Duality Types of a Monist Worldview

Duality concepts discussed in this article are part of a monist worldview. They should not be confused with the dualities mentioned in dualism.

“The term ‘dualism’ has a variety of uses in the history of thought. In general, the idea is that, for some particular domain, there are two fundamental kinds or categories of things or principles. In theology, for example a ‘dualist’ is someone who believes that Good and Evil – or God and the Devil – are independent and more or less equal forces in the world. Dualism contrasts with monism, which is the theory that there is only one fundamental kind, category of thing or principle; and, rather less commonly, with pluralism, which is the view that there are many kinds or categories. In the philosophy of mind, dualism is the theory that the mental and the physical – or mind and body or mind and brain – are, in some sense, radically different kinds of things.” – Stanford Encyclopedia of Philosophy

Cosmos is whole-connected therefore unified but there are infinite number of perspectives within Cosmos. Monism tries to unify these perspectives in a rational framework.

The models and theories of the Monist framework are supposed to be simple, explanatory, and predictive. Simplest models have two explanatory factors. It makes sense to construct models using two explanatory factors in the beginning until it becomes necessary to use more factors to explain the finer details of observed phenomena.

Instead of developing a single theory of everything (ToE) with hundreds of free parameters we may try to accumulate explanatory power by finding as many complementary pairs (duality pairs) of explanatory factors as possible.

Explanatory factors are supposed to be distinct (orthogonal) but in reality there is always some degree of coupling between them. Coupling may trigger many inter-play modalities among the factors. By discovering these modalities and combining multiple two-factor models representing different perspectives we can achieve a simpler and better explanatory framework than a ToE. This requires a lot of work but ultimately it may be easier to construct such a framework.

What follows is a categorization of duality types. To repeat, I have a monist worldview. The term “duality” here means complementary pairs (two aspects of the one unified reality seen from different perspectives). Physicists use the term “duality” in a different sense. Physics duality refers to an “equivalence”. You may also take a look at different categorizations of dualities here, and here.

List of duality types of a Monist framework

  1. Cognitive / Creative
  2. Centrifugal / Centripetal
  3. Horizontal / Vertical
  4. Circle / Line
  5. Confinement / Liberation
  6. Positive / Negative
  7. Particle / Wave
  8. Tanmatra / Bhuta
  9. Time-domain / Frequency-domain
  10. X / Rate of change of X
  11. Dimension / Attribute
  12. Positive curvature / negative curvature
  13. G and 1/G
  14. Physics dualities
  15. Mathematical dualities

Cognitive and Creative

Cognitive/Creative, Puruśa/Prakrti, Shiva/Shakti, Yang/Yin, Nirguna/Saguna

“The Cosmic Operative Principle, or Cosmic Creative Principle, or Causal Matrix, is sheltered in the Transcendental Entity, the Supreme Cognition” — Shrii Shrii Anandamurti [1]

“Nirguna and Saguna are two aspects of one and the same Brahma. They are not two different Brahmas. It should be clearly mentioned that Ananda Marga is absolute monism – it is not dualism. A question may arise: How can Ananda Marga be called monism when it declares that Shiva and Shakti are separate entities. The answer is that in Ananda Marga philosophy, Shiva, or Cognitive Force, is both the material and the efficient cause, whereas Shakti, or Operative Force, is only the efficient cause. Shakti is merely subservient to Shiva, Shakti has no existence separate from Shiva. So we can safely conclude that Ananda Marga philosophy is based on monism.” — Shrii Shrii Anandamurti [2]

Centrifugal and Centripetal

Shrii Shrii Anandamurti used the centripetal and centrifugal terminology in connection with the vidya and avidya concepts.

vidya: introversive principle; divine attraction; centripetal or introversial force; movement from the crude to the subtle.

avidya: extroversive principle; ignorance; centrifugal or extroversial force; movement from the subtle to the crude.

Horizontal and Vertical

Horizontal attributes are associated with collectivity and multiplicity. Vertical attributes are about individuality, individual histories and individual characteristics.

All entities are mixtures of vertical and horizontal attributes. All entities exhibit individuality, but they also belong to various groups. More on this can be found in this article.

Circle and Line

Circle/Line duality goes deep.

Circle is a symbol of confinement. Dimensionless point symbolizes freedom.

Straight line is a symbol of the escape from confinement. Straight line cannot symbolize freedom because line is a form. All forms are bounded therefore not free.

Circle is a form. Line is a form too. Forms have boundaries. Circle can be infinitely big but it has a boundary. Line can be infinitely long but it has a boundary as well.

Dimensionless point is the only symbol of freedom because it is the only boundless entity.

All geometrical forms are composed of formless points. All dimensional objects emerge from dimensionless points.

When the dimensionless point becomes a line an infinite number of points appear to be forming the line. The line can be viewed as a point by changing the viewing angle but the point cannot be viewed as a line. The point has to become a line.

Circle symbolizes the ego because ego confines the soul. Dimensionless point symbolizes the soul because soul is our connection to freedom.

When a circle is infinitesimally small it appears as a point. The symbolism suggests a way to attain freedom.

An investigation of circle/line and horizontal/vertical dualities in particle physics can be found in this paper.

Confinement and Liberation

I have been developing the conceptual framework of the Confinement/Liberation hypothesis in the blogposts shown below. The paper mentioned above develops it further and establishes connections to physics.

Positive and Negative

Positive/negative, left-handed/right-handed, spin-up/spin-down

Particle and Wave

In the context of quantum physics particle and wave perspectives are complementary. Light has both wave and particle characteristics. In the context of quantum field theory there are various fields and their quanta. Field has wave characteristics; quantum of that field has particle characteristics.

Bhuta and Tanmatra

The five “bhuta”s or rudimental factors are rather abstract. Shrii Shrii Anandamurti refers to bhutas as eternal flows. In Sanskrit tat means “that”, mátra means “minutest quantity”. Hence the term tanmátra denotes a microscopic fraction of “that” (of “that bhúta”). The tanmatras are the tangibles. We percieve the tanmatras not the bhutas. The similarity between the “bhuta/tanmatra” and the “field/quantum” concepts is interesting.

Time-domain and Frequency domain

Time-domain signal and its frequency spectrum are dual in the sense that they provide complementary perspectives into the same reality. In the picture below, on the left we see the time-varying signals. On the right we see the frequency spectra of those signals. A shorter pulse in time-domain has a broader frequency spectrum. Conversely, longer pulses, or signals with milder amplitude variation have sharper spectra.

Neurons in our bodies carry time-varying electrical signals (pulses). Brain/mind effectively converts the time-domain signals into frequency-domain pictures. Yes, there is much more to perception but neuroscientists should not ignore the frequency-domain aspects of perception.

Dimension and Attribute

Dimension and attribute are dual concepts. Dimensions are degrees of freedom before the interaction takes place. Attributes are the specific outcomes from the interaction. Attributes are the resultants of interactions among cognitive cores. Attributes manifest in the arena of space and time.

There may be a conservation law involving dimensions and attributes. The hypothesis claims that dimensions are converted into attributes in such a way that (number of dimensions + number of attributes) remains constant during cosmic evolution. A hint about this was given by Shrii Shrii Anandamurti.

“Thus we find that the stronger the bondage, the cruder the thing becomes with the origination of more attributes. Due to external static pressure, the number of attributional peculiarities increases, but not the attributional capability.” [3]

Phase Space

Variable X and its rate of change X’ are dual as well.

The phase-space is a plane where the horizontal axis is any variable X; the vertical axis (X’) is the rate of change of that variable. One of the classic examples is the Lorenz attractor.

The phase-space is similar to frequency spectrum in the sense that it also hides the time-dimension. If there are cycles or repetitions in time one can devise procedures to extract a static mental picture of that process and be cognizant of the structures in the frequency-domain or the phase-space.

Positive and Negative Curvature

Another hypothesis: conservation of curvature. We know from the General Relativity Theory of Einstein that matter bends space-time. Matter represents positive curvature. When matter (positive curvature) is created, negative curvature of space-time must come into existence simultaneously to maintain the zero curvature of the space-time-matter.

G and 1/G

Even more ambitious hypothesis: the primordial fabric of the universe has a fundamental invariance symbolically represented by the golden equation G – 1/G = 1 which is telling us that if the primordial fabric is distorted it will be distorted in such a way that the manifestation and its inverse will maintain unity. Any distortion in the primordial fabric has to have a dual distortion as to leave the unity unchanged.

Physics Dualities

In physics the term “duality” refers to equivalence. Dual theories are equivalent because their equations have the same form. The physical quantities, however, are different. For example, an electron in this universe may appear as a magnetic monopole in the dual universe. In both universes the physical law is expressed using the Maxwell equations. The equations are exactly the same but the physical quantities have been switched with their duals.

Mathematical Dualities

Atiyah’s Grand Survey of Duality in Mathematics and Physics

References

[1] Shrii Shrii Anandamurti, “Supreme Cognition”, published in Subhasita Samgraha Part 24, Ananda Marga Publications

[2] Shrii Shrii Anandamurti, Philosophical Treatise of Ananda Marga

[3] Shrii Shrii Anandamurti, “Concept of Gunabhivyakti and Jadasphota” published in Ananda Vacanamrtam Part 33, Ananda Marga Publications