Mathematical Novelties in Vedic Philosophy

This is the transcript of the eighth episode of my podcast. In this episode, we talk about a number of unique problems that arise in trying to make Vedic philosophy more rigorous in a logical and mathematical sense. I have been presenting some of these ideas while discussing the theories of creation, cosmology, linguistics, the nature of space and time, etc. But there is no single place where we have collected them so far. This is what this podcast achieves to do. I will follow this up with a few posts on the nature of numbers.

The Need for Alternative Mathematics

In some of the previous books and articles, you have argued for the need for an alternative logic and mathematics to describe the Vedic philosophical ideas. What makes you believe that an alternative mathematics and logic are needed and how is it related to Vedic philosophy?

Since Greek times, it has been believed in Western science and philosophy that the world is consistent. Indeed, logical consistency with axioms has been the bedrock of modern thinking. However, in both Vedic and Buddhist philosophy, which constitute the basis of practically all Eastern thinking, many of these fundamental ideas about logic and consistency have been disputed. For example, in the depiction of yin and yang in Taoist philosophy, the classical contradiction between opposites such as black and white is not accepted. Rather, there is black inside white and there is white inside black.

One way to understand this white inside black is to think of the concept of color, which is both immanent and transcendent to white and black. It is transcendent because there are other colors beyond white and black. It is also immanent because white and black are colors. So, when you see the two colors, there is a sense in which the property of color is present in white and black and yet it is not exhausted by white and black. Since color includes white and black, when color is immanent, then black enters white and white enters black. The reason is that color is in white, and black is in color, so black is in white.

The key idea here is that color is both immanent and transcendent to white and black. As a transcendent entity, it includes all colors, and as an immanent entity, those other colors conceptually enter inside the individual color. Therefore, even though white and black are separate colors, through the concept of color they become interrelated due to which you cannot truly separate anything from anything else in the classical logical sense.

Western thinking has been torn between these extremes of immanence and transcendence. In Platonic philosophy, the forms are transcendent, and in Aristotle’s philosophy, they are immanent. In modern set theory, the set includes the object, but the object doesn’t include the set. This was the basic point of Russell’s theory of types, in which he constructed a hierarchy of concepts to get rid of the paradoxes of set theory. However, you cannot get rid of this paradox because language operates in two modes as universals and particulars. You can call the universal concept of barbers by the word ‘barber’ and you can also call the individual barber by the same word ‘barber’. So, the only way you can solve this problem is by changing language and using one language for concepts and the other language for individuals, and by that so-called solution you will end up with a mind-body problem in which concepts are in one world and matter is in another world.

So, the basic problem throughout Western philosophy and science has been this dual nature of ideas which are both immanent and transcendent. And because the West could not deal with this problem, they created a world of duality in which two things are either identical or independent, but not related via immanence. This separation or identity is what constitutes Western logic, and it is a false idea because it is built upon the notion that the idea color is not immanent in the individual colors black and white. In a simple sense, the need for alternative mathematics arises from this dual nature of concepts as both immanent and transcendent, because it creates a logical contradiction.

The Solution in Vedic Philosophy

So how does Vedic philosophy solve this problem of immanence and transcendence?

There are two apparently contradictory statements in the Bhagavad-Gita. In the verse 6.30 Krishna says that for one who sees everything in Me and Me in everything, I am never lost to him nor is he lost to Me. So, here Krishna is saying that He is both immanent and transcendent. Then in verse 7.12 He says that everything is manifested from Me but I am not in this manifestation. Here He says that He is transcendent but not immanent. This contradiction again comes in verse 9.4 where Krishna says By Me, in My unmanifested form, this entire universe is pervaded. All beings are in Me, but I am not in them. Here, Krishna says that I am in everything as avyakta-murti or unmanifest form. And this is a murti or a form, so even the pervasive form of God is not impersonal. Prabhupāda explains in the purport that God is everywhere but He is invisible to the senses. But by loving devotion He becomes manifest, and then we can see how God is immanent.

So, mukti or liberation means that we see that transcendent form of God in the spiritual world. But bhakti means that we see that immanent form of God even in the material world. In many schools of Vaishnavism, the idea of mukti is rejected. Sri Chaitanya says: mam janmani janmani ishvare bhavatad bhaktir ahaitukik tvayi, which means birth after birth I desire your devotion. Repeated birth means I am in the material world, so I’m not seeing that transcendent form. Then how can I see God? It is because God is immanent. When we love God, then we can see that immanent representation in the soul. So advanced devotees say that they have captured God in their heart and He cannot leave.

In many places in Vedic texts, it is described that there are two primordial entities—namely, God and His energy or śakti. This energy or śakti is like a mirror in which God sees Himself. And when He sees, there is a representation of God inside the mirror. So, the God looking into the mirror is transcendent, the reflected representation inside the mirror is immanent, and there is a mutual attraction between God and His śakti. So long as this attraction exists, there is a reflection inside the mirror. But the transcendent form of God is not that reflection. So, in one sense He is transcendent and yet immanent.

You can also put this idea in a different way by saying that in each individual thing, the ideal thing is immanent. This ideal is called Paramātma Who exists inside each atom. However, as things become non-ideal, this ideal form is hidden, so it becomes avyakta or unmanifest. It is like a dirty mirror in which you cannot see the image. So, when we cleanse the mirror which is called cheto darpan marjanam or cleansing the mirror of chitta then the image is visible. The Paramātma form in the material atoms is temporary because the material world is temporary. However, in Śrīmad Bhagāvatam it is said that the Absolute Truth is understood in three ways as Brahman, Paramātma, and Bhagavan. The Bhagavan form is transcendent, the Paramātma form is immanent, and Brahman is when God and His śakti are not individuated, so immanence and transcendence don’t arise. Thus, the term Paramātma is used to describe the immanent form in matter or immanent in the soul. The form immanent in the soul is eternal, but the one in matter is temporary.

As a transcendent individual God contains as parts all the individual things. But as an immanent individual, He is inside all those parts. So, even though the parts are different from the whole, they are not completely separated from Him. Indeed, this idea that the parts are separated from the whole is called the illusion of the material world.

The problem of immanence and transcendence is ultimately a spiritual problem. But we can state this problem in secular terms as the problem of concepts. It is this one problem that appears in many forms in logic, mathematics, physics, and all other areas.

This problem has also been debated for centuries in the Vedic tradition as part of Vedānta philosophy. The Advaita system says that we should get rid of the idea that there are parts, and just consider the whole. The Dvaita system says that the whole is indeed separate from the part, but it is not completely separable. And there are many different schools that iterate over this theme in different ways. Sri Chaitanya articulated this idea of achintya-bheda-abheda tattva in which the whole and the part are separate and inseparable, and because this is a contradictory idea you cannot articulate it in classical logic. However, the issue is that if we cannot understand it, then every other thing is unknowable since every problem involves concepts that are immanent and transcendent. So, by saying that this is achintya, which means inconceivable, all knowledge becomes impossible. Therefore, we must transcend classical logic, and then the achintya can become chintya.

The essence of this transition is that there are three kinds of relations between the whole and the part. I call these relations is-a, has-a, and wants-a. For example, the concept color has a color called black. This is a relation from color to black. However, the inverse relation from black to color is different. It is an is-a relation where we say that black is a color. The has-a relation leads to transcendence and the is-a relation leads to immanence. And then there a relation of mutuality of wants-a, in which there is a mutual attraction between whole and part. If this attraction is removed, then the other two relations are also removed, and we think that there is no whole; there are just parts and these parts are independent of each other, and that ultimately leads to reductionism and materialism.

So, when I speak about an alternative logic, I mean that we must describe this tripartite relation between whole and part. Since there are three aspects of the relation it appears to be inconsistent if we think of the relation as only one thing. In classical logic for instance when we describe a relation R between two entities A and B, then this R doesn’t have parts or aspects. But we are talking about a relation that has three aspects. One aspect results in immanence, another aspect in transcendence, and the third aspect in mutuality. In one sense this is the solution to millennia of outstanding problems. In another sense, it is also the answer to the debates within Vedānta philosophy. If we can solve this problem, with the scheme I outlined, then we can bring a new view of both religion and science.

Historical Precedents of Alternative Ideas

Since this problem is so old and as you mentioned above there have been many attempts to solve it, what are some of the interesting ways in which a solution has been attempted? Does understanding these solutions tell us what to do and what not to do going forward?

Well, I have talked about the different schools of Vedānta and they are all interesting in how they deal with this issue. In Buddhism, there is the thesis of Pratītyasamutpāda or the apparent co-dependent arising out of nothingness. You can think about this using the example of numbers if you say that the opposites like white and black are like numbers +1 and -1, and these opposites are co-created from the zero. Since they are co-created we cannot separate them as independent individuals. So, we can say that they are two sides of the coin like head and tail, and the coin is the unity of the two sides. However, that coin is represented by a zero, and the co-dependent parts are +1 and -1. You could say that zero is inside all the numbers which is the immanence, and yet zero is transcendent to all numbers because it contains all the other numbers in a combined form. So, you get both immanence and transcendence, and it is, therefore, an interesting answer.

But it inevitably leads to the idea that the origin of everything is nothingness, and opposites emerge out of that nothingness. And if you can find that nothingness, then you have reconciled the opposites, but it is not a Western logical reconciliation. It is rather a reconciliation in which opposites originally sprang from nothingness and then they dissolve back into nothingness. Even to think like that we are required to reconceive logic in which nothingness creates logical opposites and absorbs them back into itself.

However, this solution in Buddhism is incomplete because how and why that nothingness expands into opposites is not described. What, for instance, causes the opposites to come out of nothingness when they were previously reconciled within nothingness? Similarly, what causes the opposites to go back into nothingness when they were already separated? If nothingness is all that exists before the opposites were separated, then the creation of the opposites and then the merger of the opposites become unexplainable. The Buddhist solution becomes incomplete because it doesn’t explain creation and annihilation. Therefore, you can build a transcendent philosophy but not a real science.

In Vedic philosophy, this so-called ‘nothingness’ is called Pradhāna which is the pre-separated state of matter. It is like a zero but this zero contains all the opposite numbers within itself. And the opposites are split from this unity by the effect of time. Similarly, by the effect of time, the opposites collapse back into the unity. This so-called ‘nothingness’ is the primordial Sakti or creatrix and the time is called Siva or creator. The manifest world is the combination of the creator and the creatrix, or time and space. They are identified as male and female, so these are personalities. We will see the reason for this personalization later, which is that ultimately choice is involved in creation and annihilation.

We can also say that Pradhāna is the origin of space, and from this origin, the space of opposites expands forming the manifest world of opposites. It is like a big bang where space expands from an origin and the expanded space has the opposites. The trigger for this expansion is time, and there is hence a big crunch when it all collapses back inward. Since time is cyclic, there are innumerable repetitions of big bang and big crunch. The crucial problem is how to conceive the existence of a zero. This zero is not ‘nothing’ in the sense of non-existence, but the combination of all existents. It just so happens that the existents are opposites, so their combination is logically like nothingness.

Now this creates a problem of logic because this zero is neither of the two opposites. If the two opposites are conceived as true and false, then the primordial state of matter is beyond classical logic because it is both true and false. So, this introduces logically forbidden states and the universe springs from this logically incoherent state. That’s why you can see in Zen and other forms of Buddhism the use of paradoxes by which you can conceive of this logically paradoxical state but not in terms of classical Western logic. Since this is the state from which everything springs, one must solve this paradox before you can begin anything. In short, you must deal with the problem of origin right at the outset.

Cognitive and the Precognitive

It seems like you are talking about a precognitive state of matter from which the cognitive state springs. I recall you talking about manifest and unmanifest states of matter, and this unmanifest state is the primordial possibility of being the entire universe. Does this have something to do with the fact that the conscious state springs from the unconscious state? In Vedic philosophy, the deep sleep state is identified as being prior to the dreaming and waking states, so this primordial state of matter would seem to correspond to deep sleep.

Yes, the deep sleep state is also material, but it is a precognitive state of matter in which there are no distinctions; just a singular yet unending repository of everything. In psychology since the time of Freud people have spoken about how the conscious states spring from the unconscious states, which is why this unconscious is very important.

The destination of Buddhism is this deep sleep state, which is a state devoid of distinctions. The distinctions are cognitive and conscious but the state of matter prior to these distinctions is non-cognitive. But since the cognitive state springs from this non-cognitive state, we must understand its nature before we can understand cognition. In other words, there can be a logical description of the world that contradicts classical logic. Or, we must go beyond the classical logic and speak about a new category like both to understand it.

Enfolded and Unfolded Order

You said above that time splits the duality out of a unity and then collapses this duality back into the unity creating a cycle of creation and destruction. How do we understand this time and how should we conceive this causality of cyclic creation and destruction?

As we have discussed in earlier podcasts, space is like a tree, which means that there is a root, which constitutes the everything, and then there are branches which split from this everything, and these branches are again split, and this process can continue indefinitely. Similarly, these branches can collapse back into the trunk, and the trunk can collapse back into the root. In a sense, before the branches are split, they are existing inside the trunk, but they are not visible. And when they are split from the trunk they become visible. So, there is this notion that the entire universe exists in an enfolded form which is called unmanifest. And then under the influence of time it begins unfolding which is called manifest.

In one sense, the past, present, and future exist right now in an enfolded form, and hence everything is eternal. In another sense, time unfolds and refolds due to which everything is temporary. This is described by saying that matter is eternal, but phenomena are temporary, where the phenomena represent the unfolded state and matter is enfolded. As a result, causality is not in matter. It is rather in time because time is causing the enfolding and unfolding. In modern thinking we say that time is just a parameter and it has no causality, which raises the problem of why time doesn’t go backward but only forward. This problem doesn’t arise when we say that the causality is in time.

But now someone can ask that if matter is enfolded then is time also enfolded? The short answer is yes. That enfolded time represents eternity; it includes every moment in the past, present, and future. But time is also unfolding, and that unfolding time creates the sense of passing or that there was a past which doesn’t exist right now. So, Siva is that enfolded time or Eternal Time and the manifest phenomena are the unfolded time. But this enfolded state represents only one aspect of Siva called the sat or eternity. There are two other aspects called ānanda, which represents desire, and chit which represents cognition. The desire is the cause of unfolding and the cognition is the result of unfolding or the unfolded state. So, there is an Eternal Time which is sat, then a desire which is the cause of unfolding, and then there is the phenomenal or cognitive time which is the unfolded state.

This is the reason why we must say that Time is a person—it is due to desire. Without desire there will be eternity but no sense of passing or past, present, and future. That’s why if the soul is freed from desire, there is eternity and no passing of time. When the universe is annihilated, Eternal Time exists in the enfolded state, but there is no past, present, and future. The universe is created due to desire, which produces the sense of passing.

Now, somebody can ask: What is the cause of this desire? How does Siva get desire? Why can’t He remain in the enfolded state? The short answer is that Sakti creates desire in Siva. To create this desire, Sakti must have desire. Therefore, both Siva and Sakti are persons, and Sakti creates desire in Siva and Siva creates desire in Sakti. This is recursive causality, due to which you can never truly say Who is the original cause of desire. As a result, Siva and Sakti are never separated. In many pictures they are depicted as a single person who is half male and half female, and the reason is that we cannot trace the origin of desire.

Should you say that you see an ice cream and then you get the desire to eat ice cream? Or should you say that you got the desire for ice cream and then you got the ice cream? Both alternatives are possible and potentially true, but in one case you get the ice cream before you get the desire, and in the other case you get the desire before the ice cream.

In the same way, you can say that space is the cause of unfolding of time, which then becomes the cause of unfolding of space. Or you can say that time is the cause of unfolding of space and this space then becomes the cause of unfolding of time. Prabhupāda writes in one purport that “Time and space are two correlative terms”. This has perplexed me for a long time, but I think we can understand it by the idea that both space and time are in an enfolded state and to unfold them there is a need for desire and what triggers that desire is not some third entity but this mutuality between the two correlated entities.

So, when I speak about a new geometry, I’m struggling to describe this new idea in which space and time are enfolded, and they are unfolded by their mutual effect on each other. Similarly, they become enfolded again by their mutual effect on each other. How can we express this idea geometrically using a non-traditional logic – because we need a non-traditional system of logic to describe the enfolded state? Can we even express it? That’s the big question I keep thinking about and I don’t have an answer to it, but I like to think that it is possible, but how we get to that geometry is an open issue.

If we can do that, then there is theism, personalism, semanticism, transcendent logic, and the question of the origin of the world and why it is eternal and temporary, all answered through it. It is a question that can have a very big impact on scientific thinking.

Phenomenal vs. Eternal Time

The idea of eternity or Eternal Time is sometimes described as the eternal present. For example, freedom from desire and lamentation means that you don’t look to a future and you don’t lament the past. So, this leads to a state devoid of hope and despair, which is why people talk about ‘living in the present’. Is this commonsense notion about transcending the pleasures and distresses of the world by staying in the present related to Eternal Time?

This is a great point, and perhaps a good starting point to think about time in a new way. In our current modernist thinking about time, we believe that the past is fixed but the present and the future are changeable. In deterministic theories we believe that even the future is fixed and only the present is changing. But if we allow the idea of choice, then we think that the present and the future are open to change, although the past cannot be changed.

Now, this is based on the belief that time is an effect and not a cause. This is because we are thinking about what can change or not change, which is an effect. If we instead think that time is the cause, then we will not ask whether the past and the future are fixed or changing. We will rather ask whether the past and the future are causally efficacious. So here is a new way to think about time. There is Eternal Time, which is neither past, nor present, nor future. And there are parts of this Eternal Time, which have different semantic properties and these parts become causally efficacious one after another.

There are two key ideas in this new way of thinking. First, all moments in time are not the same. Rather, time itself has a semantic property, which creates effects. So, when a given part of time becomes causally efficacious a new effect is created. The second important idea is that many such parts of time can be efficacious simultaneously, and they are going to create effects simultaneously. You can combine these two ideas through an example if you think of a man tied by many ropes, which can pull in different directions.

This is not a vague example but derived from the notion that the soul is bound by the ropes of material nature, and these ropes become tight and loose at different instances of time. When the rope is loose, then the soul feels relaxed and confident. But when the rope is tight then he feels the pressure and is pushed by the force of time. When the soul is relaxed he wants to make independent decisions and he thinks that there is no God and I can do whatever I want. When the pressure builds up then he begs God for help. So, most people turn to religion when their life is not going well. When life becomes comfortable then they forget God and think they are independent and free. The relaxed state is called avaranatmika and the state of pressure is called praksepatmika. It is like a man tied by ropes and the ropes become tight and loose due to which different effects are created.

Now the current scientific thinking is that pushing and pulling is the effect, and the present moment is the cause of this effect. For example, in science we input time as a parameter into some dynamical equation and the push or pull comes out of the equation. So, the present moment is the cause or input and the pushing and pulling is the effect or output.

But you can invert this idea and say that the pushing and pulling is the cause and the present moment in time is the effect of that push and pull. Or, that the present moment is being created as the effect of some push and pull. And as the push and pull change, the present changes. But if the push and pull stop then the present remains still or unchanging. This type of thinking comes from the experience of meditative practices where if you can overcome the push and pull of desire and lamentation then the present becomes still. So, the present is a created effect, but the cause is that desire and lamentation.

Now we can distinguish between a Causal Time and a phenomenal or experienced time. The Causal Time is that Eternal Time which has parts that become causally efficacious one by one. And the phenomenal time is the effect produced by these parts. Phenomenally speaking there is nothing other than the present. Factually, you can never experience the past or the future phenomenally. But you can remember or imagine the past and present cognitively. And even if you remember or imagine, you have the experience in the present. So, we can say that something that created an effect in the past is again creating an effect right now, and I call that remembering the past. That thing which is creating the effect is eternal, but for me it is creating an effect right now, so it appears as my present.

With this type of thinking we can go beyond parametric or changing time, into the Causal or Eternal Time and say that this time is all the moments existing simultaneously which have different characteristics. However different parts of this Causal Time act in order one by one. That Eternal Time is sat, the selection of which part acts in which order is ānanda and the phenomenal effects created due to this action is the chit. So, effectively, we are talking about three kinds of time. The first is the eternal causes. The second is the ordering of these causes. The third is the effect produced due to the combination of causes.

With this distinction we can understand what yogah chitta vritti nirodhah, a famous aphorism from Patanjali’s Yoga Sutra, means. The basic idea is that if the desire becomes steady, then the chitta is not modified by different parts of Eternal Time, so I don’t feel that the present is changing. Hence, the present is not a parameter or the cause of change. It is the effect of something which exists eternally but acts occasionally. Therefore, I may have a past, but it may not haunt me or constrain me or create fear in me. But someone else can also have a past which haunts them, constraints them, or even motivates them.

The past can be objectively real and yet have no effect on the present. Alternatively, the same objective past can influence the present. So, we must remember that because the past and the future can influence the present we have to say that they are objectively real. But because they may not influence we have to say that the influence is occasional. Then we must explain why something acts occasionally although it exists eternally.

The basic principle is that because everything is created by the combination of space and time, even our memory has imprints of the place and time that caused its existence. And if that place or time becomes active again then the past becomes active again and becomes the present. The reason is that we are carrying this material covering created in the past at some place. So, automatically by the effect of space and time we are reminded of this past and by that reminding we create the present. If we become free of this material covering, then the effect of space and time ceases upon us and we become liberated.

The understanding of how the soul becomes liberated changes the understanding of space and time. These are no longer parameters but causes, which is why I call this semantic space and time because the causality is in the space and time, and what we call matter is nothing but the differentiated part of space and time. We have made this differentiated part our identity, so it affects us, but we can be liberated from it. This means that the fundamental premise underlying the new theory of space and time is that the soul can be liberated from this space and time. This is not ordinary material science, in which there is no liberation from space and time. So, the notion that we can be liberated from space and time is not just about the soul but also about the nature of space and time.

The Spiritual Basis of Logic

In some places you have previously talked about how logic springs out of the nature of choice and therefore logic has its foundations in the soul. Can you quickly recapitulate that idea because I have some follow-up questions based on it? Basically, I want you to talk about how this precognitive state doesn’t allow choice, but the cognitive state allows it.

This is a good segue into other interesting issues. The soul in Vedic philosophy is said to have three aspects called sat, chit, and ānanda. In terms of choice, suppose you are offered the alternative between chocolate and vanilla ice cream. Assume you are desirous of having some pleasure so you cannot reject both alternatives. This is called mutual exclusion in logic, by which you must choose either chocolate or vanilla, and you cannot deny both. This is a consequence of the ānanda aspect of the soul. It arises because you desire some happiness and therefore you will choose something even if it is not the exact thing you wanted to have. Then the nature of choice is that you cannot choose both vanilla and chocolate ice cream. You are allowed only one alternative. This is called non-contradiction in logic, and it corresponds to the chit of the soul, which will allow only one out of the many possibilities. Once you have rejected the categories both and neither then you can choose one of the two, and the one that you choose is called sat. This is called the identity principle in logic, which means that the thing you choose is itself without contradiction.

So, classical Western logic can be derived from the understanding of the soul. However, this logic corresponds to the cognitive state and not the precognitive state of matter. The precognitive state, as we have discussed, pertains to the categories both and neither. This means that in the precognitive state choice cannot operate, because things are not separated and if you choose, there is only one thing to choose from, so you cannot say that I have ‘choice’ because there aren’t multiple alternatives to choose from. And once you choose that nothingness you become that nothingness, which is why Buddhists say that this precognitive state of matter is nothingness and the self is also nothingness. Factually, there is still the soul with three aspects, but unable to use the faculty of choice. And since this precognitive state transcends the manifest world, it is in some sense transcendent.

But in Vedic philosophy it is not considered a spiritual state. Hence, we draw a distinction between the deep sleep state and the transcendent state. In that transcendent state, the soul chooses itself and becomes conscious of itself. Again, there is no alternative other than the self, so the both and neither categories are inapplicable. The ānanda becomes the choice of that one thing, and the chit is the experience of that one thing. And that one thing is the self. So, Advaita Vedānta speaks about the state of identity or oneness as the self as opposed to Buddhism which speaks about nothingness as the origin of all things.

The difference between Buddhism and Advaita Vedānta is that the former is the deep sleep state of experience, and the latter is the transcendent state of experience. However, even in this transcendent state only the sat is dominantly used. The chit is not used because there is no alternative, and the ānanda is forced because you must choose something and there is no other alternative to choose from due to lack of variety. So, even though all the three aspects are present, oneness leads to the denial of alternatives and hence choice.

Therefore, in Vaishnava Vedānta we speak about a transcendence where the chit and ānanda are dominant because there is variety, and you can distinguish between the alternatives, and then select some alternative as opposed to the others. Now, somebody can say that if you can choose these alternatives then this spiritual world is just like the material world, and in one sense that is true. The main difference is that in the material world, the variety is always changing. Something is hidden today, and it becomes manifest tomorrow. And what is manifest today will become hidden tomorrow. In the transcendent world, all the possibilities are always manifest, so what you like today will never disappear. Changes in the material world are caused by the shifting desire in Lord Shiva, or we can say that Lord Shiva moves His attention to different parts of the material possibility. As a result, everything possible in theory is not always manifest or present in the universe. Other than this difference, the other principles of diversity and choice remain intact.

So, whether we want to understand the origin of the material world or the nature of the spiritual world, the main issue is understanding this unity underlying the diversity. It is a precognitive state that defies classical Western logic, but it can be understood as the origin of the cognitive reality. The precognitive state doesn’t allow choice, but the cognitive state permits choices. So, the creation springs from this precognitive state to enable choices. The One becomes many because then you can choose and hence you can enjoy.

The Three Modes of Language

If the three aspects of the soul are aspects of choice and cognitive logic is created from this choice, and this logic creates opposites such as head and tail, then how do we understand the three-dimensional structure of the universe? These logical opposites can be sequenced into a single dimension, just like all the numbers can fit into a straight line. So, if all the numbers can fit into a single line, then how do we require three dimensions for space?

These three dimensions are called the three modes of nature. We have talked about this in an earlier podcast. Basically, language operates in three modes, which are called manas, prana, and vāk. In a simple sense, you can think in terms of two modes as nouns and verbs. Adjectives and adverbs are properties of nouns and verbs. In terms of the semantic tree, you can say that the adjectives and adverbs are branches emanating from the noun and the verb. And the third mode is the higher or more abstract level noun and verb.

So, now we can combine the idea that there are dualities with the idea that there are three modes of nature. The duality is the positive and negative directions on a single dimension. And the three modes of nature are the three dimensions of space. But these are defined semantically rather than physically. In terms of mathematics, all the numbers fit into a single straight line. But we need three such lines to describe the world. The problem goes to the root of incompleteness in mathematics where the same number can be used as a concept or abstract noun and an object or contingent instance. Similarly, you can use a number as a noun in arithmetic and as a verb or instruction in a computer program.

So, once we understand the problem of logic, namely that we create numbers out of a precognitive state which cannot be captured in the classical logical categories, then we can talk about semantics namely that something is a noun or a verb, abstract or contingent. So, these constitute the problems of logic and mathematics, respectively.

Flat vs. Hierarchical

So, you are basically saying that logic and mathematics will be redefined considering the big bang and big crunch, namely that the world emanates from a contradictory state, and then collapses back into the contradictory state, and when it expands it creates a language comprised of three modes in language using which we create everything else?

Yes, you can put it like that. In modern science, we think of the world as different kinds of numbers, which are properties of material objects, and to an extent we also speak in terms of nouns and verbs as objects and forces, but we never speak about the hierarchy. In effect, we are living in a flat space of two dimensions from a cognitive standpoint, which are represented by the senses of knowledge and action. Basically, you do a state preparation by the senses of action and you perform a measurement by the senses of knowledge. The correlation between state preparation and measurement is called science. But as we say sometimes, correlation is not causation. The cause is missing in science.

However, in Vedic philosophy, there is a mind beyond the senses of knowledge and action, which perceives the individual object and the intellect assigns a concept to this object or judges the object to be of a certain type such as a table. This constitutes a hierarchy, and this conceptual hierarchy constitutes the cause beyond the correlation. The senses of knowledge and action are measuring properties and the mind and other subtle senses are measuring the objects. This hierarchy constitutes semantics, and it is the cause. We can also say that language is basically numbers operating in three modes. But when we add these modes, then we bring in grammar by which different kinds of numbers are combined. So, there are simple arithmetic operations of numbers, but there are more sophisticated operations of grammar which are also structurally combining numbers.

So, the recognition of three modes creates a three-dimensional semantic space, but then also introduces a new type of structural arithmetic of combining numbers. We must first deal with the problem of opposites on a single dimension, which is about a new type of logic that accommodates logical contradictions, and then we can deal with the problem of semantics in three dimensions which involves a new mathematics. If we can’t solve the first problem, then we cannot solve the second problem either. This is because when we speak about nouns or verbs we speak in terms of opposites like black and white, hot and cold, rough and smooth, bitter and sweet, etc. We cannot induct a semantic mathematics unless we have resolved the problem of the co-creation of opposites in logic.

Causality from a Conflict

Let’s go back to the problem of logic or the co-creation of opposites. We just discussed that these opposites enable choice and the three aspects of the soul are three aspects of cognitive choices. In the book Emotion you have talked about the conflict between these three aspects, and the result of that conflict is that one of the aspects dominates the other aspects, and this dominant subordinate relationship creates a pattern of choice and personality. The reason I bring this up is because you are speaking about a precognitive state that is contradictory but even the cognitive state involves contradictions, which must be resolved in making a choice. This would seem to imply that the problem of logic is further complicated.

Yes, we can differentiate between contradiction and conflict. There is a precognitive state, which appears contradictory from the cognitive state because the opposites are present simultaneously. However, these opposites are in a reconciled state rather than in an actively conflicting state. Then there is the cognitive conflict, which is in the actively conflicting state. Conflict is between the three aspects of the soul which manifest in matter as desire, ability, and opportunity. For example, sometimes you have the abilities but there is no opportunity. At other times, you have a desire and opportunity but there is no ability. So, the world presents itself as a problem of conflict between the three aspects, a mismatch between desire, ability, and opportunity. And the soul tries to solve the conflict.

Now you can ask: Why is this conflict a problem? The reason is that the three aspects must be combined to create an experience. You cannot have an experience unless you combine these three things. But you cannot combine them if they are providing conflicting alternatives. Or, you can say that to combine them, I must compromise, and this compromise is created by one mode of nature dominating over the other two modes. You can choose how to construct this compromise, and that choice dictates which ability is combined with which opportunity to fulfill which desire. But since it is a compromise you will not be able to perfectly match ability, opportunity, and desire. So, even though you find a solution to the problem, the solution is a compromise and hence another problem.

The soul is not comfortable in the material world. The discomfort is caused by the conflicts. And we are constantly trying to become comfortable by making new choices that seem to resolve the conflict. In effect, we are trying to go back to the state of zero conflict. But the nature of the world is that no matter what choice you make, you may solve one conflict but create another conflict. The nature of the world is that you can never solve all the problems; you can only replace one set of problems with another set. This means that there is a cycle of choices in which one solution leads to another problem, and the solution to that problem leads to another problem, until we get back to the original problem. The problems are therefore connected by solutions and the solutions are connected by problems. In making a choice, the soul jumps from one problem to a solution to another problem, and this causes the soul to remain in a cycle of successive problems and solutions.

So, we need to separate two kinds of issues. The first issue is that the precognitive state is apparently contradictory, although it is the reconciliation of opposites. The second issue is that the cognitive state is indeed conflicting. The superficial contradiction is between the opposites, but the real conflict is between the modes of nature. Once we separate these two issues then we can deal with them in two different ways. We have already discussed the problem of logical opposites being reconciled in the precognitive state. The new problem is that in Western thinking we are accustomed to the idea that the world is logically consistent and therefore the soul has no role to play because logic itself can be used to derive the future state from the present state. However, in Vedic philosophy, our experience is built out of three aspects which are always mutually conflicting. And we must combine them to create an experience, and we must find a compromise to do that.

We can call this the causality that results from a conflict. In modern thinking, causality is an inference based on premises and the conclusion follows from the premises. For example, there is an initial state of matter and then there is a law of nature, which constitutes the inference. By applying that inference on the initial state, you get to the next state, and so on ad infinitum. This is the Western causal paradigm of consistency. In contrast, the causal paradigm in Vedic philosophy is that the current state is conflicting, and you make a choice to resolve the conflict but the moment you make that choice and solve one problem of internal conflict, another problem of internal confliction would be created.

So, to do science in this kind of paradigm we have to completely forego classical Western logic. We cannot derive the future state based on the present state and some inference. We rather replace the inference by a choice, and the future state is also conflicting just as the present state is conflicting, although the nature of the conflict can change. This is an even more profound change than the previous two changes, because it completely overturns the idea of rationality as inference and replaces it by problem solving by a compromise. We are not in this world to make inferences from premises. We are here to solve problems, and no matter what problem you solve, you are going to create a new problem.

The inevitable conclusion is that we must think of rationality or logic in a new way as the dynamic of problem solving rather than the dynamic of inference from the premises.

Constraint Based Problem Solving

We are going from one serious problem to an even more serious problem. Where does it end? Is problem solving through the resolution of contradictions the end of the issue?

Well, it’s not truly the end. Every problem must be solved under some constraints. In the case of the soul trying to solve problems, these constraints are moral principles, also called mahattattva, which include ideas such as truthfulness, kindness, austerity, and cleanliness. These abstract ideas or principles have numerous manifestations. For example, cleanliness is not just taking bath but also keeping things systematically organized. Likewise, austerity is not just voluntary suffering but also the idea of simplicity. When we solve problems, we must do it under the constraint of these imperatives. For example, if you have two solutions to a problem, the solution that is simpler would be automatically preferred. People call this Occam’s razor, but at a deep level this is the moral stricture of simplicity.

Problem solving is studied in Operations Research and it has a precedent in physics where it is called the Least Action principle. The simple idea is that when we solve a problem, there are many potential solutions. So, how do we identify the best solution? This is achieved by minimizing some factors and maximizing others. For example, you could say that in a business problem we try to minimize the cost and maximize the profit. But in minimizing the cost we might indulge in unsystematic ways of working, or unkindness to the workers such as by not paying them adequately. And in maximizing the profit we might lie about the qualities of the product we are selling, which constitutes deceit. So, the principles of minimum and maximum are good, but they must be guided by moral principles, and within those constraints we can find the most optimal solution to a problem.

So, problem solving is a complex process in which we try to balance the conflicting demands and we do that under constraints. The basic structure of a problem is that there are three types of conflicting demands and four types of constraints. It is said that in other universes there are even more constraints so the problem solving is even harder because as you add more and more constraints the available alternatives decrease and finding an alternative that satisfies multiple constrains is a much harder problem.

So, identifying the solution within constraints constitutes the new dynamical model of change. This model is different from premises to reasoning to conclusions. The model comprises of a problem, constraints, optimization, and solution. This means that sometimes there may not be a perfect solution, but within the constraints it is the best solution. Similarly, under the circumstances there may be less than perfect solutions.

Now in physical theories nature always follows the path of Least Action, which is described as the shortest path between two locations. You can say it is the most optimal path and nature is supposed to be optimal. However, in problem solving we don’t necessarily follow the most optimal path. We might not balance the conflicting demands perfectly and whatever we balance may violate the moral principles. These less than optimal paths are allowed by nature, in contradiction to the Least Action principle, but there is a consequence of these choices, which is called karma, or the consequences of choice. So, the most optimal solution is called dharma and the less than optimal solution creates karma.

So, the basic idea is that we have a new type of dynamical model which is based on conflict between components of experience that presents itself as a problem. And we try to solve this problem under constraints and we are expected to find the most optimal solution. That most optimal solution is free of karma, but the less than optimal solution creates karma. So, karma is associated with the choice of solutions to a problem, and it is incorporated within the dynamical model of change. This dynamical model is the counterpart of what we call the equations of motion in modern science that determine the trajectory. The novelty is that there is morality woven into the dynamical model of change, which means that morality enters the laws of nature in every activity of solving problems. The deterministic dynamical model has no role for choice, but the problem-solving model has choice because there are potentially many possible solutions to a given problem. And this freedom of choice comes with a responsibility that we must make an optimal choice.

Conscious Control of Automatic Processes

But in modern science we say that nature is working automatically. Even in Bhagavad-Gita it is said that nature or prakriti is doing things automatically which the soul falsely attributes to itself. So, how does this conscious intervention reconcile with the automated working? If there is conscious intervention, then there could not be any automation. For example, we would have to be conscious of our bodily activities such as digestion, breathing, immunity, and blood circulation, but we are not actually consciously controlling these things.

This is a good point. Both the problem and the solution, including the constraints of problem solving are in matter. The entire dynamical process of change is in matter, and it is working automatically. The automatic working is due to time itself being the cause of change, as we have already discussed. But the soul has the choice to reject the solutions produced by matter. So, the soul is not solving the problem; the problems are being automatically solved. However, the soul can intervene in the process of solving problems by rejecting some of the solutions. Therefore, we don’t have free will but we have free won’t. This free won’t entails that we are rejecting the automatically created answers.

So, there are both automated and conscious processes of problem solving. The automation is in matter, but the soul can change its focus and reject the solution. Now when the soul rejects the solution, it doesn’t mean the solution disappears. It just ceases to be my solution. If you reject the automatically produced solution, then you move to a new body and mind. The solution produced in matter will be adopted by someone else. So, there is a difference between automatically solving a problem and something being my solution.

By changing our focus, we change our experience, but we are not changing the automatic computation. Nevertheless, by changing this focus we change karma. Some people worry about all the evils in this world and try to stop the evil. The fact is that you cannot stop the evil, but you can stop yourself from participating in that evil. That evil is also an automatic computation of nature, but nobody is forcing you to participate in it. Evil is also automatically created by God’s desire, but you are free to accept or reject it. So, the problem solving is automated, but my association with the solution is my credit or liability. This means that all kinds of people will exist in this world, but I don’t have to be like them. This is the essence of choice; it is not about changing the world but changing oneself.

Looking Forward

This has been an enlivening conversation. Beginning with the problem of logical contraries, to the ideas about space and time causing mutual expansion, to the notion of time being the cause of change, and material dynamics emerging from contradiction and problem solving, there appear to be several different problems that span logic, numbers, geometry, and algebra, which are fundamentally different from the current modes of thinking. But I have a more basic question. For thousands of years these ideas have existed in Vedic philosophy without being formally systematized in the way you have presented them. What is the need to change the approach now, and bring them to mainstream logic and mathematics?

Well, for thousands of years there wasn’t a real alternative. People understood these ideas intuitively and practiced them, because they can be intuitively understood and practiced. There was no need to state them more rigorously because there was implicit acceptance of these ideas. That is not the case anymore. The world is swept by atheism and materialism, and even the theists are highly influenced by materialism. Under that influence, even the understanding of the ideas is disappearing rapidly. The so-called theists tend to perform the rituals without understanding the underlying science and philosophy.

So, there is a need to revitalize intellectuals with a different set of non-materialistic ideas. For these to pose a tangible alternative, the answers must match the precision and rigor with which modern science is practiced, because otherwise it cannot be a good alternative. So, that’s the dominant reason to do what hasn’t been done in the past.

But before we can make these ideas more formal and rigorous, we must intuitively grasp them at least at the level at which they were formerly understood. Formalization and rigor are consequences of ironing out the details from a less formal intuitive understanding. So, before we can formalize we must understand them as a natural philosophy. This is what I have attempted to do so far, as a way of laying the groundwork for further progress. Only time can tell how far we can take these ideas in terms of precision and rigor.