What Goes Without Saying

Buckle up, sunshine! This is going to be a challenging post. I will describe reasoning, intuition, allegories, etc. I will do my best to be specific so that you can start implementing those features. I don't want to sound like one of those many who talk without saying anything. Expect value.

Iceberg

Objects are multidimensional in terms of their properties. But only a subset of those properties is affected by any action. Just like the tip of an iceberg.

Object recognition uses only a fraction of an object's properties to classify it. I described multiple times how intelligence does that. The algorithm is similar to that of the game 20 Questions. We start with a set of all possible classes. At any stage, we consider properties that split the remaining classes in that set roughly in half. "Is it tangible? Yes." As a result, we eliminated all the abstract classes like "democracy" and now we can classify our object as Tangible. The object may have many more properties. We used only one to classify it. "Is it animate? Yes. Is it an animal? Yes. Does it feed offspring with milk? Yes." And we arrived at Mammal. Only 4 properties. The tip.

References in natural languages also use only a subset of the relevant object's properties. There are many approaches to pick that subset but the core requirement is that the properties from that subset differentiate the relevant object from the current context. Categories and names narrow down the set fast but sometimes they are insufficient. "Footbal player" leaves you with 22 objects. "John" in a big audience most likely filters many fitting objects. "Einstein" will be utterly useless to filter the required person during the Einsteins family dinner. If one property is not enough we add more.

The filtering algorithm used above is in fact the core algorithm of cognition. Here it is - the selection of the most fitting option among the available ones based on relevant constraints.

The fact that the algorithm uses only a subset of properties of the options considered makes its performance fast and good enough for real-time applications. If the tip of an iceberg is enough why bother with the whole of it.

You may now suspect that this algorithm is somehow used in reasoning, intuition, etc. Indeed, it is. But be careful. The whole of the iceberg becomes relevant in the process.

Formulas

Language is formulaic in terms of constituents. Take any sentence and replace one constituent with another fitting one and you will get a valid sentence.

Constituents in sentences are references. We have already mentioned that they rely only on a subset of the referent's properties which depends on a given context. The referent itself has many more properties. The below of the iceberg.

Just like we have SVO and SVC sentence types we store information about classes of objects and their unique instances with respect to their dynamics and statics. "John is a teacher" provides information about a specific instance of the class Human and its property "occupation". "John hit a teacher" provides information about one interaction of a specific instance of the class Human with another specific instance of the class Human having the value "teacher" of the property "occupation".

Every phenomenon (be it a class or an instance) has its properties which may change over time. Not only objects. Actions, locations, time points or periods also have properties. For example, the action "hit" requires a subject and an object and possible a tool. It may affect the states of all three - physical, emotional. When we say "hit" we only gently touch the tip of the iceberg.

If sentences are formulas then questions are equations with one unknown (questions with two or more unknowns are not much more complicated). Sentences rely on a context and questions rely on the same context. How do we answer questions?

In physics, when we know time and distance we apply a formula and calculate the speed. In natural languages, the formula metaphor no longer works because we do not compute the answer. Rather we select the most fitting phenomenon (remember about actions and locations?) from the context. If you are attacked by a lion and see only a stone and a stick nearby you may ask yourself, "What weapon should I use to defend against the lion?" "Calculation" would give you "a gun", the context only leaves you with the stone and the stick. Consider the multiple-choice questions with no perfect options as a better metaphor.

Answering questions, intelligence uses its core algorithm - the selection of the most fitting option among the available ones based on relevant constraints. In the above case, the constraints may include: "is the stone or the stick close enough?", "is the stone light enough for picking and heavy enough to inflict a harm on the lion?", "is the stick thin enough to grab and thick enough to hit the lion hard?", etc.

Why do we pick those constraints and not such ones as "color" or "does it remind me my grandpa?" Because of relevance. Each action may or may not move the needle, bring us closer to the goal, solve our problem. If it may it is relevant, if it may not we do not consider it.

Recipes

Is it OK to add mint to the dough? You will never know if you don't try. In fact, believe me - you don't want to try. We only want reliable recipes that produce tasty meals.

We may not understand why somethings works as it does but we value reliability. The typical religious approach to causality - "Why does X lead to Y? By God's will. Why sometimes does X lead to Z? God's will is incomprehensible." If we are after reliable recipes the religious approach is unacceptable.

Recall Einstein's definition of insanity - "doing the same thing over and over and expecting a different result."

What results are different for us? What subset of properties are we interested in? What actions affect those properties? What subset of properties are required by those actions? What values of input properties lead to the desired values of output properties?

As children we run multiple tests to figure out those causal relationships. When we are old enough we speed up the process by asking questions, "Why?" or "How?", and running more tests.

What Is Knowledge?

We know how to classify objects when we know the defining features of classes (a tip of an iceberg). We know additionally what other properties the objects of each class have (the below of the iceberg). We know how to affect objects when we know which actions affect the required properties and which input properties cause the required resulting values. That is what is known as "knowledge how".

The "knowledge what" includes facts. Where the knowledge-how is vague the knowledge-what is precise. The range of possibilities vs one actual occurrence. Facts include a lot of information. "I picked up a black stone to hit a lion" will transform "anyone can hit any animal with any stone". Generalization forgets irrelevant bits in knowledge-what to enrich our knowledge-how.

What Is Reasoning?

Roughly, reasoning is rotating the iceberg to observe all possible of its tips. One good aspect of reasoning is that its scope is limited to one question, one unknown. Again, it is easy to expand the framework to multiple questions and unknowns.

Consider an apple, for example. If we want to eat, we view it as food. If we need a weapon it may serve as a projectile. If we need a prize for a beauty pageant, well, it was used that way once.

But such a direct usage is not what makes reasoning useful. Consider planning. We may know a lot about building houses. For example, how to make a roof, how to make walls, how to install windows, etc. But each of those actions has not only resources and algorithms but also prerequisites. For example, you need walls before making a roof and walls should have proper holes to install windows. As a result, the house is considered complete if the roof is completed, but before that, the walls should be built with holes and windows installed, before that the foundation should be prepared, before that all the materials and equipment should be acquired. Prerequisites are one of the manifestations of constraints mentioned in the core algorithm.

It is possible that we don't know something. Like ancient engineers did not know about resonance when building bridges. What happens after a failure? One more constraint is added into consideration or one more option.

Now consider detective investigation. Suspects are our options, clues are our constraints, but what about lies? If we believe them the resulting set of options after processing all the constraints will be empty. In that respect, lies are similar to inaccuracies or misunderstandings. They also lead to empty resulting sets. The problem may be solved by expanding one of the constraints so that it does not filter the set too strictly. Which constraint to choose for that or which statement to suspect as false is beyond the scope of this post.

Bolts from the Blue

Intuition is often about comparing the incommensurable. And yet we find something commensurable. The second-order properties if you will. For example, if numerical estimates of two properties increase, like height and blood sugar level, we may apply the terms from one of them to the other, as a result the blood sugar level may "grow".

Time is unidirectional. What other processes are unidirectional? River flows, aging, destruction? Can we use destruction as a metaphor for time?

The number of properties to consider is limited but still big that is why we require time to get valuable insights from our subconscious "computer".

Genius of Language

Instead of figuring out the defining features of multiple concepts and connections from actions to properties, consider taking those from natural languages that followed the practical needs of multiple generations of speakers to fine-tune languages accordingly.

The role of language, as I see it, is pointing at phenomena and their connections. But language keeps only those words and phrases that passed the test of time, that is, those standing for important phenomena and everything related to them. Checking concepts referred to by content words is a promising research direction.

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But do not expect much from language. Respect also other components involved in reasoning - memory, perception, imagination, and the multidimensional modeling of phenomena by our intelligence.