Do we understand the word “understand”?
To understand a concept is to be able to connect the concept to other concepts that are already understood. Of course, this explanation is also quite vague.
Let us see if the concept of “understanding” can be broken down in a structured way.
At the bottom of the whole understanding hierarchy are things that are more sensed than understood. For example, the concept “blue (color)” is sensory despite the scientific method to defining blue using a range of frequencies. As we grow up, we build up a “vocabulary” of these ground concepts based on sensory experience.
Related to STEM are ground concepts involving quantities. The concept of “two (2)”, for example, is a basic quantity that most of us can perceive easily using visual, auditory or touch sensory inputs.
Once we have the basic sensory ground concepts and their corresponding lexicons (words), we can then connect concepts both in speech and thought. For example, the concept of “two green apples” connects quantity, color and a specific fruit together.
At this level of understanding, it is about the connection of concepts to describe facts. However, even at this level, there are unintentional traps to watch out for.
Natural languages are not precise nor concise, and thus often can lead to misunderstanding or confusion. Let us take a closer look at these two communication obstacles. Both of these obstacles occur when one party intends to communicate a concept to another party.
A “misunderstanding” occurs when the original concept is understood to be something else. This can be rather problematic because most misunderstandings are silent until the misunderstood concept is applied.
A “confusion” occurs in one of two situations. First, a description can be interpreted in different ways and results in different understandings. Second, a description does not specify how individual concepts are connected.
How does one find out that a concept is misunderstood?
There are two main venues. First, explain the concept back to the originator but do not use the same words. Second, try to apply the concept and find out whether the understanding is correct.
More importantly, however, how does one even start to suspect a concept is misunderstood?
This has to do with a constant and subconscious cross checking mechanism in the mind. We will get back to this later (TODO).
Confusion is not as difficult to detect because a described concept “is not clear”. The question is what to do with this description that is not clear. We will get back to this later, as well (TODO).
A higher level of understanding involves concepts that are connected not by association (“a green apple”) but by logical, causal or consequential connections (“drinking black coffee turns people psychopathic”).
In the STEM field, most concepts involve this kind of connections rather than the more superficial associative connections.
Let us consider an example.
The description: A heavier car leads to higher accident survival rate. There are two levels of understanding. The first is to associate the concepts correctly, and most people do not have any problem with this part. The second is to fit (or not) this concept into an internal logic framework.
A person who is exposed to physics may connect “heavy” to “more mass”, “accident” to “high deceleration/high force” and “deformation of vehicle”„ “survival” to “avoidance to damage to vital organs”. This is a form of connection, but the connection is no longer to concepts in the description itself, but to other learned concepts.
Once the new description connects to other learned concepts, one can start to determine whether the new description fits and therefore can add to the existing logic framework. This is where logical steps occur.
However, a person who is also exposed to vehicle dynamics and actual crash test data may not stop at this point. Additional concepts and facts may get connected:
In light of the conceptual connections to these known facts, and based on the reasoning, the new claim is not as readily integrated into the logic framework.
Given logical connections that suggests consistency and also inconsistency, the resolution requires additional data, information or concepts. For example, it may be helpful to look up statistics collected by the government or insurance industry, or narrow down the claim to a specific vehicle instead of applying the claim in general.
Within a sentence, paragraph or section, which word is associated with which other word in what way? This is a reading technique. The key is to find out:
Note that when reading a technical document in STEM, the techniques used in reading novels should not be applied! Do not skim, do not just look for keywords. Every word counts!
This part does require focus because it involves mechanical reading efforts. Being distracted when reading text is not productive. Sometimes drawing diagrams, writing notes and comments can help the mind stay in focus.
This is about establishing a context of a description. What known concepts are a description connecting to?
In the mind, it is about “this reminds me of (?)”. Too little cannot establish the right context, but too much can also lead to much distraction.
It may be helpful to sit down and actual write out concepts that form the context of a description. This part cannot be done by determination or a mindset of accomplishment. Instead, it is often beneficial to let the mind roam free and let the subconscious make the contextual connections. Consciously thinking with focus is often not productive.
Note that to store contextual concepts, studying can be helpful. Reading textbooks, notes, watching fragments of a recorded lecture can all help build up a contextual database.
This is about reasoning and establishing reasoning connections between a description and the context.
In STEM, this part of understanding is often the most challenging part. It is crucial to make logical connections between a new description and concepts connected by context. Not all contextual concepts may apply, but some logical connections to already well understand concepts should be made.
Trying to explain a concept to another person can be very helpful with this part of understanding. Another suggestion is to apply the concept and see if the outcome is consistent with the prediction based on the understanding of the concept. Of course, this means the inability to come up with a logical predication automatically suggests a lack of understanding at the logical level!