How you model a concept in your head determines depth of understanding of the concept – and what use you can make of it.
When I need to travel to a new location how well I recall the route depends on one of the following:
I was taken there.
I used a GPS
I made a mental model of the route – this means taking a journey in my mind, seeing the turns and land marks as clearly as I can. This technique is even easier now with Google streetview.
If I use either 1 or 2, I may never fully know how to get to a new place without the assist. However, if I use 3, I nearly always drive straight to it.
Point 3 is an example of a mental model; it's creation requires specific attention and technique – it's simple, even obvious yet unless I use it, it would seem I didn't have any sense of direction in a new location.
The same notion of creating deliberate models of ideas applies to anything we can learn. Some material lends itself directly to making easy mental models – basic mechanics, carpentry, building are good examples. They require concrete interaction, it's quite easy to imagine seeing and feeling how things go together and what the end result might be. This does get more challenging at the more expert end of the scale as there are more concepts to work with. For example, trying to imagine how a change in alloys used in a cylinder head affects it's material properties when running is a task for computer modelling tools. However, even here an experienced engineer may well have a reasonable estimate between widely contrasting alloys: too hard = fracture risk; too flexible = wear risk.
This idea of making mental models is one that can make a tremendous difference between understanding and using knowledge vs merely memorising pieces of it.
For example:
I have a machine that takes in a list of numbers, grouped in batches of 3. You feed the instructions into a slot that pulls the list in, one batch of 3 at a time – each batch is an instruction, each instruction requests one of twenty shapes.
On the top of a machine is a large tank that has thousands of tiny geometric shapes inside. There are only 20 different types of shape. Each one is a type of magnetic - think of magnetic toys like this Magnetic Toys
On the back of the machine there is an output pipe, with a chain made from the shapes in the tank. As the length of the chain increases, it flexes and warps due to the combined influence of the different shapes that make it up. This time, it comes out coiled.
A machine like this is easy to imagine. You can also imagine how the list is made – perhaps stamped out, instruction by instruction from a template.
Once you have imagined such a machine, it's fairly easy to remember and perhaps even apply the idea to another type of machine.
In this instance, in a simplistic* fashion, I described the notion of RNA → Polypeptide synthesis via ribosome. In other words, how you get from DNA to a protein.
In terms of learning new concepts, the idea of deliberately choosing how to make a model in your mind of what you are learning can be very powerful. When I first learnt to program, copy and paste coding was common. Fortunately, this stage lasted for a short time as such a method means you can't understand the why behind the code.
Still, for a long time, a lot of coding I worked on I found syntax to be a constant bane. The simplistic answer would be to memorise syntax – a question seen on StackOverFlow and Quora quite often.
Yet, such a task – even if successful – lends itself to a low return on investment (ROI). We arrive at the point of mental models : return on investment.
Each fact, that is rote memorised, in relative isolation yields a linear ROI. Your skill and knowledge of an area can be charted on a small graph directly in proportion to the number of facts you learnt. This is the land of trivial pursuit mastery. That is not to say facts are not important, quite the reverse, but the rote memorising of them is the least efficient method of knowledge acquisition I know of.
Like many things, knowledge itself has structure – for the purposes of this article, I'm simplifying this idea enormously.
So, what is more useful to learn than facts?
Rules and the principles behind them. Rules in many systems of knowledge generate facts of various kinds – whether we are using engineering calculations to work out what our ideal alloy should be for that cylinder head or whether we can predict from an RNA sequence that we will get a beta sheet or alpha helix secondary structure for our new protein chain.
The principles are the foundations from which the rules will spring – there are often many of these at play to produce the rules we can rely on. Going back to RNA → protein as an example, what are the principles then? Here are some, loosely summarised:
Magnetism and polar vs non polar molecules.
For the shape of a molecule, we can look at valence shell electron repulsion theory to derive bond angles, from there we have aS model of how a collection of hydrogen, oxygen, carbon and other atoms will bond together.
Lowest energy principle will guide what the model of this collection will actually look like.
From these we can predict which direction the next amino acid will bend towards based on it's charge profile vs it's predecessor. To do this we can also build a model of how each shape will actually look and finally, to determine the secondary structure – sheet or coil – we can use calculations based on the ideas of the lowest energy principle**.
The example above is rather rough example of deriving knowledge, rules from a principle. However, principles or underlying theory, often lend themselves to being mentally modelled.
For me a test of understanding is simply whether I've been able to construct a model that I can use about the theory or principle in question.
To understand RNA transcription, an small mental animation, similar to my description, gave me a foundation to hang finer details on. The nice part about any mental model that can be seen and touched, is you can hang finer detail onto it, refine it over years and work with it.
The subject of metaphor and analogy becomes central to the creation of mental models.
To create a mental model is a deliberate conscious act: You see, maybe feel how the thing goes together and you may well have to talk your way through it as you build the model.
Diagrams, physical models, searches online for suitable analogies are often required. Metaphors and analogies are bridges between concepts, known and unknown. Creating or finding ones that are useful for understanding new ideas is a critical practice as this is the core of understanding how exactly you think about a new idea.
Understanding how you think or represent new pieces of knowledge to yourself lies at the root of meta cognition or learning how to learn.
Here, I've attempted to illustrate the general idea of how and why you would examine your own internal representation of any new concept. And the benefits of deliberately creating a metaphorical mental model that you can see and touch.
*In this example, there is an important aspect to mental models that needs addressing: when you create one, it is a product of your thoughts and as such can also become a limiting bias if it is not sufficiently tested and validated against reality. A model is a simplification and by it's nature omits information. Here, I skip the precursor of DNA->RNA transcription mechanisms, the finer details of exactly how the amino acid shapes are joined to the resulting polypeptide and much more.
** To get a mental model of this idea – think of a bubble, whether it's on a surface like water or in the air, it always tends towards a spherical shape. It's the simplest for the conditions at hand. Another way to see it, a ball always rolls down the steepest gradient.
We could easily elaborate on the notion of the steepest gradient by asking the question – if the ball is balanced on a hill – a tiny hill – and it can choose any direction possible, which way does it go. In an abstract mental model, you can imagine no other forces other than gravity and an ideal surface. So no gravel, fine bumps on the ball surface or any other interference. It's that model I use for my example!