Discontinuous space

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    Akhil Babu

    Hare Krishna Prabhu. Is space continuous or discontinuous? After reading your articles and Quantum meaning I am confused about the continuity and smoothness of space. I am  not sure whether I have misunderstood what what you have written or not. It would be helpful if you give some clarity to this topic. In Nyaya and Vaisheshika, I have read that paramanu is only for 4 elements(Prithvi, Ap, Tejas, Vayu) and not for Akasha. Even if there is Akasha paramanu is that finite or does it have infinite subtle aspects? In Madhvacharya’s Vedantha Darshana, Acharya doesn’t accept the finite nature of paramanu. He says that the paramanu is infinitely divisible. He classifies material space into three: Avyakruthakasha (Eternal causal space), Bhutakasha(Temporary manifested space), Padartha Avayava(Quantum of space occupied by a paramanu). But this space inside paramanu is not finite.

    Ashish Dalela

    Space is both infinitely divisible and discrete (or discontinuous). You have to think of an inverted tree. A branch is one location. It is discrete. But its subdivision is the twigs and leaves coming out of it. So, both discontinuity and infinite divisibility are supported. But that divisibility is not in a straight line as in the case of modern mathematics. It is along the branches, twigs, and leaves of the tree. A straight line is discontinuous. But there are deeper-level realities not on the line that make it continuous.

    Space and matter are not fundamentally different things. In BG 15.7, Krishna says: prakṛiti-sthāni karṣhatiPrakriti is space. In that, each location is a sthāna or place. That place is also an object. And each object is pulling or pushing because it comprises guna and based on our guna (e.g., the guna of our senses) there is a natural likeness and dislikeness to that thing. Likeness attracts and dislikeness repels. So, if your senses have some guna, then the senses will be automatically pulled toward some objects like an irresistible force. So, the same thing is object, space, and force. This is modal behavior. The space mode of something is in sattva, the force mode is in rajas, and the object mode is in tamas.

    All five elements are comprised of guna. Even the mind and other subtle elements comprise guna. And space is the collection of guna combinations. So, everything is discrete. But because everything can be subdivided, therefore, it is also infinitely divisible. But it is not a straight-line continuity.

    In BG 9.4, Krishna says mat-sthāni sarva-bhūtāni, which means that all bhūta have a location in Krishna. Even Prakriti has a location in Krishna. Then the subdivision of Prakriti are locations in Prakriti. In this way, there is a nested containment, just like a trunk, branch, twig, and leaf emanating out of a root. So, the parts of Krishna are discrete, and then each part is infinitely divisible.

    The term avyākṛta means unmanifest. This is just like a branch. The term bhūta means something is manifest from it. This is like a twig. Then because this twig manifests a leaf, so, there is a subdivision, which is called padārtha, which means a meaningful and purposeful part. So, because of padārtha, each bhūta becomes a space. Similarly, because of bhūta, each avyākṛta becomes space. So, it is space inside space inside space. We use three words to distinguish space, object, and property.

    For example, a room has a table which has a length. So, the room is a space, the table is an object, and length is property. But that length is another space, in which there are smaller objects, which have their own length. In this way, we talk about discrete and continuous. Context decides what is called a space, object, or property. When the context is beginning with the room, then the room is a space, the table is an object and its length is property. But if we make the table the context, then the table is space, parts of the table are objects, and they have their properties. So, the same thing is spoken of in three different ways.

    Akhil Babu

    Thank you so much Prabhu. This has solved many confusions I had. Now there is more clarity to my understanding of space.

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