11/01/2013

When thought doesn't proceed in a straight line

DISCLAIMER:  Some of my posts summarize research; others are inspired by research but are just speculation.  This post falls into the latter category.
 
Kathryn Stewart, director of the Orion Academy, argues that Aspergers and nonverbal learning disabled kids have "no internal organizational system" because they have "no hierarchy for ordering the information as more or less important" (italics mine; from the 2002 edition of "Helping a Child with Nonverbal Learning Disorder or Asperger Syndrome").  Notice that she assumes the only way to organize ideas is a linear, hierarchical format, as in this taxonomic map I made:
Above: This concept map is meant to be read from bottom to top; for example, "wolverine is a placental mammal is a mammal."

This assumption shortchanges thinkers who use other methods of organization--most of whom, if taught by people who think like Stewart, must learn how to organize their knowledge on their own.

In fact, several non-hierarchical, even non-linear organization systems exist.  They even rival hierarchical systems in both complexity and efficiency.  At best, they let people maintain the greatest possible amount of information in the smallest amount of "mental space."  At worst, they could make writing more difficult.

To better understand non-hierarchical organization systems, we first need to familiarize ourselves with the easiest way to represent them: concept maps.

How do concept maps work?
A concept map is a way of representing the connections between ideas.  Concept maps consist of nodes (circles or boxes with ideas in them) that are connected by links (lines or arrows).  


Concept maps have a long history both in research and education.  Ragette learned about them as a tool for teaching LD students in 1982.  Teachers still use them today, often in mainstream classes, and often instruct students in how to make them.

The fundamental unit of the concept map is the "proposition," or single-idea unit.  The sentence "I hate mosquitoes because they bite me" consists of two propositions linked by "because": "I hate mosquitoes" and "mosquitoes bite me."  In a concept map, each proposition consists of two nodes with a link between them.  For instance, the proposition "mosaicofminds writes about autism" would look like this:


Hierarchical/Vertical Concept Maps
One can arrange the information in a concept map from most specific at the bottom to most general at the top.  For example, a concept map about evolution might have the processes involved (such as "natural selection" or "speciation") closer to the top, and specific examples (such as "peppered moth" or "Galapagos finches") nearer the bottom. In general, experts have more levels, and more links between higher and lower levels, than less knowledgeable people.

This format fits perfectly with taxonomy, as can be seen in my original example of a hierarchical concept map, above. Note that each "level" has its own color: yellow for species, blue for class, and green for intermediate category).


Even in a basically hierarchical map like this one, we can have connections between concepts at the same level, either two higher level or two lower-level concepts.  For example, you can compare a hawk to a viper, in that "hawks and vipers both eat mice."

Now you might say, "why can't you just put both hawks and vipers in a higher-up category called 'things that eat mice?'"  You could, but if you made an ad-hoc category like this every time you wanted to make a comparison it would be incredibly inefficient.  Your mental "desk" would be full of folders you used once and never referred to again.  Given how rarely most people think about "things that eat mice," it wouldn't be useful to have such a category.  You'd never file any other examples, or retrieve the relationship again, so you might as well just directly compare hawks and vipers when you need to.

Horizontal links start off as one-time comparisons like this, for which we don't need a category.  However, if we routinely compared hawks to vipers in at least one way, the connections would strengthen.  If we compared hawks with vipers more often than we thought about the fact that hawks were birds and vipers were snakes, we would actually associate hawks with vipers more strongly than we would associate hawks with birds or vipers with snakes. Vertical categories aren't necessarily better or more informative than horizontal relationships; we simply use them more often.

Horizontal Concept Maps
Now look at this concept map about the brain that I made based on a cognitive neuroscience textbook.*

This map contains some hierarchical relationships--for example, the cell body and membrane are parts of a cell and the dendrite and axon are both parts of a neuron.  But is "communication" at a higher or lower level than "neuron?" Does the question even make sense?  Once you start to incorporate many types of relationships beyond categorization--cause and effect, temporal, spatial, shared features, and more--concept maps start to look more horizontal, like this one.  True expertise, of course, involves exactly this diversity of information.

Thus, contrary to Kathryn Stewart's assumptions that only hierarchical organization contains information, this horizontal concept map may be even more informative than the taxonomic one shown previously.

Mixed Vertical/Horizontal Maps
Most of the time, we use both vertical and horizontal connections between ideas--most notably, when reading.  The sounds of words follow a vertical organization, from the basic auditory signal to phoneme to syllable to word.  Similarly, the written word runs from the features that make up a letter's shape to the letter itself to the clusters of letters that form "words within words" (like "butter" in "buttercup") to the word itself.  However, at each of these levels, we find horizontal connections between the sound and the written word.


Linear Maps
Concept maps also differ in their linearity.  Some concept maps follow one or two simple paths, and all the information contained in them can be turned into a few sentences without much difficulty.

You might wonder: why bother making a concept map?  For those without reading disabilities, the visual format adds no information that couldn't be conveyed just as easily in sentences.

Complex/Web Maps
On the opposite end of the complexity spectrum are maps that resemble webs.  See this example by Meren Tamm:
http://moonladder.files.wordpress.com/2011/10/meren-tamm_final-concept-map.jpg

It's not important to be able to read the whole thing. One need only notice the rightmost column of four nodes, the topmost green one labeled "digital ecosystem."  One can get there from the green "new media" node via two different routes, as well as via the green "knowledge" node.

Such complex maps have linear sections branching out from central nodes like the spokes of a wheel.  However, these branches reconnect with each other at one or more points.  If two branches go their separate ways for a while, then reconnect, one must simultaneously follow, or remember, both in order to understand the connection.  Thus, listing all the information in the map requires many sentences.  Switching from one branch or pathway to the next without abrupt, jarring transitions can also pose difficulties.

Thus, unlike with simpler linear maps, the visual format matters: it's the most economical way to represent a great deal of information.  Using a complex map rather than verbal statements saves both time and working memory--which may be one reason they're sometimes recommended to learning disabled students.

Notice that these maps can be perfectly logical without necessarily being linear.  The branches within the map can follow a traditional a-therefore b-therefore c-therefore d structure.  Furthermore, the map can be logical in that it lacks propositions that contradict each other or links that involve logical fallacies.

Strengths and Weaknesses of Complex Maps
Try putting Meren Tamm's map into sentences that flow well together and you'll immediately see the advantage of this sort of map: its economy.  You'll also encounter the disadvantages: the nonlinearity makes it difficult to figure out, when writing, the appropriate order in which to arrange these propositions.


At some point, even maps like this become too complicated to follow.  In certain concept map-generating programs, one will literally run out of room on the screen.  An expert person knows far more than this amount of information about their topic, though.  So how do people file and retrieve knowledge when they know more than will fit on their mental "screen?"

Let's consider how you would solve the problem if you were filing papers in folders instead of ideas in interconnected nodes.  If you just got a new credit card and you know you're going to be getting statements every month for a few years, you'll create a folder for it and label it with the name of your credit card.  Similarly, if you're interested in autism and know you're going to learn a lot about it, you'll create a mental folder and label it "autism."

When you have ten credit card statements, you can easily open up the folder and look at all of them at once if you want, without investing much time and energy.  Therefore, you can easily detect the approximate amount you spend per month.  If you have five years of statements (or sixty individual ones), it becomes much more difficult to look at them all at once. Similarly, if you only know ten things about autism, you can call all of your associations with "autism" to mind when you choose to think about the topic.  But when you know thousands, you need some way to block out all the information you don't need so your working memory won't short-circuit.  How do you do this?

One answer is to create a "gist," a rough definition of the topic or a summary of what's in the folder, with pointers to specific topics you might want to retrieve.  The "pointers" in your credit card folder might refer to particular years, from which you can further retrieve an individual monthly statement.  In my autism folder, pointers lead to topics like "language," "special interests," "autism community," and other subtopics I think about often.  Eventually, the folder's label, "autism," becomes a sort of shorthand for a huge complex of information that I never entirely unpack--and couldn't if I wanted to.

If I did not pack all my ideas and emotions and memories about "autism" into a compact package with the label "autism," I would have to retrieve all the thousands of things I knew about autism every time I wanted to think about it, or say something about it.  This would take hours, and probably more working memory than I possess.  Thus, I create a folder, label it "autism," and retrieve only the gist most of the time.      

It would be hard to overstate the sheer amount of information you can learn and retrieve through these compact bundles--far beyond what the limitations of short term memory in particular should allow you to achieve.  However, the very need to unpack these bundles, plus the nonlinearity of the complex information maps they contain, make it difficult to communicate your ideas to those who do not already share the same mental folders you have.  You must retrieve every single relevant subfolder and reconstruct it for your audience.  In particular, writing becomes extremely difficult.

In other words, these idea bundles exaggerate the strengths and weakness of complex maps.  In fact, a complex information map is itself only a partial unpacking of these huge idea bundles--often, one you could further unpack, if you wished.  

Are Complex Maps Just for "Visual Thinkers?"
Complex maps are a visual representation and are notoriously difficult to translate into writing.  Visual thinkers, by definition, think in visual representations, and they are often said to have difficulty with writing.  Thus, some people think that complex mental maps and the idea packages from which they originate are characteristic of visual thinkers.  For example, Gerald Grow, describing the writing problems of visual thinkers, says:
"Such thinkers may use a few key words repeatedly, without elaboration, as if each word contained and powerfully expressed a complex thought in its entirety. The reader, though, sees only the words and does not have the writer's mental pictures that are necessary to convey the real meaning. The words are cryptic."
I doubt that this thinking style is limited to those who think in pictures.

I use labels as a shorthand in the same way myself, using words like "autism" or "learning disability," or "flow" to point to complexes of ideas that would likely take hundreds of pages to explicitly unpack.  (This blog itself, with its fragmentary entries that can be read in any order and tagged by topic, gives me the freedom to unpack such complex ideas).  Yet pictures make up only a small part of these compact idea-packages.  Instead, a label like "autism" evokes stories, memories (involving more than just vision), emotions, quotations, and study results, all interwoven in myriad ways.  In fact, sometimes when I think about autism, I don't see any pictures at all, I just hear words in my head, as if I were reading or writing.  One need not think in pictures to use words as labels.

Similarly, I've gotten stuck on writing a book--for which each specific chapter has an outline--precisely because my ideas take the form of a complex map.  Several groups of chapters exist, each of which makes a linear argument.  Yet, for example, Group 2 may provide the justification for Group 3, yet rely on Group 1, which in turn references Group 3.  Many of the ideas I wish to express do not involve pictures.

One can't build a theory on a single case, of course.  But if even a single non-visual-thinker uses a thought process identified with "visual thinking," it must be available to at least some people who aren't visual thinkers.

Why Neurodiverse People Can  Look Disorganized

A neurodiverse person who thinks in complex maps and uses words as shorthand for complex idea-packages will have difficulty communicating with those who do not share the information in his idea-packages.  Having ASD or nonverbal learning disability increases the odds that one will have different information and experiences than one's listeners, especially if one additionally has unusual special interests like trains or washing machines.  Add in the verbal dysfluencies common even in highly-verbal autistic people, and you get communication that seems cryptic even to a generous neurotypical listener.

It takes experience to learn what information you have that others don't share, working memory to unpack all this information so you can explain it, verbal ability to convey it to the listener.  Until they develop these, neurodiverse people will likely seem disorganized or illogical, and people like Kathryn Stewart will think their minds look like messy desks.

But we need not make the same errors.  Instead, we can learn more about logical thought that organizes itself in ways other than a straight line.

   
 *The textbook is Michael S. Gazzanigga, Richard B. Ivry, & George R. Mangun (2009). Cognitive Neuroscience: The Biology of the Mind, 3rd edition. NY: Norton & Company.