Sunday, April 04, 2010

Samkhya : The arithmetic of nature's evolution

Let me introduce you to the most important thinker of India.

His name might surprise you; you might not have heard of him, even if you are an Indian. But his philosophy is the anchor on which Indian culture rests. Indeed, the thousands of religions that took birth in India can be merely considered as footnotes to what he said. They consider him as the greatest of saints ever lived, even though what he said is essentially atheistic !

A.N.Whitehead has once said that western philosophy is merely a series of footnotes to Plato. Such is the influence that Plato exerted on western thought. But here is the Indian counterpart to Plato, who has brought in far more lucidity in thought, and whose metaphysics is more relevant to modern science. Who is he ?

He is the sage Kapila. In an ancient time, at least 3000 years ago or more, Kapila reflected thus.

"Whatever can be named in this universe, I shall name it.
Whatever can be measured in this universe, I shall measure it.
Whatever can be enumerated in this universe, I shall number it.
For what can be named, can be measured. And what can be measured, can be enumerated."

And the legend goes that he has succeeded in doing it ! And that through this success, he achieved enlightenment. We do not know whether this is true. But the questions that Kapila posed himself have never lost their relevance - they are exactly the same questions that science addresses. So it is interesting to tally what Kapila said with experimental evidence in the modern day.

The first thing Kapila observed was that nature is dynamic, and that every object in nature evolves from one form to another. The second thing he observed was that every natural phenomenon has a cause, and every cause has a deeper cause. So if Kapila's philosophy has to be summed up in two words, it will be evolutionist and causal. Since Kapila wanted to enumerate every object in nature that can be enumerated, he proceeded to do it in a way which respects the evolutionary and causal relationships between objects. In fact, the treatise that he propounded is called Sāmkhya (enumeration), and it is the topic of this blog.

The order of complexity in natural objects

Kapila found 5 different layers of complexity in which natural objects exist.
  1. Annamaya : The very first layer (colored indigo) is that of inanimate matter, composed of matter and energy.
  2. Prānamaya : The second layer (colored blue) is that of life, composed of life-forms which breathe. So far, the only planet that we are aware of to consist such life-forms is the earth. This second layer is exponentially more complex than the first one, and it is reflected in the size of molecules that comprise organic matter.
  3. Manomaya : The third layer (colored green) is that of mind, composed of life-forms that have a brain through which they monitor reality in a dynamic way. We can loosely say that this layer consists of animals, as most of them have brains. This third layer is exponentially more complex than the second one, and this complexity is reflected in the electrochemical signals that are transmitted between the nerve cells.
  4. Vijnānamaya : The fourth layer (colored yellow) is that of understanding, composed of life-forms that can speak of both space and time in an abstract language of symbols. So far, we are aware of only human beings to possess this kind of communication capabilities. This fourth layer is exponentially more complex than the third one, and it is reflected in the size of messages that can be transmitted across people. We can consider computers to also belong to this layer as they communicate in very complex symbolic languages.
  5. Chinmaya : The fifth layer (colored red) is that of ego and consciousness, composed of life-forms each of which has a self-image of itself, makes plans and executes them to achieve its desires, and reacts to the environment in a self-conscious way. Most human beings are in this level, except when they are very young children. But so far, we have not built a computer that achieved this level of consciousness. This fifth layer is exponentially more complex than the fourth one, and it is reflected in the complexity of plans (in space and time) that a conscious human being executes.
Of course, Kapila was not aware of computers, or bacteria, or the various types of elementary particles in modern physics, but the levels of complexity that he described are still as valid today. Kapila has also identified a cause for this exponential increase of complexity between successive layers - recursion. For example, the second layer is built by the same elements as those of the first layer, but whose interconnections form self-loops. Such recursion always produces an exponential increase in complexity.

The word "maya" which suffixes the words for each of these layers means "measurement", making clear Kapila's philosophy that all of these layers can be measured and thus enumerated in order. We can visualize all these five layers as consecutive circles. The outermost indigo circle represents the entire universe. The next blue circle represents the universe of life-forms which breathe (as far as we know, it is just the planet earth) and so on.. The layers of higher complexity are shown in smaller circles because they are much fewer complex objects in nature than the objects which are simpler. I showed the circles with linearly decreasing radius for easy visualization, but in fact, their radius is "exponentially" decreasing. The same layers can also be visualized with respect to their complexity, and this resembles an object similar to a Mexican hat, of the following image.

Kapila observed that the various forms in nature evolve across these 5 layers, and that the higher layers are built from the lower layers. What he set out to do was to enumerate all the objects in nature in all these 5 layers, and how they evolve between each other. He would give a number to an object based on how complex it is in this scale of evolution.

The reminder : what cannot be enumerated

There is a phenomenon in nature that Kapila observed, but judged that it cannot be either measured, or named (explained in words), or enumerated. That is the phenomenon of the conscious feeler who experiences sensations from nature. Kapila said that such "feeler" is present in all forms of life, including human beings. He named this feeler Purusha and held it in contrast to all the 5 layers of Prakriti (nature), including the layer of ego. He said that such a feeler cannot be evolved out of any of the these 5 layers of natural forms. He used the masculine to denote the Purusha and the feminine to denote Prakriti (nature). I will do the same in this blog, even though a Purusha can be present in women too.

What Kapila said was that either Purusha exists by himself, or he does not exist at all. Literally, this footnote of Kapila's philosophical system has become the bone of contention of million thinkers in India who gave million different answers to who this Purusha is and if he exists (some thinkers have answered in the negative), how he is related to the 5 layers of nature. This spawned a million religions in India, all of which recognize the validity of Kapila's 5-fold division of nature. They also follow the masculine / feminine division of Kapila. So any female goddess that you find in Hinduism is an aspect of Prakriti and any male god that you find is an aspect of Purusha (as reflected in Prakriti, because by himself Purusha cannot be described by any word or image). The totality of Prakriti and Purusha put together is called Brahmān, or the Absolute, which contains all types of existence within itself (please note the neuter gender for the Absolute).

We can loosely translate Purusha as the western concept of soul, but it is not at all the same. Firstly, a soul is created and then judged by God. In contrast, Purusha has no birth and suffers no change. He is constant and eternal - the closest western counterpart for that is God Himself ! Secondly, unlike God, the Purusha has no special powers. He cannot tamper with the laws of nature, nor the evolution across forms. Thirdly, unlike the soul, the Purusha is held completely distinct from ego (self-image), which is considered to belong solely to the realm of nature.

In Kapila's own system, the Purusha exists and stands at the very centre of these 5 circles (shown in the picture as a tiny grey circle), or right in the middle of the Mexican hat (in the 3D analogy). Of course, Kapila didn't call this a Mexican hat, but termed it the mountain/tower of Meru. This Meru mountain has mythic significance in all Indian religions, and indeed forms the architectural basis for every Hindu temple.

Kapila said that the vertical distance to the walls from where a Purusha stands in this tower of Meru gives the amount of happiness that is felt by him. Thus, if a Purusha stands within the outermost indigo rim of inanimate reality, he can feel only a minute amount of happiness. He feels an exponentially higher amount of happiness if he can somehow jump upwards into the layer of life, and so on. Ultimately, if a Purusha manages to reach the very centre of this tower, he would never touch the tower walls of happiness, and thus feel infinite bliss (termed as ananda). This infinite bliss is said to be within the reach of every human being.

In a Hindu temple, the main idol (murti) sits right underneath the vimana tower (symbolizing the Meru mountain) - signifying the infinite bliss of Purusha seated at the very centre of Meru. Devotees circumambulate this idol in an act of worship - in a symbolic act of witnessing the Divine from all possible views. They ultimately seek to merge in the Divine, which is supposed to reside within their own innermost selves.

Kapila says that this desire for higher and higher bliss is what prompts nature to evolve into more complex forms of existence. Just as the branches of a tree and its leaves go upwards to reach to the sunlight, the branches of the tree of life go upwards to layers of higher complexity. We cannot say how every single twig faces in a tree (and some of them do face downwards), but the general direction of growth would be upwards. Kapila has a name for the tree of existence -Ashwattha (which encompasses not only various forms of life but also inanimate objects). This Ashwattha tree is said grows on the walls of the Meru mountain and tries eternally to reach up to the top.

The arithmetic of nature's evolution between layers

Depending on the height at which an object of nature stands on the Meru mountain, it gets a number according to Kapila's scheme (To be short, I will call this the "Kapila number") . Every such object has a finite existence - both in space and in time. Eventually, it will die and a new object will take its place. In this finite existence, Kapila observed that it moves along the mountain, in a step-size that is capable of its finite reach.

Kapila mentions that every natural object has a decision with 3 choices with respect to the Kapila number :
  1. To increase : proclination to do so termed rajas quality
  2. To stay the same : proclination to do so termed tamas quality
  3. To decrease : proclination to do so termed the satvik quality
Here is the most interesting (and most misunderstood) part of Kapila's philosophical system.

Let's observe choice 1. An object can only increase of a step-size that is delimited by the layer in which it exists. Since the next layer is at an exponentially higher level, irrespective of how much an object tries to increase, it can never reach to this next level. Consequently, the rajas quality (greediness) is disparaged by the Sāmkhya philosophers.

Let's now inspect the choice 2. For any object of finite existence, staying the same means only one thing - death. Consequently, the tamas quality (inertia) is considered the most harmful by the Sāmkhya philosophers.

Now, let's see the choice 3. Surely, decreasing would only mean the object goes down the Meru mountain. How can it be a good thing ? But indeed, it is so. To understand this clearly, we should see the number system that is most directly inspired from the Sāmkhya philosophy : the system of counting with zeros, which originated in India. If we use the base 10 for counting, the numbers go


If you look at the last digit, it goes to zero before the number advances to the next level. The same is true at every decimal level. This is exactly how the Kapila number of an object changes. It has to renounce (make zero) its current level of existence to proceed to the next level. This is the only way a finite object can advance up the Meru mountain and reach heights that are incapable of the rajas method of increasing.

This paradoxical quality is the reason why renunciation (of sensual desires, wealth, fame, ..) is so valued in Indian culture. Consequently, the satvik quality (translated properly as transparence or lucidity) is valued the highest by the Sāmkhya philosophers, despite it standing for decreasing / making zero the respective Kapila number.

However, each person is exhorted to cultivate all the 3 qualities in equilibrium. When the three qualities are exactly equal with each other, a person would not make a decision, but maintain equanimity against nature. This poise is considered essential for a person to make the right decision when the right time comes. Amongst Indian religions, only Buddhism exhorts people to renounce immediately, so that one can reach enlightenment. Other Hindu religions ask people to wait and take the right decision at the right time of one's life.

Pitfalls of excess greed

I will conclude this post with the practical system for ethics that is provided by the Sāmkhya philosophy.

Irrespective of where an object stands in the Meru mountain, it suffers from the temptation of excess greed. This would magnify the rajas quality and render it blind to the true reality of the mountain. Amongst the 5 layers of existence, the layers 1 (matter), 3 (mind) and 5 (ego) are considered primary. The other layers 2 (breath) and 4 (understanding) are considered as intermediate sheaths that connect the upper and lower layers.

When one tries to advance in the matter layer, one receives the pleasure of taste. When one tries to advance in the mind layer, one receives the pleasure of possessions. When one tries to advance in the ego layer, one receives the pleasure of fame and recognition. Each of these pleasures will blind oneself to the deeper reality of nature, and the greater happiness that is obtained by jumping to the higher layer. When one desires too many tastes, this excess rajas quality is termed as lust. When one desires too many possessions, it is termed as greed. When one desires too much fame, it is termed as pride. These three are considered the 3 primal enemies of one's journey life. They all occur due to excess rajas quality in a person.

The clarity that is provided by the satvik quality at the respective layer is considered essential to counter this pitfall. In order to prevent oneself succumbing to lust, one must sacrifice sensual pleasures and seek the higher pleasures of learning. In order to prevent oneself succumbing to greed, one must sacrifice the pleasure of possessions and seek the higher pleasures of recognition. In order to prevent oneself succumbing to fame, one must sacrifice the pleasure of recognition and seek the higher pleasures of self-knowledge. This is Kapila's advice for any man or woman on how to lead one's life.

In this blog, I presented a modern perspective of the Samkhya philosophy. I have used concepts and terms that were not known during the ages when Samkhya was developed, but which would help us modern people understand Samkhya in an easier manner. To compliment this understanding, an interested reader can refer to a traditional version of Samkhya philosophy, such as Samkhyakarika. A very good traditional explanation of Samkhya is available from Deshpande Ji's blog.