It is not hard to find debates today between “flat” and “round” Earths. Many of these debates are founded on conspiracy theories, but discussing those conspiracy theories isn’t the intent of this post. This post discusses a completely different notion of flat Earth which is found in Vedic cosmology texts, where space itself is viewed differently than in modern science. How this flat Earth is different from what generally people call “flat” Earth is discussed. The post also discusses how the four ethers described in the previous post appear to have different dimensions.
Table of Contents
- What is a Dimension?
- Space in Sāńkhya
- The Is-A vs. Has-A vs. Does-A Distinction
- Two Kinds of Functions
- The Three Dimensions of Space in Sāńkhya
- The Meaning of Directions in Space
- What is “Flat Earth” Really?
- Information and Complexity
- Four Descriptions of Material Space
- What is Two-Dimensional Space?
- Why the World Appears Three-Dimensional
- The Four Ethers and Their Dimensions
- Dimensions are a Function of Our Perception
- The Model of the Universe in Vedic Cosmology
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What is a Dimension?
A dimension is any property that is first used to distinguish and then used to order. For instance, objects can be distinguished and then ordered based on color from red to violet and then labeled as first, second, third, etc. Practical experience shows that all objects can be distinguished and counted based on their location in space. Such objects may have additional properties such as color, size, speed, etc. but these properties are not needed to individuate, distinguish, and count objects because their location in space suffices for this purpose. A scientific theory, therefore, only needs a spatial location to completely count objects.
In current science, however, spatial location doesn’t suffice to describe an object’s behavior and properties completely, although the location is adequate to distinguish it from other objects. For instance, if we specify an object’s coordinates in space, we don’t know its color, taste, smell, weight, speed, etc. This is the reason that science needs to postulate additional properties besides the object’s location. Thus, while we can see that location is sufficient to distinguish objects, it is not an adequate description of the object in current science. This has to do with how the location is presently conceived, as we will shortly see. An ideal natural theory is one in which the location in space itself is necessary and sufficient to individuate an object completely, and knowing the location of the object in space would be enough to completely describe all its current properties and future behavior.
Space in Sāńkhya
As we have seen previously, spatial location in Sāńkhya suffices to know everything about the object, because that location represents all its conceptual properties (e.g. color, taste, smell, touch, etc.). We don’t need other physical properties—e.g. mass, charge, temperature, speed, etc.—because the object’s location suffices to completely characterize an object. Thus, being in a different location is a necessary and sufficient condition to know how an object is different from other objects.
Such a space, however, is structured like a tree rather than a box. The dimensions of this space are the branches and the locations in it are the points at which the branches emerge. Each location in this space branches off another space with multiple dimensions, just as twigs emanate from a branch, or branches from a trunk. As the tree diversifies, it literally has infinite dimensions, and yet, all these dimensions are constructed using only three modes of nature called sattva, rajas, and tamas.
In some earlier posts we have seen the mechanism for diversification from ideas to sensations: the higher node is the tree is called manas or meaning, and the lower node is called vāk or the word, and these two are connected by prāna. The sattva-guna is represented by manas or idea, which is connected by rajo-guna or prāna to tamo-guna or vāk.
The Is-A vs. Has-A vs. Does-A Distinction
The instantiation of an idea into an object, however, is inadequate without further details. For example, we can instantiate “mammal” into a “dog” but this is inadequate without the dog being further divided into its body parts such as legs, head, stomach, etc. The instance of an idea produces an is-a object (e.g. a “dog is a mammal” where “mammal’ is an abstract concept and “dog” is relatively more detailed). This instantiation has to be further elaborated using a has-a process—e.g. a dog has a leg, head, stomach, etc. Each part performs a specific function: stomach digests food, legs transport, hands hold, etc. but the functionality of a part is completely defined by the part’s location in the whole. This is because the location of the object in space encompasses all its properties and behaviors.
Apart from “internal” functions of parts within the whole, there are functions that the whole performs in relation to the other wholes. These functions are not fixed because the structural relation between the various wholes is not fixed. For instance, we can use a knife to tighten a screw, cut fruit, or pierce a hole into a wooden block. These functions are not fixed because the knife is not in fixed relation to the rest of the world. These “external” functions of an object are created by the mode of nature called rajo-guna which represents the functional relationships between various objects.
Before we create parts in a whole, we must define the external functionality expected of the whole. In that sense, rajo-guna is higher than tamo-guna because the functionality definition precedes the parts that together produce that functionality.
The tree of the material world is thus created from only three guna, which can be understood as three processes that we can call is-a, has-a, and does-a.
Modern science discards ideas and their instantiation. It also discards the questions of the function because no object is believed to have been designed for a purpose. Finally, parts are studied but not in relation to ideas or functions. Thus, science discards the sattva-guna and rajo-guna components of nature and only studies tamo-guna. Why this science is incomplete is not difficult to see. The fix for such problems is also not “spirituality”. It is only advancing knowledge from tamo-guna to rajo-guna and sattva-guna.
Two Kinds of Functions
Consider a table with four legs. Each of these legs performs a function within the table—i.e. supporting it and providing it stability. However, the table as a whole also performs a function in relation to me, namely, that I can use it for studying. The functionality of the leg within the table is given by the well-defined structure of the table and if we know the table’s structure then we don’t have to separately define the functions of the parts. The functionality of the table as a whole, however, isn’t fixed in relation to me because I and the table are not part of a fixed structure. Therefore, I can use the table as a chair, as a bed, or as a ladder to reach higher parts of my room. There is, hence, a function defined by the table’s structure and there is another function given by the table’s relation to other objects which does not constitute a fixed structure and can keep changing over time.
The relation between two objects is simply the path connecting them, but this path is not a straight line. It is rather a way to traverse up and down the tree from one location to another. Thus, an object can in principle perform as many functions (in relation to other objects) as there are paths connecting it to other objects. But in practice, such paths are very few. For instance, I typically use a table to read and write, and rarely as a chair, or a bed, or a ladder. The reason is that all the possible paths are not always real.
A path between objects is a channel of communication but all possible channels are not available simultaneously. Such channels are opened and closed by karma thereby enabling or blocking the transfer of information between objects. Thus, even though the object can potentially be used as a table, chair, ladder, or bed, only some of these phenomena will be visible—enabled by karma in both directions.
The Three Dimensions of Space in Sāńkhya
The three dimensions in science are interchangeable through coordinate transforms. For instance, there is no reason to label something “east” or “west” because this is only our “relative perspective” in a physical space. Such dimensions in Sāńkhya are not interchangeable because they denote three different modes—instance, part, and action. We cannot equate a dog with the legs of the dog, or the legs with an activity such as running, or the activity like running with the dog. Any attempt to interchange these properties would result in many contradictions. For instance, if we equate the dog to its legs, then we must also equate the dog to its head, and by the law of equals, the legs would now be equal to the head. Interchanging the dimensions lead to contradictions, and such interchanges must be avoided to maintain consistency.
This is the reason why space in modern science is “relative” but space in Sāńkhya is “absolute”. Every dimension in the space—i.e. the branches of the tree—has a fixed meaning, which cannot be interconverted if we have to avoid contradictions.
The Meaning of Directions in Space
Using this understanding of space in Sāńkhya, we can discuss the controversy around flat and round Earths. Planetary systems in Vedic cosmology are “flat” surfaces. The bhūloka (of which the Earth is a small part) is a flat surface. This flatness leads to much controversy among people who compare this to the “round” earth. In order to explain this flatness, without creating a conflict with our observations of “round” earth, some earlier interpretations have equated bhūloka with a projection of the solar system. Such an interpretation, however, misses a very deep point about the nature of space in Sāńkhya, namely that its dimensions or directions have no relation to those that we see.
Going “up” in Sāńkhya means rising in sattva-guna by which the gross material body comprised of details disappears, and only subtle matter remains. In fact, the living entity is given a new kind of body in which what was previously subtle (e.g. the mind) now becomes gross (e.g. the body). Thus, a higher living entity has a gross body comprised of ideas. Similarly, going “down” in Sāńkhya means adding more material details to the ideas, and a living entity is now accorded a body in what was previously gross now becomes subtle. The matter comprising my gross body becomes the ideas in someone’s mind, and a new gross body with more details is produced. Since the details are created by tamo-guna and rajo-guna, the lower parts of the universe dominate in tamo-guna and rajo-guna.
Going “down” means creating more material structure and relationships with other objects. Going “up” means reducing the material structure and relationships to other material objects. The material structure is produced by tamo-guna and the material relationships are created by rajo-guna. Thus, living beings in the higher planetary systems are reducing the extent of their material bodily manifestation and its relationships to other material objects. Similarly, living beings in lower planetary systems are creating even more intricate material technology and life is even more entwined with this material intricacy. Those in the higher planets are, therefore “detached” from the material enjoyment and those in the lower planets are similarly more “attached” to material enjoyment.
What is “Flat Earth” Really?
The flatness of the bhū-loka represents two dimensions—tamo-guna and rajo-guna which denote the internal structure (the complexity of a macroscopic object) and external relationships (information exchange between objects) respectively.
At the center of this space is the instance of the higher planetary system called the Meru Mountain. This “mountain” is higher than the rest of the bhū-loka not as a physical height but in the sense that it is created from sattva-guna which is “higher”. At the top of this mountain are all the instances of demigods, which representatives or “ambassadors” of the demigods in the higher planets, created through the is-a process. These demigods are also more abstract compared to the other living beings in bhūloka—which means that their bodies are not as complex as our bodies, and their material interactions are fewer.
All distances in the bhūloka are measured relative to this “center”, which constitutes the “origin” of the space. Thus, going closer to the center entails lesser material structure and relationships, and going outward means greater material structure and relationships.
The “outward” regions of bhūloka are more complex (in structure and relationships) in a specific sense, namely that they have bigger bodies, their houses are bigger, their cities are bigger, and their countries are also bigger. Similarly, to communicate information in this material region, they have more veins and nerves in their bodies, more doors in their houses, more roads in their cities, and more flights between their countries. The outer regions keep doubling their sizes relative to the previous region, which means the size of the material entities keeps quadrupling (a surface that has twice the radius has four times larger area). Their growth in complexity emerges due to their increasing sizes.
Contrast this method of increasing complexity with the one that involves going “down” in the universe. In going “down”, we make the same object more intricate. The bodies in the lower planetary systems are therefore more “dense” relative to the bodies in bhūloka. Owing to this “density” every contact between two material objects creates many more atomic exchanges or sensations. The simple act of touching will produce fewer sensations on Earth and far more sensations in a lower planet. Since the pleasure of sensation is proportional to the number of atomic sensations, as the number of sensations increase, the pleasures accompanying those sensations increase proportionately.
There are thus two ways in which to grow complexity by increasing sizes or density. The outer region of bhūloka increases the size, while the lower regions of the universe increase the density. This constitutes the difference between “outward” and “downward”.
Information and Complexity
The two dimensions of the flat earth are the two ways in which we characterize complexity—by its internal structure, and by the interconnections between these structures. This is a technical definition of space as a measure of complexity in matter. Go towards the center and the complexity reduces. Go outward from the center and the complexity grows. The “distance” from the center is not physical; it is a measure of complexity. This is a different kind of space in which distances represent a measure of complexity, not length.
We can add information by consuming more space—i.e. making the tree broader—and this corresponds to going “outward” in a “flat” earth. We can also add information by elaborating each idea in greater detail—i.e. making the tree longer—and this corresponds to going “lower” in the hierarchical direction. Similarly, we can reduce information and complexity in a material system by going “inwards” and “upwards”.
These words—“inward”, “outward”, “upward”, “downward”—have commonsense meanings often used to describe our psychological state. For example, a person who intends to become materially detached is advised to go “inwards” and “upwards”. Those who are going “outwards” and “downwards” are similarly getting more attached. These directions are not metaphors. They are rather an accurate description of the material position in a different theory of space—not the physical space.
Four Descriptions of Material Space
What I described as “complexity” above (as the internal structure and interrelation between objects) is perceived by the senses of knowledge and action respectively. Beyond these senses is the Antahkarana or the “inner organ” which has four parts—mind, intelligence, ego, and mahattattva. While the senses perceive the above complexity as sensations, the mind perceives it as meanings. Thus, what we call the two types of “complexities” above is also perceived in the mind as structure and functions. Beyond the mind are three other descriptions perceived by intelligence, ego, and mahattattva—each of which has two aspects similar to that of the mind: internal and external.
The intellect performs judgments of truth and false. These judgments can be based on two criteria broadly called rationalism and empiricism. Rationalism refers to the truth condition in which the meaning of a proposition is internally consistent with other such propositions called axioms. A mathematical proposition is true based on such consistency, and the “truth” of such a proposition depends on the truth of the axioms themselves. If the axioms are false, then despite proving that the proposition is true, we have only proved that is it consistent with the axioms. To prove whether the axioms themselves are true we often resort to an external confirmation—i.e. experience or empiricism. Something may be internally consistent, but we have to show that the ideas on which it is based are also compatible with the world of facts. The intellect performs these two kinds of truth judgments—assessing whether the claims are consistent with axioms and facts.
If the claims are consistent with the internal axioms of a person, we can conclude that the person believes in his claims and therefore we would caveat it with the warning “to the best of my knowledge”, “in my opinion”, “according to my understanding”, etc. If the claims are inconsistent with the facts, we would say that the person believes in what he or she is saying but they are factually wrong. If, however, we realize that the claims are internally inconsistent then we would say that the person is “confused” or “deliberately lying”. The function of the intellect is to determine which of these the case is.
Higher than the intellect is the ego, which perceives intents. If I utter a sentence such as “the moon has dark spots”, the mind cognizes the meaning. But the ego then asks: Why did I say this? Am I implying that the moon is ugly because it has dark spots? Or am I indicating that even something as beautiful as the moon has some dark spots which would mean that every beautiful thing will have some ugliness in it? Or maybe I mean that the dark spots in the moon are enhancing the beauty just like dimples and moles can give the face more character? What was my real purpose in uttering the sentence? Was it to criticize the moon’s beauty, resign to the fact that everything in the world is flawed, or imply that the beauty of the moon is heightened because it has got some dark spots?
The ego is also a sense, but it grasps the connotation rather than the denotation. Connotation, like denotation, also has two dimensions—one internal, which we call “intention”, and another external, which is the external “purpose”.
For instance, you can figure out the internal intent of “the moon has dark spots” depending on whether the sentence is uttered in a critical, resigned, or appreciative tone. The sound of the sentence exists physically. From this sound, the ear extracts pitch and tone. The mind then gives these properties meanings. The intellect then decides if they are true. The ego then determines the intent underlying the sentence’s utterance based on the tone in the utterance. There is also an external purpose implied in my words namely that based on my utterance I intend to do something about it. For example, if someone said “this carpet has many dark spots” one conclusion may be that I’m going to clean the carpet or ask someone to clean it, or I am implying that it should be cleaned.
Finally, the mahattattva, or “moral sense” decodes the morality of the utterances, and also has internal and external components. The internal component judges the nature of a person or whether they are good or bad. The external component only judges the rightness or wrongness of their actions. Thus, I might judge a person to be normally evil but specific actions good, or judge a specific action to be bad but the person to be generally good.
What is Two-Dimensional Space?
The entire subtle body comprised of the senses, the mind, the intellect, the ego, and the mahattattva, therefore, presents itself as a two-dimensional space, but all these spaces are stacked one atop the other connected by prāna, which creates or manifests the lower space from the higher space. As we have seen earlier, the perception of the material world by the subtle body is called madhyama. Each organ in this space measures the world in two ways—internally and externally—thus creating a two-dimensional space.
The “flat earth” described in Vedic cosmology corresponds to this subtle perception created from rajo-guna and tamo-guna. While there is a third dimension of sattva-guna, this dimension indicates a “higher” position in space becomes the “vertical” dimension. In the vertical dimension, we can connect the lower space to the higher space. Similarly, we can also see a third dimension in each of the tiered spaces. For example, mental ideas are not limited to how I perceive an object and how I want it to be used; these ideas can also be based on received knowledge, or “I was told to view the world this way”. Similarly, intellectual evidence is not limited to reason and experience, but the third type of evidence (called the word of the authority) is also considered evidence. Similarly, my intents can what I want to understand and how I want to do things, but there is a higher kind of intent in which I’m following the command of an authority. In this case, my intention is not truly my intent, although it has become my intent due to an authoritative command. Finally, my moral judgments of right and wrong may not be defined in relation to my perception if these judgments are based on laws and rules previously enacted by an authority.
Many people normally ignore the role of authority in knowledge acquisition, the judgment of truth, goal formation, and moral conscientiousness, because we consider everyone as “equal” in modern society. And due to this rejection of authority, the present world appears flat even though there is a hierarchy even in the present world.
Each of the senses of knowledge and action also detects two properties, but a third property often remains hidden. For example, the ear detects pitch and tone, which we call amplitude and frequency, which are then used to construct a word. The fact is that due to many accents of speaking, the words are not exactly reducible to amplitude and frequency, and yet, this reduction is dominant in all mechanical devices which try to recognize the language just based on frequency and amplitude. Similarly, the eyes detect brightness and color, which are then used to construct forms. The fact is that due to the use of different fonts, color and brightness are not adequate to understand the form, and yet, we presume that all forms are derived through color and brightness perception.
In many ways, the three-dimensional world is reduced to two dimensions in the subtle body because we are unaware of the hierarchy or we reject hierarchy.
Why the World Appears Three-Dimensional
The picture, however, changes suddenly once we cross the subtle body into the gross body. The gross matter comprises the five gross elements called bhūta. For instance, the eyes perceive color and intensity (two dimensions—which are called tanmātra and reside in the subtle body) but the color itself can only be represented completely using three types—e.g. cyan, magenta, and yellow. Similarly, taste and smell require three fundamental types—bitter, sweet, and sour. Unlike the subtle body whose properties are often reduced (at each tier) to only two dimensions due to rejection of hierarchy, the properties of material objects require at least three dimensions (for each tier and for each type of property).
We can thus give a sensual description of vision using only two properties—e.g. color and intensity (the tanmātra)—but to describe the color we need at least three types of colors. Thus, the space that seemed two-dimensional for the senses and the mind becomes three-dimensional for the external property values. Owing to this fact, the gross material world is perceived to be three-dimensional by each of the senses, while the subtle world is perceived to be two-dimensional by each of the subtle organs in the Antahkarana. Ideally, even the subtle world is three-dimensional, but we ignore or reject the third dimension.
It is important to note that the three dimensions of color are not the same three dimensions of taste or smell. Rather, each property (tanmātra) needs three dimensions. Even if you shut your eyes, the sound will appear three-dimensional. If you shut your ears, you will still see a three-dimensional world using your eyes. Each sense is perceiving a different three dimensions, which are combined in our perception.
In the combined picture, the world appears to be a single three-dimensional space—creating the impression that we are living in a box when the truth is that each of the senses is emanating three branches (the properties) which in turn are emanating three branches (their subtypes). E.g. the sense of sight is emanating three branches—form, color, and intensity. The color branch is emanating three branches—e.g. cyan, magenta, and yellow. The “space” of the subtle sense, therefore, seems two-dimensional (due to rejection of ideological hierarchy), but the world seen by the senses is three-dimensional (because we are unable to reject sensual hierarchy). To us, who are absorbed in the sense perception, therefore, the world appears to be a box of three dimensions. And yet, if we formulated a scientific theory of perception then that world would be seen as a tree of many dimensions. The senses of knowledge and action would be two dimensions by which we can perceive and act, but these are ineffective without the third dimension called the mind.
The Four Ethers and Their Dimensions
In an earlier post, I described how the Sāńkhya philosophy presents the universe as four ethers—vaikhari, madhyama, pasyanti, and para. We have now seen that vaikhari is three-dimensional and madhyama appears to be two-dimensional although there is a third dimension that remains hidden. Similarly, the pasyanti ether—which comprises the material desires of the living being—appears to be single dimensional because all these desires are prioritized and appear one by one because the living entity is incapable of desiring more than one wish at a time, and from the standpoint of the living entity’s will the universe appears single-dimensional—i.e. a personal trajectory of evolving desire. Finally, the para ether—owing to the fact that it lies outside the material space, although not outside time—becomes a zero-dimensional space (i.e. outside material space).
The para space is zero-dimensional. From it, the pasyanti one-dimensional space is created. From the pasyanti, two-dimensional spaces called madhyama are created. And from there three-dimensional spaces called vaikhari are created. The world at the level of vaikhari has 3-dimensions. The same world at the level of madhyama has 2-dimensions. The same world at the level of pasyanti has only one dimension. And if we see the world from the level of para then it has zero dimensions—i.e. it becomes a point.
Karanodakaśāyī Viṣṇu (who creates the numerous universes in Vedic cosmology) sees the universes from the para space, and each universe is a point for Him—i.e. zero-dimensional—which are described as “mustard seeds” in the Vedic texts. These “mustard seeds”, however, are embedded in another three-dimensional space called prakriti which comprises three modes of nature in their most primordial form.
Dimensions are a Function of Our Perception
In one sense, everything is created from three modes of nature, and therefore the world always has three dimensions. And yet, our perception only reveals a different number of dimensions. For instance, madhyama has three dimensions if we include the vertical dimension created by authority. However, it seldom appears in our perception because we keep rejecting the method of knowing, judging, intending, and moralizing based on authority. Those who can accept authority, have a three-dimensional mind. Those who reject authority have a two-dimensional mind. Thus, while the madhyama space is a three-dimensional space, it appears to be two-dimensional to most people.
Similarly, the different souls are covered by māyā in pasyanti and while they can perceive their desires (which create the succession of their experiences) they do not normally perceive the desires and individuality of other living beings. We call this the lack of “empathy” in which a person considers himself alive and the world just objects. The pasyanti ether is also three-dimensional if we can see all the other living beings but we don’t. Common examples of such lack of vision are considering that trees, mountains, rivers, and land are “lifeless”. As this vision is further clouded, we consider that animals, birds, fishes, etc. are not living beings just like us. And as the vision is further clouded, we objectify and dehumanize even other human beings. Thus, successively the pasyanti ether includes only our personal desires and it appears to be single-dimensional.
Finally, even the para ether is three-dimensional as it contains all the universes like “mustard seeds” or points, but to know that this space is three-dimensional, we would have to see all the other universes. If our consciousness is focused on a single universe, then space will appear to be zero-dimensional—i.e. a point.
In the material vision, therefore, space expands from zero-dimensions to three-dimensions, although the space is always three-dimensional. These dimensions are however not physical: they denote properties that are used to distinguish and count. Color and taste are not the only properties; meanings, truth judgments, intents, the morality of an action, are successively deeper “material properties” too.
The Model of the Universe in Vedic Cosmology
Vedic cosmology—as understood in light of Sāńkhya philosophy—is a very sophisticated science. Unfortunately, when this science is not understood, a variety of misconceptions (such as flat vs. round earth) are created. The world we perceive as sensations is indeed three-dimensional. The world we perceive at the level of the mind is two-dimensional under material conditioning but three-dimensional in a hierarchical social structure. The world of subtle and unmanifest desires seems one-dimensional to the selfish. And beyond each universe is a space called prakriti in which the entire universe is zero-dimensional. And yet, these dimensions are only products of our limited perception because the material universe is always three-dimensional due to the three modes of nature.
The science of Vedic cosmology goes far beyond the present material science which is focused on simply the sensations and creates the impression that the universe is a single three-dimensional space when there are as many three-dimensional spaces as there are sensual properties even at the level of sense perception.
The description of the universe in Śrimad Bhāgavatam and other Purāna is at the level of madhyama or subtle body where the vertical dimension is various planetary systems and each planetary system is itself “flat” because the differences between different living entities (relative to the differences with living beings in higher planetary systems) are very small. The world is not actually flat if we can organize the society hierarchically such that there is a hierarchy of authority in knowing, judging, intending, and moralizing.
The flatness of the Vedic cosmological models has nothing to do with the “flat earth” theories that preceded Copernicus in which the earth was regarded physically flat, although it is possible that as the Vedic descriptions spread to various parts of the world, but the accompanying science did not spread proportionately, or was lost in due course of time, a misconception about the earth being physically flat was propagated widely and incorporated into other religious cosmologies as the Biblical cosmology.
Only when Vedic cosmology is understood in light of a theory of material nature—i.e. Sāńkhya—that such misconceptions can be corrected. Otherwise, Vedic cosmology appears to be a source of many confusions, as seems to be the case presently.