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The Mathematics of the Self
Om Purnamadah purnamidam Purnaat purnam udachyate.
Purnasya purnam adaya Purnameva avasisyate.
Isvara, pure original consciousness (adah), is full. Jiva, Isvara plus a subtle body (idam), is full.
Jiva is seemingly born from Isvara (by avidya) like a mirage is born on the desert.
Therefore if you add jiva to Isvara or subtract jiva from Isvara, Isvara remains.
Reality is only non-dual consciousness.
Mathematics of Atma
The invocation is not a good mantra for beginners because the literal meaning – if you add jiva to Isvara or subtract jiva from Isvara, Isvara is unaffected – creates confusion. So you need to take the implied meaning: brahma satyam, jagan mithya. The implied meaning is necessary because the Upanishad does not state directly that jiva’s and Isvara’s bodies are apparently real (mithya). They have to be arrived at from an analysis of the implied meaning of the words. Fullness can’t come from fullness, because there are not two fullnessess, i.e. consciousnesses/existences.
This problem is caused by the use of transitive verbs such as “comes from, is born, adds and subtracts,” which reinforce the belief that freedom can be gained by action.
Here is the logic: when the jiva is present the body exists, but when the jiva isn’t present the body doesn’t exist for it, so the body is not real. It is seemingly real, dependent, mithya. Ask yourself if you have a body if you don’t exist, i.e. aren’t conscious.
The direct meaning of jiva is consciousness plus a body-mind-sense complex, meaning a human being. So this definition doesn’t work. The implied meaning is jiva minus a body-mind-sense complex, which exposes the identity of jiva and Isvara.
Consciousness (Isvara) as the Creator plus the creation is the direct meaning of Isvara, which also doesn’t work, because the world is included with Isvara, which is free of the Creator and the Creation. The implied meaning, Isvara minus cosmos and jiva minus the five sheaths works because both jiva and Isvara can’t operate their instruments unless they are conscious, which they borrow from consciousness. They are both actually limitless ever-full consciousness. If they weren’t, their upadhis wouldn’t function and there would be no world.
Isvara is full (fills everything) and jiva is full. This statement creates a problem because jiva has a body and doesn’t fill anything. Nobody knows about Isvara, because nobody has seen Isvara, so the statement about Isvara needs to be accepted on the basis of faith in the scripture (sraddha). Because reality is non-dual, they can’t both be full. But accepting the identity on faith doesn’t produce moksa. I need to know I’m free. Jiva needs to understand what it means.
Jiva is born, but Isvara is not born. Isvara is sat, existence. The problem is that the Upanishad does not explain how Maya gives birth. It resorts to logic to show that jiva’s body and Isvara’s body (the cosmos) are mithya and that the essence of both bodies is satya, limitless existence/consciousness.
You can’t say that Isvara was born, because Isvara exists in all periods of time, before the past and after the future. Jiva is “born” out of Isvara. What kind of a birth is it? If jiva is full, how can it be born? It is “born” only from the standpoint of its gross and subtle material bodies. Jiva is Isvara plus a reflecting medium, a subtle body, and the reflection.
For instance, pot-space is “born” out of universal space, which is unborn. It is a matter of experience and knowledge that there are not two space elements. If there were, there would be two or more existences because space is a material element that depends for its existence on existence/consciousness, which is not possible. It is also a fact that there are not two existences. Jiva’s physical body is born of Isvava’s macrocosmic physical body – material elements – so there is even identity at that level because there is only one cosmos.
1. Poornamidam (objects are whole and complete). Poornamadah (the subject is whole and complete).
The pronouns “that” and “this” are reversed in this mantra. Idam, this, should refer to the subject which is near; and adah, that, should refer to objects which are away from the subject. But this mantra is given from the jiva’s point of view, so the relationship between subject and object has already been reversed by Maya/avidya before the jiva understands that it has happened. It is duality because each pronoun excludes the other. If you look at the mantra from the Self’s point of view, the duality of “this” and “that” are included and resolved. “That” creates “this” and vice versa. In other words, they are not real, meaning they don’t stand on their own, but depend for their existence of the presence of their opposite.
The problem occurs because the Upanishad does not introduce the concept of Maya directly. So we have to infer Maya as the Bhagavad Gita does. We make the inference by resorting to the implied meaning (lakshyarta) since the direct meaning doesn’t leave us with moksa, understanding the identity of the jiva and Isvara, limitless fullness, consciousness. The keyword is “idam,” this. If it means the totality of all names and forms, the verse is true insofar if you subtract the totality, all the objects in existence, Isvara, pure limitless consciousness, remains. But subtracting the totality from Isvara doesn’t give jiva liberation. So the meaning of “this” has to be: jiva is pure limitless consciousness plus the subtle body, and moksa is jiva minus the subtle body, which seemingly limits it.
In effect the verse says, “Nothing is missing anywhere, since both the subject and the objects are complete. If you think you’re incomplete, you are taking the subject to be an object (viparaya).
Why doesn’t the verse just say, “Everything that is is existence/consciousness”? Because it contradicts our experience. We see limitation in the subject, which is actually an object and which is defective because it is an object. Objects on superficial analysis are definitely limited. Furthermore, we can’t perceive formlessness, i.e. Isvara, or Paramatma. Because we are so attached to the belief that the knowledge we have gained from our experience is actually knowledge and not erroneous knowledge in the form of beliefs and opinions, we can’t figure out how the duality we experience, and indeed experience itself, is non-dual existence/consciousness. So we are usually hostile to the idea.
Completeness, absolute fullness, is formless/limitless because to include everything it can’t have boundaries. The subject has to be formless because to establish its completeness requires another consciousness which requires another consciousness, etc. The mantra’s revelation of the formlessness of the ever-present ever-experienced “I” is confirmed by inquiry as a logical necessity for the ultimate subject, but neither the revelation nor the confirmation by logic change the fact that this knowledge is contradicted by experience. Everything seems to limit me and I seem to limit everything else. So I strive to remove my sense of limitation. The mantra removes duality by negating experience as non-real, not non-existent.
An experiential elimination of duality brought about by a special “non-dual experience” of one’s Self that resolves duality would only be a temporary resolution, not limitlessness. A fullness dependent on experience grants reality to the “before-after” duality. The mantra flatly rejects duality because it states that both the subject and object are full, formless, undivided, etc.
To teach this mantra other Upanishadic statements about the limitlessness of the subject needs to be included, including statements that it is the material cause (Taitirriya Upanishad) of the cosmos, but no Upanishad states that the subject is the efficient (i.e.) intelligent cause, because to do so would imply a duality between the Creator and its Creation. But logic demands that original limitless awareness is also the intelligent cause because reality is non-dual. So the material and the intelligence cannot be different. If the subject were not capable of apparently becoming a limited entity, the Upanishad’s statement that everything is existence/consciousness would be untrue, because it would exclude the Self’s experience as a finite entity, which is the reason scripture is necessary. But because it provisionally accepts duality, there is scope for Vedanta to remove its “sense” of limitation.
A common material and efficient cause are necessary to claim that the subject and the objects are non-separate. If you say, “The vase sitting on the table today is the same vase that was at the flea market yesterday,” the time-space duality of the “two” vases is a functional linguistic convenience insofar as both have the same material and the same creator and can’t be in two different locations at the same time. Therefore, if a creator is required, it will necessarily be limitless, etc. A dream provides a good example, not only of a single material and efficient cause, but also of effects of the cause which appear to be different but whose difference resolves in their common source. Both the dream’s substance and the intelligence shaping the dream abide in the dreamer. A dream is duality, a witnessing subject experiencing dream objects, including a dream ego/doer, which is resolved in the dreamer.
2. Poornat purnam udchyate. Completeness is born of completeness.
Completeness can’t be born of completeness, so the only kind of change that can bring about the world of experience is a seeming change, aka ignorance, i.e. failing to resolve duality by inquiry. Water undergoes no change to appear as a wave.
If you don’t include your Self, the word “this” refers to the objects produced by the subject (consciousness plus Maya). The verse says that mithya, fullness, comes from satya, fullness, i.e. borrows fullness so that it is clear that reality is non-dual, i.e. complete, formless, limitless, etc. The creation of a ring, for instance, involves no intrinsic change to the gold. Creation seemingly generates various forms out of consciousness. The relationship between subject and object is not causal, and therefore is not duality (although it looks like it is), because the cause and the apparent effect are in different orders of one non-dual reality. A cotton shirt is not caused by cotton, because both the cause and the effect are cotton.
We don’t use the snake-and-the-rope metaphor here, because an inquirer may think that knowledge only removes ignorance of the subject, whereas Self-knowledge needs to remove the belief that the world is real also. No analogy is required, because it is clear that any creation involves no substantial change, only an apparent change. Water does not cease to be water when it appears as an ocean. An ocean does not undergo an intrinsic change to become a wave, etc.
3. Poornasya purnamadya poornam evavasisyate.
Subtracting fullness from fullness or adding fullness to fullness involves no change even though the words “add” and “subtract” imply change. If you take the vase away from the clay, the clay is unchanged. If you add the vase to the clay, the clay is unchanged. So there is no difference between the subject and the objects.
In a dream I am fighting a fire with water because the fire seems to be real and can only be quenched by dream water. The fire, the firefighter and the water seem real as long as I am a prisoner of the dream state, but are resolved into the waker when the dreamer wakes up and finds itself imprisoned in the waking state. My pajamas and mattress are not charred and stained with muddy water. The dream and the dreamer are negated, leaving only me – consciousness.