Using Knowledge Maps for Learning Comprehension
Building reason around spacetime sequences (for advanced readers)
子曰。由、誨女知之乎。 知之爲知之、不知爲不知。是知也。
The Master said: “You, shall I teach you about knowledge? What you know, you know, what you don’t know, you don’t know. This is knowledge.”
— Confucian Analects
“…never let him know that you know what he thinks you don’t know you know. You know?”
— Sneakers, 1992
In previous articles, I’ve discussed how we can better represent the needs of human reasoning by accommodating spacetime concepts into knowledge graphs. This is a departure from the way knowledge maps are designed according to industry standards–which attempt to start with a logical catalogue of parts and then to impose relations onto them. The more natural process of thinking begins with some kind of improvised, ad hoc linguistic representation. It might be spoken, written, or visual, but it has a way of coming together in our heads like a scene and narrative. Mapping out such a scene is essentially a process of stripping away the trust-building irrelevances that pad out our speech, and deconstructing it to reveal the intrinsic skeleton of pieces, rather than trying to piece the skeleton of a scene from a jumble of imagined parts. But why go to all that trouble if the result is hard to understand?
This is an article about human learning. It is a follow up to a series of articles about using Semantic Spacetime (available through the SSTorytime Project) to understand. However, it is not about technology, but about how we should be trying to use knowledge maps–i.e. how we as humans can build our own confidence as we learn and get to know things. That challenge takes place in an increasingly contested and difficult educational environment.
In the graph technology realm, graphs are currently used mostly in one of two ways:
- As a representation of social networks with centralities and flow patterns, link weight as contact frequencies (a fancy telephone directory).
- As property graphs over ontologically restricted entities (used to express hierarchy of concepts).
These are specialized and limited uses, for which the SSTorytime software can be used perfectly well, but both are narrow and unsuitable as broad semantic representations for learning. They become little more than taxonomic telephone directories. In this article, I want to consider only a version of the second possibility, optimized for human consumption.
The goal of the SSTorytime project is to function as an asset to human learning, to give us tools to keep us afloat in a world where information could easily drown us. Even as we apply it to “AI” and artificial systems, the thoughts need to be compatible with human needs if they are to be of any use to us.
Supervised and unsupervised learning in humans
Plenty has been written about how to construct knowledge maps along different philosophies. But we need to think now about how to use knowledge graphs, because without an understanding of that, we couldn’t construct useful graphs.
If we try to build a representation of knowledge against the natural grain of how we think, it leads only to unnecessary difficulty in learning and comprehension. Some of us experience those difficulties as dyslexia, ADHD, recall issues, and other cognitive disruptions. Some, like me, are visual thinkers who rely on actual sensory cues for memory. Memory is, of course, tied to our motor cortex or “muscle memory” too, so it is easier to remember things we have done and rehearsed over and over again, especially when there is physical involvement. Modern computer systems often try to bypass these necessities and offer “market knowledge” at the push of a button, as if from a vending machine.
Let’s try to do the opposite and think about how maps can support human involvement.
Semantic Spacetime and its SSTorytime model support several knowledge processes that are poorly supported in other industry standard technology. It prioritizes different views of knowledge as alternatives in a landscape of processes–of journeys or stories, in which the narrative threads are the crucial “red threads” lifelines through a labyrinth of detail, like that which allowed Theseus to escape the Minotaur’s clutches, and find his way back to the light.
I’m always thinking of what might have made my own educational experience better–what I can do for my students to help them in ways that I missed. We could do this for every possible subject on the curriculum, but let’s start with the traditional 3 Rs.
Language (e.g. English) comprehension
In school, we are often asked to read something, then perform a “comprehension” study on it (perhaps a poem or a piece of prose). To show that we understand what was written, we are then asked to deconstruct the scene and answer questions about it. I recall this as a particularly dull exercise, often based on texts that held little interest for me. It could be so much more interesting!
We could imagine using Semantic Spacetime to make this more “physical”, something like a crime scene investigation (CSI). Consider the following “classic poem”, which I learned from my mother decades ago. Our goal is to make a “knowledge map” of this to help us to know it.
Without any further ado, we simply write down the original text into N4L, adding nothing except to give it a title and using the _sequence_ feature to link up the lines in a SSTory map. This will create the red thread.
This text sets the raw “scene”. There is no need to do any violence to it, or dream up an ontology for it. It is interesting because it is the actual experience, not a distorted facsimile of it.
Without stress, we can now start adding notes–whatever occurs to us about the text. There is no right or wrong here. To get really advanced, we’ll eventually need to have a basic familiarity with the arrow types. But, in practice for something like this, we can get away with just a few arrows to begin with.
(note) to remark on something or add a related note(e.g.) to give an example of somethingWe can then begin to add notes (no matter how obvious) to the text. As we type them (a tedious task), we use the layout of the page to keep the columns tidy. For example, the obvious thing to point out here is to explain the puns that underline the poem. Now it looks like this:
Notice by the way that, since the last line is a bit long, we can use the ditto mark to carry it over to the next line and keep the text from wrapping around. We don’t have to, but the goal is to make the experience comfortable.
This is already a valid N4L notes file. We can upload it to SSTorytime, like this:
N4L -u astronomy.n4lWe can now search. If we simply list the sequence it looks something like this:
The story view is clean and simple. The presence of the [LT] links tells us that the items are part of a “leads to” path.
The value of knowledge that we seek will come from explaining the scene, describing the encounter, perhaps learning the series to perform it, or forming a process or a story that we can apply, in a way that will be of lasting value to us. If it is not of lasting value, we can simply get disposable knowledge from any push button ATM, LLM, or Wiki.
To see the notes in full form from SSTorytime, we can search the page note view:
\notes astronomyThe check boxes can be clicked to mark the text as read. You can check how when you last looked at something on the \stats page.
For a third view, with more details, we may click on any specific item, we see an “orbital” view of the topic, with the clicked item at the top-centre, and connected items at a distance 1 and 2 from the centre (see below).
These “orbital” references are something like footnotes: more than just a hyperlink. There is also a semantic interpretation: a promise of what. The use of colour sometimes helps to enliven the text for visual thinkers, as well as expose the different kinds of relationship between the parts, telling us something about the structure, and perhaps inspiring a new idea.
I recall how I despised a university lecturer who told me to make my lab notes as dull as possible. Of course, I paid no attention to him. I didn’t want to become that person!
Adding our own thoughts
Clearly, we can now go on to add more and more notes and other things that occur to us as we browse. These should be things we care about. The goal isn’t to write an encylopaedia, but to equip ourselves for the future. We don’t have to stop at annotating the original text. Our notes can have notes too, to any level! For example, picking out one of the notes, we might offer a remark:
It doesn’t matter that we repeat text (as long as it’s exactly repeated). The compiler will only create a single node for all references to it. We can also make life easy by tagging words with % and other “annotations”, which automatically generates a “discusses” link. So the entry above generates two new links:
These references seem trivial, but they will catch our eye later when browsing and lead us to examples of the use of “to” and “two”.
If we browse the arrows in the SSTconfig directory, we can find new things to mention
And so on. Add your own. None of this is rocket science (unless, of course, we are actually making notes on rocket science), but it turns the process of wracking our brains into a kind of carpentry puzzle in which we can join dots and saw off the ends of paragraphs to highlight ideas.
By making our own notes, we can turn the chores into a scrapbook project that adds interesting colour to what might otherwise seem dull.
Perhaps, too, this simple feedback loop of collect, annotate, compile, browse, can help learners see a kind of “result” for their efforts and their choices–to empower them with much needed self-confidence. You see: I didn’t break it! Perhaps, too, the colours, sizes, and different views might help dyslexic readers to see what is in front of them quickly.
A map is a chain of reasoning
We call the resulting construct a knowledge map, even though we didn’t need to think about the nodes and arrows explicitly and make a meal of the process. We had only to jot down our thoughts as notes, as we might on a notepad. Ironically, knowledge map is something of an oxymoron. The truth is that we only need a “map” of something when we don’t actually “know” it well. A map helps us to recognize the terrain, but it isn’t strictly knowledge until we know it well enough that we don’t need the map. So we might call it a concept-experience map or simply a memory map. It’s a kind of assistant, like the GPS SatNav in our cars.
Maps have deeper virtue though: the act of making them puts us through the motions we need to learn. “The point of the journey is not to arrive” but rather to visit the places along the way and even revisit them until they are familiar.
Another kind of knowledge oriented map is the Wardley Mapping technique introduced by Simon Wardley (see my Semantic Spacetime #2 article), used to think about the evolution of processes and outcomes–strategies if you like. We can use this as a second example. It’s unrelated to SSTorytime or Promise Theory, but it is neatly compatible with both. In a strategy we are not looking at just a single possible future story, but several alongside one another. A strategy has many active players and components. Weaving them together is a kind of semantic graph.
The examples contain this as a case. We simply create this picture as a set of notes, by introducing a few vector relations for the different line directions “northeast” and “northwest”, etc. Compiling that view allows us to search it. Unlike the cases above it has several narratives side by side–something like those novels where you have a choice about how you want them to end. We can then view it in the browser
This is simplistic. We could imagine embellishing the link names in red to describe the meaning of the arrows in more detail, i.e. to tell the story in the best possible way. Using this SSTorytime approach, the goal is to tell the most appealing story. By appealing we mean: the one that will resonate best with us in future.
Selection of good names is important, because this is how we make sense of knowledge. Without sensemaking, knowledge becomes mere trivia. With meaning (clarity over semantics) we can put the knowledge to use (see Designing Nodes and Arrows in Knowledge Graphs with Semantic Spacetime).
From the basic input of the Wardley map, we can search and click our way around to see the statements, as before. Things are now spelled out explicitly. We might underestimate this simple step of speaking each fact out loud. Reading and repeating — the telling of the story, is what gives it vitality.
It’s surprising how quickly these views show us unexpected information. Seeing the result of even a basic amount of information can stimulate new thoughts and ideas.
Please Sir, must we read Moby Dick?
Back to school! In our school days, we are all asked to read books and write about them. If we believe Hollywood, Americans only read one book in school: Moby Dick. It’s a masterpiece on many levels, but it’s not an easy read for an inexperienced (especially, modern) reader. I expect many students loathe the experience and learn little from it.
The novel is excellent, in some sense, but it could be made so much more interesting. One way to get an appreciation of the book (without forcing yourself to parse every sentence in order) is to browse and search the text, making notes as we go. For a book, like Moby Dick, where the text is in the public domain, it’s easy to read the text into a learning graph. Using the tool,
text2N4L mobydick.txtwe generate notes in N4L compilable format that we can add to. Measuring the intentionality of the text, the program samples some percentage of the book and turns it into a graph–even without any initial effort on the part of the reader. We can now browse and search within it, glance at it sentence by selected sentence to see what catches our eye. Such a rich book has many fascinating episodes, but an oppressed reader (already hating the experience before reading a single word) would never find them if forced to read from start to finish as a kind of mandate.
Transforming the book into a basic knowledge graph, the strategy now becomes as follows. First, we find our way around the book first like shopping in a mall, wandering at random, stopping to look where we please, savouring the language in small doses. We can see what is interesting and what we want to know more about. Then, having done our reconnaissance (and with some thoughts about it under our belts), we might actually discover some motivation to read the story, even the style of the language, we can indeed go back to the beginning and read the book with actual intent. It’s like watching a movie trailer, with action clips.
Even so, at this stage, all we have is a partial sample of the book’s significant moments. At any time we can ask: how might we add our own thoughts as notes? That is the stage at which we can become involved in the story ourselves– when we ourselves become a part of the narrative. What might we add? Random thoughts first.
- Moby, not to be confused with the pop artist.
- There is a famous reference to Moby Dick in the classic Star Trek movie: the Wrath of Khan (but Khan is not to be confused with Khan academy.)
Not all of these will be useful later. It doesn’t matter. The fact that we have an intention to make a note suggests that they could be. It’s better to be safe than sorry. We can search and edit the N4L notes to add these:
After recompiling the map, they appear as part of the map.
As an aid to comprehension, to self-learning, this resource could be a game changer. But let’s be clear: the resource is not so much the database as it is the process involving it.
Books contain all manner of unexpected gems that we may not recall. Now we can explore them and become creative without having to treat the task as a punishment.
Mathematics comprehension
As a final example, we turn to the least popular topic of all: math(s).
Mathematics books are notoriously bad at helping the student to learn technique. They rarely show every step in a calculation, and often resort to: “This step is left as an exercise for the reader”! While some pretend to believe that this is for the student’s benefit, it’s more likely just lazy and it undermines the confidence of many students who need to be taught that they too could master the art of solving a problem. We can use a knowledge graph to retain those details.
I recall my advisor at university was always able to pull brilliant mathematical moves out of a hat, making impossible things seem trivial. As the tears rolled down my cheeks, he would shrug and say: “It’s just a matter of experience”. Ten years later, I could appreciate what he meant, but I might never have persevered without being shown how to go about thinking calmly and cleanly. To this day, I feel a certain fear of being inferior.
Years later, I now know that the key to solving mathematical problems (like all techniques) is, in fact, narrative thinking. As some story unfolds in your mind, experience kicks in and your intent to reach an eventual answer guides you to try to right kinds of move, like climbing a rockface. The reason? We learn to know ourselves (and our battery of techniques) over the years by repeated experience, by practice. We learn to know them like a friend. We know what to expect, and like a friend we know what to expect, what the answer should look like. We’ve trained ourselves to ask the right kinds of questions–even simply to play and have fun.
Here’s a simple example. An integral like this one looks deceptively simple, but the moves one needs to calculate it are far from obvious to the inexperienced.
By making detailed notes, as we pick up hints and see others’ solutions, with every step laid out, we can learn, look up, and even cross reference the techniques. We can quickly build a personal dictionary of solutions. Of course, there are famous catalogues of solutions to integrals stemming from the pre-computer age (“Gradshteyn and Ryzhik”), but these are huge and extremely difficult to find one’s way around. Our own notes are always preferable to us, because they mean something to us. We trust what we’ve experienced with our own senses.
Again, the more we document, the more interconnected the graph becomes and the more our browsing experience resembles a shopping mall rich with content, and less a single example.
This is just one example in an endlessly rich area. Of course, mathematics is also part of our culture. It’s meaning can only be understood by knowing how to use the word itself. A quick search locates even the term in our earlier example–the infamous Moby Dick.
What could this possibly mean? Well, now you can find out.
Summary
Using knowledge maps as a way of strengthening human learning, rather than replacing it with automata, is how we shall weather the storm of information that technologists seem wont to throw at us.
SSTorytime and the Semantic Spacetime approach to knowledge representation was devised as an antidote to the overly rigid methods of applied logic, through ontology. A little ancient wisdom from the Confucian Analects tells us:
In Star Trek, the Vulcans (apparently modelled on the Chinese and their passion for the dispassionate) had plenty to say about the pitfalls of uncritical adherence to logic too. Their version of this was presented in the Star Trek VI: The Undiscovered Country:
Spock To Valeris: “Logic is the beginning of wisdom, not the end…”
In each of these cases, you might have noticed that there is a simple pattern to the examples. There are sequences at the heart of these studies. Knowledge tends to begin with sequences, threads, stories, whatever we want to call them–because such stories are at the core of how we experience the world. Our timeline, our actions. We are story driven.
As a lifelong teacher, I note that–often the reason students can’t get to grips with subjects is that they see no story to write themselves into. For me, nearly every successful project I can think of began with such a narrative in my head. This is why making maps is a helpful device for learning. It isn’t knowledge until the map is redundant by repeated use. And that space in which we imagine mapping to acquire knowledge is a space of events, things, and concepts — none of which are knowledge by themselves. They are merely occurrences or events that are meaningless in isolation. They need context and connection.
A knowledge map is not like an LLM (Large Language Model chatbot): we can’t ask SSTorytime to provide a detailed question and get an oracular answer in fluid prose. Rather it shows us pathways through a labyrinth. It doesn’t try to disempower us by seizing the reins–it hands us the reins. We have to dig in like an investigator and think of the right questions to solve the mystery ourselves. But this is the fun of learning, of research, and it can add a new dimension to reading and writing if we use it well. In the hands of an exploratory teacher or a curious student.
Curiosity is the beginning of a path to knowing, and knowing is a stepping stone on the road to wisdom.
