An intro to better Mental Models, part 1

Creating a framework for our mental models

• Google learns the internet by repeatedly scanning or canvassing it and then examining the results of those scans.
• We learn things through direct experience and by analyzing those experiences in retrospect.
• Google builds a model of the internet when it scans and then examines.
• We build mental models by having experiences and then looking back on those experiences.
• Google builds its mental model equivalents so that it can respond to search requests.
• We build mental models so that we can respond to life. These mental models are what we use to solve problems. And they are what we use to make life easier.

One of the problems with our built in mental models is that we don't a framework that ties together our mental models meaningfully. Such a framework might make learning more efficient, and could give us the ability to view our mental models (and the systems they represent) from different perspectives.

We also may not have an understanding of the steps required to create mental models or to make them more effective.

Making mental models easier to learn

The purpose of this article is to introduce a modular approach to mental modelling that can make mental models easier to learn, more effective, more efficient and provide a framework that makes it easier to change our perspective.

Why?

One reason is so that we can learn more efficiently (and if you like, more effectively). The sooner we learn, the quicker we can use that learning. And so that we can learn quicker it helps to have a general process to understand what learning is, and also to make the process of learning anything a little easier.

The ability to change perspectives easily can make it easier to solve problems or at the very least make it easier to understand the actual problem. That then makes it easier to get to work on solving the problem (if there is indeed a solution).

In general, the easier it is for us to create mental models, the easier it is to get on with using them to act more intelligently and more meaningfully, without thinking, should and when we choose to.

Making mental models relevant

Something else that we can take from google is the idea of relevance. Google not only indexes web pages, it also ranks them. Ideally it ranks them so that the pages most relevant to our needs are at the top of the pile of search results.

The aim of this article isn't to rank models, but instead, to show you how we can model the same thing in different ways depending on our intent.

The idea is to create models that are relevant to that intent.

And so if we have a number of options for modelling something, the idea is to choose based on what we aim to do with the model. This includes picking the scale of the model or the level of detail or zoom at which it models the system in question. And it can include choosing which parts of the system to model.

The idea is to model as generally or as specifically as required.

Another idea of this article is to help you understand that we can always improve or augment mental models. So if we start of with the purpose of learning a model based on one particular intent, we can always build on that model at a later date with a different intent.

Four basic types of mental model

On occasion it can help to think of mental models in terms of four basic types.

The idea of categorizing mental models is to make it easier to understand how the same basic modelling process can be applied to all four types. Or rather, how the same basic mental machinery can be used to create these four types of mental model.

• A functional mental model is one that represents how a system works.
• A predictive mental model is one that, ideally, helps you to predict how the modelled system will respond to various changes.
• An informational mental model is one that stores information and allows for its retrieval.
• An executive mental model is one that generates a particular thought or action in response to some stimulus. We tend to call these habits or "muscle memory".

A necessary part of effective mental models, is having some sort of "experience" of the system in question.

Another necessary part is being able to view component parts of the system in question. With informational and executive models, this "experiential" view is a way of uniquely identifying and connecting the "component" parts.

Learning 101 models versus learning 4 models.

An article on the Farnam Street blog (FS for short) was the main inspiration for this article. The post in question lists about 101 different types of mental model (The article actually mentions over a hundred!). A mental model is a way of seeing the things in the world or ourselves in the world.

The idea of the FS article is to help us learn models that we otherwise might not be exposed to, and in turn embed these models in a latticework of theory so that the models as a whole are more useable.

I'll suggest here that the models that the FS blog refers to are the rough equivalent of the exercises a coach might assign an athlete. Generally, particular exercises are used to target particular muscles. So for example:

• If you want to work on your pecs, do bench presses or push ups.
• If you want to train your lats, do pulls ups or chin ups.

Now imagine if muscles could be trained, in part, by directly controlling those muscles. Then, instead of proscribing a particular exercise, the idea instead is to train a particular muscle in a variety of different exercises. You would no longer be reliant on just bench pressing or push ups to train your pecs. Nor would you be reliant on just pull ups for training your lats.

What if we could use a similar approach for mental models?

Instead of learning 101 or so different models, we learn the basics of modelling itself.

Instead of a latticework of different models, what we potentially end up with is a latticework of concepts that can be applied easily to any situation and to any system.

Now, instead of thinking "which of those 101 mental models applies" we instead get on with modelling the system (or the problem, or even how we relate to the problem) directly using a set of simple and re-usable components.

So what might some other advantages of taking this approach?

The advantages of a general approach

Going back to the coach and the athlete for a moment, if an athlete learns to feel and control different muscles, they can, rather than just using different exercises, use their muscles in different ways while doing the same exercise. This can allow them to find, on any given day, some muscle activation (or relaxation) that allows them to do an exercise with greater ease or efficiency. Or if they are weak on any given day, it gives them the tools to remedy the weakness.

A more general advantage is that if someone learns to feel and control their muscles, they can use that sensitivity and control in any endeavour.

Muscle control in this case isn't just flexing muscles as a body builder does. (And this isn't meant to disparage body builders.) It's actually activating muscles in such a way that we use the sensations that they generate, both muscle activation sensation and connective tissue tension, to actually get a sense of what our body is doing at any moment in time.

And so, muscle control involves sensing out body (via out muscles) as well as controlling it (again, via our muscles).

This, along with noticing how we interact with things, via pressure and skin contact, is something that can be applied to anything we do, whether laying a table for dinner, practicing calligraphy, partner dancing, using tools and so on.

A flexible and general approach to mental models

With mental modeling we can take a similiar approach. Instead of learning 101 or so different models, we learn how to make models themselves using a set of simple and reusable components.

The idea is to be able to use the same concepts over and over again when creating mental models for different systems.

By learning to feel and control muscle, we can then use that ability in any physical endeavour. With mental models, if we use the same basic conceptual building blocks, we can re-use these same components over and over again.

Rather than thinking about how to model a system, we can get on with the process of modelling it. And we can use the same basic process, and the same basic conceptual components no matter what the system we are modelling.

Using another analogy, what we end up with is the equivalent of lego blocks, (and included in this set of leg blocks, motors, and means of transmitting force so that our resulting constructs can actually move and do things) that we can use to create a wide variety of things.

Or going back to the smart device analogy, what we end up with is the equivalent of a smart phone that can be programmed to do anything, versus an old style phone with physical keys that can only do one thing when we tap them.

Instead of learning 101 different models, we learn four basic models, and more importantly, the basics of mental modelling (that we can apply to any of these 101 different models if we choose).

We end up with a flexible mental modelling system that makes it easier to model any system directly (or in the case of predictive mental models, indirectly).

A systematic approach to learning anything

We can equate the process of creating mental models to the process of learning.

Mental models are what we build and develop as we learn.

If we equate the creation of mental models to the process of learning, what we can end up with is a simple tool for learning.

This mental-model-learning-system can be applied to systems outside of ourselves. It can be used to model systems that contain ourselves. And we can even use it to model the various aspects of ourselves.

Note also that mental models as described here aren't ways of thinking. They are instead representations of different systems that we have learned.

And this isn't to say that thinking is unimportant. Instead, thinking is the process we can use to help develop these mental models and to help improve them.

Built in error-detection

One of the mental models that the FS blog includes is one for bias detection.

With the zeroparallax "mental modelling system", error and bias detection are built-in to the model building process. Or it might be better to say that the modellling process involves looking at the same system from different points of view. These different points of view help to improve understanding. And they also help us to see how we relate to the system in question.

Solving problems

Mental models are also very useful for solving problems. I'd go as far to say that they are necessary for solving problems.

Part of dealing with problems is learning how a system is supposed to work. If we know that (or learn that) we can then work towards getting the system to work as it is supposed to.

When we learn how a system, or part of a system, works, that learning becomes a mental model. Or in more common word usage, we understand the problem. We can then go about fixing it.

If we don't understand the system where the problem lies, part of the solution is learning how the system works so that we can fix it.

A system for modelling systems

One of the main aspects of the FS approach to mental modelling is creating a latticework of models. The purpose of this latticework is to give mental models some sort of unifying cohesion much like google gives the internet some cohesion.

In this article, and on this website (zeroparallax) in general, the idea is to introduce a system for creating mental models. This systematic approach to mental modelling (call it the "zero parallax" approach) has the "latticework" already built in. The latticework is actually a fundamental aspect of any and all non-shallow (or non-superficial) mental models. If a particular mental model doesn't contain some sort of lattice for holding the component parts together, then it is a very limited, and not very useful, model.

This systematic approach to modelling in general helps to hold the various mental models together by building them from the same basic "conceptual" components.

Mental models are like maps

A mental model could be thought of as a representation of a system in a way that a map is a representation of a piece of earth. One major difference between these two is that with a mental model, you aren't just taking a single view of the system in question.

As an example, the plastic models of various war planes and tanks that I used to build as a kid could be thought of as surface representations. They capture the outer appearance only. On the other hand, a fully working but miniaturised model of a car engine, that when you add gas and then crank up so that it fires up and works, that is a rather more detailed representation. It is an actual "scaled" model.

This isn't to imply that maps are useless. They obviously are otherwise we wouldn't use them.

The point of using maps

The point with maps is that they help us to see where we are with respect to the land.

While we are actually on the ground, i.e. in the territory, it can be hard to know where we are. And so we stop, noting obvious landmarks and use them to help figure out where we are on the map and thus where we are with respect to the land. Generally, in order to check the map we stop walking.

As another analogy, when an artist paints of sculpts or draws, they will, at times, take a step back from their work. They rest from the work to see how they've progressed and to see how what they've done matches the idea of what they want to do. They can then carry on or make corrections if they are required.

Driving solo and without the aid of GPS a driver can stop their car from time to time, perhaps at a convenient layby, to check their map to make sure they are still heading in the right direction.

And in the same way, someone navigating their way by foot can stop from time to time, look for landmarks, references so that they can see where they are on the map, and thus where they are in relationship to where they want to go.

While an artist can physically step back from their work to see their progress, with navigating, that's a bit harder to do. Hence the need to stop and check a map.

Is GPS a good thing?

I wrote the above from the perspective of someone who doesn't often use GPS and in general dislikes it.

There are arguments how relying on GPS isn't a bad thing. But, if you understand how to use maps, then you understand how the map relates to the environment. Via the map, if you can figure out where you are on the map, you can then figure out where you are with respect to the environment.

With GPS, you don't get that opportunity to problem solve, to figure out where you are on the map, and thus where you are with respect to the earth.

This idea of understanding how things relate is an important part of mental modelling.

That being said, whether we use GPS or a map, what can be even more important is gaining enough experience of a region that we don't need either. (This assumes we are visiting the same territory more than once!) Then the understanding of the territory becomes an aspect of a mental model that we can access at any time. We then don't need a map or GPS.

The two necessary view points for any mental model

With mental models as discussed here, the idea is to build a mental model that not only shows the component parts, but also how they work together. What each mental model requires is two viewing angles.

This second viewing angle is, in some cases, the rough equivalent to a latticework, the same type of latticework that the FS blog uses to hold it's 101 models together.

Note that Leonardo da Vinci wrote, way back when, that in order to understand a drawing of something, you need three points of view. He was talking about when viewing something in space.

The two points of view necessary for mental models relate to both time and space.

In this case, to understand time and space with respect to mental modelling, it can be helpful to view time as a wave (or set of waves) travelling through space.

We can either be on a particular wave of time, or off it.

• Riding on a wave of time equates to the system when it is actually working.
• Not being on a wave of time equates to the system when it is turned off.

This may be easier to conceptualize by thinking of a flashlight.

• When it is turned on, and assuming it has a battery, electricity flows and the flashlight shines a light.
• When it is turned off, electricity doesn't flow. The flashlight can then be taken apart.

We can liken the flow of electricity to the flow of time.

When the flashlight is working, time is flowing within the flashlight. When it is off, time stops flowing.

The river of time

Viewing a system when it is working is the temporal view. This is the view where we see (or imaginarily see) the system experiencing change and responding to it.

Viewing a system (or a model of a sytem) when the system is turned off means that we can take the system apart if we choose. We can also then reassemble it. This is the spatial view, the view where three points of view are helpful.

To better understand the difference between these two points of view we can use a flowing river as an example.

• We can view the river from the either bank. If we turned the flow of water off, we could even look at the river bed itself. We could make changes to the river bed if we chose to.
• We could then view the river while actually in it. Now we can actually experience the flow of water. And we can allow the flow to carry us. And we can guide ourselves within the flow if we chose.

An important point is that when we are in the river we can feel the flow as it occurs. We can feel the force of the river pressing against our body (particularly if we are standing on the river bed). In this way we can directly experience the river in a way that is not possible when we simply stand at the side. Thus the temporal view can also be thought of as being in the flow.

Stepping in and out of the flows of time

Note the terminology here may not be ideal. The temporal view can be taken to mean we are actually riding the wave of time. It's the wander wandering. But the spatial view is when we step off the wave of time. This is where the wanderer checks their map and sees into the past or the future, of they simply see where they are with respect to the land.

A more important point is that rather than worrying about the names or terminology, focus on understanding the idea that we can either be experiencing a system while riding the wave of time, which equals when the system is turned on and operating. Or we can viewing the system while it is turned off, and potentially in parts.

An example of the effectiveness of models created using two points of view

As an example of the effectiveness of using both possible points of view for modelling systems, when apple designed the software for their ipad apple pencil handwriting recognition, they didn't just study previously written examples of hand writing. They also monitored volunteers while they were actually using the devices.

Via sensors they directly experienced (and recorded data from) the act of writing. As a result they were able to develop software that is local to the device being used. Instead of relying on cloud computing, an apple pencil and ipad combination can perform handwritting recognition using the database or "model" that they have developed in concert with the devices processor.

These models are a lot more compact because they were created using both an experiential point of view and an "after the fact" point of view.

And so an important aspect of building mental models is building them up using two points of view. One view is where we view the components the spatial view. The other is where we view changes in the system as they actually occur, the equivalent of being in the flow.

A Dauntless approach to modelling systems

Depending on the type of systems that we are modelling, it might seem quite daunting to look not only at all the parts of a system, but also at the changes that occur while the system is operational, particularly if we are trying to build a mental model of a very big or a very complex system.

The way of dealing with such complex systems is two-fold.

One aspect of this is to take a fractal approach and choose the scale and level of detail with which we view the parts of the system. Depending on the system, we might choose to study deeply some parts of the system while taking a shallower peak at other parts.

The other aspect is to break down the system in question, at whatever scale we have chosen, and focus on learning both the spatial and temporal views of the parts in question.

There can be some trial-and-error, both when picking the scale or level of "fracticality" and how we break the system down. This may actually be an important part of the process. (The struggle of figuring out how to model a system turns to makes the end result more joyful. But it also offers potential future avenues for exploration.)

When fractacality is self-evident

It should also be noted that with some systems, the scale of fracticality and the break down is self-evident.

As an example of this, when learning to fix small arms while in the army, we had to strip weapons and put them back together again. The parts of each weapon provided a pre-defined fractacality.

Likewise with building a motorcycle from a mix of second hand and new parts. While I didn't learn how all the systems functioned, whenever we had problems, I focused on the subsystems that we had the problems with, looking at components and trying to figure out how they were supposed to work together.

With other types of system, the level of fractacality can be chosen based on what we are trying to do.

Choosing the level of fractacality

Fractacality can be thought of as the scale and detail with which you view, and model, a system. Another term is "level of break-down" or more simply, reduction. A good example of something that can be broken down in a number of ways is Chinese characters.

Made up of brush strokes, it is possible to break down Chinese characters into brush strokes, which is handy when you are learning to paint or write them. But if you are more interested in elements of meaning, then reducing to brush strokes is useless because brush strokes don't have meanings associated with them.

And so when looking at breaking characters down meaningfully (or even phonetically) the smallest unit is a collection of strokes which can be thought of as a character element.

So for example, 日 and 月 are both characters. But they can also be character elements. As an example, in the character 明. The first means sun, the second moon (which also bears a resemblance to the character element for meat) and combined, the resulting character means bright or smart.

And so when we have the option of selecting a level of fractacality for reducing a system, it helps to know what we are trying to do. That knowing can then guide the scale with which we view a system and how we subsequently reduce it.

As an example, for a doctor or dentist, understanding different types of cells, nerves and various subsystems of the body is part of what they need to do their job. However, a yoga teacher studying anatomy doesn't need quite that level of detail.

For a yoga teacher or martial artist, learning bones, muscles, joints and associated connective tissue can be sufficient, particularly if they spend the time also learning to feel and control those structures and systems in their own body.

When looking at our own body, we can look at muscles, bones, joints etc as components. We can use anatomy texts to learn these components. From there we can turn various muscles on and off in our own body in order to directly experience them.

At what other scale we are using, we should be able to view a mental model from two points of view. We can look at the components that make up the model. We can also look at the relationships between these components, how they communicate or change each other.

Initially, our mental models might only model a system at one particular scale. (And depending on the system, this may be all we need.) But as we gain more experience and understanding of the system in question, our models themselves can become fractal meaning that we can view the system (and understand it) at varying levels of detail.

Laplace transforms: changing points of views to make problem solving easier

Since we have two necessary points of view for creating a mental model of a system it might make sense to have two types of components for modelling any system. Or to have a single component that we can view from two different points of view.

To get a better idea of this, when I was in university, (and perhaps even before that when I was studying A level maths) we looked at Laplace transforms. The basic idea was that you can look at a spiral from two points of view and get two different pictures.

• If you view a spiral from the side you see a sinusoidal wave form.
• View it from the end and you see a circle.

Big deal, right?

Well, for each of these views there is a specific type of equation. The equation taken from one point of view might be difficult to solve and so with the laplace transform you change from one view to the other. This ideally makes the equation easier to solve. You solve it. Then you switch back to the original view.

Zero parallax mental models use a similiar approach.

<Ideas> as components for mental models

With the zero parallax approach to mental modelling one of the basic components of any model is termed an [idea].

An idea is something that is clearly defined. Another way to put it is that it is something is easy to recognize.

Another way to think of an idea is that it is something that creates a change when connected to another idea.

In isolation, an [idea] is the potential for change the way a battery is the potential for change when it is still in its packet, not plugged into any device. And so an idea in isolation corresponds to the view of a system when it is turned of and potentially pulled apart.

Each component of a system can be thought of as an [idea].

Note that this view of the system can include parts in isolation. It can also include show how ideas relate to each other when the system is assembled but turned off in the same way that a battery can be inserted into a flashlight, but the flashlight is turned off.

When an idea is connected to another idea, the result is a [relationship].

<Relationships> as components for mental models

A relationship consists of two, and only two connected ideas.

One way to think of a relationship is that it is the smallest possible system.

With a relationship, the potential of the connected ideas is realizable. A battery inserted into a flashlight makes the potential of both ideas, the flashlight and the battery, realizable.

With a relationship, we can view it in terms of the two ideas that make it up. We can also view it in terms of the change that is generated by these two ideas. For the flashlight, we can think of it in terms of a battery and the flashlight itself. But we can also think of it as a source of light, of illumination.

Thus the working flashlight becomes an idea also.

Going back to the two general definitions of an idea:

• An idea is something that is easy to define or is easy to recognize
• An idea is the potential for change

The potential for an idea is realized when it is in a relationship.

So now, if we have a working flashlight, we can use it to illuminate our surroundings.

We can view ourselves, the flashlight and our surroundings all as separate ideas. We can then look at the relationships between each of them. What we then have is a [system].

<Systems> as mental model components

A system is anything of made up of more than one relationship. If we have systems, why bother with relationships? Why not just have systems and ideas?

Relationships are a basic vehicle or context for change. We can't have change unless we have two related, or connected, ideas.

In terms of a system (which is more than one relationship), relationships allow us to tour the system one relationship at a time, in particular while it is working.

Relationships and ideas make systems easier to understand from two complementary points of view.

As an example of this, there is a concept termed "Working from First Principles". It is a very powerful concept. But it is limited in that it tends to focus on breaking complex systems down into components. But it doesn't provide a way of breaking down systems into component parts while they are working. [Relationships] provide that missing link.

Relationships allow us to view a system and make sense of it while it is working, one relationship at a time.

Taking a break from mental modelling

If you've read this far, you might choose this time to take a break, or even to read over what we've covered so far. The basic ideas are: ideas, relationships and systems, plus choosing the level of break down plus viewing any system, and thus modelling it from two points of view the temporal view, when we are riding the wave of time through the system, and the spatial view where we can take a step back from it. The spatial view is where we can take the system apart view its components and how they relate because it isn't working. With the temporal view its just as important to be able to isolate parts of the system while it is working so that we can understand it.

The next part of this essay will approach the actual learning of mental models. How do we make this approach more enjoyable (or less frustrating)?

Note that when actually building mental models, aka "learning" rest is important because that is when are brain does the rough equivalent of compiling it or if you like turning it from a beta version into the version that is actually meant to be used.