One particularly useful method of thinking is that of abstraction. Abstraction is a word, which stands for the process of conceptualisation.[1] Look up the definition of “two”. You will find the dictionary say something rather disappointing like: “two is a number between one and three”, or “the sum of one and one”. Dictionaries are circular documents.[2] A word can only be defined with reference to other words. But even so. That is going a bit far. Try it yourself. Define “two.” Soon you will come to something like two is two of something: two apples. That means you have conceptualised the “twoness” of a pair of apples. You have grouped them into an abstraction of their similarities and differences.


Abstraction means “to conceptualise” or “to take away”, or “to separate”. It also means “to generalise as opposed to particularise”. You can abstract in several ways.


Formal reduction is what a painter like Raphael did with human beings. His figures do not really look like any one person, but appear more like generalised human beings. Sometimes their sex is even a bit ambiguous. Much African sculpture from below the Sahara Desert also abstracts the human figure: the statues are a formal reduction of their model. Legs are reduced to cylinders, the face becomes a schema of the real thing. Picasso adopted this technique during his cubist phase.

How has this helped people? Well, it has actually made it possible to establish comparisons: a leg is like a cylinder. That is a first step in the attempt to relate the leg to other things. That relation could become useful. It might lead to the idea of a column…. Furthermore, abstractions made the invisible visible in some way, it can help make the inside of people visible in some way.  Through complex associations involving symbols and such objects, which have a particular form also achieve a particular emotional charge. In other words, abstraction is a method whereby we become aware of connections between ourselves and the world around us.


That function of abstraction between ourselves and the world of which we are a part is related to symbolic representation. Symbols are signs, which represent desires and aspirations. They can also be used to represent belonging. Belonging is a form of attachment that is not physical but, for lack of a better word, magical.

Magic is something whereby symbols can alter the behaviour of people. In a sense the spoken words: “this watch lying on the table is mine” are magic words. They do not physically prevent you from taking the watch and keeping it, even so, they do prevent you from taking the watch. If you chose to ignore the summons you will be labelled a thief and be subject to the rigours of the law. Either way, these words of magic have changed us.

[1] Michael Bernkopf, Mathematics, An Appreciation, Boston, Houghton, 1975, p. 5 f.

[2] Ibidem.