Response by Learner JT
Sri Aurobindo starts the chapter on concentration by describing how purity is complementary to concentration. An obvious question comes why are they complementary?
The answer would be on the lines of stating what purity is and what yogic concentration is. With purity you move all that which is impure from the mind, vital and physical layers of personality. What are those impurities? In a broader sense, they are negative thoughts, negative emotions and negative sensations. The more you can move them out, more you will find that mind is getting single pointed. That is what we refer as yogic concentration. And when this single pointed-ness becomes very sharp you can use it for different reasons. One of them being that by using it you can know the inner principle of an outer manifestation, in this case it has taken the form of divine Tapas. Ideally, this would be most simplistic way: to define three very important concepts of Purity, Concentration and divine Tapas. Though purity is not a focus of this question, however purity is very basic to concentration. The power of concentration goes higher and higher with purity.
Comment by Course Facilitator LS to JT
Purity is also something else. It is a wrong mixture of different elements of the being which brings in impurity. When the mind is pure, then there is no mixture of vital or physical elements in it. That would mean, for example, that its perceptions and thoughts are not distorted by emotion or desire. It thinks and it perceives clearly. The physical tends to contribute tamas to its workings -- laziness, unclarity, dullness. With the vital and physical impurities removed, the mind can look at the truth of things clearly.
The vital's true function is to experience and enjoy the delight in things, as well as to contribute energy and force to action. But it is not its role to determine which action should be taken. That is a form of vital desire and grasping, and those are impurities in the vital. The vital actually should carry out the directions of what the mind in its purity sees to be the right action. When the mind is sufficiently quietened and receptive to the higher knowledge above rational thought and will, or to the inner promptings of the soul or psychic being, then the vital's role is to carry out the directions from those sources of the will. So purity has much to do with a proper organization of the various parts of the being, such that each carries out its own and true role, and does not interfere in the action of the other parts of the being.
At a somewhat higher level, we could say that the role of the mind is to become a quiet channel and receiver of the knowledge and will from above mind. At this level, impurity in the mind would include mental discourse itself, that is, thought activity, reasoning, etc. Actually, what is happening at this stage is that one is becoming aware of the higher mind, and one is beginning to take one's station there. So this quiet receptivity to the higher knowledge (and not to anything else) would be the natural function of the higher mind, and the main impurity would be the interference of the normal rational mind below it.
These things are explained in some detail in later chapters of The Synthesis of Yoga.
In this conception of purity, it is easier to see its close relation to concentration. The particular part of the being is concentrated in its own proper action, and is not dispersed or mixed and diluted with the action of lower parts of the being or engaged in wrong action not consistent with its own dharma and function.
Response by Learner NJ
Divine Tapas is Being dwelling in concentration upon itself for bliss. This is how it maintains and possesses itself and by which it draws back from manifestation