Seeing vs. Visualizing – Part II

Thinking further about my previous post on seeing vs. visualizing, and doing a bit more research, there is more to add.

After falling down the rabbit hole for some considerable time, I ended up with solid footing on Korzybski’s insight:

A map is not the territory it represents, but, if correct, it has a similar structure to the territory, which accounts for its usefulness…If we reflect upon our languages, we find that at best they must be considered only as maps. A word is not the object it represents. (p. 58)

This seems obvious, but far too many people operate as if the map *is* the territory. To illustrate, I’ll start with a literal map/territory example (see Figure 1). I’ve been to Hawai’i many times, and every time I go, I spend time on the North Shore of Kaua’i, hiking the Kalalau Trail. It doesn’t look like much if you look at a high level map of the Island. Doesn’t even look like much if you look at the topographical map of the trail which includes Hanakapiai Beach and the Falls. But looking at an actual photograph of the territory begins to reveal why it is this trail is frequently included in the top 10 most difficult trails. It is rainy, slippery, rocky, steep, and hot. That’s the territory, and except for geographical references and elevations, it bears little resemblance to the map.

The Map is not the Territory

Figure 1. The Map is not the Territory

Now for a little less obvious example, consider your response as you read the word “ObamaCare.” Was your response positive or negative? Chances are your reaction is based on a combination of personal experiences and sound bites from critics or supporters of the program and not from having actually read all 2,000+ pages of the bill. Investing (and I use the word deliberately) time to develop the ability for moving from map to territory seems to be a necessary precursor to successful transfer of learning experiences. There also seems to be a kind of ferocious tenacity that drives this, an unrelenting drive to move from a map of the world based on dreams/fantasy/wishful thinking/second hand data to, at least, a map based on objective data. (Philosophers would argue that we can never really know the actual territory. Like I said, this is quite a rabbit hole.) Another way to describe this is a drive to get to the original source of whatever one is studying and distrusting any intermediary interpretations until verified against the original source.

So, where does this leave us with considering the transfer from chemical understanding to mathematical understanding to martial arts skill? It wasn’t that understanding the chemical symbols became an understanding of mathematical symbols. Rather, it was understanding that the chemical symbols represented the underlying chemistry which translated to understanding that the mathematical symbols represented the underlying mathematics. In my case, an essential element was acquiring the ability to see, literally, the underlying chemistry represented by the symbols much like I can look at a topographical map of the Kalalau Trail and see the underlying jungle trail. The experience of learning how to view stereo triptychs is directly analogous to the experience of actually hiking the Kalalau Trail for the first time.

The learning theory most closely aligned with this experience is the Four Stages of Learning attributed to Noel Burch in the 1970’s. (There is no definitive reference for this attribution, and a measure of ambiguity exists as to the origin of the theory.) The transition from conscious incompetence (“This chemistry makes no sense.”) to conscious competence (“Thanks to stereo triptychs, I understand!”) to unconscious competence, where I can visualize three dimensional molecules without the need for stereo triptychs, accurately describes the experience.

How this translated to mathematics seems to have hinged on the realization, novel at the time, that the mathematical equations were also simply symbolic representations of an underlying reality. This fundamentally changed the question and the focus of attention for understanding the problem. It was still difficult at first, but at least understanding and comprehension seemed to stick better as I spent less time struggling with the symbols. Patterns began to emerge which were not evident in the isolated symbols.

Turns out, there is a neurological basis for this kind of shift. Working from robotics as an analogy to the human neurology involved with learning, Pribram (1971) argues, “Pattern ‘perceiving’ devices build up in one manner or another a spatially coded representation, a map, of their experience. Thus they can ‘learn’ to respond differentially to a particular pattern: they can ‘recognize’ the familiar, and distinguish the novel” (p. 102). And later:

As noted, however, habituation is not an indication of some loss of sensitivity on the part of the nervous system but rather the development of a neural model of the environment, a representation, and expectancy, a type of memory mechanism against which inputs are constantly matched. The nervous system is thus continually tuned *by* inputs to process further inputs. (p. 105)

This appears to be a description of unconscious competence. But when an individual’s habituation is challenged with input that increasingly fails to match the established pattern or map (that is, the individual ‘distinguishes the novel’), it is possible that the individual is then shifted into a state of conscious incompetence from which new skills need to be learned (conscious competence) and habituated (unconscious competence). For complex information, such as chemistry or mathematics, this is undoubtedly a cyclical process. As Haskell (2001) observes:

The research on teaching for transfer clearly shows that for transfer to occur, the original learning must be repeatedly reinforced with multiple examples or similar concepts in multiple contexts, and I would add, on different levels and orders of magnitude. Teaching that promotes transfer, then, involves returning again and again to an idea or procedure but on different levels and in different contexts, with apparently “different” examples. (p. 26-27)

As for martial arts, there is another important component to the application of this skill. True enough, I was deliberately thinking about my opponents as giant molecules undergoing dramatic state changes. But there were numerous distractions that needed to be removed from the visualization which were irrelevant to the situation, such as race, gender, bulk (muscle or fat), and even clothing. Eventually, the skill developed such that attackers now look something like the image in Figure 2.

The Bare Bones Attack

Figure 2. The Bare Bones Attack

Is the attacker a man or a woman? Afro-American, Caucasian, Hispanic, or Asian? Well dressed or homeless? These are all distractions that can inhibit a proper defense or provoke an unwarranted counteraction based on prejudices and personal bias. All that matters is the attacker’s fist or what, if anything, is in the attacker’s hand. All I need to know is where the weapon (fist, knife, club, gun) is pointed, and where I need to move to disarm the rascal.


Haskell, R. E. (2001). Transfer of learning: Cognition, instruction, and reasoning. San Diego, CA: Academic Press.

Korzybski, A. (1933). Science and sanity: An introduction to non-aristotelian systems and general semantics (4th. ed). Lakeville, CT: the Institute of General Semantics.

Pribram, K. H. (1971). Languages of the brain: Experimental paradoxes and principles in neuropsychology. New York, NY: Brandon House, Inc.