Thursday, September 17, 2015

Can there be two infinities?

Vivekananda once said to one of his disciples, "There can be no two infinities.... Still further advance will show you that all things are infinite, but these infinite things are one in essence and not two. They are but different expressions of a single entity, and they must be one." This is perhaps the most clear expression of Vivekananda's opinion about the age old Vedantic debate between Advaita and Dvaita. Vivekananda did not discard Dvaita, but he always held Advaita at a higher pedestal. In simple terms, Advaita (or monism) says that the individual soul (Atman) is essentially same as the cosmic soul (Brahman). And Dvaita (or dualism) says that Atman is distinct from Brahman. Indian scholars have been debating on this for many centuries with no clear resolution in sight. 


This question of infinities also arises in mathematics and is considered to be a very important problem. In 1874, Georg Cantor provided the first mathematical proof that there could be more than one kind of infinity. Unlike usual mathematical concepts, this idea of multiple infinities is very easy to understand. Consider the set of all natural numbers (1,2,3,4,...) called 'N' and the set of even numbers (2,4,6,8,...) called 'E'. Now, clearly both the sets are infinite. The main question is : does the set E contain the same number of elements as N? It is obvious that all elements of E are contained in N and hence E must be a smaller set. But one has to be more careful when it comes to infinite sets. In set theory, if we can show that there is a one-to-one correspondence between the elements of two sets, then they are said to have the same number of elements. Now, if we multiply each element of 'N' by 2, we get each element of 'E'. Hence, there does seem to be a one-to-one correspondence between the elements of these two sets and thus, they must contain the same number of elements!

From the above example, we can well imagine how complicated the concept of infinity is! From one point of view, the set E is a subset of N and contains less number of elements. But from another point of view, there is a one-to-one correspondence between all the elements of these sets and hence, they must contain the same number of elements. So, from one point of view the two sets represent different realities (dualism) and from another point of view they represent the same reality (monism). Hence, when it comes to infinity, it is very important not to form any rigid notions and be open to other kinds of ideas which may be quite contradictory to each other with all of them being 'right' in their own way. 

One of the most famous verses from the Rig Veda is 'Truth is one, sages call it by various names.' What is important to note in this context is that the various expressions of truth may be exact opposite of each other and still be equally valid. It is not necessary that one expression be lower and another higher. Truth is not just a ladder but also a landscape. There are deep seas and high hills. Diving the ocean is as adventurous and rewarding as climbing the everest! Living in the midst of a multiplicity of life forms can be as soothing as the serenity of solitude. As AR Rahman once said, "Each one of us has our own evolution of life, and each one of us goes through different tests which are unique and challenging. But certain things are common. And we do learn things from each other's experience. On a spiritual journey, we all have the same destination."

12 comments:

  1. Comments received over email:

    Your poser and the article both are interesting.
    To your poser, philosophically, I would like to say that there are infinite-infinities. If the infinity can be restricted to one or two, it is not infinite but a finite-infinity, which is not correct. The zero itself is infinite. There is no difference in zero and infinity, only a difference in perception. If zero denotes absolute non-existence, is that absolute non-existence not infinite in itself?
    Perhaps one can say that every particle in the cosmos is a reflection of cosmos and as infinite as the cosmos itself. At the very core of that particle exists that, which cannot be defined or found. From this non-beingness emerges the beings.
    In my opinion the very existence is relative and there is nothing which is at rest. How a thing which is not at rest perceive and declare about the status of another thing? The mind unless quietened cannot perceive the Truth.
    With Kind Regards,
    RKGupta

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    1. Thank you very much for your wonderful comments! I totally agree that
      it is absurd to put a limit on the number of infinities. And as you
      rightly said, zero itself is another kind of infinity.

      Regards,
      Kushal.

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  2. Kushalji, 'Infinite' by its very connotation suggests all-pervasive or all-inclusive, meaning, there is nothing beyond it. If you envisage two infinites, your presumption s that both are mutually exclusive, as otherwise, there cannot be two but one infinite. It is fundamentally flawed and absurd to describe or enumerate 'infinite' by number. This is precisely the reason why the concept of zero (Sunya) as symbol for infinite came into existence in India, as has been pointed out by Guptaji. Infinite has no number.

    Samkhya was rich in its philosophical content but flawed in its presumption that there could be two infinites, viz. Purusha and Prakriti. Vedanta corrected the mistake by going to the source of both Purusha and Prakriti in Brahman which was described as infinite, purusha and prakriti being derivatives of Brahman. Dvaita Vedanta does not contest the above postulate of Vedanta that only Brahman is infinite. It only contends that duality exists in the state of manifestation only. It does not deny the existence of unmanifest Brahman Which is Infinite. Advaita Vedanta says that the ultimate Truth is that only Brahman exists, as the Infinite includes all existence and non-existence. Thus, on the question of Brahman only being infinite, there is no dispute between Dvaita Vedanta and Advaita Vedanta.


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    1. Asishji, thanks a lot for your comments! Here is my response:

      "If you envisage two infinities, your presumption is that both are mutually exclusive, as otherwise, there cannot be two but one infinite. It is fundamentally flawed and absurd to describe or enumerate 'infinite' by number."

      That is precisely why I find Vivekananda's idea of infinity being 'one' to be absurd. As Guptaji has said, infinity must itself be infinite. Also, the idea of two infinities having to be mutually exclusive is based on our idea of rigid bodies. But reality is much more porous.

      "Samkhya was rich in its philosophical content but flawed in its presumption that there could be two infinites, viz. Purusha and Prakriti. Vedanta corrected the mistake by going to the source of both Purusha and Prakriti in Brahman which was described as infinite, purusha and prakriti being derivatives of Brahman."

      There is no concrete reason to believe that Vedanta is a better theory than Samkhya. It seems to be just a matter of personal preference.

      "Thus, on the question of Brahman only being infinite, there is no dispute between Dvaita Vedanta and Advaita Vedanta."

      I am not sure if this is true. Can you please give a reference?

      Thanks,
      Kushal.

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    2. Kushalji, you are surely familiar with the word: Ekamevadvitiyam (Only one and no second). This is often used to describe infinite Brahman or a personal god as representing all-pervasive Brahman. Here, the word 'one' is used to the exclusion of all others, meaning that we all are covered in that ONE. Vivekananda used the word one to imply that Infinites cannot be two but one, and that ONE is all inclusive. I do not find anything wrong in that expression. If he had used the word ONE in the sense of Abrahamic religions to exclude all others from that ONE, you would have been justified to find fault with his expression. But Vivekananda's ONE was all inclusive. In Abrahamic religions, it is blasphemous to call yourself or anyone else as Infinite or God while to Vivekananda, all that exist is infinite and God in reality. Herein lies the difference between Abrahamic ONE and Vivekananda's ONE.

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    3. Asishji, every person including Vivekananda is certainly free to have their own philosophical preferences but there is no concrete reason to believe that one preference is better than all others. In fact, there are many similarities between the concepts of Abrahamic religions and that of Dvaita. But yes, this does not mean to say that one is free to believe whatever comes to ones mind. What this says is only that there are infinitely many possible ways of expressing the truth with none of them being higher or lower and some of them appearing to even be in opposition of each other.

      Thanks,
      Kushal.

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    4. "I am not sure if this is true. Can you please give a reference?"

      Several thousands of pages have been written by Sankara and his followers, Madhva and his followers and Sri Ramanuja and his followers in support of Advaita Vedanta, Dvaita Vedanta and Vishisth-advaita Vedanta. Their dispute centres on interpretation of Brahma Sutras of Badarayana (Vedavyasa), which are a compilation of upanishadic verses referring to Brahman. You may go through Sri-Bhasya of Ramanuja and Sankara Bhasya of Brahma Sutra to know their interpretation of 'infinite Brahman' and also the Chhandogya upanishad concept of Tat-Tvam-Asi' (That thou art), provided you have time & so much interest. Each school refutes the reasoning of the other schools while interpreting Brahman. It is Gita that takes an unified and integral approach and, therefore, most appealing to lay persons. Therefore, my sincere advice to you is that you read Gita and draw your conclusion.

      "What this says is only that there are infinitely many possible ways of expressing the truth with none of them being higher or lower and some of them appearing to even be in opposition of each other."

      In verse 12.12, Krishna says that knowledge is superior to practice, meditation is superior to knowledge and action without desire (renunciation of the result of action) is superior to meditation. Thus you will see that Krishna made a distinction and all the authorities in spiritual domain, named above or not named, swear by what Krishna said in Gita. I have no difficulty in accepting the proposition that Karma without desire is the highest goal in our life, and that the dispute about dualism, monism and qualified monism, belonging to the domain of knowledge, is less significant, going by Gita.

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    5. > You may go through Sri-Bhasya of Ramanuja and Sankara Bhasya of
      > Brahma Sutra to know their interpretation of 'infinite Brahman' and also the
      > Chhandogya upanishad concept of Tat-Tvam-Asi' (That thou art),

      I certainly don't dispute their interpretations. As far as I understand, what Dvaita says is that Atman is different from Brahman but not that Atman is finite and only Brahman is infinite. I will be glad if you can kindly point to a particular verse from Dvaita literature which says that Atman is finite.

      "I have no difficulty in accepting the proposition that Karma without desire is the highest goal in our life, and that the dispute about dualism, monism and qualified monism, belonging to the domain of knowledge, is less significant, going by Gita."

      I have no problem with this proposition that Karma without desire is the highest goal of life. But not every school of thought agrees with this. Advaita says that Jnana is the highest and Dvaita says that Bhakti is the highest. And as you have also said, all these schools derive support for their theory from the Gita itself. So, what we choose among these is only our personal preference. And let us not forget that there could be a fourth and a fifth and many more interpretations and preferences.

      Thanks,
      Kushal.

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  3. I wish to quote a Zen poem by D.I.Suzuki on the subject, which perhaps is relevant:
    ADVAITATA HI PARAM GYAN HAI,
    AUR PARAM KARUNA HAI,
    US EK KO HI,
    SAB ME DEKHNA.
    (Attaining the state of non-duality is the highest state of knowledge and to see that One in all that exist is the highest state of compassion)
    Regards,
    RKGupta

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  4. Thanks a lot for sharing these verses! But I hope DI Suzuki will not insist on Dvaitins or people following other paths to agree with him. :)

    Thanks,
    Kushal.

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  5. Everything starts with Zero and ends with Zero. If we take a car and move it with high speed the car will be everywhere. But just fast above from our reaction time, there will be no car. We starts with 0 1 2 3 4 5 6 7 8 9 10 11......................... oo 0 . They are just like clock. A bad person Ravan also get Moksha and a good person Saint also get Moksha.

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    1. Very well said! This concept challenges 'common sense' but is true nevertheless. Thanks!

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