Explanation by: Ramananda Prasad
The dictionary meanings of the most important word "Purna" in this verse are: full, whole, complete, boundless, accomplished, powerful. The word Anant (limitless) has also been used to describe Brahman in Upanishads and Ramayana. Therefore we have chosen the word limitless or infinite. Mathematically, the word "limitless" fits better than "complete" or any other word to describe the indescribable Brahman in our opinion. Taittreeya Upanishad (verse 2.1.1) defines Brahman as Satyam (existence), Jnanam (consciousness, Chitta), Anantam (boundless) Brahma. This Upanishad also states Brahman is that from which everything comes from, is sustained, and into which everything enters into in the end (verse 3.1.1). Brahman desired let Me be many (verse 2.6.1).
Looking at the literal translation, a new student or any first time reader of Vedanta can get confused. But, as we will see, this verse is very profound. It is so profound that some one said: Let all the Upanishads and Vedic literatures disappear from the face of the earth, I don't mind so long as this one verse survives and remains engraved in the mind of even a single individual. This is not an ordinary verse. It contains the Vedic vision, the universal Truth of oneself. It answers the fundamental question: Who am I and how should I live in the world?
Everything is limitless, infinite Brahman.
The first part of this great mantra says that everything, known objects of the world or unknown spirit (Atma), is nothing but the limitless Brahman. Gita also says in verse 7.24: Everything is Krishna or ParaBrahma Paramatma. There is nothing that is not Brahman. There is Brahman only and nothing else in the universe and that Brahman is limitless, infinite, one of a kind, and the source and sink of the entire cosmos.
Our experience indicates that all the objects that we see seem to be limited in space, time, and in many other ways. Then how can everything in the universe and the world be unlimited? Atma or spirit is considered limitless, but how can visible objects, such the world and our bodies, be called infinite? Can we call everything as infinite? The ocean can be called limitless, but not the waves. Some waves are quite large, some are small, but all are limited in time and space. The waves appear limited as long as we look at the waves and ocean as separate or "dual" entities. If we consider the wave as part and parcel of ocean or consider both as water only, then the wave is limitless like the ocean. From a non-dualistic viewpoint if ocean is limitless, so is the wave, because both the ocean and the wave are a single, non-dual entity. Thus from a dualistic view point, the wave "appears" incomplete, and limited, but is really infinite as the ocean itself. Thus, if there is only a single entity, then the question of one being infinite or complete and the other limited or finite does not arise at all. If we consider we are not the body, but the infinite spirit residing in the bodies, then, we are limitless and infinite.
Duality is apparent, not real.
The negation of duality means negation of the reality of duality, but not the negation of the experience of duality. The experience of duality that we see in real life is apparent or relative, called unreal in Vedanta. From a dualistic viewpoint, a small wave is afraid of being swallowed by the large wave and prays to the ocean for protection from large waves. This is what prayers and worship are. From a non-dualistic point of view, there is no such fear. Everything in the world is an interaction, a play, a cosmic drama, only. Vedanta acknowledges duality as apparent -- not real -- experience of difference between various objects. The Unity appears diversified. The experience of non-duality brings joy, bliss. Even a temporary escape from duality and the experience of non-duality during Samadhi (or superconscious state of mind) brings bliss and peace. The literal elimination of duality in Samadhi is temporary and beyond easy reach of everybody. A complete and full negation of the reality of duality has a permanent, wonderful, blissful, effect on our entire psyche.
The experience of duality does not create problem as long as we fully understand that duality is apparent and not real. And I am not different or separate from the world, and the world is not different from me. Everything is Brahman only. The limitless, infinite or non-dual Brahman also means that no entity other than Brahman exists in the cosmos. Brahman is both the creator and the creation. In other words, Brahman is both the material and efficient or instrumental cause of the creation, the cosmos. There is no other cause or existence, except Brahman.
Brahman is both the material and efficient cause.
Vedanta cites two beautiful examples of how one and the same entity can be both the material and instrumental cause of creation. One example is that of the spider who creates its web from the material within itself. The spider is both the creator and creation, the web. The entire creation, both visible and invisible, comes out during the creative cycle and gets dissolved or sucked into Brahman during great dissolution (Gita 9.07). Brahman brings the material from within, weaves the beautiful and wonderful tapestry called the cosmos, and takes it all within again and again, just as the spider does.
Another example is the dream world where the dreamer is both the material and instrumental cause of his dream world. The cosmos is created as the cosmic mind's dream creation. When we dream, both the subject (or the creator) and the objects, the dream world (or the creation), happen to be the dreamer himself. The dreamer's mind is both the material and creative cause of the dream. When we fight a dream-war in a dream-battlefield, the warriors on both sides--- the bombs, bullets, rocky terrain, the land mines, nurses, ambulance and medical supplies --- are all none other than the dreamer himself.
Thus, the first half of this great Upanishadic verse beautifully tells in a nutshell that the limitless Brahman is both the material and efficient causes of creation. The creation comes from the creator, and both the creation and the creator are infinite and the same. There is no entity in the cosmos other than the creator. He has become all, and He is all, and He is in all. Om purnamadah purnamidam purnaat purnam-udacyate.