Rituals | Recursion | Mantras | Meaning : Language and Recursion
From The hidden hyperbolic geometry of international trade: World Trade Atlas 1870–2013
Here, we present the World Trade Atlas 1870–2013, a collection of annual world trade maps in which distance combines economic size and the different dimensions that affect international trade beyond mere geography. Trade distances, based on a gravity model predicting the existence of significant trade channels, are such that the closer countries are in trade space, the greater their chance of becoming connected. The atlas provides us with information regarding the long-term evolution of the international trade system and demonstrates that, in terms of trade, the world is not flat but hyperbolic, as a reflection of its complex architecture. The departure from flatness has been increasing since World War I, meaning that differences in trade distances are growing and trade networks are becoming more hierarchical. Smaller-scale economies are moving away from other countries except for the largest economies; meanwhile those large economies are increasing their chances of becoming connected worldwide. At the same time, Preferential Trade Agreements do not fit in perfectly with natural communities within the trade space and have not necessarily reduced internal trade barriers. We discuss an interpretation in terms of globalization, hierarchization, and localization; three simultaneous forces that shape the international trade system.
When it comes to international trade, the evidence suggests that we are far from a distance-free world. Distance still matters1 and in many dimensions: cultural, administrative or political, economic, and geographic. This is widely supported by empirical evidence concerning the magnitude of bilateral trade flows. The gravity model of trade2–4, in analogy to Newton’s law of gravitation, accurately predicts that the volume of trade exchanged between two countries increases with their economic sizes and decreases with their geographical separation. The precision of that model improves when it is supplemented with other factors, such as colony–colonizer relationships, a shared common language, or the effects of political borders and a common currency5–7. Despite the success of the gravity model at replicating trade volumes, it performs very poorly at predicting the existence of a trade connection between a given pair of countries8; an obvious limitation that prevents it from explaining the striking regularities observed in the complex architecture of the world trade web9–13. One of the reasons for this flaw is that the gravity model focuses on detached bilateral relationships and so overlooks multilateral trade resistance and other network effects14.
Another drawback of the classical gravity model is that geography is not the only factor that defines distance in international trade. Here, we use a systems approach based on network science methodologies15,16 to propose a gravity model for the existence of significant trade channels between pairs of countries in the world. The gravity model is based on economic sizes and on an effective distance which incorporates different dimensions that affect international trade, not only geography, implicitly encoded on the complex patterns of trade interactions. Our gravity model is based on the connectivity law proposed for complex networks with underlying metric spaces17,18 and it can be represented in a pure geometric approach using a hyperbolic space, which has been conjectured as the natural geometry underlying complex networks19–22. In the hyperbolic trade space, distance combines economic size and effective distance into a sole distance metric, such that the closer countries are in hyperbolic trade space, the greater their chance of becoming connected. We estimate this trade distance from empirical data using adapted statistical inference techniques23,24, which allow us to represent international trade through World Trade Maps (WTMs). These define a coordinate system in which countries are located in relative positions according to the aggregate trade barriers between them. The maps are annual and cover a time span of fourteen decades. The collection as a whole, referred to as the World Trade Atlas 1870–2013, is presented via spatial projections25, Table S5, and trade distance matrices, Table S6. Beyond the obvious advantages of visualization, the World Trade Atlas 1870–2013 significantly increases our understanding of the long-term evolution of the international trade system and helps us to address a number of important and challenging questions. In particular: How far, in terms of trade, have countries traveled in recent history? What role does each country play in the maps and how have those roles evolved over time? Are Preferential Trade Agreements (PTAs) consistent with natural communities as measured by trade distances? Has the formation of PTAs led to lesser or greater barriers to trade within blocs? Is trade distance becoming increasingly irrelevant?
The answers to these questions can be summarized by asserting that, in terms of trade, the world is not flat; it is hyperbolic. Differences in trade distances are growing and becoming more heterogeneous and hierarchical; at the same time as they define natural trade communities—not fully consistent with PTAs. Countries are becoming more interconnected and clustered into hierarchical trade blocs than ever before.
Guillermo García-Pérez Marián Boguñá, Antoine Allard & M. Ángeles Serrano
Molecular BioSystems · March 2012
M. ÁNGELES SERRANO
Pol Colomer-de-Simo ́n1, M. A ́ ngeles Serrano1, Mariano G. Beiro ́2, J. Ignacio Alvarez-Hamelin2 & Maria ́n Bogun ̃a ́1
Kaj-KoljaKleineberg,1,∗ Mari ́anBogun ̃ ́a,1 M.A ́ngelesSerrano,2,1 andFragkiskosPapadopoulos
Ginestra Bianconi1 & Christoph Rahmede
Antoine Allard1,2, M. A ́ngeles Serrano1,2,3, Guillermo Garc ́ıa-Pe ́rez1,2 & Maria ́n Bogun ̃a ́
Daan Mulder · Ginestra Bianconi
Guillermo Garc ́ıa-P ́erez,1,2 Mari ́an Bogun ̃ ́a,1,2 and M. A ́ngeles Serrano
Ma A ́ngeles Serrano and Mari ́an Bogun ̃a ́
M. A ́ngeles Serrano,1 Mari ́an Bogun ̃ ́a,2 and Alessandro Vespignani3,4
Elisabetta Candellero and Nikolaos Fountoulakis
Dmitri Krioukov, Fragkiskos Papadopoulos, Maksim Kitsak, Amin Vahdat, and Mari ́an Boguna
From The Avatamsaka Sutra Francis H. Cook
Hua-Yen Buddhism: The Jewel Net of Indra 1977
Far away in the heavenly abode of the Great God Indra, the protector and nurturer of life, there is a wonderful net which stretches out indefinitely in all directions, in accordance with the extravagant tastes of deities.
At the net’s every node, is hung a single glittering jewel and since the net itself is infinite in dimension, the jewels are infinite in number. There hang the jewels, glittering like stars of the first magnitude, a wonderful sight to behold.
If we now arbitrarily select one of these jewels for inspection and look closely at it, we will discover that in its polished surface there are reflected all the other jewels in the net, which sparkle in the magnificence of its totality.
Not only that, but each of the jewels reflected in this one jewel is also reflecting all the other jewels, so that the process of reflection is infinite. As each gem reflects every other one and everything else in the universe, so are you affected by every other system in the universe.
The metaphor of Indra’s Jeweled Net is attributed to an ancient Buddhist named Tu- Shun (557-640 B.C.E.) who asks us to envision a vast net that:
- At each juncture there lies a jewel
- Each jewel reflects all the other jewels in this cosmic matrix
- Every jewel represents an individual life form, atom, cell or unit of consciousness
- Each jewel, in turn, is intrinsically and intimately connected to all the others
- A change in one gem is reflected in all the others
The moral of Indra’s net is that the compassionate and the constructive interventions a person makes or does can produce a ripple effect of beneficial action that will reverberate throughout the universe or until it plays out.
By the same token you cannot damage one strand of the web without damaging the others or setting off a cascade effect of destruction.
From The Indra’s Net
“Far away in the heavenly abode of the great god Indra, there is a wonderful net which has been hung by some cunning artificer in such a manner that it stretches out indefinitely in all directions. In accordance with the extravagant tastes of deities, the artificer has hung a single glittering jewel at the net’s every node, and since the net itself is infinite in dimension, the jewels are infinite in number. There hang the jewels, glittering like stars of the first magnitude, a wonderful sight to behold. If we now arbitrarily select one of these jewels for inspection and look closely at it, we will discover that in its polished surface there are reflected all the other jewels in the net, infinite in number. Not only that, but each of the jewels reflected in this one jewel is also reflecting all the other jewels, so that the process of reflection is infinite. The Hua’yen school [of Buddhism] has been fond of this image, mentioned many times in its literature, because it symbolizes a cosmos in which there is an infinitely repeated interrelationship among all the members of the cosmos. This relationship is said to be one of simultaneous mutual identity and mututal intercausality.”
~ Francis H. Cook, Hua-yen Buddhism: The Jewel Net of Indra
There are several aspects of Indra’s Net, as described in the above quote, that signify it as a crystal clear allegory of reality:
1. The Holographic Nature of the Universe
Long before the existence of the hologram, the jeweled net is an excellent description of the special characteristic of holograms: that every point of the hologram contains information regarding all other points. This reflective nature of the jewels is an obvious reference to this.
This kind of analogy has been suggested by science as a theory for an essential characteristic of the cosmos, as well as as the functioning of the human brain, as beautifully described inThe Holograpic Universe by Michael Talbot.
2. The Interconnectedness of All Thingss
When any jewel in the net is touched, all other jewels in the node are affected. This speaks to the hidden interconnectedness and interdependency of everything and everyone in the universe, and has an indirect reference to the concept of “Dependent Origination” in Buddhism. Additionally, Indra’s Net is a definitive ancient correlate of Bell’s Theorum, or the theory of non-local causes.
3. Lack of a substantive self
Each node, representing an individual, simply reflects the qualities of all other nodes, inferring the notion of ‘not-self’ or a lack of a solid and real inherent self, as seen in the Advaita Vedanta school of Hinduism and Buddhism in general.
Indra’s Net shoots holes in the assumption or imputation of a solid and fixed universe ‘out there’. The capacity of one jewel to reflect the light of another jewel from the other edge of infinity is something that is difficult for the linear mind, rational mind to comprehend. The fact that all nodes are simply reflections indicates that there is no particular single source point from where it all arises.
5. Innate Wisdom
The ability to reflect the entirety of all light in the universe attests to the inherent transcendant wisdom that is at the core of all nodes, representing all sentient beings, and to the inherent Buddha Nature.
6. Illusion or Maya
The fact that all nodes are simply a reflection of all others implies the illusory nature of all appearances. Appearances are thus not reality but a reflection of reality.
7. Universal Creativity
A familiar concept in various high dharmas is one of an impersonal creative intelligence that springs forth into reality through the instruments of all living beings.
8. The Mirror-like Nature of Mind
The capacity to reflect all things attests to the mind being a mirror of reality, not its basis. This is a common thesis among various schools and religions.
This article is from: http://www.heartspace.org/
The Vedic metaphor of Indra’s Net
The metaphor of Indra’s net, with its poetic description of the indivisibility of the universe, captures the essence of Hinduism’s vibrant and open spirit.
Indra’s Net is a metaphor for the profound cosmology and outlook that permeates Hinduism. Indra’s Net symbolizes the universe as a web of connections and inter-dependencies among all its members, wherein every member is both a manifestation of the whole and inseparable from the whole. This concept is the foundation for Vedic cosmology and it later went on to become the central principle of Buddhism, and from there spread into mainstream Western discourse across several disciplines.
The metaphor of Indra’s Net originates from the Atharva Veda (one of the four Vedas), which likens the world to a net woven by the great deity Shakra or Indra. The net is said to be infinite, and to spread in all directions with no beginning or end. At each node of the net is a jewel, so arranged that every jewel reflects all the other jewels. No jewel exists by itself independently of the rest. Everything is related to everything else; nothing is isolated. [i]
Indeed, the fundamental idea of unity-in-diversity underpins all dharmic traditions; even though there are many perspectives from which Indra’s Net may be viewed and appreciated, it is ultimately recognized as one indivisible and infinite unity. From the Hindu viewpoint, the One that manifests as many is named Brahman; even seemingly disparate elements are in fact nothing other than reflections of Brahman, and hence of one another. This notion of an organic unity is a signature of Hinduism, and distinguishes it from all major Western religions, philosophies and cultures.
Each jewel of Indra’s Net includes the reflections of all the other jewels; the significance of this symbolism is that each entity in the universe contains within itself the entire universe. This idea, rather than positing interdependence among separately existing entities, asserts that the whole does not owe its existence to the coming together of individual parts that have independent existence. Indeed, the existence of each individual part is contingent upon, and relative to, the existence of the whole and of all the other parts. Yet, paradoxically, each individual part also ‘contains’ the whole within itself. Put simply, the whole and the parts are inseparable.
Every jewel in Indra’s Net is a microcosm of the whole net; every component is the cause of the whole and also the effect of the whole. Nothing exists outside the net. [ii] In the Hindu worldview, the only essence that ultimately exists is Brahman; Brahman is the foundation for Indra’s Net, and no jewel exists apart from Brahman.
The jewels of Indra’s Net are not meant to symbolize static substances. Each jewel is merely a reflection of other jewels, and individual jewels always remain in flux. Each jewel exists only momentarily, to be continuously replaced by its successor, in mutual causation with other jewels. Just as the interdependent cells of the human body are perpetually changing, so also everything in Indra’s Net is perpetually in flux. Reality is always in the flux of becoming. This concept is different from the notion of real, independently existing entities undergoing modification, or static entities that happen to be woven together.
Swami Vivekananda applied the great Upanishadic saying, ‘tat tvam asi’ (‘that thou art’) as the basis for Hindu ethics. He said, in essence, that we are all jewels in Indra’s Net (even though he did not use this metaphor to say it). Thus, Vivekananda defined a Hindu platform for determining ethical conduct, not only towards all humans but towards animals and all entities in general—because everyone and everything is a jewel in Indra’s Net.
The Sanskrit word bandhu is frequently used to describe the interrelationship between the jewels of Indra’s Net. ‘Bandhu’ defines a corresponding entity; for example, a relationship between x and y can be stated as ‘x is a bandhu of y’. In traditional Indian discourse, this term is often used to explain the unity between the whole and its seemingly diverse parts. For example, ancient thinkers have described specific bandhus which express the paradoxical relationship of the microcosm to the macrocosm. While the microcosm is generally perceived as a map of the macrocosm, it is also the case that both microcosm and macrocosm continuously mirror one another.
Bandhu can also refer to the connections among various facets of our overall unified reality, linking sounds, numbers, colors and ideas together. No object—whether physical, mental, emotional, or conceptual—has any existence by itself and is merely another facet of this unified whole. In addition, bandhu describes how the transcendental worlds correspond with the perceptible world, implying that whatever we perceive through our senses is but a pointer to something beyond.
Kapila Vatsyayan, a scholar of classical Indian art, has cited many examples of bandhu in the form of common metaphors. Significant symbols may be found in the Rig Veda, the Natya-shastra (a seminal text on aesthetics and performing arts) and the Tantrasamuccaya (a text on temple architecture). The seed (bija) is often used to symbolize the beginnings. The tree (vriksha) rises from the bija and represents the vertical pole uniting the realms. The nabhi (navel) or the garbha (womb) brings together the concepts of the un-manifest (avyakta) and the manifest (vyakta). The bindu (point or dot) is the reference point or metaphorical centre around which are drawn geometrical shapes, which in turn facilitate the comprehension of notions of time and space. The sunya (void) is a symbol of fullness and emptiness. From its arupa nature (formless) arises the rupa nature (form) and the parirupa (beyond form). There is equivalence in the relationship between sunya (emptiness) and purna (completeness or wholeness), the paradox being that the void has within it the whole. [iii]
In Hinduism, the concept of unity-in-diversity can also be understood as a manifestation of Brahman, an agency that penetrates, pervades and harmonizes the entire universe. Brahman enters and shapes the mould of every entity giving it form, substance and individuality. It is only human pre-conditioning that causes us to visualize the multiplicity of forms as separate entities, and hence the world appears to be full of contradictions. The Brhadaranyaka Upanishad says:
Brahman is responsible for the interconnectedness of things and has become the living and the non-living; the visible and the invisible; the creatures which are two-footed and those that are four-footed. He became the subtle body and then the gross body by means of a subtle instrument known as the subtle body. This very Being became the vital consciousness of all. This is known as the Madhu¬Vidya, the sense of the ‘honey’ of all beings, the knowledge of the inter-dependence of things and the vital connection of everything, under every condition, at every time, everywhere. [iv]
Hinduism devotes much thought to exploring the relationships between the jewels of Indra’s Net, and how they are manifestations and reflections of each other. Hindu thought is distinct from Abrahamic religions, which are premised on the existence of one separate God, one absolute event in history, and one inviolable set of injunctions. Hindus, for better or for worse, tend to be natural de-centralists. This is why it is hard to understand Hinduism, and difficult to organize and mobilize Hindus under an overarching corporate institution. It is also why Hinduism has proved, thus far, difficult to destroy. This idea can be referred as ‘integral unity’. The integral unity of the whole manifests itself in the parts, and they, in turn, aspire to unite with the whole; this principle is reflected in every domain of dharmic knowledge, including philosophy, science, religion, ethics, spirituality, art, music, dance, education, literature, oral narratives, politics, marriage rituals, economics, and social structures. Each domain of dharmic knowledge is itself a jewel in Indra’s Net, and reflects all the others. In other words, the same underlying principles are represented in these specialties in different ways.
For example, Hindu dance is not merely an isolated form of cultural expression but a complete and rigorous discipline through which one may learn and experience philosophy. This quality of correspondences across many domains of knowledge is striking. Music and sacred dance have a formal grammar based on Hindu cosmology. The Sanskrit Natya-shastra, a seminal text on performing arts and aesthetics, treats natya as a total art form; its scope includes: representation, poetry, dance, music, make-up, indeed every aspect of life. The Natya-shastra presents an integral view encompassing the Vedic rituals, Shaivite dance and music, and the epics. The eight traditional rasas it describes (love, humour, heroism, wonder, anger, sorrow, disgust, and fear) mirror a complete experience of the real world like the jewels of Indra’s Net, and together facilitate a practitioner’s pursuit of the purusharthas(human goals).
Some other examples across various domains are as follows:
- The Vedic ritual altar is a representation of the entire cosmos.
- The architecture of Hindu temples is based on physical dimensions which correspond to various astronomical metrics.
- The yantra, an important device of sacred geometry, represents the whole universe.
- Any deity can be conceived of in multiple ways: as a personal manifestation of the divine, as a metaphor for certain cosmic qualities and powers, and as an amalgamation of qualities and energies to be invoked and established in a person through ritual, meditation and yoga. Based on individual preferences, a deity can be approached as another entity in the mode of devotion, or as an object of meditation, or as a means for self-realization within oneself.
- In Ayurvedic diagnosis, a correspondence is posited between specific points on the tongue and all parts of the entire body; thus, an expert in this field examines the tongue as a means of analysing the patient’s overall condition. The tongue is thus a jewel in which the entire physical and psychic body is reflected. The core principle of integral unity is encoded in the symbolism of Indian art, architecture, literature, ritual, mythology, festivals, and customs, all of which are intended to facilitate access to higher knowledge that goes beyond the conventional scope of any specific domain. Integration between disciplines is built-in and no effort is needed to create unity by bringing separate parts together. Even when certain disciplines and practices were destroyed, other disciplines encoding the same principles survived and helped preserve and re-ignite the overall tradition.
Dharmic cosmology is governed by bandhu interconnections among the astronomical, terrestrial, physiological, and spiritual realms; and each of these realms is itself connected, in the broadest sense, with the arts, healing systems, and culture. As discussed previously, bandhu describes a correspondence between the whole universe and the individual consciousness, which can be explored and developed from many alternative starting points. Thus, dharmic traditions have a common current that impels the individual along a natural quest to discover the reality beneath the appearances and to appreciate relationships among seemingly unrelated phenomena.
Dharmic traditions consider the common experience of reality as merely the transient reflection of a system in flux, interconnected with other realities across the past, present and future. In this flux, which affects all phenomena, repeating patterns may appear as static and independent ‘objects’, but this perception is just an illusory artifact of the limited mind. The individual person, of course, is himself a part of this flux. With the aid of meditation, he is able to witness reality as a detached observer—to see the personal ego, and indeed all fixed objects, as mere reflections of a moment in the flux.
Indra’s Net and Buddhism
Important Buddhist texts use Indra’s Net to describe an infinite universe with no beginning or end, in which every element is mutually related to every other element. Indra’s Net is a quintessential metaphor for Buddhist philosophy, describing how everything exists only in mutual causation with everything else, and nothing can be isolated.
The Avatamsaka Sutra (which means ‘Flower Garland’) of Mahayana Buddhism uses the metaphor of Indra’s Net to explain cosmic interpenetration. This sutra explains everything as both a mirror reflecting all and an image reflected by all. Everything is simultaneously cause and effect, support and supported. This important sutra was translated from Sanskrit, and its logic further developed in China under the name of Hua-yen Buddhism.
The Hua-yen tradition was developed by a series of thinkers, most notably Fa-tsang (cE 643-712). Through him, it passed on to Korea and other East Asian countries, becoming known as ‘Kegon’ in Japan. Hua-yen is praised as the highest development of Chinese Buddhist thought. D.T. Suzuki called Hua-yen the philosophy of Zen, and Zen the meditation practice of Hua-yen. Francis Cook explains the core philosophy of Hua-yen as follows:
Far away in the heavenly abode of the great god Indra, there is a wonderful net that has been hung by some cunning artificer in such a manner that it stretches out infinitely in all directions. In accordance with the extravagant tastes of deities, the artificer has hung a single glittering jewel in each ‘eye’ of the net, and since the net itself is infinite in all dimensions, the jewels are infinite in number. There hang the jewels, glittering like stars of the first magnitude, a wonderful sight to behold. If we now arbitrarily select one of these jewels for inspection and look closely at it, we will discover that in its polished surface there are reflected all the other jewels in the net, infinite in number. Not only that, but each of the jewels reflected in this one jewel is also reflecting all the other jewels, so that there is an infinite reflecting process occurring. [v]
Cook goes on to explain that Indra’s Net ‘symbolizes a cosmos in which there is an infinitely repeated interrelationship among all the members of the cosmos’. He adds that ‘the cosmos is, in short, a self-creating, self-maintaining, and self-defining organism’. Furthermore, there is no theory of a beginning time, and such a universe has no hierarchy. ‘There is no center, or, perhaps if there is one, it is everywhere.’
Hua-yen is built on the primary concern of Indian thought which is about the nature of causation. This is evident in the Sanskrit name for Hua-yen, ‘dharmadhatu pratitya–samutpada’ (the interdependent co-arising which is the universe). Key principles of Madhyamika Buddhism, regarding non-substantiality and non-origination, have exact equivalents in Hua-yen. The Avatamsaka philosophy emphasizes the illusory nature of things when they are seen separately. [vi]
David Loy, a Buddhist practitioner and scholar who has spent most of his life in Kyoto, uses the analog of lila (play) to refer to the Buddhist ideal of life. While the ordinary ego is a player struggling, out of anxiety, to ground itself in the net, the liberated player has realized that he is the net. There is no separate ‘me’ to possess anything, nor any separate thing to be possessed. He explains:
Life becomes play; … the issue is whether we suffer our games because they are the means whereby we hope to ground ourselves somewhere in Indra’s Net, or whether we dance freely within the Net because we are it. The dangers of relativism in ethics are vitiated to the extent I realize my interdependence with other beings: I shall indeed love my neighbour as myself when I experience that I am my neighbor. [vii]
It is interesting to note that over a period of many centuries Buddhist thinkers across East Asia have meticulously preserved the Sanskrit terms originally used to define Buddhist ideas, and fully credited Indian sources. Recently, however, as Buddhist ideas have travelled to the West and spread across many disciplines, the tendency has been to disconnect Hinduism from these ideas. Thankfully, the term ‘Indra’s Net’ has been preserved, and this allows scholars like myself to retrace the Vedic origins of these widely popular ideas.
Influences on modern society
Indra’s Net has inspired thinkers and movements in the West ranging from philosophy to ecology. David Loy has described how the major milestones of Western post-modernist thought resemble the ideas inherent in Indra’s Net. He cites Sigmund Freud’s approach in psychology, Ferdinand Saussure’s work in linguistics, Roland Barthes’s ideas in literary theory, and Jacques Derrida’s approaches to deconstruction as examples of twentieth-century pioneers who have utilized the ideas of Indra’s Net (mostly without explicit acknowledgement). The result of this has been nothing short of a revolution in Western philosophy, shaking the age-old Western premise that entities have separate, absolute, independent existences. Deconstructing the self-existence of things is the very signature principle of post-modern thought, and is a subset of the philosophical ideas contained in Indra’s Net. [viii]
Gregory Fahy has examined John Dewey’s idea of local, contextual and relational metaphysics as a subset of the Hua-yen thinking of Indra’s Net. [ix] Mathematicians studying chaos theory and fractals have described the beauty of structures as ‘Indra’s net’, ‘Indra’s necklace’ and ‘Indra’s pearls’. [x] In physics, the notion of quantum entanglement is a special case of the kind of interconnectivity we are describing. It is not at all surprising that Indra’s Net has been used as a metaphor to explain holograms, wherein, by definition, each part also includes the whole within itself. Indra’s Net has also been cited as the metaphor for the internet.
In the field of environmentalism, Leslie Paul Thiele has explained that Indra’s Net represents the Sanskrit concept of prajna (the wisdom of the interdependency of things), with the key implication that causes and effects are inseparable. He mentions that the word ‘ecology’ was coined in 1873 to mean the interactive relations between plants and animals, and that its meaning has recently expanded to include all of nature’s interrelationships in a wider sense. Sustainability is inherently a matter of interdependence, so the applicability of these ideas to the modern ecology movement is obvious. [xi] Indra’s Net, of course, embodies a far wider scope than just the material aspects of nature.
The basic principle is that each individual is both the cause for the whole and is caused by the whole. Ecological interdependence implies that if any one part of a system is disturbed, the whole system is affected. In this regard, Francis Cook has described Indra’s Net as a kind of ‘cosmic ecology’. [xii] Unlike in Western (disembodied) philosophy, nature is not seen as a backdrop for human existence; rather, humans are seen as inseparable from nature. A special issue of the journal Philosophy East and West was devoted to the applications of Indra’s Net to the field of environmental ethics. [xiii]
Another example of contemporary applications is an NGO called Indra’s Net Community, a South Korean movement that addresses concerns in the daily lives of lay people. Inspired by the interdependency principle of Indra’s Net, it was started by a group of visionary monks. They established grassroots communities to promote an alternative lifestyle in response to contemporary society’s emphasis on mass consumption, commercialism, competition, and the exploitation of natural resources. [xiv]
[i] The mantra is: ‘brihaddhi jaalam brihatah shakrasya vaajinivatah’ (8.8.6). ‘Ayam loko jaalamaasit shakrasya mahato mahaan’ (8.8.8).
[ii] However, from the viewpoint within the provisional reality, all jewels are not the same. We must note the Buddhist (and Vedantin) notion of two truths, phenomenal and absolute. There is spiritual progress only from a phenomenal point of view.
[iii] Vatsyayan, 1997.
[iv] Brhadaranyaka Upanishad (2:5.17-18) http://www.swami-krishnananda. org/brdup/brhad_II-05.html
[v] Cook, 1977, p. 2.
[vi] In early Pali texts, there is the notion of ‘paticca samuppada’ (dependent, co-arising or interconnected origination). Nagarjuna established one of the central principles that there are no isolated entities bearing essential natures or existing as themselves. This is referred to as things being empty of their own separate distinct existence, i.e., not having any ultimate sva-bhava or self-nature. This developed into the Avatamsaka tradition’s idea of sunyata along with interdependence comprised all reality. One of the famous chapters of the Avatamsaka Sutra includes the following explanation of interpenetration: ‘All the lion’s organs, the tip of every hair, being of gold, include the whole lion. Each of them permeates the whole lion; the eyes are the ears, the ears are the nose, the nose is the tongue and the tongue is the body. They come into being freely, without difficulty, without impediment.’ Here the gold symbolizes the substance and the lion symbolizes the form.
[vii] Loy, 1993, p. 484.
[viii] Loy, 1993.
[ix] Fahy, 2012.
[x] See, for example, Mumford, 2002 and Debnath, 2006. The metaphor has also been applied to new ideas proposed in library science (Bair-Mundy, 1998).
[xi] Thiele, 2011.
[xii] Cook, 1977.
[xiii] Philosophy East and West, vol. 37, no. 2, April 1987.
[xiv] Park, 2010. Indra’s Net has also been cited by activists who argue against climate change and other environmental concerns (Tam, 2008). There are also co-dependency arguments for helping salmon survive (Allendorf, 1998).
Please see my related posts:
David Mumford, Caroline Series and David Wright
TexasA&M University Press 2009
By David Mumford, Caroline Series, and David Wright,
Cambridge University Press,
New York, 2002,
University of Cambridge
This is the 2010 joint London Mathematical Society / Gresham College lecture.
‘Yat Pinde tad Brahmaande’
“As above, so below.” The ancient Vedas and Upanishads say, “Yatha pinde, tatha Brahmande”, translated as: “As is the atom, so is the universe. As is the microcosm, so is the macrocosm.” i.e., The individual is truly cosmic.
‘To see a world in a grain of sand and heaven in a wild flower,
hold infinity in the palm of your hand and eternity in an hour.’
Great Chain of Being
Great Chain of Being, also called Chain of Being, conception of the nature of the universe that had a pervasive influence on Western thought, particularly through the ancient Greek Neoplatonists and derivative philosophies during the European Renaissance and the 17th and early 18th centuries. The term denotes three general features of the universe: plenitude, continuity, and gradation. The principle of plenitude states that the universe is “full,” exhibiting the maximal diversity of kinds of existences; everything possible (i.e., not self-contradictory) is actual. The principle of continuity asserts that the universe is composed of an infinite series of forms, each of which shares with its neighbour at least one attribute. According to the principle of linear gradation, this series ranges in hierarchical order from the barest type of existence to the ens perfectissimum, or God.
The idea of the chain of being was first systematized by the Neoplatonist Plotinus, though the component concepts were derived from Plato and Aristotle. Plato’s “idea of the good” in the Republic, eternal, immutable, ineffable, perfect, the universal object of desire, is fused with the demiurge of the Timaeus, who constructed the world of becoming because “he was good, and in one that is good no envy of anything else ever arises.” Aristotle introduced a definition of the continuum and pointed out various graded scales of existence. Thus, in the words of Plotinus, in his Enneads,“The one is perfect because it seeks for nothing, and possesses nothing, and has need of nothing; and being perfect, it overflows, and thus its superabundance produces an Other.” This generation of the many from the one must continue until all possible varieties of being in the descending series are realized.
The scale of being served Plotinus and many later writers as an explanation of the existence of evil in the sense of lack of some good. It also offered an argument for optimism; since all beings other than the ens perfectissimum are to some degree imperfect or evil, and since the goodness of the universe as a whole consists in its fullness, the best possible world will be one that contains the greatest possible variety of beings and so all possible evils. The notion died out in the 19th century but was given renewed currency in the 20th by Arthur O. Lovejoy (The Great Chain of Being: A Study of the History of an Idea, 1936).
General Characteristics of the Renaissance
The Great Chain of Being
Among the most important of the continuities of the Renaissance with the Classical period was the concept of the Great Chain of Being. Its major premise was that every existing thing in the universe had its “place” in a divinely planned hierarchical order, which was pictured as a chain vertically extended. (“Hierarchical” refers to an order based on a series of higher and lower, strictly ranked gradations.) An object’s “place” depended on the relative proportion of “spirit” and “matter” it contained–the less “spirit” and the more “matter,” the lower down it stood. At the bottom, for example, stood various types of inanimate objects, such as metals, stones, and the four elements (earth, water, air, fire). Higher up were various members of the vegetative class, like trees and flowers. Then came animals; then humans; and then angels. At the very top was God. Then within each of these large groups, there were other hierarchies. For example, among metals, gold was the noblest and stood highest; lead had less “spirit” and more matter and so stood lower. (Alchemy was based on the belief that lead could be changed to gold through an infusion of “spirit.”) The various species of plants, animals, humans, and angels were similarly ranked from low to high with in their respective segments. Finally, it was believed that between the segments themselves, there was continuity (shellfish were lowest among animals and shaded into the vegetative class, for example, because without locomotion, they most resembled plants).
Besides universal orderliness, there was universal interdependence. This was implicit in the doctrine of “correspondences,” which held that different segments of the chain reflected other segments. For example, Renaissance thinkers viewed a human being as a microcosm (literally, a “little world”) that reflected the structure of the world as a whole, the macrocosm; just as the world was composed of four “elements” (earth, water, air, fire), so too was the human body composed of four substances called “humours,” with characteristics corresponding to the four elements. (Illness occurred when there was an imbalance or “disorder” among the humours, that is, when they did not exist in proper proportion to each other.) “Correspondences” existed everywhere, on many levels. Thus the hierarchical organization of the mental faculties was also thought of as reflecting the hierarchical order within the family, the state, and the forces of nature. When things were properly ordered, reason ruled the emotions, just as a king ruled his subjects,
the parent ruled the child, and the sun governed the planets. But when disorder was present in one realm, it was correspondingly reflected in other realms. For example, in Shakespeare’s King Lear, the simultaneous disorder in family relationships and in the state (child ruling parent, subject ruling king) is reflected in the disorder of Lear’s mind (the loss of reason) as well as in the disorder of nature (the raging storm). Lear even equates his loss of reason to “a tempest in my mind.”
According to the chain of being concept, all existing things have their precise place and function in the universe, and to depart from one’s proper place was to betray one’s nature. Human beings, for example, were pictured as placed between the beasts and the angels. To act against human nature by not allowing reason to rule the emotions–was to descend to the level of the beasts.
From From the Great Chain of Being to Postmodernism in three Easy Steps
The 14 Lokas Of Hinduism –
The concept of the 14 Lokas of Hinduism state that they are divided into 7 upper worlds or Vyarthis and the 7 lower ones, known as the Patalas.
The 7 Vyarthis –
1 Satya-loka: Brahma’s loka. Satya-loka planetary system is not eternal. Abode of Truth or of Brahma, where atman are released from the necessity of rebirth.
2 Tapa-loka: Abode of tapas or of other deities. Ayohnija devadas live here.
3 Jana-loka: Abode of the sons of God Brahma.
4 Mahar-loka: The abode of great sages and enlightened beings like Markendeya and other rishies.
5 Svar-loka: Region between the sun and polar star, the heaven of the god Indra. Indra, devatas, Rishies, Gandharvas and Apsaras live here: a heavenly paradise of pleasure, where all the 330 million Hindu gods (Deva) reside along with the king of gods, Indra.
6 Bhuvar-loka (aka Pitri Loka): Sun, planets, stars. Space between earth and the sun, inhabited by semi-divine beings. It is a real region, the atmosphere, the life-force.
7 Bhur-loka: The Vishnu Purana says that the earth is merely one of thousands of billions of inhabited worlds like itself to be found in the universe.
The 7 Patalas –
1 Atala-loka: Atala is ruled by Bala – a son of Maya – who possesses mystical powers. By one yawn, Bala created three types of women – svairiṇīs , who like to marry men from their own group; kāmiṇīs, who marry men from any group, and the puḿścalīs.
2 Vitala-loka: Vitala is ruled by the god Hara-Bhava – a form of Shiva, who dwells with attendant ganas including ghosts and goblins as the master of gold mines. The residents of this realm are adorned with gold from this region.
3 Sutala-loka: Sutala is the kingdom of the pious demon king Bali.
4 Talatala-loka: Talātala is the realm of the demon-architect Maya, who is well-versed in sorcery. Shiva, as Tripurantaka, destroyed the three cities of Maya but was later pleased with Maya and gave him this realm and promised to protect him.
5 Mahatala-loka: Mahātala is the abode of many-hooded Nagas (serpents) – the sons of Kadru, headed by the Krodhavasha (Irascible) band of Kuhaka, Taksshaka, Kaliya and Sushena. They live here with their families in peace but always fear Garuda, the eagle-man.
6 Rasatala-loka: Rasātala is the home of the demons – Danavas and Daityas, who are mighty but cruel. They are the eternal foes of Devas (the gods). They live in holes like serpents.
7 Patala-loka: The lowest realm is called Patala or Nagaloka, the region of the Nagas, ruled by Vasuki. Here live several Nagas with many hoods. Each of their hood is decorated by a jewel, whose light illuminates this realm.
Koshas and Lokas in Hinduism
The Five Koshas
Swami Satyananda Saraswati
Satsang in Toulon, France, June 9, 1984
In philosophy, the body, mind and spirit are understood as one continuity, but in fact eastern and western thought were never in agreement with each other. Western philosophy originated from Greece while eastern philosophy originated in India. Greek philosophers in general and western philosophers in particular spoke about the object. Indian philosophers in general and in particular spoke about consciousness, and for many centuries western thinkers could never accept anything beyond object as tangible: here is the object, I can see it, I can touch it, therefore it is.
However, in yoga and in vedanta, object and consciousness are interrelated. In fact, modern science, what you call physics, speaks in exactly the same way as yoga. Both modern physics and ancient yoga move absolutely parallel to each other in explaining the reality of matter and consciousness.
Body, mind and spirit are interconnected, interrelated and interpenetrating. Therefore, a person is a combination of three things: firstly, the gross body, secondly, the subtle or astral body and thirdly, the causal body or unconscious. These three bodies constitute you, me and everyone, but they are gross divisions, broad classifications.
Each body has a dimension and a layer. You can call it a field. Just as you say electromagnetic field or radioactive field, in exactly the same way there are fields in your body. In vedanta, they are known as koshas which means ‘sheaths’. These koshas are five in number: annamaya, pranamaya, manomaya, vijnanamaya and anandamaya, and are further sub-divisions of the three bodies, which represent the three states of your daily experience.
Every day you have three types of experiences. One is the waking experience in which you experience through your senses and mind. The second experience is dream. In dream you do not experience through the senses, but through your subconscious mind. The third experience is sleep in which there is no knowledge of time and space, no knowledge about yourself or about anything in sleep, but when you get up in the morning, you know that you slept well the night before.
So every day the individual self undergoes these three experiences alternately. These experiences relate to a particular field. Whenever your individual self goes to one particular realm, it has one experience, and as your individual self changes the field, realm or dimension, it has another experience. For example, if you go to the North Pole, you will feel cold, or if you go to a tropical country, you will feel hot.
The first kosha is annamaya, the physical body. Annamaya kosha can be sattwic, rajasic or tamasic. The word sattwa means harmony, balance and tranquillity, where you create a balance between activity and peace. Rajas means dynamic, active, violent. Tamas means dull and inert. Through the hatha yoga shatkriyas, you develop a sattwic annamaya kosha and when annamaya kosha becomes sattwic, then the bouncing of energy is much greater.
In modern science it is said that all the time, the whole day and night, atomic energy is bouncing in and out from this physical body like a pendulum. Of course, you cannot see it, but scientifically it has been seen that just like a pendulum swings from left to right, left to right, in the same manner everybody is emitting or throwing away these atoms. The sattwic body creates a longer bouncing, a tamasic body perhaps no bouncing at all, while a rajasic body has a bouncing but it has no limitation.
Now when these atoms or atomic particles bounce off your body and come back, there is a period of rest. That period of rest is always in the pendulum also. When it goes to the left and then turns to the right, there is a moment of rest. In the same way, when you do pranayama, in between inhalation and exhalation there is a point of rest. That is called timelessness and it is very short. Sometimes it can be a one-thousandth part of one second and sometimes a ten-thousandth part of a second. In that short period, the body transmits energy which is sattwic, rajasic or tamasic. Therefore, annamaya kosha, which is the container of the other koshas, is tackled through the practices of the hatha yoga shatkriyas.
The second kosha is pranamaya, the kosha composed of prana, or life force. This prana is a part of cosmic life. Each and every creature, each and every thing in this world is a part of cosmic life. Prana is the force or energy for all kinds of motion. Prana is a Sanskrit word meaning movement, motion or vibration.
Pranic energy is in constant motion throughout life. It is not only in human beings, animals, herbs or trees, not only in oceans and mountains, minerals and bacteria. The tiniest part of an atom has prana. This prana is both visible and invisible. We need not talk about invisible prana now. Visible prana is manifesting before you. Wherever there is prana there is movement, growth, change and activity and where there is no prana there is no activity. When we die the body dissipates because it has become completely bereft of prana.
Prana is one item of your total composition and should also be dealt with in yoga. If the pranas are agitated or there is a pranic imbalance, there is imbalance everywhere. To understand prana you need to know a little about positive and negative atoms. The pranas are in the atmosphere in the form of positive and negative ions, which keep on bouncing, migrating and reintegrating. A balance has to be created between them.
If you study the science of the behaviour of positive and negative ions, you will understand the importance of balancing the prana in the body, because prana represents the positive energy in the body, and mind represents the negative energy. When there is a balance between positive and negative energy, then you can see illumination and everything is in harmony.
This prana is responsible for the action of the karmendriyas, the organs of action, just as electrical energy is responsible for the functioning of a microphone or light bulb. If the electricity which is being supplied somewhere in 220 volts becomes 440 volts, everything will burn. If the electricity becomes 120 volts, then there will also be a crisis. Therefore, the electricity has to be adjusted according to the capacity of the microphone or the bulbs. Similarly, there has to be coordination between the prana and the indriyas or sense organs. If there is too much prana, then your children are sometimes hyperactive. Hyperactivity in the body is due to hyperactivity of the prana.
There are five karmendriyas: feet, hands, vocal cords, urinary and excretory systems. Indriya means vehicle, tool or sense. Karma means action. Through these five karmendriyas you perform five gross actions. Prana is the force behind them. You have seen how old people become slow due to lack of prana. Pranamaya kosha is the energy in annamaya kosha.
There are five main pranas: prana, apana, udana, samana and vyana. These forms of prana control various functions in the physical body. For example, urination, excretion, insemination and childbirth are consequences of apana. Then there are five auxiliary or secondary pranas.
Prana is not a mechanical outcome of the body as it is understood in modern medical science. According to the classical tradition prana enters the womb in the fourth month of pregnancy. When an embryo is developed in the mother’s womb, it is part of the mother’s body and prana. After the third month, the independent or individual pranas manifest in the foetus. That is to say, from the fourth month, the mother’s prana and the prana of the embryo become two different pranas. Therefore, remember that prana is universal energy.
Pranamaya kosha is purified through the practice of pranayama, because pranayama makes the pranic energy penetrate into each and every cell and fibre of the body. Pranayama does not literally mean breathing exercise. The word pranayama is composed of two ideas, prana and ayama, meaning field, dimension or area. Pranayama means extending the field of prana. In this physical body you have a field of prana. It is the subtle form of energy and can be measured. This prana shakti can also get blocked. It can be in excess in some parts of the body and sometimes there is an imbalance in the prana.
The third kosha is manomaya, the kosha composed of the mind. Mind is consciousness. It is a field of energy by itself. Even as prana is the positive field of energy, mind is the negative field of energy. In Sanskrit, the mind is known as manas, and has three dimensions. In fact, in Samkhya philosophy, they say that the mind has ten dimensions. Here they mean the mind of everyone, not only of human beings but of lower animals, the vegetable kingdom, the mind of each and everything in this world.
There are ten stages in the evolution of the mind from the most crude to the most fine. If you want to study those ten stages, you should read the Samkhya Sutras. However, out of those ten stages of mind, three are known to human beings: the conscious mind, the subconscious mind and the unconscious mind. Now these three stages are divisions of the human mind. The literal meaning of manas is ‘that by which you cognize, perceive and understand’. Perception, cognition and understanding are the basic and primary qualities of the mind.
This mind is connected with time, space and causality. What are past, present and future? They are the three so-called divisions of the same mind. What is the form of the mind? It is said that the mind moves at the greatest speed. Do you know the speed of an object? French trains run at 240 kilometres per hour. You know the speed of sound and of light, but do you know the speed of the mind. If only you could create a mental train! The mind is a very subtle unit and when it goes to the subconscious level, it begins to go into the unknown past.
Carl Jung used to talk about archetypes, dreams and visions. He said there is no known source of these things. Whether they are transferred to you from your parents or from a super space, from your previous incarnations or from some unknown transmissions, there is a primitive stock of archetypes within you. This is called samskara. It is known as the seed body or the unconscious. These are the three broad divisions of the mind.
Now this mind can be brought closer, that is to say, time, space and causality can be brought closer. When we are on the external conscious plane, the distance between time, space and causality is long and when you are in meditation, then the gap between time, space and causality is very short. In fact, if the mind can sometimes stop, time stops. A lot of work has been done on this by modern physicists.
The mind which I am talking about is part of the cosmic mind. Of course, I think that I have an individual mind. Everyone thinks this, but it is ignorance because we do not know, just like an ignorant person may feel that the light burning in the light bulb is individual, but another person understands that the energy is coming from the powerhouse. In the same way, this mind is part of the universal mind. How can we put this mind in touch with the cosmic mind? Through raja yoga practices.
The fourth kosha is vijnanamaya. Vijnana means psyche. Vijnana is a Sanskrit word from the prefix vi and jnana meaning knowledge or awareness, inner perception or experience. Vijnana has two meanings: external science and also inner experience. Therefore, whenever you have any experience which is subjective in nature, it is a consequence of vijnanamaya kosha. Whatever you are dreaming is a projection of vijnanamaya kosha, and in your meditation, concentration or mantra yoga, when you see lights and flowers, figures, angels or saints, smell perfumes or hear sounds, it is the consequence or result of vijnanamaya kosha.
Vijnanamaya kosha is related to a very unknown part of the universe and it is a link or sutra between the conscious mind, the individual mind and the universal mind. Universal knowledge comes to the conscious mind through vijnanamaya kosha or the psychic mind. Vijnanamaya kosha does not depend on time, space and causation factors.
You may not have seen Peking, but vijnanamaya kosha can give you a complete film of Peking because it is not limited by time past, present or future. The mind has its eyes on the object, but vijnanamaya kosha has its eye on the universe, and therefore Hindus say that vijnanamaya kosha has a thousand heads and a thousand eyes, a thousand hands and a thousand feet. This means it can see anywhere and think anything.
How can it be developed? It can be developed through tantra because tantra is related to vijnanamaya kosha. The tantric practices act as a catalyst because it is in you, just as curd and butter are in milk, but cannot be seen as separate unless they are released. Matter has energy in it, but when you look at matter, can you see the energy? No, you cannot. Even if you believe that there is energy in matter, still you cannot see it. Then you adopt a method to separate the energy from the matter. That is what nuclear energy is. All energy is inherent in matter. In the same way, vijnanamaya kosha is inherent within you but it is hidden in you like butter is hidden in milk. You have to separate it; you have to release your vijnanamaya kosha.
The fifth organism is anandamaya kosha. It is not possible to translate the word ananda. Some translate it as bliss or happiness, but ananda is when there is no happiness and no unhappiness. In happiness you are jumping, in unhappiness you are dull – sometimes low, sometimes high. So your mind is swinging. In ananda there is no swinging. There is unified experience and that experience does not change.
Death cannot change that experience; birth cannot change it; love and hatred cannot make your experiences swing. When your mind has become steady in experience and does not fluctuate under any condition, that is ananda. So we call it homogenous experience. The experience which you have in your life every day is not homogenous. It is divided and that is why swamis have ananda in their name, to remind them that they must achieve the state of mind where there is no swinging. So, anandamaya kosha means the kosha which comprises homogenous experience.
In many books, anandamaya kosha is translated as the blissful sheath. But I have thought about ananda for many years and have come to the conclusion that there is a state of mind which does not change, despite anything that happens in life. With that state of mind you can live with all the conditions of life. You can live with a good partner or a bad partner, prosperity or poverty, disease or death, in a discotheque, on a beach, a hotel, everywhere, because nothing affects you. You are where you are, firmly rooted in your own self, but at the same time you can interact with everyone. You can even fight, but still not be affected.
The three gunas
You are composed of these five sheaths or koshas, but you are not that. These five koshas belong to the lower existence, not to the range of supreme knowledge. They are controlled by the three gunas: sattwa, rajas and tamas. Guna means quality, faculty or attribute. The three gunas belong to nature. In this context nature does not mean beautiful places, mountains and hills.
In philosophy nature means prakriti, the universal law. There is a universal law which controls all, from biggest to tiniest, and it is inherent in the thing itself. Take a tree, for example. It is controlled by the laws inherent in the tree. In the same way every human being and every animal is controlled by a law which is inherent in it. My controller is inherent in me and that is the law. That is prakriti, and it controls, maintains or manages each and every law by the three gunas.
These three gunas again control the five koshas. The three gunas work in unison. Nothing is controlled by one guna. The body is controlled by tamoguna, but there is also a little bit of rajas and sattwa. In the same way, anandamaya kosha is controlled by sattwa guna, but there is a trace of the other two gunas. The mind is controlled by rajoguna, but there is a trace of the other two gunas. The three gunas control the five koshas in cooperation with each other. They all have a share. In one kosha, one guna may have a major share and in the others a very minor share, but the proportion changes from time to time.
Where can we place yoga here? First of all, the various practices of yoga purify the mechanism of these koshas. Thereby they can change the quantum of the gunas in each kosha. For example, the body is predominantly tamasic, but by the practices of hatha yoga, sattwic food and a good daily program, you can increase sattwa guna in the body. In the same way you can change the quantum of the gunas in each kosha.
When you change the quantum of the gunas in these five koshas through the yoga practices, a balance is created and when balance is created, then greater awareness takes place. These five koshas are separate classifications. You can experience them during your yoga practice. When you meditate, you pierce through or penetrate each and every kosha.
There are many books on the koshas. One is Vivekachudamani, a very famous book by Adi Shankaracharya, the second is Panchadashi, a very famous book in fifteen chapters dealing with terminologies in yoga and vedanta, and the third is Samkhya Sutras. These three are authentic classical texts.
The five koshas, five tattwas, three gunas and various forms of yoga should be studied in conjunction with each other because they are related to everyone. Even animals have koshas, but the nature of evolution is different. Animals have a well developed annamaya kosha and pranamaya kosha, but their manomaya kosha is in a rudimentary state of evolution, while their anandamaya kosha is not at all manifest. In little insects, annamaya kosha is there but pranamaya kosha is not fully developed and manomaya kosha is unmanifest there.
So the five koshas are not the sole property of human beings. Anything in this universe which has a body has five koshas, but as it goes on evolving then the later koshas become more and more prominent. A yoga practitioner has a developed vijnanamaya kosha while one who has achieved the result of yoga has anandamaya kosha fully developed. But beyond these five koshas is the absolute self. The purpose of existence is to experience that cosmic self and in order to understand and experience that cosmic self, you have to first understand these five koshas and then separate them.
Awakening the Vijnanamaya Kosha (Part 1)
Swami Satyasangananda Saraswati
Satsang to Iranian yoga students at Rikhia, 24th January 2007
Please tell us about vijnanamaya kosha and the practices to awaken it.
Shalom! Salamalekam! Shabahkher! Swagatam! Namaskar! Namo Narayan! and welcome to the land of yoga. Although yoga by virtue of being a science is the universal birthright of mankind, which necessarily implies that it does not belong to any sect or group of people, nor to any country or even religion, yet I would not be wrong in saying that India is the land of yoga because it is here that this knowledge was preserved. It was in this land that this knowledge was kept alive for centuries amidst the ravages of war and turbulence of history, and for that we have to thank those great souls, the rishis and munis, who were the original scientists on this planet.
Scientists are those who, with complete freedom of mind, without any bias or preconceived notions, explore and probe deeply into the underlying mysteries of the universe and life therein. In that sense, these rishis were scientists because they devoted their entire lives to exploring the mysterious terrain of inner life. With utmost honesty, courage, sincerity and dedication they spent their time unravelling the deeper layers of the mind and consciousness, discovering its mighty potential and the source from which it has sprung. Yes, the credit for this discovery goes entirely to these ancient scientists of the vedic era, just as the credit for unravelling the mysteries of matter goes to the scientists of the modern era.
Of course, in those times they were not known as scientists. Instead they were known as rishis, which means seer, or munis, which means sage, or sannyasins, which means one who has entrusted himself to the divine will. Although they are often mistaken to be priests or religious sectarian pontiffs, that is not the case. They may have been born into a particular religion, just as you and I have been born into the Hindu, Muslim or Christian religion, but that did not in any way influence their quest for the mystery called ‘life’. Who knows what religion they followed in those prehistoric vedic times? We cannot say for sure because we know so little about it and what the historians tell us is mere speculation.
Just as the only reality the scientists of today know and believe in is that of matter, the only reality these ancients believed in was that of consciousness. Their entire quest was in this direction for they believed that the purpose of life was to discover the infinite, that reality which is not subject to death or decay. The finite perishes and after so much spent energy, one finally realizes that the source of this finite world is what one should be able to capture, for in that lies the ability to be master of both the finite as well as infinite worlds.
It was this magnificent quest so full of difficulties and perils that led them to the awakening of the vijnanamaya kosha, and it is on account of their discoveries and the records that they left behind that today we can sit here and discuss this important subject. Otherwise we would not even know that we have a vijnanamaya kosha!
The five koshas
According to the science of yoga, there are five koshas which surround this body in much the same way as the inner core of an onion is covered by layers of skin. Only, in the case of koshas, each subsequent kosha is more subtle and unperceivable to the naked eye than the one preceding it. One can say that these koshas can only be realized with the opening of the inner eye, in the state of meditation.
The first is annamaya kosha, which is the physical sheath made from food. Anna means food. The grain which you eat is called anna and the body which is composed of food is one that you can touch, see and feel. It is the substratum for the subtler koshas, which also assume the shape and size of the body.
Subtler than that which is not visible to the naked eye is the pranamaya kosha, which instead of food is made of prana or energy. You ought to know that your body is enveloped by this field of prana and when you leave this room, you will carry it out along with your body. Although you can’t see it, the pranamaya kosha follows you wherever you go.
However, if you raise your awareness by the practices of yoga, then you will see the pranamaya kosha in the form of an aura which surrounds the body. Many people are born with this natural gift, where they are able to read the aura of people and determine what is in store for them, because this aura keeps changing all the time according to the state of health you are in at that time. Even your moods influence the pranic aura. The phrases ‘green with envy’ or ‘red with rage’ are just a few indications of the vibrations emitted by the aura according to our mental state.
Beyond the pranamaya kosha, this physical body is surrounded by a more subtle energy which is purely mental in nature, known as the manomaya kosha. It is at the level of manomaya that the chatushtaya antahkarana, comprising manas or mind, buddhi or intellect, ahamkara or ego, chitta or memory spring up and begin to perceive, cognize, record, understand, rationalize, discriminate, accept, reject, compare, to name only a few of the myriad functions that it performs effortlessly in our lives. Without the manomaya kosha we would be no better than the vegetables sitting on your kitchen shelf!
This kosha is the seat of para or empirical knowledge. It beholds the world around and although an instrument of inner consciousness, it has the capacity to externalize the awareness as well as withdraw it inwards. When it is under the sway of the senses, it is fully occupied with the external impulses that it receives from the world of smells, sounds, lights, colours, touch and taste. But there are times when, dissatisfied with the finite nature of these experiences, the mind propels inwards, and at that time it receives the impulses of the self which recharge and rejuvenate the manomaya kosha.
This happens in the state of meditation too, and that is why meditation broadens the horizons of the mind, sharpens the intellect, brings the ego in tune with nature and strengthens the chitta.
Beyond manomaya or mind is the sheath of intuition or vijnanamaya kosha, and needless to say it is subtler than all the preceding koshas. The Taittiriya Upanishad elucidates the existence of the vijnanamaya kosha in the following manner: “Separate from the self comprised of mind, there is another inner self comprised of intuitive knowledge. This one is also like the shape of a person like the preceding koshas. Faith is its head, Tasye shraddhaiva shiraha; righteousness its right wing and truth its left wing, hritam dakshinah pakshaha satyamuttarah pakshaha; yoga is its soul, yoga atma, and maha its foundation, maha puchham pratishtaha.”
Koshas and lokas
Interestingly, by stating that maha is the foundation of vijnanamaya, we derive a clue as to how the koshas are also linked to the lokas, which are planes of consciousness one experiences as the awareness gains ascent from annamaya to pranamaya to manomaya to vijnanamaya. The sapta or seven lokas are bhu, bhuvar, swar, maha, jana, tapo and satya. While bhu, bhuvar and swar, the earthly, intermediate and divine planes, are related to annamaya, pranamaya and manomaya, maha, the plane of siddhas, jana, the plane of rishis and munis, and tapo, the plane of liberated souls, relate to awakening, stabilization and illumination of vijnanamaya.
Satya loka, the plane of ultimate bliss, corresponds to anandamaya kosha, which is none other than pure consciousness. The Taittiriya Upanishad defines anandamaya kosha as having the shape or form of a person with love as its head, joy as its right wing and delight as its left wing, bliss as its trunk and Brahman as its support or foundation.
Maha loka, the plane of siddhas and saints, is the foundation or support of vijnanamaya kosha. It is from here onwards that the superstructure of heightened awareness is constructed. If the foundation is shaky, in other words if the siddhis which begin to manifest become the object of focus or enjoyment, then the siddha will surely fall back to lower planes of consciousness. However, if he does not allow them to distract the awareness, especially when he is in a state of samadhi, then ascent of awareness to higher lokas known as jana, the realm of rishis and munis, and tapo, the realm of liberated souls, the jivanmuktas and videhamuktas, is definitely assured.
From vijnanamaya to anandamaya
The above is such an important stage in the ascent of awareness that the Raja Yoga Sutras of Patanjali has devoted an entire section to this mega event, when the consciousness is able to perceive the four dimensions of time, past, present, future and eternity. Patanjali has termed this event when siddhis manifest as vibhooti. He calls it the accomplishment of yoga and has cautioned the aspirant against becoming distracted by this accomplishment. It is the state equivalent to paroksha anubhuti, or awareness of only one point without consciousness of one’s own self. Deepening awareness of paroksha anubhuti leads the practitioner to aparokshanubhuti, which correlates to the bliss of anandamaya kosha.
So you can say that vijnanamaya is the doorway to anandamaya. The experiences of vijnanamaya give you glimpses of what is in store for you as your awareness begins to experience pure bliss, but the experience again drops due to the appearance and disappearance of distractions and one-pointedness of mind. All siddhas and saints must have passed through this stage before they attained enlightenment. The tales about Buddha, where prior to nirvana he encountered the demons and bewitching damsels, as well as the forty days and forty nights when Christ encountered temptation before he experienced God, point a finger in this direction.
When there is awakening in vijnanamaya kosha, siddhis begin to manifest. The practitioner becomes clairvoyant and telepathic; he begins to know many things about people and events before they happen, which come to him in the form of dreams, thoughts or visions. He may be able to appear at many places to many people at the same time. He develops the power to read others’ thoughts and also to change them. Or else he may develop healing powers. His words, touch or glance can heal the deadliest of diseases which no doctor can cure. In some exceptional cases, depending on the extent of his advent into the level of vijnanamaya kosha, he may even be able to resurrect life or enter another person’s body. A person exhibiting such powers could easily be mistaken for God, which perhaps many did who were unaware of the manifestation of siddhis through the power of yoga when there is awakening in vijnanamaya kosha.
Yoga has boldly declared that you are not just the body you perceive with the eyes, nor are you just blood, bones, marrow, muscles, nerves and the different organs that keep you alive. You are much more than that. In fact, what you see of yourself with the eye is sustained by what you cannot see. If the unseen part of you ceased to exist, the seen part of you would wither and die. This unseen part of you is composed of the five koshas as mentioned above. The aim of all the practices of yoga, without exception, is to energize and awaken these koshas until ultimately you experience awakening in vijnanamaya kosha. That alone is the purpose of yoga.
Koshas and shariras
Now, you ought to know that these five koshas belong to or co-relate with three bodies that constitute your being. These three bodies, which are known as sthula or gross, sukshma or subtle and karana or causal, along with the koshas also influence each and every experience and reaction you face or evoke throughout your life. For example, the experiences related to annamaya kosha belong to the sthula sharira or gross body, whereas the sukshma sharira or subtle body is the arena for the experiences of pranamaya and manomaya koshas. The most subtle body, known as karana sharira or causal body, which stores all of our karmas, samskaras and impressions of many, many incarnations is the one we encounter when we speak about awakening in vijnanamaya kosha.
As life evolved through 84 lakh yonis or incarnations, from an amoeba to a bacteria or virus and then on to insects, plants, fish, birds, animals and finally to the human being, it carried the impressions of its experiences. All of these experiences, pleasant and unpleasant, are stored in the vijnanamaya kosha. In order to step into the arena of spiritual ecstasy, you have to pass through this zone and face what is stored there eye to eye. You simply cannot avoid it, just as you cannot avoid your thoughts or your feelings and dreams. The practices of yoga can accelerate this process and accomplish this in a systematic and graded manner. It is only when the awakening occurs in vijnanamaya and that experience is stabilized, that the transcendental experiences of ecstasy and bliss related to anandamaya kosha arise in the consciousness.
In modern psychology, the causal body or karana sharira is known as the realm of the unconscious. You may even term it as the psyche of man. It is the mythical Pandora’s Box, virtually the skeleton in the closet. You cannot know what is stored there until there is awakening in vijnanamaya kosha. When you experience awakening in manomaya kosha, you are still within the realm of buddhi or intellect. Everything that you experience will be within the fold of logic and reason and thus there is a degree of control of the experiences and their outcome.
The dimension of intuition
Vijnanamaya kosha transcends intellect and enters into the dimension of intuition, where the mind does not work. This mind of yours which you are familiar with does not function in vijnanamaya kosha; nor does the intellect. Each one of us operates at the level of instinct, intelligence, intellect and intuition. Till the level of intellect you are under the influence and in the field of manomaya kosha. But when you are able to transcend this intellect, even for a second, you will experience an intuitive flash about something or other that has been on your mind. All of us have at some time in our life experienced this intuition, which comes in flashes due to a sudden contact with the vijnanamaya kosha. But they drop. You get intuitive, but you are not able to hold on to that state of awareness and once again you regress to the hold of intellect and intelligence.
The aim of yoga is not just to induce these abilities. More than that, the focus of yoga is to attain mastery or control of these supernormal powers that belong to the realm of intuition. That intuition should act as a tool in your hands, just like your intellect, mind or intelligence. All the practices of yoga are designed to take you to this point. And each one of us has to find a way for ourselves, because each one of us has a different temperament and each one of us has our own dharma which determines our own individual needs.
(To be continued in the next issue)
Awakening the Vijnanamaya Kosha (Part 2)
Swami Satyasangananda Saraswati
In the journey to awaken vijnanamaya kosha, first of all, you have to find out exactly where you are standing at this present moment. What exactly is your temperament? Are you tamasic, rajasic or sattwic? While it is true that each individual is a combination of these three gunas or qualities that belong to the realm of prakriti or nature, still one or the other is predominant in us. Are you by nature a procrastinator, lazy, dull and negligent in your duties and responsibilities; if you are, then you are tamasic by nature. Of course, we are all lazy at some time of the day, but tamasic individuals are unable to rise above these tendencies, no matter how hard they try. On the other hand, predominantly rajasic people are always on the go, trying to accomplish and achieve something, having a lot of desires and passions. Or are you sattwic, full of knowledge, peace and tranquillity? Is that the point where you are going to start your journey to the awakening of vijnanamaya kosha?
Preparing for the awakening
After discovering your temperament, you have to prepare the vehicle which is this body, annamaya kosha. The journey starts from the body because it is through this vehicle that you can reach that point of intuition. The next thing you have to gear up is the fuel to move this vehicle to higher states of experience which are beyond the gross and mundane. Just as you need refined high octane fuel to drive your Mercedes Benz, Bentley or Rolls Royce, in the same way you need high octane fuel to drive this body and mind out of the clutches of the sensorial experience into the state of meditation.
According to yoga, that fuel is known as prana. Prana is not oxygen, nor is it the breath. Prana is the energy which flows in the breath. It is the vital energy, the source of life. So first of all you have to prepare the vehicle, and you also have to see that the quantum of prana which is flowing in the body is sufficient to take you to that heightened state of awareness. If there is an insufficient flow of prana in the body, then you simply cannot meditate. You may be able to meditate for a short period, but again the awareness drops. But to awaken vijnanamaya kosha you have to have enough fuel to allow unhindered and uninterrupted meditation.
So you have to find ways to increase as well as conserve the quantum of prana which is being dissipated and lost in the myriad activities you engage yourself in throughout the day. Prana is depleted in the digestion of food; you also lose prana when you talk, sing or dance. In fact everything requires prana, from blinking the eyelids and sneezing to thinking and contemplating. A lot of prana is wasted when you are worried, anxious, frightened or upset, which means you have to also learn the mental disciplines of yoga so that you don’t waste prana in useless thoughts, but instead are able to conserve it for meditation. This means that along with the vehicle and the fuel, you also have to take care of the driver, which is the mind. You have to keep the mind in order if you want to dive into the experiences of vijnanamaya kosha. By mind, I mean the totality of mind which constitutes the conscious, subconscious and unconscious.
The path of yoga
Good health or a beautiful body is not the aim of yoga. Fitness, beauty and youth are a by-product or side effect of yoga, not its final goal. Just as modern medicines produce side effects – for example, long usage of aspirin results in peptic ulcers or some other drug results in night blindness or vertigo or stiff joints – yoga too has a side effect. The difference is that the side effects of yoga are not detrimental; instead, they always have a positive and beneficial influence on the body and mind. You derive good health and attain clarity and focus of mind. Your intellect and memory are sharpened and your capacity to take correct decisions improves. You acquire confidence, poise and grace. These are only some of the side effects of yoga, but they are certainly not the aim or purpose of yoga.
The purpose of yoga is far more sublime. It is to prepare you for that ultimate state of meditation or transcendental experience. Through the practice of asana you first of all purify the entire physical structure and organs which constitute the body. The heart, lungs, liver, kidney, endocrine, nervous and circulatory systems are purified and the body is brought to an optimum condition. Then through the practice of pranayama you increase the level of prana, which increases the flow of blood to all the organs of the body and also to the brain, which is the most vital organ for meditation.
When all the organs are functioning properly and the flow of prana is unobstructed, then calmness and a peace descend on you, which is essential for meditation. In fact, peace of mind is a prerequisite and not a consequence of meditation as we normally tend to think. Unless you have attained peace of mind you cannot ever meditate, because the distractions of mind will simply not allow you to reach that heightened state. Instead of concentration, the mind will be wandering everywhere.
Asana and pranayama are practised to induce a balance and harmony between the body and mind, or you may say the physical and mental activities. Asanas do not just influence the organs, they influence your emotions as well. Together they play an important part in regulating the turbulent emotions which influence your attitude, responses and perception of the events in your life.
Through the practices of asana and pranayama you can directly instigate an immediate influence on the quantum of prana which flows through 72,000 channels or nadis throughout your entire body. Although all the nadis are to be purified, for this there are three which are most important, known as ida, pingala and sushumna.
Ida nadi, which corresponds to the sympathetic nervous system, is responsible for your mental activity, and pingala nadi, which corresponds to the sympathetic nervous system, is responsible for your physical activity. Originating at the root of the spine, they wind their way upwards, intersecting at a few junction points from where they send offshoots to all the different parts of the body, conveying prana right from your head down to your toes. An imbalance in the flow of these two nadis not only results in physical or mental sickness, but also obstructs awakening of the third nadi, sushumna, which corresponds to the autonomic nervous system.
The practices of yoga are intended to create a balance between the flow of these two nadis, which carry physical and mental energy to every part of the body, as that paves the way for the grand awakening of sushumna. Because it is only with the awakening of sushumna that experiences of vijnanamaya kosha begin to take place. Unless and until you are able to awaken sushumna through the balance of ida and pingala, you will not have the experience of vijnanamaya kosha. That is the sum and substance of what you have to do for awakening of vijnanamaya kosha.
Stages of awakening
This awakening takes place in three stages, which yoga terms as pratyahara, dharana and dhyana. As you become proficient in the practices of asana and pranayama and attain a balance in the flow of ida and pingala, you will find your mind becoming more and more introverted and that suddenly it is easier for you to withdraw your awareness from the external to the internal. That awareness, which is deeply attracted by the sense perception of sound, taste, smell, sight and touch, is able to transcend the influence of the senses and turn inwards. In other words, you are able to shut off the external world for some time and enter into the inner dimension. This is known as pratyahara and mastery of this state is essential before you can progress any further to the next stage. There are several ways prescribed to induce pratyahara, but pranayama is one of the most effective ways to perfect it, no matter whether you are temperamentally tamasic, rajasic or sattwic.
In the brief moments when you find that you are able to achieve this enormously difficult feat of sense withdrawal or pratyahara, you will need to fix that awareness on an inner point so that the concentrated energy that you are directing inwards does not dissipate, scatter or diminish. This inner focus or fixed concentration on a point is known as dharana. As you build your proficiency in these two practices with regular practice, the third stage of dhyana or meditation occurs. There are no rigid barriers between pratyahara, dharana and dhyana. Perfection of one spontaneously leads to the other.
When you do the practices of asana and pranayama, particularly pranayama, you may at any time spontaneously experience the state of pratyahara. If this state of pratyahara continues for some time, the mental energy will automatically become concentrated and dharana will occur. And as soon as the mind is concentrated, the internal state of dhyana or meditation simply happens, which is none other than the experience of awakening in vijnanamaya kosha, and glimpses of the experience of bliss and ecstasy related to anandamaya kosha begin to filter through.
Experiencing vijnanamaya kosha
The most important thing you have to know is that vijnanamaya kosha is the realm of your unconscious mind or psyche. It is a world of signs and symbols, colours and lights. And your unconscious is a part of the collective unconscious. It is directly linked to the collective unconsciousness or hiranyagarbha, the cosmic womb, that holds everything that has ever come into existence or is waiting to come into existence. It is the cosmic storehouse to which the unconscious mind of each and every individual is linked. That is why when you have experience of vijnanamaya kosha you become intuitive, because you begin to perceive things which belong to the four dimensions of time, the past, present, future and beyond that to eternity.
When your mental frequencies transcend time, space and object to attain a heightened frequency, that knowledge becomes available to you. The collective unconscious is a definite reality, where everything that has happened, everything that is happening and everything that will happen is stored. You can say it is a bank of unlimited knowledge. For example, it does not have the limitation of country. It is not Indian knowledge, nor is it American knowledge. Nor does it have the limitation of religion, because religions are man-made. This knowledge is universal. It is the knowledge of existence. It is not restricted to time and space.
Therefore, if you want to enter this realm of your being which is mystical and psychic, it is important that you should try to know a bit about your past: what is your ancestry, where do you come from, what is your heritage? Each one of us has a lineage, a heritage and a tribe from which we have descended. I may be an Indian, but that is not my tribe. That may be my national identity, but it does not indicate my tribe. The identity each one of us holds dear to ourselves of nation, religion and sect is fabricated or stitched so neatly around us that ultimately we are reduced to that and cease to be nothing more than that.
Eventually we fit into that mould, but undoubtedly there is something more to us than that. So each one of us has to go through this process of self-discovery which will take us beyond the confines of caste, country and religion back to our origins from where we descended. Who were those people from whom you descended? What was their tribe? What were their beliefs? Which rituals did they follow? What mantras did they chant? What methods did they employ to alter the consciousness?
You may be American by birth, but you may belong to a tribe that has its roots in India. From the North Pole to the South Pole, from Peru to Alaska, there are many, many thousands of tribes that have existed since time immemorial, who later congregated in different countries, different sects, different beliefs and different religions. In the course of time, they lost that tribal identity, but that does not alter the fact nor change the reality that those tribal influences will remain embedded in their psyche.
For instance, an Indian belonging to the Santhali tribe of Jharkhand will have a different psychic influence to an Indian belonging to the Toda tribe of the Niligiris. To reach the roots of your ancestry is important if you want to delve into mystic practices, because knowledge of that will help in ascertaining the practices that will yield quick results for you. This is because every tribe has its own set of mystic practices that are peculiar to them. Some tribes used mantras and mystic sounds to reach that mystical state, others used fire rituals, still others had knowledge of herbs or music and dance.
There is not one but thousands of rituals practised by different tribes, which they preserved as long as they maintained their tribal identity. Once they lost that identity, these rituals may have gradually ceased to exist in the conscious mind, but they would certainly have retained their roots somewhere in the unconscious as memory. It is this unconscious memory in the form of symbols and sounds, colours, lights and visions that comes to the fore in mystical practices and generates an altered state of consciousness.
As long as you want to develop the mind, intellect and intelligence, it is perfectly in order that you resort to the knowledge which is available according to the place where you live and your surroundings. But if you want to delve into the mystic practices that will awaken vijnanamaya kosha and develop your intuition, you will need to correlate yourself with your primitive and instinctive origins. That will give you very good results.
Instinct and intellect
Although instinct and intuition are very similar in expression, they are not the same. However, even though they are not the same, they are deeply linked and you may say that they are two sides of the same coin. At one level the consciousness expresses itself as instinct, as it does in the animal kingdom, and at the other end it expresses itself as intuition in humans.
If you observe birds and animals closely, you will find that they know of natural calamities in advance. Is that instinct or intuition? Not only that, they can know of distant events; leave some tasty meat outside in your courtyard and see the swarm of birds and animals that descend there in just a matter of seconds. This is the instinct of survival which perhaps we have inherited from them, which in the course of time can evolve to intuition if we know how to transform it. The difficulty we face is that we have lost sight of our instincts because we rely solely on our intellect and intelligence to survive. The intellect and intelligence is so highly developed in us that it has simply erased the innate instinctive responses and reactions that are still alive in animals. You have to restore that connection with your primeval past if you want to transform your instinct into intuition. Unfortunately, you have sacrificed your instinct at the hands of intelligence and intellect, which in a sense has corrupted your natural responses and led you away from your inner self.
That self, which becomes apparent as there is awakening in vijnanamaya kosha, cannot be realized through the mind. This mind which is responsible for your present experiences has to be separated and thrown out of its present field or range of experience. It is not this mind that illumines your experiences beyond manomaya kosha, but the self that illumines your path.
Intuition is born when the mind is transcended. So long as you function in this mental state of logic, reason and intellect, your intuition will not reveal itself to you. Intuition has no logic, it is pure feeling. It comes to you with amazing clarity as if that event is occurring right before you. For example, once a lady had come to meet my guru and as she entered the room I saw her in a white sari, although she was wearing a bright red one. It was just a flash of a vision and I did not give it much importance until I learnt a few days later that she had become a widow due to a tragic accident. Imagine my amazement when, two weeks after her visit, she again returned for my guru’s blessings, this time in the white sari which I had seen her in. That was intuition working.
This is an important point as well, for intuition first of all reveals calamities, destruction, fatal events, sickness, tragedy and all that is negative. This why the sage Patanjali in ‘Vibhooti Pada’ of the Raja Yoga Sutras has clearly warned against the use, or should I say misuse, of siddhis that arise as a consequence of awakening in vijnanamaya kosha. In fact, he has called them obstacles in the path of yoga – Te samaadhavupasarga vyutthane siddhayah (3:38). To an ordinary person they are a welcome achievement, one that he can boast about and maybe use to earn money, name and fame, but for a serious aspirant they act as hindrances. For if he begins to use them, in time they will disappear and leave him bankrupt. Even if you do not want the siddhis, they will come to you as you progress on the path of yoga, because awakening of vijnanamaya kosha grants vibhootis (divine attainments) and brings out the inherent pratibha (inner light, intuition) in an individual.
Beyond the mind
To awaken vijnanamaya you have to transcend the influence of mind and intellect. The easiest and quickest way to influence the analytical mind and logical intellect is to provide it with a set of practices that defy all logic. Amazingly, according to yoga and tantra, this really works. Mystic practices, involving mantras, rituals, worship, music as well as dance as in the case of the whirling dervishes and Sufi traditions which have been utilized since time immemorial by millions of races and tribes throughout the world, are a very important heritage which we can delve into. Of course, if you don’t have knowledge of your ancestral past, you can still use the practices of yoga. Because, as I said at the very beginning, yoga is universal, it belongs to mankind. And all mystic practices, all practices dealing with the esoteric, have some link with yoga. So you can easily use the practices of yoga, such as asana, pranayama, mudra, bandha, mantra, pratyahara, dharana and dhyana, to awaken vijnanamaya kosha.
The Moksha Gita by Swami Sivananda Commentary by Swami Krishnananda
Chapter 9: The Five Sheaths
1, 2. The Guru said: This Annamaya sheath or food sheath is made up of the five elements. It has a beginning and an end. It is inert and full of parts. It is an effect of the five elements. It is full of impurities. Therefore you are not this physical body or the Annamaya sheath. You are the witness of this body. Understand, therefore, “I am not the body. I am Brahman.”
The physical body is the grossest form of thought. The food consumed by the parents is converted into Sukla (semen) in men and Sonita in women and by the combination of these the physical body is formed. After birth, the body grows by suckling the milk which is only a transformation of the food consumed by the mother. The body is further developed by taking food. It gets dissolved in earth which is another form of food. The body is itself a food for other creatures. Hence it is called the food sheath, the material body or the earthly encagement of the soul. The food sheath is an object of perception. The Atman is the cogniser and the body is the cognised. Hence the Self is different from the body. In dream and deep sleep there is no consciousness of the body.
The five elements constitute the physical body. These modifications of Maya are not the Truth, the body and its Dharmas, size, form, birth and death are not actual modifications of the Self. Varnashrama, name and class differ in different births. They are mere accidental attributes of the body. There is no physical body either before birth or after death. Hence it is non-eternal.
Existence, birth, growth, modification, decay and death are the six Vikaras of the physical body. Just as the ether in a pot is not affected in any way by the destruction of the pot, so also the Atman is not at all affected by the destruction of the body or the Annamaya Kosha. Atman is unattached. Ether is subtle, but the Atman is still subtler. Atman is formless, changeless, birthless, deathless, free from old age. It is neither born nor is killed. Hence one should meditate on this Atman or Brahman.
3, 4. The Pranamaya Kosha or the vital sheath is a product of Rajoguna. It also has a beginning and an end. It is inert. It is an effect. Therefore you are not the Pranamaya Kosha. You are the witness of this sheath. Understand, therefore, “I am not the Pranamaya Kosha. I am Brahman.”
The Pranamaya Kosha consists of the five Pranas and five Karma-Indriyas or organs of action. Though the Prana is waking when one is sleeping, it does not invite a friend and entertain him; it cannot stop a thief who tries to remove the articles in a house. Therefore it is insentient. The Self is a mass of Intelligence. It is Chaitanya-Swarupa. It is entirely different from the Prana. The Self is the knower, seer and witness of this sheath.
Prana is only the active working of the mind. A pure-hearted man breathes rhythmically. The breath of an evil-minded person is disturbed. When the mind is controlled the Prana is automatically controlled. The Vedantic aspirant does not practise Pranayama, because his breath is automatically regulated and Kumbhaka naturally follows when the mental Kumbhaka or concentration and meditation are practised. The Pranas are the Rajasic manifestations of the dynamic mental force which with their ups and downs maintain the balance of individual existence even as the bicycle is kept in balance when its wheels are vigorously turning. When there is a break of this movement, the bicycle falls down and when the Prana is inhibited the individualising mind together with the ego breaks down and dies.
Hence there should be no identification with the Pranamaya Kosha and the aspirant should assert the Self-existent Atman distinct from it.
5, 6. The Manomaya Kosha or the mental sheath is a product of Sattwa Guna. It also has a beginning and an end. It is inert. It is an effect. Therefore you are not the Manomaya Kosha. You are the witness of this sheath. Understand, therefore, “I am not Manomaya Kosha. I am Brahman.”
The Manomaya Kosha consists of the mind and the five Jnana Indriyas. It is a means of enjoying pleasure and pain. The mind causes egoism in the body and “mine”-ness in house, sons, wife, wealth, etc., and passes outside through the avenues or channels of these five Indriyas. It is the internal instrument for gaining the experiences and knowledge of this world. Mind is associated with the Vrittis or waves of lust, anger, etc., and is a terrible objectifying agent. Mind is a Vikari, it constantly changes itself.
The Self is a witness of the Manomaya Kosha. The Self is Nirvikari. The mind is not the Self. The Self is the Atman or Brahman, unblemished, eternal and changeless, and one should meditate on it as such.
7, 8. The Vijnanamaya Kosha or this Buddhi sheath is a product of Sattwa Guna. It has also a beginning and an end. It is inert. It is an effect. Therefore you are not the Vijnanamaya Kosha. You are witness of this sheath. Understand, therefore, “I am not the Vijnanamaya Kosha. I am Brahman.”
The Vijnanamaya Kosha consists of the intellect in conjunction with the five organs of knowledge or the Jnana-Indriyas. During sleep it gets involution or Laya along with Chidabhasa or the reflection of Pure Consciousness. During waking state it is the doer. It is an effect like a jar and is inanimate. It shines in borrowed feathers. It borrows its light temporarily from its source, just as the moon borrows its light from the sun. It is not the eternal Self.
The Pranamaya, Manomaya and the Vijnanamaya Koshas constitute the subtle body. The subtle body is composed of the five unquintuplicated elements. There is neither breathing nor talking, neither seeing nor hearing in the dead body. There is also no warmth. The self-cognitions such as “I speak; I hear; I am hungry; I am thirsty;” and the like appear distinctly in the subtle body. The subtle body operates in the waking and the dreaming states. Ghosts and apparitions are the manifestations of the subtle body only.
The ego is hidden in the intellect and the memory (Chitta) is hidden in the mind. The subtle body thus, contains nineteen principles or Tattwas. It is also called the “Puri-Ashtaka” or the eightfold city. The five organs of sense, the five organs of action, the five vital breaths, the five subtle primary elements, the fourfold Antahkarana, ignorance, desire and action are the eightfold city of the subtle body.
The physical body is only an instrument in the hands of the subtle body. When the subtle body is disciplined through Pranayama, abstraction and concentration, the physical body also becomes very healthy and strong. Whatever the subtle body is, that the physical body also becomes. The mind which is the ruler of the subtle body gets fattened by worldly affections, by avarice for wealth, by the acquirement of women and gold and by attachment to the external fleeting forms of beauties. The mind is thinned out by eradication of the Vasanas and egoism.
The subtle body is the distracted expression of the self through Avidya, the causal sheath. Therefore it is not the Truth. Truth is Brahman and all else is false. One should meditate that he is not the subtle body and that he is the self-effulgent Atman.
9, 10. The Anandamaya Kosha or this bliss sheath is Avidya or ignorance, a modification of Prakriti. It is the effect of past deeds. It is endowed with changing attributes. It is Jada or insentient. Therefore you are not the Anandamaya Kosha. You are the witness of this sheath. Understand, therefore, “I am not the Anandamaya sheath. I am Brahman.”
The Anandamaya Kosha is made of Mula-Ajnana. It is the Karana Sarira or the causal body which is the substratum of all other sheaths which are external to it. Its three attributes or Dharmas are Priya, Moda and Pramoda, affection, delight and intense happiness. It is the indescribable beginningless Avidya, the nescience of the Atma, and is composed of Malina Sattwa. It is inanimate, beginningless, but has an end in Atma-Jnana.
The ignorance of the real nature of the Self constitutes this causal body or seed-body. It contains the potentialities or the seeds for the subtle and gross bodies. It projects the appearance of the whole universe through the subtle sheath. It is the food of ignorance for the hungry ego. The mind has come out of this ignorance and gets involved in it during deep sleep. In the sleeping state there is a vigorous functioning of this ignorance in which everything is lost as in pitch darkness. The Karana Sarira screens the Satchidananda Brahman.
He who knows the ignorance or the negation of the existence of the Atman and the denial of its appearance is the true Self, the Atman. He who knows the effects of ignorance, such as “I am a man, I am the doer and enjoyer, I am happy, I am miserable,” is the witness and the Atman. Hence in reality the Self is the seer, knower and the witness of the causal body or the ignorance. The Self is the Knowledge and the Light itself.
As the light that enlightens the jar is different from it, so is the Self different from the bodies witnessed by it. Therefore the Self is Consciousness itself and not the bodies.
The aspirant should endeavour to rise above the five Koshas to realise the identity with Pure Consciousness. Just as one draws out the thin stalk from the Munja grass by stripping off its upper layers one by one, so also one should take out the innermost essence of the Atman from all objects of perception, i.e. the five Koshas, by the “neti, neti” doctrine of negating unreality. Just as butter is removed from milk by churning the mixture of curd, so also the butter of the Atman should be taken from the mixture of the five Koshas by the churning of constant meditation on the Immortal Brahman which fictitiously appears as the sheaths, the world, etc. When the identification with the sheaths ceases, the self realises the Infinite Being and gets liberated beyond death.
Above Dhruvaloka by 10,000,000 yojanas is Maharloka, above Maharloka by 20,000,000 yojanas is Janaloka, above Janaloka by 80,000,000 yojanas is Tapoloka, and above Tapoloka by 120,000,000 yojanas is Satyaloka. Thus the distance from the sun to Satyaloka is 233,800,000 yojanas, or 1,870,400,000 miles. The Vaikuṇṭha planets begin 26,200,000 yojanas (209,600,000 miles) above Satyaloka. Thus the Viṣṇu Purāṇa describes that the covering of the universe is 260,000,000 yojanas (2,080,000,000 miles) away from the sun.
The body of the Supreme Lord, Viṣṇu, which forms the Śiśumāra-cakra, is the resting place of all the demigods and all the stars and planets. One who chants this mantra to worship that Supreme Person three times a day—morning, noon and evening—will surely be freed from all sinful reactions. If one simply offers his obeisances to this form or remembers this form three times a day, all his recent sinful activities will be destroyed.
Summarizing the entire description of the planetary systems of the universe, Śrīla Viśvanātha Cakravartī Ṭhākura says that one who is able to meditate upon this arrangement as the virāṭ-rūpa, or viśva-rūpa, the external body of the Supreme Personality of Godhead, and worship Him three times a day by meditation will always be free from all sinful reactions. Viśvanātha Cakravartī Ṭhākura estimates that Dhruvaloka, the polestar, is 3,800,000 yojanas above the sun. Above Dhruvaloka by 10,000,000 yojanas is Maharloka, above Maharloka by 20,000,000 yojanas is Janaloka, above Janaloka by 80,000,000 yojanas is Tapoloka, and above Tapoloka by 120,000,000 yojanas is Satyaloka. Thus the distance from the sun to Satyaloka is 233,800,000 yojanas, or 1,870,400,000 miles. The Vaikuṇṭha planets begin 26,200,000 yojanas (209,600,000 miles) above Satyaloka. Thus the Viṣṇu Purāṇa describes that the covering of the universe is 260,000,000 yojanas (2,080,000,000 miles) away from the sun. The distance from the sun to the earth is 100,000 yojanas, and below the earth by 70,000 yojanas are the seven lower planetary systems called Atala, Vitala, Sutala, Talātala, Mahātala, Rasātala and Pātāla. Below these lower planets by 30,000 yojanas, Śeṣa Nāga is lying on the Garbhodaka Ocean. That ocean is 249,800,000 yojanas deep. Thus the total diameter of the universe is approximately 500,000,000 yojanas, or 4,000,000,000 miles.
Vedic Cosmology – The Planets of the Material Universe
The cosmology and cosmography of the ancient Vedas is awe inspiring to say the least. The more “modern” of the Vedic texts are known to originate from approximately 3000 B.C., thus being the oldest scientific and religious doctrines known to man. The descriptions of our solar system and what modern astronomy has discovered of the visible universe corresponds with the ancient Vedic knowledge, proving that man has had advanced knowledge of astronomy for thousands of years before our modern civilization began. This article describes the Vedic version of planetary systems from the topmost, eternal planets down through the temporary planetary systems within innumerable universes of this material world.
When saying “cosmic manifestation” we speak of two separate worlds, the spiritual and the material. The spiritual planetary systems are eternal, beyond the limits of the material universes, and belong to a “super dimensional” or “anti-material” dimension. These are beyond the limitations of material time and space and therefore beyond our vision, or powers of perception. In these planetary systems there is no occurrence of creation or dissolution, and these planets are unlimited, indestructible, and eternally existing. There are descriptions of these spiritual planets in the vedic literatures, but this article concentrates on those within the material universe.
The material planetary systems are created at some point in time and will be destroyed at another. They are bound by the influences of time and space. Both of these energies (spiritual and material) are of the same divine source called “brahmajyoti”, the spiritual light. About 1/4th of this brahmajyoti is covered by the “mahat-tattva”, the material energy, where are found innumerable material universes. The 3/4th portion is the eternal spiritual sky. In the spiritual world are two realms of existence, “Goloka-dhama” and “Hari-dhama”. The material world has one realm called “Devi-dhama”.
Goloka-dhama is the topmost planet and residence of the Supreme Godhead Sri Sri Radha-Krishna. Below this is Hari-dhama where the spiritual planets of the Vaikunthalokas are situated. Below the Vaikuntha planets is “Mahesh-dhama” (also called Sadasivaloka, or the abode of Lord Siva). This is the realm dividing the spiritual from the material universes. Below Mahesh-dhama is Devi-dhama, the realm of the material universe. It is said that the systems of yoga offer different destinations. Bhakti yoga directs one toward entering Hari-dhama or Goloka-dhama. Jnana yoga directs the aspirant toward entrance to Mahesh dhama, and karma yoga directs one to remain in Devi-dhama, experiencing repeated birth and death in the material worlds.
The Planetary Systems of Devi-Dhama
In the Bhagavad-Gita we find a statement that there are three divisions of material planets in our universe. They are “urdhva-loka” (highest), “madhya-loka” (middle), and “adho-loka” (lower). Above the urdhva-lokas are the coverings of the material universe beyond which lie the eternal realms of existence. Within these three spheres of existence are 14 main planetary systems with different standards of life and duration of existence. The residents of the upper three systems have almost no disease or aging of the body, and they have no sense of fear. As the planetary systems progress downward there is lesser duration of life and standard of living, as well as a greater manifestation of disease and anxiety.
The 14 planetary systems are named as follows, from highest to lowest:
In one of the Vedic scriptures called the “Hari-vamsa” there is a description as follows: “Above the planetary systems where humans live is the sky. Above the sky is the orbiting sun, which is the entrance point of the heavenly planetary systems. This is the middle of the universe where begins the planets of those elevated by great austerities and penances. The planets above these, up to Satya-loka are the residences of those advanced in spiritual knowledge. All these planets are within the material world and under the control of Devi (Goddess Durga), and therefore called Devi-dhama.”
The term “amara” (deathless) is often used to describe the residents of the heavenly planets because their span of life is inconceivable to us, but although they live for millions of years by our calculation, none within the material worlds can live here eternally. In Bhagavad-Gita there is given a description for the life span of those living on Satyaloka. One day is equal to 4,300,000,000 solar years. On other heavenly planets the day is considered to equal six months of our time, and the night also equal to six months on earth. These souls live in their bodies for 10 million of their years.
Time duration such as day, night, months, and years are different in different planetary systems, and there are also different types of human beings, animals, trees, and vegetation. Some of the planets that are visible to us are considered heavenly planets with different timings. Jupiter, Venus, and the Moon are examples of planets where one day is equal to six months on earth. How can that be, one may ask, when we can see these planets orbiting the Sun?
One point of reference that may be difficult for some to understand is crucial to this realization. All planets have different dimensions surrounding them. The dimension of existence visible to our eyes gives us the impression that the other planets in our solar system are mostly devoid of life. In actuality astronomers have found proof of intelligent life on other planets, regardless of the fact that little is yet public knowledge. The purview discernable by our physical eyes, though, cannot enter into the heavenly spheres of these planets where devas, angels, and higher beings exist, nor even that of humans who enjoy an existence far superior to what is obtainable on our planet earth.
Just as on and surrounding earth there are realms of existence inhabited by ethereal beings invisible to our eyes, some highly advanced and others bound by unfortunate circumstances (such as ghosts), all planets have different spheres of existence. We can never gain knowledge of the multi-dimensional reality on earth with our physical eyes, so how could we possibly expect to enter into the higher realities of other planets with them?
There are also different types of oceans on different planets in the material world. “Siddhanta-siromani”, an ancient vedic astrological text describes them as being of seven varieties:
1) an ocean of salt water
2) an ocean of milk
3) an ocean of curd
4) an ocean of ghee (clarified butter)
5) an ocean of sugar cane juice
6) an ocean of liquor
7) an ocean of sweet water
Our minds may balk at such a conception of different types of oceans, but why should any of these be more fantastic than the ocean of salt water that we have here on earth?
There are also some eternal planets seemingly situated within this material universe, but they are always inaccessible for human beings. The text “Laghu-Bhagavatamrita” describes these eternal planets as follows: “Above Rudraloka, the planet of Lord Siva, is the planet called Vishnuloka. It is 400,000 miles in circumference, and inaccessible for any mortal living being. Above that Vishnuloka is a golden island called Maha-Vishnuloka in the ocean of salt. Brahma and other demigods sometimes go there to meet Lord Vishnu. Lord Vishnu lies there with Lakshmi (the goddess of fortune). East of here is the “ocean of milk” where within is the island of Svetadvipa, where Lord Vishnu also resides with Goddess Lakshmi. His transcendental island is 200,000 square miles and covered with desire trees for the pleasure of the Supreme Lord.”
This planet is called “Dhruvaloka” and we see it as the polestar. It is said to be 3,800,000 yojanas above the sun (one yojana is equal to 8 miles). Above Dhruvaloka by 10,000,000 yojanas is Maharloka. Above Maharloka by 20,000,000 yojanas is Janaloka, a further 80,000,000 yojanas lies Tapaloka, and above by 120,000,000 yojanas is Satyaloka. The Vaikuntha planets begin 26,200,000 yojanas beyond Satyaloka.
The scripture “Vishnu Purana” describes that the outer covering of the universe begins 260,000,000 yojanas above the sun. About 70,000 yojanas below the earth begin the seven lower planetary systems of Atala, Vitala, Sutala, Talatala, Mahatala, Rasatala, and Patala. Below these planets 30,000 yojanas is the Garbhodaka Ocean where Sesa Naga lies. This ocean is 249,800,000 yojanas deep. This gives an approximate diameter of the universe as 500,000,000 yojanas or 4,000,000,000 miles. These distances are calculated according to the distances between the planetary “planes” of existence. Actual distances between planets may be more.
The higher planetary systems are the realms of devas, demigods, and angels. Bhuvarloka is the abode of ghostly spirits, and the lower planets are populated by those of demoniac consciousness as well as the snakes known as “Nagas”. Development of higher consciousness, which also includes advanced intellectuality, starts with human beings and further increases among the denizens of higher planetary systems. The earth is situated close to the middle of these planetary systems.
Descriptions of the Planetary Systems
This is the abode of Lord Brahma, the progenitor of this material universe. Here there are airplanes controlled by mantra, not by any mechanical means. The residents have mind and intelligence, but no material gross bodies. They feel compassion for those suffering in the lower regions, but do not suffer fear, old age, or death. At the time of final dissolution of the material planets the residents here transform their subtle bodies into spiritual bodies and enter the eternal Vaikuntha planets. Great yogis finally reach this highest planet through the Milky Way, which is the “highway” to this most elevated planet where the duration of life is calculated as 15,480,000,000,000 years.
This is the abode of the four Kumaras named Sanat, Sanaka, Sanandana, and Sanatana. In this world many great sages also reside due to their advancement through spiritual austerity. The enjoyment available to the residents is inconceivable to us as it is beyond anything of our experience. When there is annihilation of the material universe the residents here also transform their subtle bodies to spiritual and enter the spiritual sky.
This planet, still above the heavenly realms, is another abode of great saints and sages. This planet is populated by mystics who move to higher planets, and eventually transform their subtle bodies to spiritual, when the fire of devastation consumes the material planets. These residents can move between any planets within the material universe as mystic “spacemen” at speeds unthinkable to us.
When fully purified from material desire and contamination through sacrifice, penance, and charity one can reach the heavenly planets, and if advancing further can pass through the higher orbits to reach Maharloka. The greatest of sages, such as Bhrigu Muni, live in this place. It is situated beyond the “Sisumara”, which is the pivotal point for the turning of the universe. Advanced yogis reach this planet and live here for 4,300,000,000 solar years. When the fire of devastation almost reaches this planet the residents transport themselves to Satyaloka where they live further before this highest of planets is destroyed. They then transform their subtle bodies to spiritual and enter the spiritual realms.
In every material universe is one Vaikuntha planet with an ocean of milk where Lord Vishnu resides on an island called Svetadvipa. This planet is Dhruvaloka. Living here are completely pure personalities. In our universe this planet is seen as the polestar and is situated above the planets of the Seven Rishis. As it is a spiritual planet, it is eternal and therefore remains when all other planets within the material universes are destroyed. It is said that this planet is the pivot for all material stars’ and planets’ orbits. All planets travel at high speeds in orbit, including the sun, which travels 16,000 miles per second in its orbit around Dhruvaloka. The planets of the seven sages are stars just below this planet that also orbit Dhruvaloka. They are always concerned with the welfare of the living entities within this material world and send emissaries to bring spiritual knowledge at various times and circumstances.
Saturn is considered an inauspicious planet astrologically, as he gives painful lessons to us here on earth. It is situated 1,600,000 miles above Jupiter and passes through one sign of the zodiac every 30 months.
Jupiter is considered a most auspicious heavenly planet and is generally considered favorable astrologically, depending on placement at the time of our births here on earth. It is a planet of devas, and situated 1,600,000 miles above Mars.
Mars is considered to be a malefic planet, which creates lack of rainfall on earth and almost always is capable of creating unfavorable influences here. It is situated 1,600,000 miles above Mercury.
Mercury is said to be the son of the moon and is 1,600,000 miles beyond the planet Venus. As does Venus, he sometimes moves behind the sun, sometimes in front, and sometimes along with it. Generally the influence of Mercury is said to be auspicious astrologically, except when not moving with the sun. At such times this planet causes great storms on earth.
Venus is considered a most auspicious and favorable planet, and is also of the heavenly planets. Venus is said to bring rainfall, another reason for it being considered auspicious to life on earth.
The Moon is one of the four most important residences of the demigods. Those who worship the demigods through sacrifice aimed at great material enjoyment are promoted to the Moon. Here the celestial, intoxicating beverage called “soma” is available. It is not possible to enter into or even see the actual heavenly dimensions of this planet with our present eyes. The Moon passes through the entire zodiac in approximately one month. He influences the growth of vegetation and therefore considered the life-giver for all living beings on earth.
The Sun is the source of light and heat for our universe. Modern science considers many stars to also be suns, but in the vedic literature they are considered to be planets of varying material elements, but not the center, as is the Sun. Surya, the sun god, is considered an expansion of Narayana (a form of Lord Vishnu). He controls the seasons here on earth. It is situated between Bhuloka and Bhuvarloka, rotating through the time circle of the zodiac. Yogis practicing hatha or ashtanga yoga, or those performing agnihotra sacrifices, worship the sun for their benefit. The demigods residing on the sun planet have bodies made of fire, necessary for life here.
Rahu is said to be an invisible planet, which is situated 80,000 miles below the sun. It causes solar and lunar eclipses, as Rahu, along with Ketu, are the north and south nodes of the moon respectively.
Siddhaloka, Caranaloka, & Vidyadharaloka
These planets are 80,000 miles below Rahu. The residents of these planets are born with natural mystic powers, including the ability to fly without mechanical means, even to other planets. They have all the mystic siddhis, and being materially perfect beings can control gravity, time, and space. Their arts, culture, and sciences are far superior to that knowledge possessed by we here in the earthly realm.
Yakshaloka & Rakshashaloka
Beneath these higher planetary systems, in the sky called “antariksha”, are the residences of the Yakshas, Rakshashas, Pisachas, ghosts, and other etheral beings. This realm extends as far as the wind blows and clouds float in the sky. Above this there is no air.
Bhu-mandala (Middle Earth)
The planetary systems of middle earth (Bhumandala or Bhuloka) are abodes of both standards of living such as we enjoy on our planet, as well as some heavenly abodes where living beings may “stop” on the way to, or from, births in the heavenly planetary systems. There are seven planetary systems, which are divided by seven oceans. The names of the planetary systems are Jambu, Plaksha, Salmali, Kusha, Krauncha, Shaka, and Pushkara. Each system is twice as large as the one preceding it, and each ocean between the systems are made respectively of salt water, sugarcane juice, liquor, ghee, milk, emulsified yogurt, and sweet water.
Bhumandala is shaped like a lotus flower and the seven planetary systems are in the whorl of the lotus. The radius of Bhumandala extends as far as the sunshine, and the limits of our vision here to see the stars and moon. As the sunshine reaches earth from a distance of 93,000,000 miles, this is the radius of the plane of Bhumandala.
Lower Planetary Systems
Below the earth are seven other systems called Atala, Vitala, Sutala, Talatala, Mahatala, Rasatala, and Patala. These lower planetary systems are the same size as the earth planet, and begin 560,000 miles below earth. Sunshine does not reach these planets and light comes from jewels on the hoods of serpents. These planets are populated by persons of great power and opulence, yet of demoniac consciousness, who have reached here through austerity aimed at material enjoyment without spiritual development. They do not become old and diseased and fear only the time factor, which ultimately must destroy their abodes. Therefore they are given the name of “bila-svarga”, or subterranean heavenly planets.
The residents here enjoy a standard of material comfort more opulent than even the higher planets due to their desires for high standards of sensual enjoyment, wealth, and influence. The residents are known as Daityas, Danavas, and Nagas and are all engaged in illusory material enjoyment with no thought of spiritual liberation. There are incredible feats of architecture in their cities bedecked with valuable jewels in houses, gardens, compounds, etc. All residents drink juices and bathe in herbal elixirs which free them from any anxiety or physical disease, as well as any sign of physical aging. The visual beauty of these artificial heavens surpasses that of the higher planets and this sensual atmosphere completely captures the mind, allowing no thoughts but those directed toward sensual pleasure and happiness. Since time is not divided into days and nights due to no sunshine reaching these planets, they have no fear produced by time. Only at the time of dissolution does anxiety and fear consume them.
Narakaloka, the Hellish Planetary Systems
Beneath the planet Patalaloka, and slightly above the water of the Garbhodaka ocean, are the Naralokas, or the hellish planetary systems. These planets are of different degrees of suffering for those who must endure life there. Here on earth we can see many hellish circumstances of suffering for people, but nothing like what is experienced on these planets. They are said to be a place of rectification for those who commit the most abominable actions while living as humans on the earthly plane. Although life here seems like it goes on for an eternity, in actual fact the duration of one’s “karmic sentence” here may be only seconds or moments. There are 28 different hellish planets described in the Vedic literatures.
These descriptions of the material creation, as well as the spiritual planets, may be found in several Vedic literatures to a far greater depth. I have out of necessity greatly abbreviated the information given here.
All of the planetary systems in the material world will in time be annihilated. This annihilation takes place in two ways. Partial annihilation occurs every 4,300,000,000 solar years, or at the end of each day on Satyaloka. This extends from the hellish planets through all lower planetary systems up to the heavenly planets. The highest planets are not annihilated at this time. The entire cosmic manifestation is wound up in the universal form of God every 8,600,000,000 x 30 x 12 x 100 solar years. The spiritual world, which is never annihilated, simply absorbs the material creation. It is described that before the destruction there is no rain for hundreds of years. Everything dries up and dies due to continuous sunshine. The sun becomes 12 times as powerful as was previously. Then there are horrendous rains that absorb everything into water.
The mortal bodies of living entities, including all vegetation, merge into the earth. The earth merges into its subtle sensation of fragrance. Fragrance merges into water, and water merges into its quality of taste. That taste merges into fire, which merges into form. Form merges into touch and touch into ether. Ether finally merges into the sensation of sound. The senses all merge into their origins, the presiding devas and demigods, then they merge into the controlling mind, which merges into ego in the mode of goodness. Sound becomes one with ego in the mode of ignorance, and ego (the first of all the physical elements), merges into the total nature. The total material nature dissolves into the modes (goodness, passion, and ignorance). These modes then merge into the unmanifest form of nature, and that unmanifest form merges into time. Time merges into the Supreme Godhead, present as Maha-Vishnu, the original creator of the cosmic manifestation. The origin of all life merges into God, the unborn Supreme Soul who remains one without a second, and from whom all creation and annihilation takes place. This annihilation of the material world is the exact reverse of the process of creation. Everything ultimately rests within the Supreme Absolute.
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Key Sources of Research:
Our brain is not a “stand alone” information processing organ: it acts as a central part of our integral nervous system with recurrent information exchange with the entire organism and the cosmos. In this study, the brain is conceived to be embedded in a holographic structured field that interacts with resonant sensitive structures in the various cell types in our body. In order to explain earlier reported ultra-rapid brain responses and effective operation of the meta-stable neural system, a field-receptive mental workspace is proposed to be communicating with the brain. Our integral nervous system is seen as a dedicated neural transmission and multi-cavity network that, in a non-dual manner, interacts with the proposed supervening meta-cognitive domain. Among others, it is integrating discrete patterns of eigen-frequencies of photonic/solitonic waves, thereby continuously updating a time-symmetric global memory space of the individual. Its toroidal organization allows the coupling of gravitational, dark energy, zero-point energy field (ZPE) as well as earth magnetic fields energies and transmits wave information into brain tissue, that thereby is instrumental in high speed conscious and sub-conscious information processing. We propose that the supposed field-receptive workspace, in a mutual interaction with the whole nervous system, generates self-consciousness and is conceived as operating from a 4th spatial dimension (hyper-sphere). Its functional structure is adequately defined by the geometry of the torus, that is envisioned as a basic unit (operator) of space-time. The latter is instrumental in collecting the pattern of discrete soliton frequencies that provided an algorithm for coherent life processes, as earlier identified by us. It is postulated that consciousness in the entire universe arises through, scale invariant, nested toroidal coupling of various energy fields, that may include quantum error correction. In the brain of the human species, this takes the form of the proposed holographic workspace, that collects active information in a ”brain event horizon”, representing an internal and fully integral model of the self. This brain-supervening workspace is equipped to convert integrated coherent wave energies into attractor type/standing waves that guide the related cortical template to a higher coordination of reflection and action as well as network synchronicity, as required for conscious states. In relation to its scale-invariant global character, we find support for a universal information matrix, that was extensively described earlier, as a supposed implicate order as well as in a spectrum of space-time theories in current physics. The presence of a field-receptive resonant workspace, associated with, but not reducible to, our brain, may provide an interpretation framework for widely reported, but poorly understood transpersonal conscious states and algorithmic origin of life. It also points out the deep connection of mankind with the cosmos and our major responsibility for the future of our planet.
Dirk K.F. Meijer* and Hans (JH) Geesink
Hans (J H) Geesink and Dirk K F Meijer
Hans (J H) Geesink* and Dirk K F Meijer
J.H. Geesink and D.K.F. Meijer
Dirk K. F. Meijer and Hans J. H. Geesink
NeuroQuantology | December 2016 | Volume 14 | Issue 4 | Page 718-755
Hans J. H. Geesink and Dirk K. F. Meijer
Dirk K. F. Meijer
Dirk K. F. Meijer
Dirk K.F. Meijer
Dirk K. F. Meijer
Dirk K. F. Meijer and Simon Raggett
Dirk K. F. Meijer and Jakob Korf
Boundaries precede Networks.
It is the difference which makes the difference.
The Relational Turn in Social Sciences
Recent times have witnessed relational sociology, as arguably the major form of relational scholarship, gain considerable scholarly momentum. There is a forthcoming major handbook (Dépelteau, 2018), significant edited collections such as Conceptualizing relational sociology (Powell & Dépelteau, 2013), Applying relational sociology (Dépelteau & Powell, 2013), and in the broader leadership literatures Advancing relational leadership research (Uhl-Bien & Ospina, 2012). In addition, there have been key texts from Crossley (2011), the work of Donati (1983, 1991, 2011) has become more accessible in English (to which he thanks Margaret Archer for, stating she “greatly encouraged and assisted me in presenting my theory to an international audience (Donati, 2011, p. xvii)), and – although less engaged with by English-speaking audiences—Bajoit’s (1992) Pour une sociologie relationnelle.
The Canadian Sociological Association has established a research cluster for relational sociology, with regular symposia, meetings, and events. Significantly, in 2015 the International Review of Sociology/ Revue Internationale de Sociolgie published a special section on relational sociology. Edited by Prandini (2015) and with contributions from Crossley (2015), Dépelteau (2015), Donati (2015), and Fuhse (2015), this special section sought to ascertain whether an original and international sociological paradigm entitled “relational sociology” could be identified. Prandini (2015) argues:
A new and original social paradigm is recognizable only if it accedes to the world stage of the global scientific system constituted and structured by networks of scientific scholars, scientific contributions published in scientific journals, books, internet sites, etc., fueled by a vast array of international meetings, seminars, conferences, and so on. It is only at this global level that we can decide if a new paradigm is gaining a global stage or not. Put in other words: are we really witnessing a new and emergent sociological ‘school’, or are we observing only a sort of ‘esprit du temp’ which is able to catalyse similar intuitions and sociological insights? (pp. 1–2)
At the end of his paper, Prandini (2015) contends that there is less a paradigm (in its precise Kuhnian meaning) and instead it is better to speak of a “relational turn” in sociology. Built on a strong and clear convergence toward a common critique of classic sociological theories, it is possibly the early stages of an emerging paradigm but such a label is currently premature. The real breakthrough of this turn is in forcing social scientists to specify “accurately the ontology of society and social relation and to discover new methods and research techniques well suited to study it” (Prandini, 2015, p. 13).
Relational theory is, as Emirbayer (1997) declares, beyond any one disciplinary background, national tradition, or analytic and empirical point of view. Outside of the major centers of Europe and the USA, Yanjie Bian hosted the International Conference on Relational Sociology at the Institute for Empirical Social Science of Xi’an Jiaotong University, and Jan Fuhse hosted the international symposium Relational Sociology: Transatlantic Impulses for the Social Sciences at Humboldt University of Berlin. Donati (2011) claims that interest in social relations can be found in philosophy (from the metaphysical point of view), psychology (from the psychic point of view), economics (from the resource perspective), law (control by rule), and even biology (bioethics). The interest is also not limited to the social sciences, with Bradbury and Lichtenstein (2000) noting:
The interdependent, interrelated nature of the world has also been discovered by physicists in their study of quantum reality. In their quest to identify the basic building blocks of the natural world, quantum physicists found that atomic particles appeared more as relations than as discrete objects (Capra 1975; Wolf 1980), and that space itself is not empty but is filled with potential (Bohm 1988). Heisenberg’s discovery early this century that every observation irrevocably changes the object being observed, further fueled the recognition that human consciousness plays an irreversible role in our understanding of reality (Bachelard, 1934/1984; Wilber 1982; Jahn & Dunne 1987). (p. 552)
Apart from its widespread contemporary appeal, relational thinking has a long history. The North American stream arguably finds its roots in the New York School, European scholars such as Karl Marx, Georg Simmel, Gabriel Tarde, Norbert Elias, Niklas Luhmann, Pierre Bourdieu, Bruno Latour, among others, have long argued for various relational approaches (even if not using that label), and Emirbayer traces the tradition of privileging relations rather than substances to pre-Socratic Greek philosopher Heraclitus. What is consistently germane across these various scholars is a critique of substantialism in classic sociological accounts. This also arguably speaks to the proliferation of relational scholarship in the past few decades as globalized forces are causing a rethink of spatio-temporal conditions (e.g., the nation state and geographic borders). In breaking down the substantialist approaches, and their underlying analytical dualisms, relational scholarship asks questions of the ontological and epistemological as much as the empirical.
Contemporary thought and analysis in social theory is overrun with “turns.” In this chapter, rather than be seduced by contemporary attention to a relational turn in the social sciences, I seek to highlight some major events, trajectories, or streams of relational thought. In doing so, I am critically aware of the difficulty of arguing for relational understanding and then constructing significant events as though they are entities in and of their own right. Within the confines of a single chapter, and mindful of the role that this chapter is playing the book (e.g., setting some context/trajectory for developing my argument), my goal is to cite key developments and how they relate to one another and my argument. Given my particular interest in organizing activity, my focus is on the Human Relations Movement of the early twentieth century, the New York School of relational sociology, and then contemporary developments in sociology, leadership, and to a lesser extent, the natural sciences. While I concede that there is increasing interest in what has come to be known as “relational sociology” (see also the following chapter), relational scholarship has a long and diverse intellectual history. Importantly though, as Powell and Dépelteau (2013) note, relational sociology is not a heterogeneous label and as a collection of scholars, is still quite some way from achieving any form of consensus. Whether consensus is required, or even desirable, for relational scholarship is questionable. The diversity of ontological and methodological starting points allows scholars to investigate a wide range of phenomena. This diversity, complexity, depth, and vitality enable dialogue and debate without requiring consensus. What binds them together is their scholarly focus on relations rather than alignment with a specific empirical object and/or method of inquiry
CALL FOR PAPERS
The Relational Turn in Sociology: Implications for the Study of Society, Culture, and Persons
Special issue of the academic journal Stan Rzeczy [State of Affairs]
The relational approach, which has a long tradition, has re-emerged and strengthened, forming a new, vital movement of divergent variants in sociology. Initiated and systematically developed by Pierpaolo Donati, it has grown into what is called the Italian relational turn, later followed by a proliferation of relational sociologies of various origins, including the works of Harrison C. White, Charles Tilly, Mustafa Emirbayer, Pierre Bourdieu and others. After the postmodern diffusion and beyond the stagnation of interpretative against normative conceptualizations of social life, relational sociology offers new conceptual tools and plays a leading role in reconstructing sociology both on theoretical and applied planes.
Modern sciences are founded on the study of relations, rather than essences or substances. From the outset, the relational approach has had to pave its way in sociology against holistic (“science of society”) and nominalistic (“science of individuals”) orientations. Social relations are among the key sociological concepts and have been studied as constitutive for social bonding. On the micro-level, interpersonal relations have been in the center of attention in the area where sociology and social psychology overlap. The relational turn consists not only of focusing on social relations; it also involves introducing relational categories of analysis.
The category of social relations is certainly not new in social theory. What is new is the way of looking at them. Contemporary relational thinking assumes radical changes in the ontological, epistemological, and phenomenological status of social relations. Refocusing on social relations, on their constitution and emergent effects leads us to a new way of describing, understanding and explaining social and cultural phenomena as relational facts.
A particularly significant feature of relational sociology resides in its capacity to broaden the theory of the human subject not only as a self, agent, and actor, but also through the development of the concept of the person; more precisely, through deeper research on the relational constitution of the human person as a social subject emerging from relational reflexivity (dialogue between ‘I’, ‘Me’, ‘We’, ‘You’ in a situated social context) – in other words, a view of the human person as homo relatus. Analyzing these processes leads to a sui generis relational theory of agency.
Various or divergent theories of contemporary social and cultural processes evoke relationality, but relational analysis differs from “relationistic” positions. Most existing approaches, both historical and modern, cannot be considered relational sociology in a true sense unless the social relation is conceived as a reality sui generis and society is conceptualized as a network of social relations.
“Turn” refers to a gradual transformation of the field of scientific theories, rather than to a scientific revolution. Several characteristic features of a “turn” appear to correspond well with significant traits of the relational turn: an epistemological rupture, which is brought about by introducing an innovative vocabulary that opens up new analytic perspectives; an attempt to reconstruct the scientific domains of knowledge under conditions of their growing fragmentation; introduction of a novel perspective that shows existing knowledge in a new light; moving on from the research object to the category of analysis. These are the features of a genuine new intellectual movement that enters into debates and polemics, particularly as regards various ways of understanding relations and relationality.
The synergetic effect of a creative exchange of ideas between the founders of theories that have been independently pursued – the relational theory of society developed by Pierpaolo Donati and the theory of morphogenic society, developed on the basis of critical realism by Margaret S. Archer – proves particularly fruitful for the study of the after-modern and the new possibilities of a morphogenic society, in which the challenge of re-articulating social relations remains of central importance.
The aim of this special issue is to reflect upon the innovative potential of contemporary relational theorizing of society, culture, and persons and to go beyond superficial statements on relational sociology by addressing these issues through in-depth investigations. We invite authors to take on problems of relational sociology by discussing its main assumptions, by conceptual clarifications, by re-articulating the concepts pertinent to understanding social phenomena in relational terms, and by empirical studies guided by methodological rules of relational analysis.
Please see my related posts:
Chapter of Book ME++
RWTH Aachen University
Paper presented at the International Symposium
„Relational Sociology: Transatlantic Impulses for the Social Sciences“,
September 25-26, 2008
Jia Shao, Sergey V. Buldyrev, Reuven Cohen
Maksim Kitsak1, Shlomo Havlin, and H. Eugene Stanley
Speech given by
Andrew G Haldane, Executive Director, Financial Stability, Bank of England
At the Financial Student Association, Amsterdam
28 April 2009
Kurt A. Richardson & Michael R. Lissack
Thomas Edward Webb
Sunil Sahadev, Keyoor Purani, and Neeru Malhotra
James E. Rauch
James R. Markusen
Stellenbosch University, South Africa
Understanding complex systems
Paul Cilliers, Rika Preiser (Eds.)
Authors: Eacott, Scott
By Pierpaolo Donati
edited by C. Powell, F. Dépelteau
edited by Francçois Depélteau and Christopher Powell.
Hampshire, UK: Palgrave Macmillan,
Lily Liang Sida Liu
By Nick Crossley
The American Journal of Sociology, Vol. 103, No. 2. (Sep., 1997), pp. 281-317
by Josef Langer (Klagenfurt)
Michele Lamont and Vira ́g Molnar
Special issue of the academic journal Stan Rzeczy [State of Affairs]
LILLA VICSEK1 – GÁBOR KIRÁLY – HANNA KÓNYA
Growth and Form in Nature: Power Laws and Fractals
There are several instances of power laws found in nature and in society. Some of the well known ones are:
Power laws and Scaling in Biology
After 1997 paper by West et all, many publications have analyzed empirical evidence as to what the correct exponent is and what is the fundamental theoretical basis for power law.
West found 3/4 as exponent, others have reported 1/4, 2/3, 4/5 etc.
Animals and Mammals follow 3/4 exponent. Plants follow 2/3.
The Metabolic Theory of Ecology
Scaling in biology has a rich and important history. Typically body mass, or some other parameter relating to organism size, is related to anatomical, physiological, and ecological parameters across species. Quite remarkably, diverse organisms, from tiny microbes to the earth’s largest organisms are found to fall along a common slope, with a high degree of variance explained. The beauty of such scaling ‘‘laws’’ has been the generality in biotic organization that they suggest, and the challenge (for ecologists) has often been interpreting their mechanistic bases and ecological consequences.
Scaling laws have thus far inspired scientists in at least three major areas. First, scaling laws may illuminate biology that is otherwise shrouded. For example, if scaling relationships can account for variation in a parameter of interest, the residual variation may be much more easily examined because the major influence of some trait, say, body size, is removed. Second, some scientists have taken an interest in ‘‘the exponent’’—essentially the exponential scaling values that produce the allometric relationship. What are the precise values of these exponents? Are they all from a family of particular values (quarter powers) for many different biological relationships? This area seeks to define the generality of patterns in nature and to explore the empirical robustness of the relationships. Third, from a mechanistic perspective, if scaling laws are mechanistic and truly general, then this suggests some underlying common biological process that forms the structure and function of species and ultimately generates biological diversity. The mechanistics of scaling from metabolism and the currently favored fractal network model of resource acquisition and allocation may allow scientists to understand the laws of how life diversified and is constrained. Perhaps more importantly, such a mechanistic understanding should allow the successful prediction of evolutionary trends, responses of organisms to global change, and other basic and applied biological problems.
The Ecological Society of America’s MacArthur Award winner, James H. Brown, working together with colleagues for over a decade on scaling in biology, has arrived at an outline for a metabolic theory of ecology—a proposal for a unifying theory employing one of the most fundamental aspects of biology, metabolism. This metabolic theory incorporates body size, temperature (metabolic kinetics described by the Boltzmann factor), and resource ratios of the essential elements of life (stoichiometry). Indeed, this bold and visionary proposal is likely to inspire ecologists and provoke much discussion. My goal in assembling this Forum was to work toward a balanced discussion of the power and logic of the metabolic theory of ecology. I have asked both junior and senior scientists to evaluate the ideas presented in the metabolic theory and to go beyond the listing of strong and weak points. As such, this collection of commentaries should be viewed neither as a celebration of the theory nor as a roast of Jim Brown. It should, however, serve as a springboard for future research and refinements of the metabolic theory.
Several themes and axes of admiration and agitation emerge from the forum. The focus on metabolism, and metabolic rate in particular, is an advance that most agree is the fundamental basis for the processes of acquisition of resources from the environment and, ultimately, survival and reproduction of organisms. The combination of size, temperature, and nutrients has compelling predictive power in explaining life-history traits, population parameters, and even broader-scale ecosystem processes. The key point here is that Brown et al. are making a direct link between factors that affect the functioning of individuals and the complex role that those individuals play in communities and ecosystems. Although what we have before us is a proposal for a unified theory of ‘‘biological processing of energy and materials’’ in ecosystems, Brown et al. embrace the unexplained variation and acknowledge other areas of ecology that may not be subject to metabolic laws.
The commentaries presented in this Forum are unanimous in their admiration of Brown et al.’s broad theoretical proposal and its clear predictions. Yet, points of discussion abound and range widely: What really is the correct exponent? Does the scale at which scaling is applied affect its explanatory power? Are the laws really based on mechanism or phenomena? How does the addition of temperature and resource limitation enhance the power of scaling relationships? And, is scaling up from the metabolic rate and body mass of organisms to population dynamics, community structure, and ecosystem processes possible? This Forum ends with Brown’s response to the commentaries. Although there will be continued debate over the correct exponent, the data at hand from the broadest taxonomic groups support quarter powers. There is general agreement over the issue of scale and the fact that, depending on the scale of interest, metabolic theory may have more or less to offer. Finally, nutrient stoichiometry is the most recent addition to metabolic theory, and all agree that further research and refinement will determine the role for such nutrient ratios in the ecological scaling. The benefits of a metabolic theory of ecology are clear. The authors of this Forum have outlined some of the future challenges, and tomorrow’s questions will evaluate these theses.
Metabolism provides a basis for using first principles of physics, chemistry, and biology to link the biology of individual organisms to the ecology of populations, communities, and ecosystems. Metabolic rate, the rate at which organisms take up, transform, and expend energy and materials, is the most fundamental biological rate. We have developed a quantitative theory for how metabolic rate varies with body size and temperature. Metabolic theory predicts how metabolic rate, by setting the rates of resource uptake from the environment and resource allocation to survival, growth, and reproduction, controls ecological processes at all levels of organization from individuals to the biosphere. Examples include:
(1) life history attributes, including development rate, mortality rate, age at maturity, life span, and population growth rate;
(2) population interactions, including carrying capacity, rates of competition and predation, and patterns of species diversity;
(3) ecosystem processes, including rates of biomass production and respiration and patterns of trophic dynamics.
Data compiled from the ecological literature strongly support the theoretical predictions. Eventually, metabolic theory may provide a conceptual foundation for much of ecology, just as genetic theory provides a foundation for much of evolutionary biology.
Key Sources of Research:
The Origin of Universal Scaling Laws in Biology
Geoffrey B. West
Life’s Universal Scaling Laws
Geoffrey B. West and James H. Brown
A General Model for the Origin of Allometric Scaling Laws in Biology
Geoffrey B. West, James H. Brown, Brian J. Enquist
Power Laws in Economics: An Introduction
The origin of allometric scaling laws in biology from genomes to ecosystems: towards a quantitative unifying theory of biological structure and organization
Geoffrey B. West, James H. Brown
A general model for ontogenetic growth
Geoffrey B. West, James H. Brown & Brian J. Enquist
Plants on a different scale
Lars O. Hedin
The Fourth Dimension of Life: Fractal Geometry and Allometric Scaling of Organisms
Geoffrey B. West, James H. Brown, Brian J. Enquist
TOWARD A METABOLIC THEORY OF ECOLOGY
JAMES H. BROWN,
with JAMES F. GILLOOL Y, ANDREW P. ALLEN, VAN M. SA V AGE, AND GEOFFREY B. WEST
Complexity and Transdisciplinarity; Science for the 21st Century(?)!
Scaling Laws in Complex Systems
A General Model for the Origin of Allometric Scaling Laws in Biology
Geoffrey B. West, James H. Brown,* Brian J. Enquist
Effects of Size and Temperature on Metabolic Rate
James F. Gillooly,1* James H. Brown,1,2 Geoffrey B. West,2,3 Van M. Savage,2,3 Eric L. Charnov
Growth, innovation, scaling, and the pace of life in cities
Luís M. A. Bettencourt, Jose ́ Lobo, Dirk Helbing, Christian Kuhnert, and Geoffrey B. West
Urban Scaling and Its Deviations: Revealing the Structure of Wealth, Innovation and Crime across Cities
Lu ́ıs M. A. Bettencourt1,2*, Jose ́ Lobo3, Deborah Strumsky4, Geoffrey B. West1,2
URBAN DYNAMIC LAWS AND OUR DEGREES OF FREEDOM FOR DEVELOPMENT
Francisco J. Martínez
Allometric Scaling Laws and the Derivation of the Scaling Exponent
Cities, Markets, and Growth: The Emergence of Zipf’s Law
August 10, 2011
Self-similarity and power laws
The fractal nature of nature: power laws, ecological complexity and biodiversity
James H. Brown1,2*, Vijay K. Gupta3, Bai-Lian Li1, Bruce T. Milne1, Carla Restrepo1 and Geoffrey B. West
Metabolic Rate and Kleiber’s Law
Patterns in Nature
Zipf, Power-laws, and Pareto – a ranking tutorial
Lada A. Adamic
The Power of Power Laws
Re-examination of the 3/4-law of Metabolism
P. S. DODDS, D. H. ROTHMAN- AND J. S. WEITZ
Fifth dimension of life and the 4/5 allometric scaling law for human brain
Ji-Huan He, Juan Zhang
Lack of Evidence for 3/4 Scaling of Metabolism in Terrestrial Plants
Hai-Tao LI1*, Xing-Guo HAN2 and Jian-Guo WU
Is West, Brown and Enquist’s model of allometric scaling mathematically correct and biologically relevant?
J. KOZLOWSKI and M. KONARZEWSK
Evidence against universal metabolic allometry.
An evaluation of two controversial metabolic theories of ecology
ASSESSING SCALING RELATIONSHIPS: USES, ABUSES, AND ALTERNATIVES
Karl J. Niklas1, and Sean T. Hammond
A critical understanding of the fractal model of metabolic scaling
José Guilherme Chaui-Berlinck
Allometric scaling of metabolic rate from molecules and mitochondria to cells and mammals
Geoffrey B. West*†‡, William H. Woodruff*§, and James H. Brown
Shapes and Patterns in Nature
There are so many colors, shapes, and patterns in nature.
How do we explain these from perspective of science? There are several branches of science which have explored these questions for decades. There are Reaction Diffusion Models and Cellular Automata models explaining development of patterns on seashells, plants and animal skins. There is L-system developed by Aristid Lindenmayer to explain development of plants. It is a fascinating subject.
From Exploring Complex Forms in Nature Through Mathematical Modeling: A Case on Turritella Terebra
There are several studies have been carried out in a number of scientific disciplines, such as mathematics, biology, paleontology and computer engineering to understand and decipher the relations of the seashells complex forms. Starting with Descartes, Figure 4 shows a time line in which many investigators having focused on the curves of these shells and their mathematical properties. They all outlined a number of mathematical relations that control the overall geometry of seashells.
After examining the existing seashell models in literature it is seen that they all followed Raup’s model which roughly abstracts the seashell form using three parameters; whorl (rate of expansion of the generating curve), distance (relative distance between the generating curve and axis of coiling), and translation (the change of the cone’s movement along an axis with respect to the whorl), an ellipse as the whorl cross-section as well. However, it is clear from the observations of actual shells (Figure 5) that the cross-section is more complex than the input that the three parameters allow. In the pursuit of realistic visualizations, Kawaguchi enhanced the appearance of shell models using filled polygons which represented the surface of shells more convincingly than line drawings. Similar techniques were used subsequently by Oppenheimer (1986). A different approach was adopted by Pickover (1989) who approximated shell surfaces by using interpenetrating spheres. Illert (1989) introduced Frenet Frames (Bronsvoort, 1985) to precisely orient the opening of a shell. His model also captured a form of surface sculpture. Cortie (1989) studied the pattern forms on the surface of the shell model (Meinhardt, 2003). Finally, the model of seashell geometry by Fowler et al. (2003) was similar to that introduced by Raup, and was the first to implement free-form cross sections using a Bézier curve (Farin, 2002 Rogers, 2001) as the input. It can be claimed that, studies above all focused on modeling the appearance of the shell surface.
All these approaches can be considered as a milestone for their era, as each model reflects the observation and tools of measurement, modeling and technologies of their time. In all these approaches seashells were modeled as a single surface, as a twodimensional object, and embedded in three-dimensional space. Today, such modeling research should be carried out employing observation tools, knowledge, information, and computational technologies to the maximum extent. For this reason, we developed a mathematical model that can be transformed into a computational model for further studies (such as overall behavior of shells, form-structure relations, form finding explorations etc.) to explore potentials of such optimized forms.
From Exploring Complex Forms in Nature Through Mathematical Modeling: A Case on Turritella Terebra
From Computational models of plant development and form
A broad program of using mathematical reasoning in the study of the development and form of living organisms was initiated almost 100 yr ago by D’Arcy Thompson (1942) in his landmark book On Growth and Form (see Keller, 2002, for a historical analysis). One of his most influential contributions was the ‘theory of transformations’, which showed how forms of different species could be geometrically related to each other. The theory of transformations was extended to relate younger and older forms of a developing organism (Richards & Kavanagh, 1945), but did not incorporate the formation and differentiation of new organs. This limitation was addressed a quarter of a century later by Lindenmayer (1968, 1971), who introduced an original mathematical formalism, subsequently called L-systems, to describe the development of linear and branching structures at the cellular level. By the mid 1970s, computational models based on Lsystems and other formalisms had been applied to study several aspects of plant development, including the development of leaves and inflorescences, and the formation of phyllotactic patterns (Lindenmayer, 1978). The questions being asked included the impact of distinct modes of information transfer (lineage vs interaction) on plant development, and the relationship between local development and global form. Similar interests underlied the independent pioneering work of Honda and co-workers on the modeling of trees (Honda, 1971; Borchert & Honda, 1984).
Another class of models was pioneered by Turing (1952), who showed mathematically that, in a system of two or more diffusing reagents, a pattern of high and low concentrations may spontaneously emerge from an initially uniform distribution. This was a surprising result, as it appeared to contradict the second law of thermodynamics: the general tendency of systems to proceed from more organized states toward disorder (the apparent paradox is resolved by jointly considering the reaction–diffusion system and its surroundings). Related models were introduced, under the name of activator–inhibitor and activator-substrate (depletion) systems, by Gierer & Meinhardt (1972), and extensively investigated by Meinhardt (1982). Reaction–diffusion systems showed how, in principle, molecular-level interactions may lead to morphogenesis and differentiation. In plants, reaction– diffusion-type models have been used to explain the patterning of trichomes in leaves and hair cells in roots (Digiuni et al., 2008; Savage et al., 2008; Jo¨nsson & Krupinski, 2010; Benı´tez et al., 2011). Nevertheless, the extent to which reaction–diffusion models apply to the plant kingdom appears to be limited (Kepinski & Leyser, 2005; Berleth et al., 2007). A significant role is played instead by mechanisms involving active transport of the plant hormone auxin (Section V). In some cases, such as the generation of phyllotactic patterns, this reliance on active transport is difficult to explain in evolutionary terms, as reaction–diffusion systems can generate the same patterns. Spatio-temporal coordination of other developmental processes, however, such as bud activation, requires long-distance signaling. Active transport may thus have evolved to overcome the limitations of diffusion, which is very slow over long distances (Crick, 1971).
In the last decade, computational modeling has become a mainstream technique in developmental plant biology, as reflected in numerous reviews (e.g. Prusinkiewicz, 2004b; Prusinkiewicz & Rolland-Lagan, 2006; Grieneisen & Scheres, 2009; Chickarmane et al., 2010; Jo¨nsson&Krupinski, 2010; Jo¨nsson et al., 2012). On the one hand, the sequencing of the human genome put in focus the chasm between knowing the genome of an organism and understanding how this organismdevelops and functions.Computational models bridge this chasm. On the other hand, successes of early conceptual models that relate patterns of gene expression to the form of animals (Lawrence, 1992) and plants (Coen & Meyerowitz, 1991) have prompted a quest for a comprehensive, mechanistic understanding of development (Coen, 1999). Current experimental techniques for tracking growth and observing marked proteins in living tissues (Reddy et al., 2004; Fernandez et al., 2010) are yielding a wealth of data that correlate molecular-level processes with plant development and form. Computational models play an increasingly important role in interpreting these data.
The use of models has been accelerated by the advancements in computer hardware, software, and modeling methodologies. General-purpose mathematical software (e.g. Mathematica and MATLAB), modeling programs built on the basis of this software (e.g. GFtbox, Kennaway et al., 2011) and specialized packages for modeling plants (e.g. the Virtual Laboratory and L-studio (Prusinkiewicz, 2004a), OpenAlea (Pradal et al., 2008) and VirtualLeaf (Merks et al., 2011)) facilitate model construction, compared with general-purpose programming languages. Furthermore, current computers are sufficiently fast to simulate and visualize many models at interactive or close-to-interactive rates, which is convenient for model exploration.
From The reaction-diffusion system: a mechanism for autonomous pattern formation in the animal skin
In his paper entitled ‘The chemical basis of morphogenesis’ Turing presented a ground-breaking idea that a combination of reaction and diffusion can generate spatial patterns (Turing 1952). In the paper, he studied the behaviour of a complex system in which two substances interact with each other and diffuse at different diffusion rates, which is known as the reaction–diffusion (RD) system. Turing proved mathematically that such system is able to form some characteristic spatio-temporal patterns in the field. One of the most significant deviations is s formation of a stable periodic pattern. He stated that the spatial pattern generated by the system might provide positional information for a developing embryo.
In spite of the importance of the idea in the developmental biology, his model was not accepted by most experimental biologists mainly because there were no experimental technologies available to test it. Therefore, most of those who took over and developed the Turing’s idea were applied mathematicians and physicists. They proposed various types of model that developed Turing’s original equation to fit real, naturally occurring phenomena (Meinhardt 1982; Murray & Myerscough 1991; Murray 1993; Nagorcka & Mooney 1992). Although the equations for each model differ, they all share the basic requirement of the original model; that is, ‘waves’ are made from the interactions of two putative chemical substances which we refer to here as the ‘activator’ and the ‘inhibitor’ (Meinhardt 1982).
Key Sources of Research:
On Growth and Form
Thompson D’Arcy W.
The Algorithmic Beauty of Plants
Prusinkiewicz, Przemyslaw, Lindenmayer, Aristid
The Algorithmic Beauty of Seashells
Meinhardt H, Prusinkiewicz P, Fowler D
(Springer, New York), 3rd Ed.
The Algorithmic Beauty of Seaweeds, Sponges and Corals
Kaandorp, Jaap A., Kübler, Janet E.
Models of biological pattern formation
The chemical basis of morphogenesis.
Pattern formation by coupled oscillations: The pigmentation patterns on the shells of molluscs
Hans Meinhardt, Martin Klingler
The Self-Made Tapestry Pattern formation in nature
Models of biological pattern formation in space and time
Models of biological pattern formation
Cellular Automata, PDEs, and Pattern Formation
The Computational Beauty of Nature: Computer Explorations of Fractals, Chaos, Complex Systems, and Adaptation
By Gary William Flake
The Curves of Life
Dover Publications, Inc. New York.
Reaction-Diffusion Model as a Framework for Understanding Biological Pattern Formation
Shigeru Kondo1* and Takashi Miura
The Hegemony of Molecular Biology
Deborah R. Fowlery, Hans Meinhardtz and Przemyslaw Prusinkiewicz
The neural origins of shell structure and pattern in aquatic mollusks
Alistair Boettigera, Bard Ermentroutb, and George Oster
Mechanical basis of morphogenesis and convergent evolution of spiny seashells
Régis Chirata, Derek E. Moultonb,1, and Alain Goriely
The Geometry and Pigmentation of Seashells
PATTERNS IN NATURE
Forging patterns and making waves from biology to geology: a commentary on Turing (1952) ‘The chemical basis of morphogenesis’
Mollusc Shell Pigmentation: Cellular Automaton Simulations and Evidence for Undecidability
INGO KUSCH AND MARIO MARKUS
Pattern Formation in Reaction-Diffusion Systems
The Natural 3D Spiral
Gur Harary and Ayellet Tal
A Model for Pattern Formation on the Shells of Molluscs
HANS MEINHARDT AND MARTIN KLINGLER
The reaction-diffusion system: a mechanism for autonomous pattern formation in the animal skin
Mechanical growth and morphogenesis of seashells
Derek E. Moulton, Alain Goriely and R ́egis Chirat
Scaling of morphogenetic patterns in continuous and discrete models
On the Dynamics of a Forced Reaction-Diffusion Model for Biological Pattern Formation
A A Tsonis, JB Elsner, P A Tsonis
A Model for Pattern Formation on the Shells of Molluscs
Impact of Turing’s Work
The possible role of reaction–diffusion in leaf shape
Nigel R. Franks1* and Nicholas F. Britton
Pattern regulation in the stripe of zebrafish suggests an underlying dynamic and autonomous mechanism
Motoomi Yamaguchi*†, Eiichi Yoshimoto‡, and Shigeru Kondo
MODELS FOR PIGMENT PATTERN FORMATION IN THE SKIN OF FISHES
Web Resource for Algorithmic Botony
FRACTAL GEOMETRY AND SUPERFORMULA TO MODEL NATURAL SHAPES
The Geometry of Seashells
Dr S Coombes
SEASHELLS: THE PLAINNESS AND BEAUTY OF THEIR MATHEMATICAL DESCRIPTION
Models for the morphogenesis of the molluscan shell
Modeling Seashell Morphology
Exploring Complex Forms in Nature Through Mathematical Modeling: A Case on Turritella Terebra
The Neural Origins of Sea Shell Patterns
Biological Pattern Formation : from Basic Mechanisms to Complex Structures
A. J. Kochy and H. Meinhardt
Form-Optimizing in Biological Structures The Morphology of Seashells
EDGAR STACH University of Tennessee
A Theory of Biological Pattern Formation
A. Gierer and H. Meinhardt
Cellular Automata as Models of Complexity
Nature 311 (5985): 419–424, 1984
Website on Oliva Porphyria
Evolution of patterns on Conus shells
Zhenqiang Gonga, Nichilos J. Matzkeb, Bard Ermentroutc, Dawn Songa, Jann E. Vendettib, Montgomery Slatkinb, and George Oster
Theoretical aspects of pattern formation and neuronal development
20+ Photos Of Geometrical Plants For Symmetry Lovers
Computational models of plant development and form
Przemyslaw Prusinkiewicz and Adam Runions
Periodic pattern formation in reaction–diffusion systems: An introduction for numerical simulation
Takashi Miura* and Philip K. Maini
Dynamics of Complex Systems