is not a christian concept is as ancient as the human.

 

[John G]

I think Jung was confused about the application here of the concepts trinity and quaternity.
One thing is quaternity derived of four, in this case 3+1: 3 is "good" and 1 become "evil" (accord to Jung) and other thing is the dark side of all things or in others words the dark side of christian trinity: the "good" trinity and the "evil" trinity. and with this, we could have two very importants concepts: the number "zero" meaning the other "side" of the things or better "the non seeing", and the concept of antimateria. By the way the Trinity is not a christian concept is an ancient as the human.

Those two views could be two ways to look at the same thing. You can look at spacetime being three space dimensions plus a time one or think of time creating two (or more) space configurations. Those 4 arrows are a two bit thing (static point bit plus transformation bit) and two bit things are math-wise a way to represent the quaternion (3 imaginary numbers plus one real number) so it makes sense math-wise too.

Which arrow would be "evil"? Maybe it's the "do nothing" transformation when one is away from the starting static location or maybe it's an initial "fall" transformation from the starting static location?

Yeah this forum has Gurdjieff as well as Jung gnostic-like views and for Gurdjieff "Christian" goes back long before the Christianity we know. Humans have likely known a law of 3/trinity for as long as they've been Adamic.

 

[Jones]

I'm here and reading and struggling to understand. I have some ideas that may just be noise though so apologies in advance.

If the quaternion can be reflected in all things then I can see the both the motivation matrix and the symbol for paleochristianity as quaternions.

The motivation matrix has its binary element: punishment and reinforcement.

This can be further divided - in the punishment element there is positive punishment and negative punishment.
- in the reinforcement element theres is positive reinforcement and negative reinforcement.

So there's the quaternion...if I've understood that term correctly. Also there is the reflection of the double yin-yang in the symbol for paleochristianity.

They all can be further divided by the terms 'intrinsic' and 'extrinsic'; coming from within or coming from without. Which actually leaves us with a total of 8 segments to the motivation matrix. Here the eight is also reflective of the symbol of infinity surrounding the two yin-yang symbols in the paleochristianity logo.

But there is also another element to the motivation matrix - neutral stimuli. So now there are 9 elements all up. Neutral stimuli can be seen to exist, but they have no effect. However they can become any of the above depending on the nature of interaction with them. So I'm thinking that the neutral stimuli as proposed by the motivation matrix in this context has to do with the interaction, reaction, focus or intention of the observer.

The number nine is interesting because in the version of the enneagram that has 9 points it is a combination of the the law of 7 and the law of 3. But its curious that it has only nine points when 7 + 3 equals 10. Perhaps the 10th element is the integration of all of the above?

 

[kenlee]

It could easily be inferred that the fourth represents the devil.

I don't know if what I'm about to say accurately relates to Jung's quote (I might be so off the point here so as to "not even be wrong"). Anyway here it goes. The fourth aspect might be what brings the trinity together in a kind of synthesis. So its a question of a balance in a way (I guess) but what's really balanced is the three aspects of a trinity coming together in the proper ratios (like the baking of bread) and allowing for their transformation into something else. The 'direction' of the transformation (and I could be wrong on this) might relate to the fourth aspect of Jung's. In other words, very simply put, you have the three points of the trinity as the base of a triangle (tetrahedron) and they come together to an apex (fourth) point, the apex point giving space, direction and depth to the transformation process.

It may be that the true opposite of evil is not really good at all, but the true opposite of (outer) evil is the evil, the darkness, the mechanical programs within ourselves that we don't see. Not seeing it within, not being conscious of it, is what allows for its projection onto the outer world allowing outer evil to further mechanically propagate itself all in the name of 'good.'

The three forces of the trinity can come together in outer life to produce events where things 'happen' but maybe the fourth aspect (the inward direction of consciousness) is where a space exists so as to allow for the outer world events to inwardly transform themselves with an "inner direction." Potential evil can be in that inner space which will be projected onto the outer screen of life if we are not more conscious of what's going on inside ourselves. The lack of seeing it might be the 'devil' of this fourth aspect that Jung speaks of. FWIW on all this (this is just my interpretation on what Jung might have meant).

 

[Esote]

Back to the fundamental groupoid - the atom or monad of the Universe:

There are also four arrows. Four has also an esoteric meaning: it is enough to recall Jung’s quaternity. Quoting Karl Gustav Jung (Jung, 1938):

I cannot omit calling attention to the interesting fact that whereas the central Christian symbolism is a Trinity, the formula of the unconscious mind is a quaternity. As a matter of fact even the orthodox Christian formula is not quite complete, because the dogmatic aspect of the evil principle is absent from the Trinity, the former leading a more or less awkward existence as devil. Since a God identical with man is a heretical assumption, the "God within" is also dogmatically difficult. But the quaternity as understood by the modern mind directly suggests not only the God within, but also the identity of God and man. Contrary to the dogma there are not three, but four aspects. It could easily be inferred that the fourth represents the devil.

Fourth aspect as Challenge :
As an (mine, for now) interpretation of Trinity, we have 0, 1 and information (the link, the movement in between).
What else, but Awareness ?
Which could mean that the Fourth Force is itself ambivalent, part of it being ignorant awareness, the other one Consciousness with Knowledge...
Ignorance, Dualism, Devil, Time... versus Atemporal Knowledge, beyond words but mathematically probable ?

Makes me think about the Yi-King hexagrams, with a dual trinity in the trigrams transforming in another one, and giving 64 hexagrams to complete the cycle. By the way, 43=64

 

[John G]

For me the last three posts seem very related with the I-ching related to Clifford Algebra (binary); the Enneagram related to Lie Algebra (root vector polyhedron projection); and an inner-outer evil (axis) related to how one gets Lie Algebra geometry out of Clifford Algebra bits.

Getting back to the math of the quaternion; the real number timelike Jungian 4th is actually a 0-vector scalar which means it's like an empty set, none of the bits (neither transformation nor static location), it's nothing which sounds very much like an STS definition (at its limit which one never gets to).

 

[ark]

Here I will go into some more details. It will be slightly more technical. But then we can discuss the essence in plain terms.

Groupoid in algebra clothing
When building a house, we start with the construction of a scaffolding. Eiffel Tower is an example of an almost pure scaffolding. Even if today it houses a dozen of restaurants, nevertheless it is largely open to the winds does not attract an average human being to stay there for long. Statue of Liberty, the gift of French people to America, started also with the construction (in Paris) of a clever frame. But it was then covered with copper sheets, so the Statue of Liberty looks more solid and more habitable than Eiffel Tower - it even houses the so called Dormitory Room (that served, in the past, for detaining immigrants).

Our groupoid, consisting of a couple of points and of connecting them arrows, is just a frame, a scaffolding, and, as such, not very attractive to our minds. Therefore, in order to make our structure more “habitable”, we will cover it with a smooth structure – much like Bartholdi covered the skeleton of the Statue of Liberty with copper. Instead of copper we use another smooth material, this time of a mathematical nature, that is with numbers. Copper was the right material for the sculptor Frédéric-Auguste Bartholdi. We will use the right material for our construction complex numbers. The details of the construction are in Appendix. Here it is enough to say that our mathematical sculpture, based on the fundamental groupoid skeleton, when finished, has the shape of the algebra of 2x2 complex matrices:

[a b]
[c d]

where a,b,c,d are complex numbers, each having a real and an imaginary part. WE have four complex numbers, that is eight real numbers. Our complete construction spans therefore an eight-dimensional space!