Universality Lives in Structure

If you are a software engineer, you have likely imagined creating something versatile - software widely utilized by many. An open-source project boasting ten thousand GitHub stars, a social network with hundreds of millions of users, or mission-critical systems that keep the world functioning. Moreover, the operating systems that uphold this entire infrastructure.

In the realm of software, we often discuss value as being applicable in more scenarios. Generality, in practice, proves to be genuinely significant. However, generality isn't eternal. Once renowned, Flash faded with its era. XML, designed as the universal standard, fell out of favor. jQuery, which once powered nearly every web page, is seldom selected for anything new.

Generality hinges on the expansion of cases. A web framework like Rails or Laravel can construct most web applications independently. If I were to advise a novice, I would recommend starting with one of these; learn it, and some work will become accessible. Yet, this multitude of cases evolves with time. Single-page applications, Progressive Web Applications, WebAssembly - the list goes on.

Consequently, generality, by its very nature, diminishes over time. Instead of adding more cases, consider altering the circumstances from which you observe. Change the era, culture, representation, or the level of observation. In doing so, you commence to discern what shifts and what remains constant. Relativize, and the core essence persists.

What remains? For Rails, perhaps it is its conventions. As eras and cultures evolve, adhering to conventions in governing a codebase preserves its value. For React, the enduring aspect may be the presence of pure functions - a concept from functional programming brought to the frontend. Rendering the view as a pure, idempotent function offers benefits that outlast the era.

Only by altering how you perceive does the outline of the universal become discernible. This does not imply that everything is relative. We relativize to discern what is not relative. That which remains through relativization - that is universality. The essence of Buddhism, which is approximately 2,500 years old, traversed East Asia and branched into numerous schools.

While doctrine, practice, and precepts vary across schools, the questions persist. Why do we suffer? Where does attachment originate? What is the self? How should we live? The answers differ per school, relative to place and time - yet something endures. These questions themselves constitute universality. The teaching that emphasized impermanence has endured for 2,500 years.

Lehman's inquiries Returning to software. Fifty years ago, Meir Lehman published his laws of software evolution. Eight laws, describing how software utilized in the real world evolves over time. Software in use must undergo changes, or it loses its value. The more it changes, the more complex it becomes. Features continue to expand, and without maintenance, quality seems to deteriorate.

Evolution unfolds through layers of feedback. There was also a law stating that the work rate of a development organization remains roughly constant. Not all eight laws are universal. Alter the condition termed "era," and they diverge: some persist while others evolve. The constant-work-rate law has aged. It was a statistic derived from the development organizations of its time, and those organizations no longer exist.

Currently, AI is reshaping the work rate itself. Yet, the law that software in use perpetually changes remains. It is not a statistic; it stems from the relationship between software and the world. Software intertwined with reality alters the world, and thus must continually adapt to the world it transformed. This reciprocal exchange persists, regardless of the proliferation of languages and frameworks.

What Lehman left behind was not the statistics of an era, but the questions arising from a relationship with the world. The Age of AI We are currently experiencing a turning point. AI now generates code at a pace surpassing human capabilities. AI excels at identifying commonalities across vast datasets. The speed at which general software and frameworks emerge will accelerate dramatically.

However, the era itself also transforms more swiftly. What is deemed general in August may become obsolete by December. What endures? What persists when conditions change? Precisely because this is the epoch of AI, universality is what retains value. Algebraic Architecture Theory (AAT): The enduring elements found in Buddhism and Lehman echo a concept known as structure.

AAT, the theory I am researching, endeavors to express the structure of software architecture using the language of algebraic geometry. It quantifies the gap between parts and the whole. Each individual modification is accurate and passes review. Yet, the entire, when interconnected, is somehow flawed. AAT provides mathematical expression to this phenomenon - something every engineer has experienced.

Software metrics are typically established by people. We agree upon a method of computation, then measure the result. This is why metrics are abundant, and the rationale behind measuring a particular metric is weak. The central quantity in AAT operates differently. Frame the question - why can the parts be correct while the whole fails to assemble? - and mathematics inherently reveals the location where the answer resides.

Not chosen. Obligated. Generality can be selected. Universality cannot. The Atlas Theorem, recently proved, encapsulates precisely this universality. When examining source code, there exists a resolution to the observation: whether it is coarse or fine-grained. The Atlas Theorem offers a sufficient condition under which the review outcome remains unchanged despite alterations in resolution.