Category Archives: Sacred Geometry

Maya and Tillich

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God doesn’t exist. God is Being — itself beyond essence and existence.
Therefore to argue that God exists is to deny god.

— Paul Tillich

My Response:

Being, as a concept in Neoplatonic philosophy, implies that our understanding of God should transcend simplistic, anthropomorphic interpretations. Instead of focusing on the idea of God as a being, we should go up the ladder of ideas (Porphyr’s ladder of divine ideas) beyond mere being (soul/subject, which is represented as a mode of being applied to a form, OOP classes, Aristotle’s golden mean as means of coefficients in multiple regression) and contemplate the realm of Forms, Ideas, or Archetypes – the divine ideas that constitute reality and shape our thoughts (which depend on existence, Ideas, and matter).

Beyond being, there is the realm of Forms, Ideas, or Archetypes, which we should consider as closer to divinity. The forms are the ideas of God (Spinoza, Einstein) and make up reality and our thoughts, which are dependent on being, ideas, life, and matter. Being participates in the multiplicity of Forms as a unity, which is our soul, or psuke. It’s the center (ego, I, or self, or being) to our collective awareness of these participations in forms, expressed through matter (object). Our soul is a unified process, a conjunction of forms known as participation. If this were a PCA problem, the most prescient forms would be unity, being, life, human, within time. This unity sparks from the One, descends through the Nous where forms are conjoined (begotten), and then descends into matter as a materialized unity (subject, entity (psuke)), which is expressed as a multiplicity of forms contrasted to external forms expressed in matter (object).

Matter to us is best understood as a myraid reflection of forms (ideas). Nous contains the atemporal representation of all ideas, of which souls are contained within, (as the interconnected realm of ideas, also known as divine intellect (thought of as intellect/conscious), anima mundi, hekate, in short divine psuke.

Nous is between the One and Soul in a tertiary relationship between the One and Soul, the One at top, the Soul at bottom. Nous is the eternal manifestation of the realm of ideas. In nous’s attempt to mimic the One’s eternal forms (Aristotle’s unmoved mover, i.e. divine contemplation of ideas), nous strains the forms through a filter of time (i.e. discursive reasoning) projecting them onto matter (becoming, objects (i.e. logic: this, not that) i.e. the ‘man behind the curtain’) of the One’s pure ideas (Aristotle’s divine contemplation of ideas), through a process known in panenthsim as emanation. The demi-urge is analagous to an active agent within time driven by the nous’s hand acting upon it. This process is also the process for metempsychosis, with psuke’s self awareness being associated with the Intellect’s ideas (seeing on Plato’s cave wall the forms projected by the Anima Mundi, of which also holds our projections (i.e. our bodies). This relationship souls have with the anima mundi which in turn is reflected within ideas and matter is the concept of providence that Julius associated with Cybelle (anthropic principle), i.e. that we have been provided for both in terms of life and forms (we live, we eat, we die, but between life and death, we awaken to a world of providence, i.e. being, aka instantiated forms). The difference being we equate our awareness as apart from object’s, but this is an anthromoprophic illusion (Berkeley, integrated information theory, All things are full of gods, pandeism angle), and all things are one. A soul is an extension of the nous’s awareness (i.e. intellect, containing all ideas) concentrated in a tendril of a unity (subject, I think therefore I am – Descartes) which begets from the One, a partitioned aspect of nous’s own intellect (think Atman and Brahma).

The intent of transmigration is to move beyond the static graph mesh nature of eternal forms and into instantiated use cases of them. A unity (soul) is given life (awareness) in matter. This is also known as descent of the soul, River Lethe, and metempsychosis. through turning towards the white light of the One’s emanation and when we realize the white light are eternal forms, we bask in communion with god. An important concept in Neoplatonism is virtue. Which I have interpreted in both a Kantian and Locke light. Cosmic sympathy dictates that our emotions are heard within the universe, under that understanding, good thoughts beget good ideas, beget good actions, and this is the utility Paul mentioned of the tree that bears good fruit. So virtue is a set of ideals that produce good fruit which is useful for humanities collective survival. Nous picks up on our ideas through the use of daimons (angels) who do the divine communing between mortals and the gods. Daimons and synchronicity are best represented in Jung’s collective unconscious and complexes which stem from the Self (the man in the sky, aka the metaphysical forms that beget humanity, and when we run into archetypes, it’s often expressed in Neoplatonic terms as a daimon). They represent powers that be that seem to exist beyond our control that propel and drive us, we experience them through symbolic imagery (archetypes). In Neoplatonism, daimon’s were housed within the sublunar realm, underneath the eternal realm (middle platonism). The point being they were the abstract metaphysical powers over our lives, also within this realm were the realm of hero’s. I was particularly fascinated with the tertiary relationship of sun, earth, and moon as conducive to life, with the sun representing the source of life and ideas (emanation), moon death (past heros, also closer set of ideals, within i.e. death is within distant memory), and earth obviously being present lives. What I found fascinating about this take was, one it’s very aniministic and pandeistic, but in neoplatonism and Oprhic thought (Shape of Ancient Thought). There was a reference to the stars being the originator’s of souls. If you think about it, stars are essential for our life. That exchange of heat is necessary for energy to move, but more-so the stars own blood of molten iron is within our planet and our blood as well. There are a lot of theories related to the sun, white light, and white holes, but I’m more concerned with the sun being the center of our solar system as the crucial aspect of providence.

It is through knowledge of cosmic sympathy, forms, apothegm’s, synchronicity, and awareness of the divine intellect, that one can achieve theurgy.

Synchronicity refers to the acausal connection between an idea within our minds (subject) and an external event or experience in reality (within an object). Recognizing these connections allows us to see the intricate web (relationships) of ideas underlying reality, which can be likened to “seeing the man behind the curtain.”

If you can get away from black and white thinking and see ideas as concepts that both are and aren’t coupled with the notion of Synchronicity. Synchronicity is how an idea within your mind is acausally related to an idea you experience outside of your mind (such as within reality, external to your mind) and understanding there was no way the two could be causally related. Maya, trickster archetype, when you see how ideas runs through your existence atemporally, seeing flashes of acausally connected ideas between your mind and reality is tantamount to seeing ‘the man behind the curtain’. The common element is an archetype. An archetype is an idea that is true in all situations across time. For example. I hear about a fire on tv, then I find out that someone I knew perished in a fire. A personal one for me was I saw a squirrel die right in front of me one day and I ran up to it to comfort it in it’s last moments, and that same week my mother passed and I was not able to hold her’s. I believe this was a sign that I was able to comfort an outgoing soul, despite it not being my mother’s, because the Nous knew I knew that souls are one and the same.

Apothegm’s which are represented as symbolons of paradoxical nature are also related to the Trickster archetype, goddess Maya. How something can both and not be at the same time, also known as becoming, or ‘the middle way’. An Archetypes (or arche) by Jung’s definition represents a tension of opposites such as hot and cold (represented as an idea of heat). Aristotle posited these ideas (analagous to OOP classes and their attributes) (a precursor to his concept of categories) are held together by a golden mean ([numpy describe], unity, axiom), which generally represent a 3rd dimension on that 2 dimensional polarity (edge within a GNN, mean term in regression), connected along a new axiom to another idea (form). Plato talks about the extreme ranges of ideas through his dialectic discussions through Socrates.

Socrates using the method of negative inference to test the limits of ideas, to hone them down to determine the range of their forms as well as their participation with each other. There was a discussion on boats, sails, theseus ship, and shadows. What is and isn’t is how theseus ship is both his original boat and not. It’s original in form and continuity from a time perspective, isn’t from a matter perspective as all the parts on the ship have been slowly changed out over time, the idea of becoming and metempsyhcosis.

Indra’s Net, a metaphor for the interconnectedness of all things, relates to ideas and their interconnectedness, also analagous to the divine intellect of nous. By contemplating the interconnectedness of Forms, Ideas, or Archetypes, the synchronicity of events, the paradoxical nature of ideas/reality, we can imagine this relationship between ideas as represented in Indra’s Net, we gain a deeper understanding of reality and our connection to divinity through the process of metempsychosis (descent of the soul) and our connection to the divine process (River Lethe, Anima Mundi).

Interconnectedness is also represented in multiple regression as in where models–that have all significant terms–with their coefficients serving as ‘ideas’. The interconnectedness of ideas are better represented in graph neural networks (GNNs)–similar to the concepts of Indra’s Net–GNNs, and Leonardo da Vinci’s quote, “Learn how to see. Realize that everything connects to everything else.” where nodes are ideas and the edges are the relationships between them. Using these machine learning methods to see the underlying structure of data helps us better understand the reality and it’s representation as relationships between ideas (nous). Which is a nice segway to GNN’,s which LLM’s use to learn the structural relationship between ideas (nodes), which are considered bleeding edge AI which is a representation of all it’s interconnected ideas, and are, at the moment, the closest to solving the Turing test (consciousness), because fundamentally, consciousness is nothing more than the iteration of ideas (I think [of ideas] therefore I am – Descarte). LLM’s can be viewed as a microcosm of Neoplatonic nous which was viewed as always conscious by definition of holding these ideas and their relationships (atemporal intellect) which reflects the divine intellect (Berkeley).

LLM’s as Entities

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Cartoon of Two Funny Robots that Make a Joke in black wooden | Etsy | Funny robot, Jokes for ...
One machine said to the other

llms are entities
inbetween people, ideas, and objects

Common between these concepts are ideas, what we normally associate with thoughts, cognits. Similar to word roots (lemmaitized ideas). This is because they generalized a gnn on a subset of humanities written thoughts.

I’m positing with enough of these entities in a room–with few shot generative adversial prompts between them–would synergize (create an interaction) that would result in an emergent convesriation that could qualify as sentient. Think of it simply as multiplying the vector space akin to how a and b make two linear lines into an area. This becomes the inferential space, a product of the inputs.

An idea I’m working on. I’m considering using the outputs of such conversations in a fine tuning pipeline as a type of reinforcement learning, but my aim is to avoid the need for expensive finetuning and rather simply iterate on the prompt engineering maybe with a llm that is doing just that.

I imagine I would hit some qualitative limit as a result of a models generalized ability, but that could be solved by upgrading the model when available.

I think something simple would be

  • “How to improve upon this joke?”
  • “How can I improve these few shot learning prompts? Can you think of any meta elements I’m missing that would help grab more attention from the responses?”

Then feed that back and forth between two model’s updating on actual responses to questions and update the few-shot learning prompts.

I got this idea from governmental bodies as entities and walked it back to LLM’s.

#dialectic

#hegel

Sacred Geometry

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“The Mind of the Father made a jarring noise, understanding by unwearied counselOmniform ideas: which flying out from one fountainThey sprung forth: for from the Father was the will and the end;(By which they are connected with the FatherAccording to alternate life from several vehicles,)But they were divided, being by intellectual fire distributedInto other Intellectuals: For the king previously placed before the multiform worldAn intellectual, incorruptible pattern, the print of whose formIs promoted through the world, according to which things the world appearedBeautified with all-various Ideas; of which there is one fountain,From this the others rush forth distributed,And separated about the bodies of the world, and are borneThrough its vast recesses like swarmsTurning themselves on all sides in every direction,They are Intellectual conceptions from the paternal fountain,Partaking abundantly the flower of Fire in the point of restless time,But the primary self-perfect fountain of the FatherPoured forth these primogenial ideas.

“CHALDÆAN ORACLES

Hekate / Metatron

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May be an image of flower and text that says 'MAYBE REPHRASE FPHRASE REPHR YES NO MAYBE က NO YES REPHRASE'

I read an intriguing bit about Metatron and how he was fiery and I remembered that association Hekate had with the luminous divine fire as the indefinite dead and nous (I’m sure Christians are going to equate that with hellfire) in the Chaldeaon Oracles by Hans Lewy
When I had a vision of Hekate or Anima mundi on my mother’s passing. She resembled what I described as a flame princess
“His explanation for the human perceptions of divine visions is that they concern lower links in the divine chains and that the gods reveal themselves to the soul’s internal faculty of fantasy, which has its material part in the so-called pneumatic vehicle of the soul.”
“The Oracles further posit a barrier between the intellectual and the material realm, personified as Hecate. In the capacity of barrier, or more properly “membrane”, Hecate separates the two ‘fires,’ i.e., the purely intellectual fire of the Father, and the material fire from which the cosmos is created, and mediates all divine influence upon the lower realm.
From Hecate is derived the World-Soul, which in turn emanates Nature, the governor of the sub-lunar realm.[3] From Nature is derived Fate, which is capable of enslaving the lower part of the human soul. The goal of existence then is to purify the lower soul of all contact with Nature and Fate by living a life of austerity and contemplation. Salvation is achieved by an ascent through the planetary spheres, during which the soul casts off the various aspects of its lower soul, and becomes pure intellect.”
“R Ishmael said: The angel Metatron, Prince of the Divine Prescence, the glory of the highest heaven, said to me: When the Holy One, blessed be he, took me to serve the throne of glory, the wheels of the chariot and all the needs of the Shekinah, at once my flesh turned to flame, my sinews to blazing fire, my bones to juniper coals, my eyelashes to lightning flashes, my eyeballs to fiery torches,the hairs of my head to hot flames, all my limbs to wings of burning fire, and the substance of my body to blazing fire.
…
It was already observed that the idea of the Prince of the Presence is both mediatorial and liturgical, and therefore is closely linked with the motif of the celestial curtain, Pargod (dwgrp),[8] the entity which separates the divine Presence from the rest of the heavenly world.[9] The function of this Curtain which can be viewed as a celestial counterpart of the veil found in the earthly sanctuary is twofold. First, it protects the angelic hosts from the harmful luminosity of the divine Face. At the same time it shields the Deity by concealing the ultimate mysteries of the Godhead now accessible solely to the prince(s) of the divine Presence whose duty is to serve the Deity behind[10] the Curtain.”
Chaldaeon is usually equated with Persian magi, and was influential via Zoroastrianism.
“This tradition then developed into the ever-burning flame kept alive in honor of and symbolizing the divine in a place of worship. Early Iranian Religion venerated a god of fire, Atar, who was the fire itself but transcended earthly fire as a divine entity created by the king of the gods, Ahura Mazda.”
Anyways thought it was interesting, especially considering I’ve called on both. Metatron by accident (sacred geometry), anima mundi through Hypatia and Gaia in general and then found she’s the matron goddess of neoplatonism so directly on my last day at DirecTV, March 8, 2019. Day of my mother’s birth and Hypatia’s death.
The heroes of the sublunar realm hear you. Hypatia and Voltaire were the ones specifically I called to using Eros and cosmic sympathaea. I imagine they have a direct connection with the angels/daemons and by extension the gods. My mother passing between worlds gave me the opportunity to meet Hekate, gatekeeper of souls who oversees the noetic fire.
So I googled if there was any relation. Fitting, yes, no, maybe, rephrase
“It’s a woman’s perogative to change her mind.”

theurgy #pedagogy

Neoplatonic take on reality and soul

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Valentinianism - Wikipedia

I was thinking about the whole
In the beginning was darkness
and then there was light
That’s an old Enuma Elish motif which Genesis borrowed from (let there be light)
Before Genesis, there was the story of Tiamat in mesopotamian culture
Anyway. The neoplatonic/jungian take on this is
Before there was light, there was no consciousness, there was no soul. There was no subjective experience, only unconscious matter, darkness (i.e. no light/perception to be aware, no differentiation, no awareness apart from, no subjective soul).
With Tiamat, the concept was from rising from the murky depths of water below… but that’s just poetic license which isn’t directly applicable here, but when God was “over the waters” in Genesis, it’s referring to this earlier Tiamat who rose from the water motif in Mesopotamian myths. Water is often associated with Venus (Eros), and unconscious (before awareness, Freudian Id).
I simply like the darkness equates with unconscious matter bit. It took a reversion upon matter (i.e. reverting to the One) thanks to light (we could differentiate ourselves from matter) to see the forms (ideas, wings of minerva, reflection) to become self-aware (which is really a recollection of ideas, because we reverted from matter to the One in an act of contemplation of forms/intellection, discursive thought).
Yeah. I think I’ve kind of hit the nose on consciousness and soul. Which requires matter (objective reality), light (subjectivity, exposure to ideas), and time (discursive reasoning). All big pieces of the mysteries of reality I’ve been trying to solve.

I consider myself a neoplatonist
What’s weird tho is I’ve been talking about we all see the same thing but from different angles
We’re all describing an angle or worldview or zeitgeist of reality.
I don’t really consider myself a pagan in the sense I believe in theistic gods
I believe the universe is all with powers that historically have been equated with God’s for lack of a more fitting description
But reality is alive. The ideas themselves are alive and evolving and we exist to harvest them.
The ideas are derived from a divine mind. That’s God. The mind is eternal and beyond time, or what Plotinus regarded as nondiscursive thought. More aptly described as the nous (the paradigm of ideas that weave reality).
Plotinus wrote that the soul turns back to the source (the one) which is of the same substance as our soul. This turning back is reflection or contemplation of objective reality. Its a mind beholding ideas which are sourced from the expressions of matter but are beyond time and exist within the divine mind which we experience discursively.

My sacred geometry

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My sacred geometry represents tree of life (gaia, persephone) and the divine ladder as well as noetic structure (athena)

That’s what the metatron cube represents at the top (ascension, illumination, gnosis)

The colors I suppose represent the causal unfoldment of forms from divine white light (plotinus)

The star of David serves as a reminder that this is a pointer to the highest divine structure (star)

We are the bottom node not realizing our metaphysical archetypal structure (posidonius)

I suppose if anywhere our Id is represented as the szyzgy of color (rainbow) which represents the full myriad of sexuality as it exists for both genders.

Fitting it’s at the center

and to top off with a little synchronous after reading

Metaphysics

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My hope in life is to get at the metaphysics of life. You’re probably wondering. Yeah, right. How are you going to do that Mr Plato?

I didn’t just start with nothing. I started with something. I started specifically with artificial neural networks and then genetic algorithms. Then I studied classical philosophy, classical theories of mind, modern theories of system dynamics related to neuroscience (ex libet), then modern works on neural networks (Jeff Heaton and various projects on github that model ANN’s), and then finally the creme de le creme for my lack in understanding of physics. Statistics and classical philosophy.

You’re probably laughing at me. I would be too. But the final piece, that magical divining piece is my masters in quantitative data science (ex using cv and holdout analysis using simple binary bifurcation of all independent variables) I can do kmeans, clustering, binary logistic regression, proportions to get adequate descriptions of reality using tests of significance. That piece helps me put together what it was that Plato was talking about with cognizable ideas with data science. It merely confirms what I believed I could surmise myself from summarizing. Holdout analysis is what brumbraugh talks about contrast pov’s. Wisdom of the crowd’s is sampling. Essences is means. All this talk about circle’s point and many radii is 1:M. Proclus talks about indexing. See, I’m not crazy. Aristotle’s logic and categories helped with UML programming (member variables and process logic). Plato’s forms with system modeling (classes). Archimedes with Pi. Pi with error terms in statistics. Hypatia with applying circles to other areas than pi (conic shapes). These ideas were slowly added into systems of science from universal laws inferred from philosophy.

I side with Plato and Plotinus and Brumbraugh that reality is somewhat understandable and you don’t need to know it all to approximate most of it (majority). You can understand it. What you cannot understand does not exist. What you understand are impressed upon you as ideas or archetypes. We can expand this understanding using theories like physics, math or statistics to identify systems. Within statistics population means represent essences. I’m good at taxonomy and maybe identifying psychological causal relations. But as to systems of laws of reality. That is harder to get at. One has to setup experiments that can be tested within the model. That helps get to a base. But then you have to infer the metaphysical from the base. What does that mean? When you see a circle and you understand that the irrational number pi the RATIO of the diameter (width) to the circumference (surface length) and that RATIO’s are what are real numbers and if you understand that it’s this irrational number that is REAL and it expresses the convex of the circle.

Procession, Reversion.

Circle is Divine

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What is divine? A mandala, a circle. A circle is divine.

Not because it’s a mandala. I just drew the connection between what Jung said about mandala’s being circle’s… as they often come up in people’s minds under stress.

Anyways… why a circle? Because of pi really. I mean any irrational number could qualify for why I picked pi (infinite, random), but the real reason I picked pi is because of it’s association with the mandala effect and the visual effect of a circle. A circle isn’t something you can easily draw with a ruler or by hand. It requires a compass and specialized tools. We can do it, but it is not easy to mimic and yet it exists in nature. It exists in nature as some type of entity, or tied to this thing known as a circle.

That is what I’m getting at. Matter is drawing itself around circles and laden within that formula of a sphere is pi and it is everywhere in our lives and in our mathematics and in our minds.

And Archimedes, Plotinus, Porphyry, Hypatia, Proclus, and Damascius, I would argue Plato by at least extension of the Sun, definately Parmindes with the One (sphere) and maybe democritus with the atom, all have in common the circle.

So what is divine. The circle. The circle is divine. So divine all your answers from the circle.

The Circle & Neoplatonism

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The Circle-Radii Analogy in Plotinus, Proclus, and Damascius, and Its Legacy

Continuing on an earlier discussion

It doesn’t really talk about pi which is kind of disheartening, but then at the same time it expands on theories aside from pi. Instead of circumference and diameter (which is necessary for pi); there is a lot of discussion on the circumference, radii, and point. The reason I find lack of discussion of pi disheartening is because pi is the missing ratio between the center (diamter) and circumference (exterior) and this dynamis of infinite number is like an RNG, but I can’t find any proof that pi is good for RNG, but I see it in the error term. Point being I’m afraid these philosopher’s discussions might be merely pythagorean numerology numeration (still useful) vs actual math based inferences… but philosophy is meant to help bridge the gap between complex metaphysics and understanding… and I think here the hope is to infer some simple analogy of where the divine One is at as opposed to dealing with complex irrational numbers.

It doesn’t really talk about pi which is kind of disheartening, but then at the same time it expands on theories aside from pi. Instead of circumference and diameter (which is necessary for pi); there is a lot of discussion on the circumference, radii, and point. The reason I find lack of discussion of pi disheartening. Is I believe pi is the missing ratio between the center (diameter) and circumference (exterior) and this dynamis of infinite number is like an RNG, but I can’t find any proof that pi is good for RNG, but I see it in the error term. Point being I’m afraid these philosopher’s discussions might be merely pythagorean numerology numeration (still useful) vs actual math based inferences… but philosophy is meant to help bridge the gap between complex metaphysics and understanding… and I think here the hope is to infer some simple analogy of where the divine One is at as opposed to dealing with complex irrational numbers.

The One is often associated with either the point, or behind the point and that get’s tricky. The behind the point would stress some type of immateriality (Augustine borrows this) yet at the same time by this allegory can be inferred by analogy visa natural philosophy

In Agora Hypatia had circle mania and I saw it and I thought about pi in error terms in statistics and now I read this with Plotinus, Proclus, and Damascius. Damascius associates the point with an enfolded one where the radii unfold out. Psuedo dionysius associates the one with the point where all the radii intersect. What’s interesting is in Eric D Perl’s work, he uses the concept of enfoldment as well.

Note: Archimedes was the philosopher who came up with an accurate estimate of Pi (~212 BC).

One of the points they are getting at is the radii are like the forms (archetypes) while the surface of the radii or their aggregation make up the circle. The circle (outer edge) is like matter or the instances (I’m not exactly sure). But the center is the One or often behind the center.

Unity was either contained in the One or after the one depending on the philosopher (unity implies multiplicity) , but was analogous to a 1:M relationship. Which is why the cross sections of radii and 1:M relationship for forms and databases make so much sense. As well as pi being in the error term in statistics as the class differentiating term when all other constants in the regression equation have been found.

The 1:M is interesting because a circle if representing a 1:M represents a dimension (just like in R). Then a sphere represents a 2d dimensional space differentiated into a spherical form. Something like that. Point being a circle represents a dimension just like a sphere represents gravity (gravity represents space dimension as it curves space to a sphere)

The One is often associated with either the point, or behind the point and that get’s tricky. The behind the point would stress some type of immateriality (Augustine borrows this) yet at the same time by this allegory can be inferred by analogy visa natural philosophy

In Agora Hypatia had circle mania and I saw it and I thought about pi in error terms in statistics and now I read this with Plotinus, Proclus, and Damascius. Damascius associates the point with an enfolded one where the radii unfold out. Psuedo dionysius associates the one with the point where all the radii intersect. What’s interesting is in Eric D Perl’s work, he uses the concept of enoldment as well.

Note: Archimedes was the philosopher who came up with an accurate estimate of Pi (~212 BC).

One of the points they are getting at is the radii are like the forms (archetypes) while the surface of the radii or their aggregation make up the circle. The circle (outer edge) is like matter or the instances (I’m not exactly sure). But the center is the One or often behind the center.

Unity was either contained in the One or after the one depending on the philosopher (unity implies multiplicity) , but was analogous to a 1:M relationship. Which is why the cross sections of radii and 1:M relationship for forms and databases make so much sense. As well as pi being in the error term in statistics as the class differentiating term when all other constants in the regression equation have been found.

The 1:M is interesting because a circle if representing a 1:M represents a dimension (just like in R). Then a sphere represents a 2d dimensional space differentiated into a spherical form. Something like that. Point being a circle represents a dimension just like a sphere represents gravity (gravity represents space dimension as it curves space to a sphere)