Uses

Derivation would encompass a wide spectrum of different uses, essentially concerning everything, as long as it has a logical dimension which can be systematized, when this aspect of it is not realized to the ultimate potential, which it hardly could be currently, considering the pretty much constant interrelational relevance to other fields and aspects of reality, and their relative lack of systematization as well. Fields would, in this massive relation between different fields in reality, only be realized to their ultimate potential, when every other field is also realized to its ultimate potential. This process was of course started at the time where the first beings recognized knowledge.

Architectural and Engineering Applications

Similar to the Finite Element Method, you could design an architechtorial model using formulas that account for the strength of walls, volume, and other mechanics. For example, the mass of a wall depends on its volume, the strength of the floor it's on, and other factors. These formulas come from the materials and conditions the model needs, like the environment, weather, and use - say, if you're designing terraced houses in an area that sometimes has minor earthquakes. From there, you can generate the best design and construction options based on materials, energy, and time availability. But some models might be impossible - like if you need a material stronger than tungsten but lighter than helium, which doesn't exist. When precision is lacking, the model requires a larger margin of error. The idea is to make these formulas as extensive and far-reaching as possible to avoid design issues. The ultimate goal is to create a vast knowledge network, linking everything from the smallest to the biggest details. This network would help spot errors more easily and simulate reality.

Historical Research and Analysis

This process can also be applied to exploring and mapping history. Historical facts can be likened to puzzle pieces; in the sense that the more you have in place, the easier it is to find where others fit. Different epistemologies have different ways of understanding history, and that can lead to various interpretations, and because history is so complex, it's rare for these interpretations to overlap perfectly with others. Since tracking every detail in reality is hard, we often use statistics to estimate the likelihood of different historical events. If theories change, so do the odds of certain events happening, which can shift our understanding of history. But if everything is connected through formulas, these changes would be updated automatically. With enough resources, you could even use a trial-and-error approach to analyze history, like solving a sudoku puzzle. If you assume one possibility and it doesn't work, you can rule it out to learn from it. But of course, this point is very far from where we currently are.

Enhanced Communication and Discourse

One perspective from which Derivation can be viewed is for improving communication, like discussions in forums. Instead of risking rhetorical tricks or logical fallacies, people could refer to arguments in Derivation, which are based on transparent premises and logic. You could then identify where contradictions exist, how they can be avoided, and investigate possible inconsistencies. For polarizing issues, you could set up all known, relevant data, compare it, conduct experiments, and figure out the root causes. This would help move away from misunderstandings and ignorance. Even if contradictions aren't resolved, you could break them down to the core, moral perspectives and address them directly. This would help explore why certain premises are polarizing and find the fundamental differences in perspective. With Derivation, discussions could be more factual, goal-oriented, and productive. The results of these discussions could be saved and referenced later, so people don't keep repeating old, refuted arguments. A project based on this idea is the Democratic Evolution of Politics.

Political Applications and Resource Optimization

With enough systematized knowledge, you could identify and address injustices based on faulty (inconsistent) perceptions. You could also calculate the resources available in society and how they could be used to achieve goals like human rights, environmental targets, and automation. When taken to the fullest extent, you can create a proof of the feasibility of this. This could be explained clearly and simply to inspire change by showing what's possible. By using as much shared knowledge and logic as possible, you'd try to minimize ideology in decision-making. A political perspective utilizing this idea is Expediency.