What is true comprehension and knowledge?

True comprehension bursts forth when the light of the consciousness illuminates a problem or an idea and we exclaim (silent or loud): "Aha - I see!". The idea then becomes knowledge and the kind of knowledge that is duly comprehended, digested and assimilated - not the sort of superficial knowledge that we put in our memory and that just serves to torture and nag our minds because it is not perfectly assimilated.

Comprehension, reflexion and understanding are of receptive nature. In school they didn't teach us to contemplate a problem, that is to reflect and see the nature and solution of the problem with our intuitive and reflective part of thinking. Instead we have learned to force ourselves to perform disciplined concentration and attention, to struggle between concentration and distraction and force our feminine and sensitive memory to work. The true joy of thinking, the true joy of knowledge and learning is when we see the very nature of a problem and its solution. Such comprehension is silent and without effort!

Higher thinking consists of perfect will and perfect reflection / intuition in harmonius proportions,  prior experiences / knowledge and finally a superior element that brings order and perfection to the whole process - this element is the light of consciousness, the very antithesis to the chaos of our lower, egoistical part. The light of consciousness allows us to be inspired, to be creative, inventive and to see things in new, positive ways. Subjects as maths, physics, aesthetics should cultivate this higher form of thinking.

With the light of consciousness we understand the undefineable essence we all have inside that makes us alive, joyful, inspired, creative and good to other people - we are all familiar with this undefineable higher faculty. As Humanists we don't believe that human nature is evil in its essence, on the contrary we think it is goodness, love, inspiration, illumination, etc., it is our consciousness in its most elevated and Human form.

Two kinds of understanding

The 1-dimensional, linear and deductive understanding

All comprehension in this 1-dimensional domain can be described as a linear, logical or deductive process, where we are trying to show a statement G from a statement A and in which we apply known rules B,C,D,E,F to show the way to statement G. We know that A is true and we will also show that G is true by applying known rules and logical deduction. A gives B and B gives C and C gives D and D gives E and E gives F and F gives G. That is: G is true. This kind of comprehension is legal and true in a logic sense, but it is purely linear, logical and one-dimensional.

This kind of understanding represents the dark shackels and labyrinths of the intellect. Remember the dark and tricky labyrinths in the Greek mythology. The labyrinths were 1-dimensional (as the pure rational and logical thinking) and if we were able to see it from above, in the light, in two dimensions we immediately would have known its solution and we would have performed the other type of understanding :

The 2-dimensional, direct comprehension of a seeing or intuitive character

Here we see the true nature of the problem, its true connections, etc. Here we get exalted and exclaim "Aha - I see!". It is a spontaneous, natural and effortless comprehension that have the characteristics of seeing. It is 2-dimensional because it doesn't follow a line in time, it gives the picture directly. It is enlightened because it has similarities with the physical seeing wich is dependent on light. The following example will show a concrete math application of the two types of understanding.

A concrete example

We will now present a very concrete example of the above:

Suppose we will show that

(a + b)² = a² + 2ab + b²

Following the linear, deductive model (the standard in schools) we arrive at:

(a + b)² = (a + b)(a + b) = a(a + b) + b(a + b) = (aa + ab) + (ba + bb) = a² + 2ab + b²

But here we don't actually see that (a + b)² = a² + 2ab + b², we have just performed 4 steps that lead to the desired result (of which each step is based on a mathematical, abstract rule).

But suppose we apply the intuitive, visual model on this formula. Then (a + b)² can be viewed as a square having sides (a + b) and we arrive directly at this figure:

Here we can see directly that a square with sides (a + b) consists of four fields: one a², one b² and two ab:s, that is, the total area of the figure - (a + b)(a + b) - is a² + 2ab + b² ! We can now rightfully exclaim: "Aha!, now I see why (a + b)² = a² + 2ab + b² ! ". Very simple, isn't it?

This model is not general

Of course, this theories of thinking and comprehension are not applicable to subjects in school generally. In maths and physics we may apply this model, but for instance, in languages it is a different matter. Speaking and learning a language is a very motoric and instinctive process. We should not let the intellectual faculty interfere with the practical thing of speaking. We should focus much more on the practical side - to talk and write etc. - when we are learning a language, than on the grammatic or theoretical side. The grammar should only be a map in the beginning, when we are learning the correct forms, etc., but when this is accomplished we must just talk, write and talk so as to be virtous on expressing ourself in the language. It is absurd to learn a language in an intellectual and grammatical way. Language is practical, motoric and instinctive, the intellect is slower and must not interfere with the sensitive memory or the faculty of speech.

The importance of Relations and Connections

Another important matter is to connect, to relate the diferent topics (in maths: the different theorems, rules, etc.) to each other in a harmonius and comprehensible way. If someone says to us: "Please go and buy 1 pound of butter, 1 pound of flour, 5 ounces of salt, three eggs, strawberry-jam and some cream.", it would be much easier to memorize and comprehend if the person added: "...I'm going to make waffles.". (Waffles is the connection). Let this picture talk: