Understanding

We need to understand the legitimacy of the procedures and applications contained in the previous explanations. Therefore, we either understand, fundamentally, the mathematical tools and techniques used in carrying out the rules of the system or believe in the validity of the body of theory which leads to them. If we are only interested in the abstract concept of emergence then this is a sufficient characterisation.

Otherwise, if we are interested in legitimising the applicability of a particular system to an external field of study, we must understand how that field incorporates the system into its own phenomenology. For instance we may wish to use our results to make statements about physical or economic systems, and in such a case we would like to justify the legitimacy of such claims within an accepted framework of such fields.

Let us now examine successive levels of understanding, in an analogous manner to that for explanation.

``I understand the rules which govern the actions of every single agent and interaction in the system, precisely.'' I could carry out a simulation of the system to explain precisely why (in the first sense above) happened.

``I understand the rules and the arena in which they operate sufficiently well that I can make predictions of the outcome very rapidly from the initial state alone, without having to calculate every interaction.'' I have some deeper understanding of the system and the legitimising tools, such that I can perform an analysis which reveals some symmetries (probably abstract) which enable me to calculate the outcome more directly. This analysis will presumably reveal at least a partial characterisation of the space of initial states, whose boundaries may have to be sharpened by means of simulation.

``My analysis and understanding of the system is sufficient to give a clear, precise classification of the space of initial states in terms of the system's outcome.'' Here we have achieved complete success with the previous method of analysis, and developed a mapping from the space of initial states to the space of outcomes described by, for example, a closed-form expression.