This second article of the series of articles “The stuff that I think you should know” will attempt to explain some concepts that allow you to change your perspective in the context of problem-solving.
Categories can encompass a variety of things that share one or various properties between themselves, they can contain, be contained, be independent and overlap with other categories, relations between categories can many times be context dependent.
Examples: If one is told to organize the categories “Horses” and “White” in a realistic way he can’t put “Horses” inside “White” as not every horse is white and he can’t put “White” inside “Horses” as not everything that is white are horses, due to some horses being white he can’t separate them either, so, these categories necessarily intersect, but, if the context was “colors of horses” then it would become perfectly acceptable to put “White” inside “Horses”.
Abstraction is a way to make complex things more manageable (seemingly less complex) by producing abstract concepts of those things or by simply ignoring less important details.
Think of a tree, not a specific tree, just a tree. Most people will imagine something with a dark brown vertical wooden trunk with some simple or ambiguously shaped crown with a lot of green leaves, not all trees have these characteristics, obviously, if we see a tree with a white trunk and a purple crown we will certainly mention those categories along with the word “tree” if we want to communicate what we saw to another person because we believe that the other person’s concept of “tree” is similar to ours, which is probably true. In this situation the general look of all trees was reduced to that basic description that is our abstract concept of “tree” because there was no need for more detail.
Think of what trees do for us humans and our environment. Suddenly, the look of the tree becomes a secondary or irrelevant thing and what’s in your mind is more likely to be that it provides oxygen, shade, fruits, lumber, and so on. In this situation trees were reduced to a simple narrow set of characteristics because, again, there was no need for more detail.
Draw something that’s enough to be identified by most people as a tree. A brown vertical line with a green circle on top is probably enough.
These are examples of how abstraction works and how we use it in our daily lives.
Blackboxing is a kind of abstraction that focuses on cause and effect. To open a locked door to his house the owner just inserts the key in the hole in the lock, rotates it a certain way, and the door opens as a result, it works even if he doesn’t know anything about how the lock works inside, this is an example of blackboxing, the owner can treat the lock as a metaphorical black box, as something mysterious, the only thing he needs to know about it is that when the lock is supplied with a certain input (key + rotate) a certain output occurs (door opens).
This is a powerful abstraction method that allows to very quickly determine how to do something complex by taking several “black boxes” and organizing them together until a certain input results in the desired output. Each successive black box that is connected will output a modified output of the previous black box until the desired result is reached.
Let’s say that someone wanted to build a flashlight but knew next to nothing about electricity and electrical components, he would essentially need some source of light that operates on electricity (so a black box that takes electricity as input and outputs light) and a source of electricity (a black box that outputs electricity). Now he would begin his search for the real components represented by the black boxes, he would find that for the “electricity black box” there are rechargeable and non-rechargeable batteries in a great range of different chemistries, dynamos, photovoltaic panels and so on, as for the “electricity as input, light as output black box” he would also have some choices like incandescent, fluorescent or LED, the point being, without even being aware of his choices he was capable of identifying at least two hypothetical crucial components, their rough properties and how they related to each other to achieve a certain goal. Sometimes the available choices for the real world representation of one black box don’t exist or don’t seamlessly connect with the choices for other black boxes, the solution for these cases is to either pick alternative components or add intermediary black boxes that convert the output of one to an input that the other can work with.
Analysis consists of breaking things down (concepts, hypothesis, sentences, etc..) to it’s constituent parts and examining them in depth as the situation may require in order to obtain a more complete understanding of said thing.