Types of Analysis

In googology there are various ways to demonstrate the strength of a given notation, and this is called analysis. There are different ways to analyze notations, here are some of them.

List analysis:
List analysis is analysis of a notation that usually takes the form of a list or table where the notation will be compared with a more familiar notation. The benefit of list analysis is that it may be done by people who lack the formal knowledge required for an in-depth proof of a notation's strength, and it is intuitively clear to most who see the list how strong expressions in the notation are.

The down-side is that the list analysis does not explain why the notation is as strong as it is and can be likened to a log table, where the logarithms are all written down but no explanation is made about how you can derive your own logarithms.

For an example of a list analysis, see my Analysis of TON.

Explanatory analysis:
Explanatory analysis is superior to list analysis because it explains why a notation does a certain thing or has a certain strength. It takes more thought than a list analysis but is more rewarding because then when you understand how a notation works you can devise more powerful notations.

Explanatory analysis will often go beyond the strength of already established notations and compare a notation with the strength of a mathematical theory. This often requires knowledge of set theory and formal mathematical proofs which is why explanatory analysis is less common than list analysis.