Knowledge, Optimized

Hierarchy provides a way to quantify the information we have about something. For example, if we witness a _cat_ or a _dog_ from a distance without being able to distinguish which it is, we can still identify it and reason about it as an _animal_. Using a classification higher in the hierarchy implies less information and a wider error bar on our recognition. Sometimes, even if we know that an animal is in fact a cat, it can be useful to reason about it as an animal. The simpler summarizing category may be enough for the current purpose and may free up space in our mind for other things. Summarizing a complexe situation by abstract categories that ignore irrelevant details allows more things to be reasoned about at the same time than if every small detail of the situation was taken into account. Another case where hierarchical order is useful is when we are dealing with circular definitions. Sometimes, learning a new concept relies on the comprehention of another concept which in turn relies on knowing the first. Dictionaries are one of the best example of this problem. The purpose of a dictionary is to define every word in a language. However, each definition is written quite circularly in terms of other words of the same language. Other examples of circularity of concepts include: *When learning about a species of animal, it can be important to understand its habitat, but habitats may be influenced by the different species within it. *It may be difficult to understand an historical figure without understanding the political context he or she emerged from. However, to understand the political context, you need to understand the important figures that influenced it. *Circularity is often present in theoretical versus practical aspects of subjects. It is often difficult and tedious to learn detailed theory about a subject without knowing the practical use for the theory. However it is difficult to learn advanced practice without knowing the theory. **For example, it can be uninteresting and tedious for a medical student to learn the details of complexe biological and chemical processes without knowing that there are useful medications that influence these particular processes. However, it is difficult to understand these medications without understanding the biological processses they influence. Although we have to rely on peripheral knowledge for "bootstrapping" when we learn concepts with circular definitions, hierarchical organisation can help by providing a learning path. In the above cases, it is easier to ignore the details and learn subjects superficially first and then alternate reading about each subjects going deeper each time until the required advanced knowledge is understood. In the case of circular information, taking a breadth first approach makes things easier. There are also times when concepts are not circular and instead build on top of each other. In these cases, it is better to learn the foundational subjects in depth before moving to the next subjects. For example, one should understand addition and multiplication very well before doing any calculus or statistics. Here a depth first approach is better. Other times a reader simply doesn't need all the details and an overview is sufficicent for his or her purposes. Hierarchical organisation allows readers to dig down to the level of details they need and come back later and dig deeper if or when more is needed. Laying out the building blocks of "is a" and "has a" relationships Our mind makes abundant use of "is a" and "has a" relationships to identify and reason about things. Everything _is a_ something because it _has_ parts and properties that characterizes it and allows it to be described as this something. Each of these parts can in turn be identified as instances of categories (_is a_) with a degree of abstraction and detail determined by the occurences of their own sub parts. We can identify and decompose knowledge about complex objects following alternating "is a" and "has a" relationships into the simplest forms of recognizable order. Hierarchical organisation of information can make more obvious the varying levels of details needed for this decomposition and allows us to carry and convey the right amount of uncertainty in our knowledge. Our brain relies on a delicate balancing of facts about uncertainty and amount of details when reasoning. It is important for information to be organised in a way that helps us avoid cognitive traps that can lead to over generalizing or over specifying and to making bad predictions. A Bookvoid section can contain both information about the parts that make up a subject and information about the different subcategorizations, sub species, types, notable instances and examples used to classify the subject further. Lengthy details about parts or sub categorizations can be hidden in collapsed Bookvoid sub sections.