Advanced concept maps#

Concept maps are not just simple tools. NASA for example used the IHMC concept mapping software (described in module 6) to model pages and pages of knowledge relating to the recent Mars Rovers exploration program. Other scientists use various forms of concept maps to help decode the human genome (DNA). In this module, I introduce you to some more advanced forms of concept maps, including:

Systems concept maps. These model natural and man-made systems in which there is often no start or end point. They are often cyclical (circular) in nature.
Decision Trees. These help model mathematical options and help you make financial decisions.
Logic Trees. These use deductive and inductive logic to help you construct a convincing argument.
Software-Based concept maps. The frontier of concept maps. See how concept maps are changing the way we interact with knowledge via computers.
Other types of maps. Some examples of other types of specific concept maps.

Systems concept maps#

A systems concept map organizes information in a format that’s similar to a circular flowchart. It can show a cycle or cycles in a system.

In the following basic example adapted from Peter Senge’s book, The Fifth Discipline, the concept map shows how each element in the simple act of filling a bucket with a hose influences the other elements. For example, your perception of how full the bucket is influences the degree to which you will turn the handle on the faucet. This, in turn, influences the water flow and the current water level. You continue in this cycle until the bucket is full.

You can see from this example that filling a bucket with water is not a simple linear task. Your brain evaluates a feedback loop several times a second. Using this method you can also start to understand why it’s difficult to get the temperature of the water in the shower just right. There is often a delay between turning the faucet and the resulting water temperature. The more the delay, the more you over-correct and under-correct the faucet several times until the temperature is right. This pattern of behavior plays out in small and large systems – for example the flow of products in an industry, the movement of investors in financial markets, or the wastage of clothes in the fashion industry.

Senge chose this method to illustrate his point that we should stop using straight-line (linear) thinking and should instead see the world in terms of “circles of influence”. Seeing things in terms of circles of influence gives us a better understanding how dynamic systems work. Unlike traditional writing which take a straight-line approach to a subject, systems concept maps can account for complexities in many situations. In other words, you can see the whole of a dynamic system rather than just the parts.

Systems concept maps can show the cycles in everything from engines to sewage treatment. The following example shows the cycle of the internal combustion engine.

Such a systems map allows you to see how the elements of an engine interact to produce power and electricity in a vehicle. Describing this concept in words would take much longer and, most likely, wouldn’t be as effective in explaining how an auto engine works.

Decision Trees#

Businesses and people often need a way to figure out and clarify complex problems before committing considerable money, time and resources to a project. To do that, they can use decision trees to try to account for all variables and to figure out the best solutions. Below is an example of a decision tree. The example represents a decision that a bottled water company has to make. The company needs to decide whether to do market research before launching a new bottled water product aimed at high-performing students. The dollar amounts are in thousands of dollars (‘000s’).

As you can see in the decision tree, each option branches into the factors involved in each option. Each of these factors then branches into costs and the possible outcomes for each of the choices. Actually, this decision tree is only the first in a series of decision trees. As the company refines the chart down to the best option to take, it will revise the chart to account for all variables and then choose the most effective course.

Using this decision tree, the business people can see that they are better off not doing market research! Let’s see how they arrived at this conclusion.

Constructing a decision tree#

A decision tree has two main parts. Decision nodes represent a choice to make. Event nodes represent outcomes. Let’s look at these in more detail. Here’s what a decision node looks like:

In this example, the business people have two choices—do market research or don’t do market research. Market research will cost $50,000 though, so you write this as a negative amount below the market research option. There is no cost for not doing market research. Now let’s add an event node:

If the company does market research, history shows that, on average, 60% of the time market research is positive whereas 40% of the time research is negative (i.e., the product may not sell well). You enter these probabilities as “0.6” and “0.4” in the boxes above the event outcomes.

You build a tree using these components first, and then you “calculate the tree”. This involves working “forwards, then backwards”. Let’s look at an entire branch in our example:

Working forwards means you add all the boxes along each branch to arrive at an expected monetary value (EMV) for that branch. In the example above, you add a+b+c+d to give e. Using the numbers (-50) + 0 + (-200) + 1000 = $750. In other words, if the company does market research, and the product is successful, they will receive $750,000.

Working backwards involves using probability to work out the most effective decisions. You then work out the numbers below each option.

For an event node, e.g., point k above, k = (g x f) = (h x i). Without going into a lot of detail, this simply means that if you launched 1000 products with these same probabilities, on average you’d receive $660,000 per product.
For a decision node, e.g. point m above, you simply look at the values of each branch and choose which one is better. In our example, $660,000 at point k is better than $-50,0000 at point l, so you write 1 (for branch 1) it in the box representing the decision. You then fill in the winning value, i.e. at point m you write 660.

You continue working backwards until you arrive back at the left hand side of the graph. Once you have done that, you now have the right path mapped out for you.

Go back to our example at the start of this section. Which is the right path, according to the numbers? It’s to do no market research, and launch the product.

The chart above only covers the financial aspects of a decision. You may need to incorporate non-financial factors that may eventually have a financial impact. For example, “product failure” may affect “corporate image.” A negative impact on corporate image could result in a 10% reduction in sales of this product and other products.

Keep in mind that decision trees are useful in many areas beyond business. You can use them to help decide whether to change jobs, where to live, and what course to study. They’re useful in many areas of your life.

Logic Trees#

A logic tree is a diagram that starts with a key statement and then branches out with further logic or key points that support the statement. There are two types of reasoning—deductive and inductive—that you can use to establish logical relationships between ideas. Let’s look at each of these types in turn.

Deductive reasoning#

Deductive reasoning involves moving from things you know or assume to be true - called ‘premises’ - to conclusions that must follow from them. In other words, deductive reasoning presents a line of reasoning that leads to a “therefore” conclusion. Below is an example of deductive reasoning:

The first two statements are premises (Birds fly, I’m a bird), and the third statement is a conclusion (Therefore, I fly). By the rules of deduction, if the first two statements are true, then the conclusion must be true. Any deductive argument needs to accomplish three things:

Make a statement about something that exists in the world; i.e., Birds fly.
Make another statement about a related situation that exists in the world at the same time: i.e., I’m a bird. The second statement relates to the first if it comments on either its subject (birds) or its predicate (fly).
State the implication of these two situations existing in the world at the same time; i.e., Therefore, I fly.

Deductive statements can sometimes become too long and boring if you include every step included in the process. In cases like that, you can skip a step and “chain together” two or more deductive arguments. Here’s an example: Assume that the issue under consideration is aluminum production in Australia. The deductive argument might look like this in text form:

Australia produces enough aluminum to meet its own needs.
But exports to Asia have increased, reducing supply to below domestic demand.
Therefore, Australia has a shortage.
A shortage of aluminum causes a shortage of manufactured goods.
We have a shortage of aluminum.
Therefore, there is a shortage of manufactured goods.

This material contains a lot of information. However if you skip steps and consolidate their information into other steps, then you get a “chained” deductive argument that appears this way in concept map form:

The key in deciding whether to use a chained deductive argument is this: The reader must be able to understand the missing steps and agree with them.

Inductive reasoning#

The second type of reasoning is inductive. With inductive reasoning, you move from a set of examples to a theory that you think explains all the examples, as well as examples that will appear in the future. Inductive reasoning is often more creative than deductive reasoning as deductive reasoning tends to be “straight-ahead” logic. It’s more creative because the mind is required to notice that several things (ideas, events, facts, etc.) are similar in some way. It then needs to group these things together and comment on the significance of their similarity. Below is an example of an inductive reasoning concept map:

As a reader of the map, you’re required to infer from the lower four nodes that these factors can hurt your family in the future if the property is jointly owned.

A conclusion deduced by deduction must be true if the premises are true. But, the conclusions induced by induction may or may not be true. For example, people who visit a rainy city like Seattle in America for short periods may find that it rains every day of their visit. They could induce (or infer, or draw the conclusion) that it rains every day in Seattle. However, their conclusion would be wrong. It does rain a lot in Seattle, but not every day!

Using logic trees#

Logic trees are useful in many different disciplines—math, logic, computer science, etc. They can also help you build up a logical structure for a report or presentation. Look at the following diagram:

This diagram shows the structure of a logical argument. The main argument at the top is deductive; however, lower level arguments support each higher point. An inductive argument supports the first point, whereas deductive arguments support the next two points.

Once you have your argument laid out like this, you can then structure your report or presentation along the same lines. The top point is your executive summary; the second level points become chapters; and the third and fourth levels become sections within those chapters.

Software-based concept maps#

I’ve now covered many forms of concept maps you can draw yourself. In this last section of this module, I’d like to introduce you to some more advanced types of visual mapping techniques. I won’t be covering these in detail as my aim is to give you a taste of the variety of visual mapping tools and techniques that are available.

All of the concept maps in this section use some form of software to create and view them. Often they provide better ways to view large amounts of data that would be impossible to understand in raw form. As available computer power and software technology increases, the possibilities are endless. For example, real-time interaction with maps in three dimensions is now possible on desktop computers, and you will see some examples of 3D maps below.

The types of maps I cover are:

Concept maps with automated layout. These maps automatically arrange themselves based on the data provided, and can be re-arranged based on user actions.
Hyperbolic tree maps. These maps provide both context and detail while browsing large amounts of hierarchical data.
Squarified tree maps. These maps use layout, color, and size to provide additional insight into large amounts of data.
General 3D concept maps. Think of your standard concept maps but in 3-D.

Concept maps with automated layout#

Here we look at two forms of concept maps using automated layouts. The first uses a fixed layout format, and the second uses a force-directed layout.

Fixed layout#

The first example here uses software called PersonalBrain. The topic is the Memletics Accelerated Learning Manual. As you can see below, the concept map lays out six main parts of the Memletics Manual.

Let’s say you wanted to understand more about the Memletic Techniques. When you click on the techniques concept, the map rearranges itself as follows:

As you can see, the concepts not in focus have moved up and to the side, and techniques concept has expanded to show the six main groups of techniques described in the manual. Clicking for example on the Visualize concept, results in the tool showing the next level of detail:

The tool allows you to associate documents, image, videos, notes, web pages and other files to each concept. It also keeps track of how much time you spend in each concept. It will then rearrange the concepts based on the ones you spend the most time in!

Force directed layout#

Here’s an example of a force-directed concept map using a thesaurus as the data. Force-directed means that the software works out where to position each element based on some formula that models attraction and repulsion. If you start with the word “accelerate” you see this example:

You can see the tool placed some synonyms and related words near each other on the right. You also see that the tool placed an antonym, decelerate, on the opposite site with a dotted line joining it. Synonyms attract each other whereas antonyms move away from synonyms. The tool also models some repulsion between synonyms so that if they get too close, it moves them away slightly. This improves the overall layout.

Let’s look at what happens when you click on speed:

The map redraws itself to show words related to speed. You can hover the mouse over nodes to see more information on that node. If you wanted to hear how to pronounce the word, you can click on the small speaker next to it.

You can play with this tool online using their free trial.

See http://thesaurus.plumbdesign.com/index.html

Hyperbolic tree maps#

Hyperbolic tree maps also use force-directed layout, however they also use a view filter based on some complex mathematical functions. As you move around the map, branches that are further away disappear, while those nearer to your point of view become larger and more spaced out.

Let’s see an example. The following hyperbolic tree map shows the structure of a NASA website – the Planetary Data Store. When the map first opens, it looks like a regular concept map:

http://starbeam.jpl.nasa.gov/pdsstartree/PDSStarTree.html

The grey lines on the diagram give you hints to where more data is. See the lines below Mars? When you click and drag Mars towards the center, the map changes in real time to look like this:

As you can see, the concepts below Mars have expanded, while concepts further way have receded. You can still have a sense of where you are on the map though. When you click on any of the concepts, the map displays a web page for that concept!

Here are some more you might want to play with on the Internet:

Understanding the USA: http://www.understandingusa.com/understanding.html
Data needs planning: http://www.nass.usda.gov/research/mexsai.html
Medical research example: http://rami-s383.stanford.edu/StarTree/HPMR/hpmr.html

Squarified tree maps#

Most of the concept maps you’ve seen lay out concepts in an open space and use lines to link them. Let’s look at a completely different type of concept map. Squarified tree maps lay out concepts in squares or rectangles, and then use size, position and color to show relationships. Here’s an example:

http://www.cs.umd.edu/hcil/treemap/

This is a squarified tree map providing a view on the common causes of death for those over 65. The medical classification of the causes drives the grouping of the squares (rectangles in this case). The frequency for each cause drives the size of the squares (the bigger the square, the more deaths from that cause). The color indicates the change over the previous 17 years—green being a reduction, yellow a moderate increase and red being a large increase. (Note: you may have difficulty identifying colors if you are reading a black and white printout of this page.)

By only spending a few minutes studying this data, you can see:

The two biggest causes of death are cardiovascular diseases and cancer (neoplasms). You can compare the size of the squares to see that, for example, these two causes account for far more deaths than say Alzheimer’s disease.
The most progress over 17 years appears to have been made in cardiovascular diseases, as there is the most green area for these causes.
Progress in these areas may partially account for the significant increase in deaths from Alzheimer’s disease. As people live longer, diseases of the brain appear to be increasing.

While this is a relatively morbid topic, you can see that this view of the data provides far more insight than trying to understand text-based data. With a few clicks of the mouse, you can drill down into interesting areas, or change the data settings to look at the data in a completely different way.

Let’s look at another example. When your hard drive fills up, how long does it take you to find which files and directories are taking up the most room? The following squarified tree map provides a 3-D view of the data partition on our server.

The map shows the relative size of files and directories (surface area), the number of files, the directory level (layers) and the file types (color). Instantly you can see which are the biggest files and directories and which are the deepest directories. Moving the mouse over each block provides more data about that file, and you can click on any element to drill down to the next level. You can also move the map and zoom in to see more detail in any area.

http://www.sm.luth.se/csee/csn/visualization/filesysvis.php

Three-dimensional concept maps#

Often concepts and relationships are too complicated for a simple two-dimensional map. For example, a chemist might use only words or 2-D diagrams to explain the structure of a molecule. However, this would likely take a considerable amount of time, and, as a learner, you still might not have an adequate picture of the structure of the molecule. A better choice would be for the chemist to give you a 3-D concept map, and then use words and further illustrations to explain the molecule. More than likely, you would then have a better understanding of the molecule structure.

On the right is an image from JMol, a tool that models molecules. Notice that it’s similar to a standard concept map. The atoms themselves are the concepts and the bonds are the links. You can rotate and zoom the model in the tool to understand each of its parts. This tool also provides an additional feature that allows you to measure the distance between atoms.

http://jmol.sourceforge.net

While I still haven’t found a good tool that allows you to model concept maps in full 3D, there are some examples that go part of the way. For example, the following illustration shows one tool’s view of the Water concept map shown earlier in the book.

Created by axon http://web.singnet.com.sg/~axon2000/

I envisage these tools becoming more complex and integrated over the next few years. Imagine a tool that allows you to model knowledge and then display it in full 3D. It changes shape over time as you learn more. Concepts rearrange themselves as you add new links and work with the map. You can add in a new map from someone else, and the tool rearranges your existing map to show what’s common and what’s new. Perhaps this tool might one day replace books as the way we transfer knowledge between each other!

Other types of maps#

Here is a brief summary of other concept maps you might want to investigate further.

Gantt charts and PERT charts. Project managers often use these charts to model the sequence of tasks over time. Links between tasks show dependencies, and positions of tasks show when the tasks should occur. Various other visual elements show task completeness, delays in schedule, overruns and other information.
Data Flow Diagrams and Entity Relationship Diagrams. These diagrams model the flow of data in a computer system or database. Computer professionals use these to design and communicate information about computer software.

Summary#

Systems concept maps show a cycle or cycles in a system. They’re useful in depicting the complexities of a concept or process. They do this by showing the whole of a dynamic system rather than just the parts. Logic trees are diagrams that start with a key statement and then branch out with further logic or key points that support the statement. When constructing logic trees, you can build them with two types of logic—deductive and inductive. Deductive reasoning presents a line of reasoning that leads to a “therefore” conclusion. With inductive reasoning, you move from a set of examples to a theory that you think explains all the examples as well as examples that will appear in the future. Decision trees help you figure out and clarify complex problems before considerable time, money and resources are committed to a project. Decision trees try to account for all the variables in a situation so the best decision is clear. Decision trees have two main parts—decision nodes and event nodes. Decision nodes represent a choice to make. Event nodes represent outcomes. From these parts, you can build very simple or very elaborate decision trees. Software-based concept maps use the power of computers to help you see and visualize information new ways. They will likely change the way we learn in future.

Exercises#

Exercise 1 - Deductive Logic concept map#

Construct a visual logic map from the following information about a company:

Any corporation meeting three specific criteria is worth buying.
Company X meets all three criteria.

Remember, a deductive logic concept map must follow three criteria:

Make a statement about something that exists in the world; i.e., Birds fly.
Make another statement about a related situation that exists in the world at the same time: i.e., I’m a bird. The second statement relates to the first if it comments on either its subject (birds) or its predicate (fly).
State the implication of these two situations existing in the world at the same time; i.e., Therefore, I fly.