Degrees of Cleanliness

Do you cook your own food? My own meals tend to be boring - I optimize for speed and efficiency when cooking for myself, but I become passionate when I do it for a loved one.  I’m occasionally creative, but I prefer to base my efforts off a recipe.  It can be passed down from my parents, from a cooking blog, or even generated by AI, but I like to have some kind of concrete list of ingredients and steps that guides the process.  If I ruin the dish, I can at least compare my actions with the instructions to get a clue of where things might have gone wrong. 

Recipes, like all abstractions, aim to distill complex processes into manageable steps, but they are never perfect reflections of reality.  They are a virtual analogue, an information unit that uses a system of information to represent something about the physical world.  By following the recipe’s steps, I can change objective reality to match the intended design.  
​
Having a good recipe does not guarantee a good meal.  Even if I follow the recipe perfectly, I might still accidentally make inedible slop. There are countless variables that go unaccounted for, such as ambient temperature, humidity, or even my current mood.  Even measuring by volume instead of weight, for instance, introduces variability that cleaner systems like weight-based measurements aim to reduce.

This illustration shows how measuring by volume introduces variability—demonstrating the inconsistency that cleaner systems aim to reduce.

Approximating reality

Like recipes, all systems of information simplify reality, capturing some aspects while inevitably losing others. The ‘cleanliness’ of a system’s information determines how faithfully it reflects the original.  The more ways that something can be interpreted, the less reliable the information becomes. 

In other words, the recipe becomes an abstraction of experience, and the original act of cooking is reduced down to words on a page.  The abstraction is composed of information units, such as the ingredients, the steps, temperature and time. If the recipe’s information is clean enough, it will result in only one very specific flavor experience: the meal intended by the original chef.  Most of the time, however, it’s an approximation of an experience, and the actual outcome varies significantly from the original vision. 

This degree of deviance between abstract information and objective reality is the focus of the ‘cleanliness’ metric in blob theory.  Although clean information is my preferred personal terminology, I’m not the only one to investigate it.  Scientists and logicians throughout history have been concerned with connecting abstract information to the physical world, and the methods of precision have evolved over the ages. Yet, as we’ll see, this pursuit of cleaner information systems reveals a surprising paradox: the very tools we use to define clarity are themselves imperfect.

Chasing precision

Recipes aren't very scientific.  They use some standards of measurement, like cups or grams, but they are ultimately written in simple English. English itself is a system of information units: it is composed of patterns of sound that mirror the objects and phenomena of objective reality.  As systems of information go, it's a relatively informal system. It’s not consistent or permanent enough to produce high purity information: words change meaning over time, and can have different meanings depending on context. 
​
For example, consider how “gay” as happiness and “mad” as insane have fallen out of fashion. This inconsistency over time limits English’s ability to function as a clean system.  Words can also have their meaning change depending on the context, like how ‘mad’ can mean insane, but it more likely means angry and on occasion means smitten.  This inconsistency does not disqualify language from being useful - language is obviously the dominant strategy of information transfer we have.  That being said, English is not optimizing for precision because words are naturally ambiguous.

A comic (not made by me) mocking the ambiguity of the English language

​The inconsistencies in natural language, such as evolving meanings and contextual ambiguity, highlight the need for systems like ‘syllogisms’ that aim to reduce such ambiguity and bring consistency to reasoning.  This tool can be traced back to Aristotle, whose formal logical systems are still present in our modern day technology. In order to clean up the system of plain language, his ‘syllogisms’ make statements with high standards for truth and cleanliness.  The syllogistic format is pretty straightforward: it proposes premises then draws conclusions based on the laws of logic.  You can think of it as an if/then statement.  

As an example, consider the following statement: 
If I have a brother and his mother is alive, then my mother is alive. 
​
The premise does not explicitly state that I have a mother or that she is alive, but it provides enough information to easily come to the logical conclusion.  This ability to draw conclusions relies on clean information that satisfies Aristotle’s three laws.  This means the concepts of ‘mother’, ‘brother’, and ‘alive’ all being well defined, consistent, unambiguous and non-contradictory.  By avoiding most of the ambiguity found in language, it revolutionized how information could be treated to be more reliable and consistent. Aristotle's syllogisms were a groundbreaking tool for cleaning information, and their influence persists in everything from formal education to computer algorithms.

The path to clean information didn’t stop there.  The evolution of cleanliness took a fundamental leap with Boolean logic, which fused logical principles with symbols and equations.  Instead of expressing a statement with the natural language of syllogisms, you can use mathematical signs to manipulate information with greater rigor and precision.  This can mean using operators, like ‘>’ meaning ‘greater than’, or ‘+’ meaning ‘and’.  This symbolism gave rise to statements such as the following symbolic representation of the first law (the law of identity) =

A=A
Units have consistent identities that do not change over time

This equation effectively says something is equal to itself, using the symbology used in formal academia.  This example is one of many forms that the symbols took, and they continually evolved across separate disciplines and across history from Boole to Gödel to Turing.  The trend of cleaner and cleaner information units has continued through the modern age: the codes that power the content of your digital screen are built from binary bits of logic that have passed through the evolutionary pipeline of information purification.  

Yet, in this process, it was proven that perfectly clean information units can’t be achieved. Gödel demonstrated that no system of logic can be both complete and consistent. Even the cleanest systems contain truths they cannot prove, revealing the limits of absolute precision.  

Perfectly CleanJust as recipes aim to standardize cooking, syllogisms and Boolean logic aim to standardize reasoning. But like recipes, they simplify reality and can never fully eliminate ambiguity. Despite being relatively cleaner than English, they still all sit on the same spectrum that describes different degrees of cleanliness. There is no binary distinction between ‘clean’ systems and ‘dirty’ ones. 

All systems require some blurring or editing to translate objective reality into information units.  As an example, imagine building a perfect map of a territory, a map so detailed it includes every blade of grass. At some point, the map becomes indistinguishable from the territory it represents, defeating its purpose as an abstraction.The closer you get to including perfect detail, the less practical the map becomes. Similarly, logic seeks perfect cleanliness but collapses under its own weight when pressed to its limits.

If information can’t be described in binary terms, then it means that information is in some sense illogical, meaning that it doesn’t satisfy Aristotle’s 3 laws (despite being built upon them).  After all, logic fundamentally relies on binary validation. If cleanliness itself is a gradient, then it fails the expectation of classical logic’s rigid requirements. This contradiction suggests that even the foundation of logic itself rests on imperfect ground—a flaw baked into the very tools we use to understand the world.

This paradox is more than an intellectual curiosity—it challenges the foundations of how we process, categorize, and act on the information that shapes our lives. Despite being the foundation of the modern Western world, logic is a system that somehow doesn’t abide by its own rules. The concept of units themselves, or categories themselves, is contradictory. How does this make sense?

Rejecting Logic

This episode, I’ve explored how we use clean information units to reflect and capture objective reality, whether through recipes, language, or formal logic. I’ve also shown that, despite forming the guidelines for logical thought, the idea of ‘cleanliness’ itself can’t exist as a binary category. This contradiction aligns with insights from Eastern philosophies like Taoism and Zen Buddhism, which reject binary thinking as part of their core beliefs.

This rejection of binary thought and categorical thinking can feel deeply unintuitive to the Western mind. After all, our default intuitive model is built on clean information units. Still, in the next episode, I’ll introduce my own model of inverted logic: a conceptual system that uses gradients of concentration and solidity to describe reality without relying on classical logic. This approach has guided my decisions, and I hope to make its value accessible to you.