ThreeMinds
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Under Construction!
This will be the first essay in a collection of dozens of essays describing the structural frameworks that make up Wondrous Wisdom.
Three Minds
An exposition by Andrius Kulikauskas
Answering, Questioning, Investigating
In this essay, I argue that we experience life by alternating between three faculties, which is to say, three minds:
- A mind that knows answers.
- A mind that asks questions, for it does not know.
- A mind that investigates, thereby bringing the other two minds into accord, what we know and what we don't know.
We can learn to introspect these three minds by noting the different ways we approach our lives, appreciating the inner conflicts that arise and how they are resolved or not, and collecting examples of how others have talked about these three faculties, their properties and consequences.
We can learn to untangle these three minds. This untangling is done by the investigatory mind. We can then live harmoniously and help others likewise. This is the foundation for flourishing in every way.
Historical Accounts of These Three Minds
The Theory Translator database abounds with examples illustrating the opposition of the Answering mind and the Questioning mind. Several distinctions have been drawn.
- senses vs. intellect Western philosophers Aristotle, Augustine, Descartes, Spinoza, Locke, Hume, Kant, Brentano, James
- irrational vs. rational psychotherapist Ellis
- unconscious vs. conscious
- emotion vs. cognition neurologist Jackson
- pictorial vs. verbal neuropsychologist Milner
- sensations vs. representations Lotze, von Helmholtz
- instinctual vs. learned Baldwin
These three minds express three levels of awareness.
- Minimal awareness: The Answering mind presents us with a single answer but does not explain how it got that answer. It works unconsciously, instinctively, intuitively, confidently, averaging and summing up all of our experience to yield that answer.
- Increased awareness: The Questioning mind does not know thus asks a variety of questions, consciously, conceptually, verbally, rationally, thereby building, updating, revisiting models of possibilities, where each possibility can be checked and the relationships can be validated.
- Maximal awareness: The Investigating mind takes responsibility to make sure that the other two minds are truly in agreement, thus is ready to let go of the Answering mind's experience and the Questioning mind's model and reconsider them from scratch, in parallel, as necessary. And once the same information is expressed in two different ways, the Answering mind's integrated answer and the Questioning mind's web of questions, then the Investigating mind oversees which mind should behavior proceed from.
We experience life through all three levels of awareness and we can add to them a zeroth level of nonawareness which we do not experience but which may be consequential nonetheless. There may be complicated processes taking place within us that we are completely unaware of yet they affect us profoundly. The Answering mind is likewise mysterious but at least we are aware that it is giving us an answer.
In contemporary, every day English, we typically speak of the Answering mind as the Unconscious ("my unconscious tells me") and the Questioning mind as the Conscious ("I consciously know"). Metaphorically, we can imagine the Unconscious as setting up objects or actors on a stage, and the Conscious as shining various lights upon some of them. When we speak of Consciousness ("I have full consciousness"), then we refer to the Investigating mind, which has an even greater level of awareness, directing the show, deliberately, willfully, self-reflectively, cognizantly.
The purpose of this website, Theory Translator, is to describe these three minds as well as other important conceptual structures, and to overview evidence that they may indeed be universal, considering hundreds of examples from the history of world culture to show how they appear in different contexts under a variety of names.
Examples of Answer, Question, Investigation
- #621 Indo-European hunters guessed (inferred) an animal (the answer) from its tracks (the question) by stepping into them with their minds.
| answer | question | investigation | |||
| -2500 | Proto-Indo-European | animal | tracks | guess | #621 |
| 1926 | physics | Bose-Einstein statistics | Fermi–Dirac statistics | #131 | |
| 1932 | quantum mechanics | state | observable | measurement | #51 |
| 1971 | physics | bosons | fermions | #130 |
Logical dialogue between a mind that knows and a mind that does not know
We can think of the first two minds, knowing and not knowing, as in a dialogue which the third mind facilitates. All manner of thinkers have noted various characteristics which distinguish the first two minds. These distinctions express the difference between knowing and not knowing. The third mind, by which these thinkers make these distinctions, is often left unacknowledged, although it may be inferred as facilitating the proper relation of the other two minds.
We can focus on the knowledge that these minds know or do not know. The logical square of classical logic can be interpreted as this dialogue between what is known and what is not known, manifesting their duality, where basically the same information can be expressed in these two different ways.
The distinction between not knowing and knowing grounds a distinction, respectively, between variables and the specific values they may take.
- #655 Socrates: "I was conscious that I knew nothing at all."
| know | not know | ||||
| -399 | Socrates | think one knows | know nothing | be conscious | #655 |
| 1794 | William Blake | experience | innocence | solidarity | #144 |
Also: what is and is not.
| 580 | Tiantai | existence | emptiness | middle | #684 |
| assertion | negation | integration | [1] | ||
| 1781 | Immanuel Kant | synthetic a posteriori | analytic a priori | synthetic a priori | #29 |
| 1794 | Johann Gottlieb Fichte | thesis | antithesis | synthesis | #6 |
| 1817 | Georg Wilhelm Friedrich Hegel | fixed concept | engendered opposite | revealed unity | #363 |
And the logic of success - the lucky intuitive mind, and the counterfactual logic of failure - the unlucky rational mind. For we can't only learn from success. We need to be able to model death and injury and avoid them. And we need to be able to choose which logic to apply. Which makes sense of the traditions of oracles.
Mathematics: Duality
This duality is important in mathematics. Sometimes it appears exactly, as in set theory, where we can think in terms of the elements that are in a set, or equivalently, the elements that are not in a set. The duality may appear with a slight modification, where the two perspectives differ slightly but essentially, as in topology, where the definition of open set ensures that arbitrary unions of open sets are open but only ensures that finite intersections of open sets are necessarily open. This grounds a duality between continuity and discreteness.
Mathematics: Adjunctions
In mathematics, and in particular, in category theory, the concept of adjunction grounds a mathematical analogy expressed by a pair of adjoint functors.
Philosophy: Introspective distinctions
- #673 Goethe, in The Sorrows of Young Werther, juxtaposing innate free natural instinct with the narrow limits of an antiquated world.
Experimental pscyhology: Evidence for two minds
System 1 and System 2
Polanyi: Tacit and Explicit
- Understanding has us empathize with the tacit, as consciousness does.
- Tacit knowledge is of what we know, not of what we don't know. Thus know-how is the maximal konwledge of the unconscious. Consciousness distinguishes what we know and don't know.
- Forgetful functor yields tacit, free functor yields explicit. The same information in two different ways.
| intuitive | logical | ||||
| -350 | Aristotle | sensitive | rational | #42 | |
| -275 | Zou Yan | yīn | yáng | #3 | |
| 53 | Christianity | carnal | soulish | spiritual | #24 |
| 1516 | Thomas More | imprinting | #114 | ||
| 1620 | Francis Bacon | induction | syllogism | #46 | |
| 1677 | Baruch Spinoza | random experience | reason | intuition | #11 |
| 1739 | David Hume | impressions | ideas | #26 | |
| 1748 | David Hume | matters of fact | relations of ideas | #27 | |
| 1776 | Sturm und Drang | emotionality | rationality | #672 | |
| 1811 | Jane Austen | sensibility | sense | #20 | |
| 1868 | Hermann von Helmholtz | stimuli | sensations | #32 | |
| 1873 | Franz Brentano | sensory consciousness | noetic consciousness | #585 | |
| 1890 | William James | associative thought | true reasoning | #10 | |
| 1894 | Library science | principle of least effort | #15 | ||
| 1907 | William James | facts | principles | consequences | #324 |
| 1907 | William James | sensations | relations | previous truths | #667 |
| 1958 | Hannah Arendt | labor | work | action | #335 |
| 1960 | Aldous Huxley | personally | objectively | universally | #475 |
| 1958 | Michael Polanyi | tacit knowledge | explicit knowledge | #642 | |
| 1965 | Isaiah Berlin | inner voice creates | external voice reflects | #670 | |
| 1966 | Gene Rodenberry | McCoy | Spock | Kirk | #19 |
| 1969 | neuroscience | appositional | propositional | #615 | |
| 1969 | Julian Jaynes | sense perception | metaphors | introspection | #619 |
| 2001 | Jonathan Haidt | intuition | rationalization | discussion | #658 |
| 2004 | Social psychology | impulsive | reflective | #23 | |
| 2005 | Daniel Kahneman, Jason Riis | experiencing self | remembering self | #9 | |
| 2005 | mathematics | even part A of superalgebra | odd part eA of superalgebra | induced R-automorphism a→a' | #129 |
| 2016 | Michael Graziano | attention | awareness | #94 | |
| 2018 | Lois Isenman | unconscious | conscious | attending to inner experience | #113 |
| 2023 | Jaemin Frazer | victims | workers | winners | #108 |
| 1866 | neuroscience | emotional speech | intellectual speech | #611 |
Philosophy: Thinking Styles
From observing individuals and also the history of human culture.
- #668 Archilochus: a fox knows many things, a hedgehog knows one big thing.
| divergence | convergence | ||||
| -650 | Archilochus | know many things | know one big thing | #668 | |
| -250 | Xun Kuang | meandering mind | fixated mind | empty mind | #120 |
| 1872 | Friedrich Nietzsche | disorder | order | #651 | |
| 1953 | Isaiah Berlin | wide variety of experiences | single defining idea | #669 |
Philosophical introspection: Unconscious and Conscious
| unconscious | conscious | consciousness | |||
| 1946 | Paramahansa Yogananda | subconscious | conscious | superconscious | #577 |
| 1946 | Paramahansa Yogananda | body | mind | soul | #576 |
| 1949 | Gilbert Ryle | machine | ghost | #629 | |
| 2012 | Richard Barrett | ego | soul | #573 |
Philosophical introspection: Past, Present, Future
| past | future | present | |||
| 1997 | Eckhart Tolle | past | future | present moment | #641 |
Neurological evidence: Preconscious and Conscious
Preconscious processing and Conscious processing
Modeling Particular and General
| instance | language | ||||
| 1050 | law | exception | rule | #649 | |
| 1856 | Rudolf Hermann Lotze | muscle sensations | local signs | #30 | |
| 1874 | Rudolf Hermann Lotze | facts | laws | standards of value | #31 |
| 1905 | Theosophy | color | form | clarity of outline | #561 |
| 1905 | Theosophy | radiating vibration | floating form | #562 | |
| 1781 | Immanuel Kant | quid facti | quid juris | quid jus | #25 |
| -200 | Buddhism | concreteness | emptiness | #685 | |
| 1949 | neuroscience | language | #614 | ||
| 1958 | neuroscience | pictorial | verbal | #612 | |
| 1958 | mathematics | forgetful functor | free functor | #671 | |
| 1967 | Neuroscience | right hemisphere | left hemisphere | #21 | |
| 1971 | neuroscience | analogue codes | symbolic codes | #616 | |
| 1972 | neuroscience | judge difference | judge sameness | #617 | |
| 1973 | neuroscience | parallel processing | serial processing | #618 | |
| 1974 | Cognitive psychology | performance | introspection | #16 | |
| 1975 | Neuro-linguistic programming | neuro | linguistic | programming | #427 |
| 1980 | Persuasion | peripheral | central | #12 | |
| 1980 | Persuasion | heuristic | systematic | #13 | |
| 1984 | cognitive psychology | heuristic | analytic | #17 | |
| 1992 | David McNeill | gesture | speech | #582 | |
| 1992 | John Gray | counting units | measuring sums | #145 | |
| 1996 | Cognitive science | associative | rules based | #14 | |
| 1997 | John Cutting | individual things | classes of things | #593 | |
| 1998 | John Templeton | brain | mind | laws of life | #35 |
| 1998 | Robert Horn | images | words | shapes | #93 |
| 2005 | Malcolm Gladwell | thin-slice | analysis paralysis | #111 | |
| 2006 | cognitive psychology | heuristic | analytic | dispositional | #18 |
| 2006 | Karl Friston | sensory input | internal model | #33 | |
| 2006 | Jonathan Haidt | automatic | controlled | #657 | |
| 2009 | Iain McGilchrist | whole-oriented | detail-oriented | #328 | |
| 2011 | Daniel Kahneman, Amos Tversky | System 1 | System 2 | #1 | |
| 2013 | Lois Isenman | holism | #112 | ||
| 2024 | Gabrielė Aleksė | water | stone | #594 |
| focus | framework | ||||
| 100 | Jesus | truth | word | free | #485 |
| 1650 | Quakers | inward light | ministry | silence | #589 |
| 1774 | Johann Wolfgang von Goethe | innate free natural instinct | narrow limits of an antiquated world | #673 | |
| 1776 | Thomas Paine | society | government | #87 | |
| 1797 | Johann Gottlieb Fichte | self-acquaintance | self-explanation | self-consciousness | #591 |
| 1800 | William Wordsworth | overflow of feelings | simple language | recollection in tranquility | #674 |
| person-in-particular | person-in-general | God | [2] | ||
| 2021 | Anoop Kumar | individuality | shared identity | absence of differentiation | #688 |
| 2023 | Lucy Weir | self | context | observer | #359 |
| faculties | |||||
| 1748 | Montesquieu | judicial | executive | legislative | #34 |
| 1781 | Immanuel Kant | judgment | practical reason | pure reason | #28 |
| -350 | Aristotle | possible intellect | agent intellect | #43 |
Neural network vs. conceptual language
| nervous system | conceptual language | [3] | |||
| 1941 | neuroscience | language | #613 | ||
| 1955 | artificial intelligence | neural networks | symbolic processing | combined | #36 |
Neurological evidence: Right and left hemispheres
User requirements for a brain.
Right Hemisphere and Left Hemisphere
- Wikipedia: Lateralization of brain function
- Consider split brain patients.
Rational, typed, linear
Gender Studies: Differences and Stereotypes
| feminine | masculine | ||||
| -250 | Judaism | Eve | Adam | God | #203 |
Traditional Understandings of Female and Male Preferences
- Wikipedia: Gender
- Wikipedia: Gender identity
Gender role
- Social construction of gender
- Sex differences in psychology
- Sex differences in cognition
Concepts to consider that may be related
- Anima and animus Jungian concepts. Animus is the unconscious masculine side of a woman, and anima is the unconscious feminine side of a man. My point here is not to embrace Jungian psychology but to show that Jung is distinguishing femininity and masculinity and asserting that they are both found in every person.
Balancing the two minds
- #121 Plato, in Phaedrus, presents the metaphor of a charioteer (reason) driving a pair of horses, irrational appetite and moral impulse.
- #5 Plato, in the Republic, expands with Subjects, Warriors, Rulers
- #4 Freud: Id, Superego, Ego. The id is referred to as "It", the superego is "Over-I", which means that it is speaking of "You". The ego is refering to "I". But here we have an inversion due to socialization, participation in society with many actors. Originally, from its own point of view, our Unconscious id lives as our "I", our Conscious superego lives from the vantage of "You", our Consciousness - our ego - lives from the vantage of "Other".
- id is the set of uncoordinated instinctual desire
- superego plays the critical and moralizing role
- ego is the organized, realistic agent that mediates between the instinctual desires of the id and the critical superego
- #6 Fichte: Thesis, Antithesis, Synthesis
| balance | |||||
| -375 | Plato | appetite | spunk | reason | #5 |
| -370 | Plato | irrational appetite | moral impulse | reason | #121 |
| -350 | Confucius | duty and sense of shame | laws and punishments | virtue and propriety | #117 |
| -250 | Xun Kuang | naturally selfish | conscious effort to do good | conscious development of proper standards | #119 |
| 100 | Jesus | flesh | spirit | watch and pray | #38 |
| 1283 | Kabbalah | instincts | moral virtues | understanding | #470 |
| 1860 | Horace Greeley | slaves of appetite and sloth | subduers and cultivators of the earth | God who decrees, grants, eradicates | #147 |
| 1864 | Robert Browning | half monster | half human | his creator | #164 |
| 1895 | Gustave Le Bon | revert to instincts | sacrifice personal interests | follow excitable leaders | #148 |
| 1896 | James Mark Baldwin | instinctual behavior | learned behavior | aptitude for learning behavior | #115 |
| 1920 | Sigmund Freud | id | superego | ego | #4 |
| 1929 | Anthropology | economic | martial | sacral | #22 |
| 1957 | Eric Berne | child | parent | adult | #141 |
| 1964 | Eric Berne | child | parent | adult | #140 |
| 1967 | Thomas Anthony Harris | child | parent | adult | #139 |
| 1955 | Albert Ellis | irrational | rational | education | #661 |
| 1986 | Marsha M Linehan | emotional | reasonable | wise | #682 |
| 2019 | Jessica Lock | emotional | rational | wise | #679 |
Expectations of unity
There is a curious trichotomy (beauty, good, truth) known as the transcendentals, which sometimes includes unity, making for a tetrachotomy. These are the latent expectations of each of the three minds, thus the purities, the unities and essences that each mind is attracted to, of itself. The answering, sensory, unconscious mind is attracted to beauty; the questioning, calculating, conscious mind is attracted to good; the investigating mind, governing the other two, working towards their correspondence, is attracted to truth. The overall expectation, general speaking, is unity.
One's ideal sweetheart meets these expectations, if they could ever possibly be met. They appear beautiful to the eyes, they are good in all they do, and in this they are true, that they seem as they are. Thus one adores them absolutely.
John Levi Martin details the history of this trichotomy in his paper, The Birth of the True, the Good, and the Beautiful: Toward an Investigation of the Structures of Social Thought. He finds it as far back as the Greek historian Herodotus, who noted the Athenian expression kalos kagathos (beautiful and virtuous), by which they characterized the ideal warrior, and how they spoke of themselves. I note here the significance of the concept and which is explicit in the construction k + agathos where agathos means good and k means and. The word and emphasizes that the person is not only beautiful, and not only virtuous, but is both. This is one of the oldest recorded expressions of the three minds.
This trichotomy otherwise seems quite odd, as the three qualities are of such different phenomenological appeal, ontological character and existential significance. They resemble a hodge podge list of incongrous animals. But let us exercise our imagination, what creatures are these? Perchance, beauty is the flower, good is the bee, and truth is the pollen which bees carry from flower to flower, as they feed on their nectar, proliferating bees and flowers.
| beauty | good | true | |||
| -430 | ancient Greece | beautiful | virtuous | and | #7 |
| 1711 | Earl of Shaftesbury | beautiful | good | true | #8 |
| 1820 | John Keats | beauty | immortal work | love of principle | #162 |
| 1916 | Max Scheler | beautiful and ugly | right and wrong | true and false | #601 |
Grounds for Assent
Aristotle, in his Rhetoric, pragmatically noted three very different grounds for assent: pathos, logos and ethos. Each of these grounds appeals rhetorically to one of the three minds.
What speaks to them
- #97 Aristotle's Rhetoric explains what speaks to them: pathos, logos, ethos.
| Appeal to: | unconscious | conscious | consciousness | ||
| -357 | Aristotle | pathos | logos | ethos | #97 |
| -357 | Aristotle | rhetoric | logic | dialectic | #124 |
| 1240 | Sakya Pandita | see | talk | #570 | |
| 1650 | Confucianism | see | hear | speak | #104 |
| 1976 | Julian Jaynes | verbal hallucinations | obeying | consciousness | #620 |
| 1982 | Chaïm Perelman | rhetoric | logic | dialectic | #126 |
| 1990 | Joseph Wenzel | rhetoric as process | logic as product | dialectic as procedure | #127 |
| 2021 | Adam Grant | preaching | prosecuting | politicking | #666 |
Perspective, perspective on perspective, perspective on perspective on perspective
| onefold | twofold | threefold | [4] | ||
| 1857 | Karl Marx | consumption | production | distribution and exchange | #652 |
| 1867 | Charles Sanders Peirce | firstness | secondness | thirdness | #2 |
| 2022 | active inference | enactive | predictive | cybernetic | #142 |
- Peirce: Firstness, Secondness, Thirdness
- Categories (Peirce)
First, Second, Third Person
As with God's Dance: I am God, You are God, They are God.
The structure of interpretations of the divisions of everything, with the third person (Consciousness, Thirdness) yielding the three-cycle.
Selfishness, selflessness
Answering mind is selfish. Questioning mind is selfless but may serve and accentuate the selfish. Investigating mind has selfishness serve selflessness, making us truly selfless.
Emptying the mind
| emptiness | |||||
| -325 | Daoism | gentleness | economy | shrinking from taking precedence of others | #166 |
| 1237 | Dōgen | motherly | joyful | vast | #675 |
| 1969 | Pete Townshend | pinball wizard | engaging the mirror | deaf, dumb, blind | #580 |
What, how, why
Three minds express What, How, Why from the idealist point of view. Whether is God.
Why functions like a break, allowing How to shift to What upon release, at which point Why becomes Whether.
Perception-Action Loop. Consciousness acts as a brake.
Consider how to interpret the opposite direction as given by version 2.0 of the Meaning of Life.
How does this relate to the equation of life?
Narration: Ways of creating tension
Four voices creating tension
- Reality forces
- Unconscious commands
- Conscious explains
- Consciousness cares
Mathematical models
Unreflected and reflected
Consider
- O(n),O(∞). Rotations and rotoreflections.
- Linear operators and antilinear operators. Complex conjugation as reflection.
Simple roots of G₂. Consciousness functions as a brake that the arrow from the unconscious to the conscious must wait for. Consciousness functions as a virtual unconscious.
Compare with a transistor.
More examples of the three minds
Galileo inaugurated modern science by dividing the world into the quantitative realm of science and, on the other hand, the qualitative realm of subjective experience. https://en.wikipedia.org/wiki/Philip_Goff_(philosopher)
https://en.wikipedia.org/wiki/Philip_Goff_(philosopher) book Why? The Purpose of the Universe
Quantum mechanics axioms in terms of C* algebras.
| Unconscious | Conscious | Consciousness | Wondrous Wisdom |
| first person | second person | third person | grammar |
| first person | second person | third person | narration |
| comprehension | apprehension | Iain McGilchrist | |
| mother | father | child | R.Buckminster Fuller 1200.00 |
| female | male | gender stereotypes | |
| autonomous mind | algorithmic mind | reflective mind | Keith Stankovich |
| descriptive | normative | prescriptive | Bell, Raiffa, Tversky |
| William James | |
| associationism, spiritualism | William James |
Under Construction: Three Minds
- answer, question, investigation
- dialogue: know, not know, discover
- direct, model, apply
- adds perspectives: P, P on P, P on P on P
- level of knowledge: what, how, why
- dialogue: child, parent, grandparent (status free)
- dialogue: woman, man, child (gender free)
- attracted to: beauty, good, truth
- I, you, other
- personality, character, God
Also appearing structurally
- Flow of experiences - three minds
- Six visualizations
- Narration - voices for creating tension
- Dialogue of two minds: foursome, fivesome, sixsome, sevensome
- Eightsome
- Emotion (boundary of self vs. world: sadness vs. surprise)
- Emotion - Cognition loop
- Truths of the heart and the world
My Relevant Writings
- Poster: What Minds Require of Brains: A Phenomenological Consideration of the Evolution of the Central Nervous System Towards Abstraction?
- Santrauka: Išgyvenimų kalba: Sąmonės išplėtimas pasąmone, šneka ir tikrove
Three Minds
- https://www.researchgate.net/publication/6531370_Dimensions_of_Mind_Perception
- {$3\times 8$} theory of {$3$} minds and {$8$} mental states
- Janet Pauketat
- Megan M. Callahan, Terre Satterfield, Jiaying Zhao. Into the Animal Mind: Perceptions of Emotive and Cognitive Traits in Animals
- Kara Weismana, Carol S. Dweck, Ellen M. Markman.Rethinking people’s conceptions of mental life
- Hideyuki Takahashi, Midori Ban, Minoru Asada. Semantic Differential Scale Method Can Reveal Multi-Dimensional Aspects of Mind Perception.
- Megan N. Kozak, Abigail A. Marsh, Daniel M. Wegner. What Do I Think You’re Doing? Action Identification and Mind Attribution
- Bertram F. Malle. How Many Dimensions of Mind Perception Really Are There?
- Kallie Tzelios, Lisa A. Williams, John Omerod, Eliza Bliss‑Moreau. Evidence of the unidimensional structure of mind perception
- Consciousness +3 is self-reflection (which switches the direction of the twosome's mental shift). Is it then possible that the fractional charge of quarks indicates the Unconscious (1/3) and the Conscious (2/3) and so we have Consciousness (1) for electrons and protons?
The disembodying mind results from evolutionary pressure to devote more resources to modeling the unknown.
- A mind that knows answers represents almost 100 billion neurons
- A mind that does not know but asks questions represents perhaps 100 thousand concepts
- A third mind that is just 8-fold (thus merely 3-bits) balances the two.
If we focus on user requirements than on neural implementation, then it makes sense to talk about left and right hemispheres as champions of these two mindsets.
Constructive hypothesis C:A->B for communication yields the 3 minds.
Work-in-progress
Andrius: I am thinking about the various manifestations of the three minds and how they are related. I am working on the diagram below.
