Abstraction

Abstraction is the ability to boil things down to its core by ignoring unnecessary details and instead focusing on whats common with something else. The ability of abstraction is a defining characteristic of humanity: We can talk about a book, even though every book has a different content, color, languages or size. The concept of a book is an abstraction of all the different concrete books and every other human understands what we mean. 

Through abstraction we are able to draw connections between seemingly unconnected things. Making sense of the world requires abstraction. In his famous monologue Goethes Faust wishes in German

Dass ich erkenne, was die Welt
Im Innersten zusammenhält

That I may detect the inmost force
Which binds the world, and guides its course

The better we can abstract things, the better we can model the different aspects of the world around us. This enables us to better understand how things effect each other, allows us to make better predictions of the future and most importantly make better decisions in the present. 

Without abstraction we can see the dots, but can't draw a connection between them. 

In his book "Die Kunst des digitalen Lebens" (The art of living in the digital age) the author Rolf Dobelli argues why consuming media can easily give us a wrong impression of the world. At one point he compares each article with a single dot, representing some event. Because the format of an article is often not long enough to represent the complex background of the event. Instead most articles represent a simple cause-effect relation that is often not accurate or even wrong. In that sense the author of the article makes an abstraction of the matter for us. Details are left out to obtain a stripped down image of the event. But that abstraction is not made to better understand "the inmost force which binds the world, and guides its course", but as Dobelli argues is optimized to grab our attention in the first place. There are useful abstractions that give us a better understanding of the world, but abstraction can also lead to the opposite. We still connect dots, but maybe the wrong ones. In each step of abstraction we need to be careful if we abstracted away irrelevant details or if we stripped away details of "the inmost force which binds the world". 

Solving complex problems with abstraction 

Abstraction allows us to focus on the relevant parts of a complex issue. If we want to solve a complex problem, the first step should always be gain a deep understanding of the problem. We can do this by finding good abstractions for it. This way we understand, which parts are important and which ones are rather noise instead of information. Often we find out that certain aspects of the problem are similar to problems we know from other areas. Sometimes we can reduce the problem to an abstract model we already know. For instance, in mathematics we could find out that the problem can be reduced to a graph-theoretic problem or that it can be represented with a finite state machine. If we can find such an abstraction and the abstraction is abstracting the right parts, we can often apply generic solutions that have already been researched. Suddenly we might solve our problem by using an existing graph-based algorithm. If we are not able to see the similarities between different issues, we have to start from scratch every time. We can not transfer the insights from other problems to the current problem. This might take us more time than necessary and the outcome probably is of lower quality. Moreover, abstracting a problem to an already known theoretic model has the enormous advantage that it is much easier to communicate to other people. There is an abundance of literature about all kinds of theoretic models. If you can reduce your problem to a theoretic model other people know, they can instantly apply their generic knowledge. This increases the probability of finding a good solution even further.