On Tue, 29 Aug 2006 03:04:03 on another list, John McPherson wrote: "... yet the maps can be made progressively more similar in structure to those realities ... and in fact the maps become more and more useful as we do so."

I find this not to be the case. My dad has a great relief map of the Panama Canal showing where the canal will be built. It was constructed as a scale model of the territory - It is horizontally to scale, but I think that vertically the scale is exaggerated so that we can visually and tactilly experience the elevation. It is painted to show the foliage and other topographical features as they might look from an aerial perspective - looking down on the earth from space. This map is FAR LESS USEFUL that a conventional road-map or even a flat topographical graph with lines for elevation, yet is much more similar to the territory. It is "useful" only insofar as it provided the "big picture" to the politicians who had to approve funding. There is no "absolute" usefulness.

"Usefulness" depends on the level of abstraction of the perspective of the user. Maps are only useful to the degree that they represent the territory in symbolic structures - non-similar - that can evoke our cognitive experiences for understanding how to use the territory. (Useful <==> use) Maps are useful only to the degree that they allow us to navigate, and that requires that the structure of the territory be transformed or translated into non-similar symbolic entities that hook into our semantic environment.

The more "similar" a map is to a territory, the more details must be included representing smaller and smaller bits of the territory. But we understand in terms of abstractions, particularly at higher levels of abstracting, and that means less detail. The map with a great many details becomes useless because we cannot see the forest for the trees. It overwhelms us with information we cannot assimilate. A "useful" map has the "right amount" of abstractness - non-similar to the territory - that allows us to see the "big picture", depending on how precise our need for navigation is (level of observation of the observer). A "map" that show every pebble in the driveway, every crack in the road, every anthill beside the street, will normally be of no use, because we won't be able to orient to gross features that interest us. Try to find the pebbles you are standing on in such a map by looking at the detailed features shown. It cannot be done without possibly years of searching and comparing details. One has to stand back, blur the details, and abstract the larger patterns using our own abstracting process. Then we narrow down, allowing ourselves to see more and more detail, but we have to orient or position ourselves in terms of "objects" we experience that are proportional to our own size and perspective.

So the general idea that the more similar a map is to the territory, the more useful it is, is simply wrong.

A map is most useful only when it is an abstraction that presents the level of detail that the observer is interested in. If I'm going cross country, then I need a map showing major highways, not every street, house, and cul-de-sac. When I get to the city of my destination, THEN I need a local area map. And when I get to the suburb, THEN I need a local street map. To be useful, a map must EXCLUDE as much detail as possible that does not relate to the purpose of its use. In short, the theory (not "fact") that "the more similar a map is to the territory, the more useful it will be" is false.

It's not John's personal premise. He is just reporting the common view expressed frequently in general semantics circles.

How can a map be "ideal" if it cannot be used effectively by humans? I do not consider a map that is more and more detailed as approaching "ideal". The "ideal" map is the one that is most helpful to me in my need to navigate at a time and place. So there is no "absolute" "ideal" map. The idea that the more "exact" a map is, the better it is is clearly not helpful.

Nora wrote: "then your territory is not the rocks and mountains,". Whenever you say what is a territory, you are already at verbal levels of abstraction - no longer at the level of the territory.

According to "metaphors we live by" we normally associate "up" with "higher" and "more", and hence "more abstract" with "higher levels". I wonder why people don't see the "ladder of abstraction" as simply another map of the structural differential that reverses the up and down directions and changes the shape of the parts. Korzybski chose physical "down" to represent "higher levels", and that goes against our normal metaphorical perspectives.

Quantum mechanics is a very abstract theory that describes the smallest entities postulated to explain physical interactions. Do you equate small with detailed? I do not, because I think of detailed as including many instances. A "detailed" map would include many small features, but it would exhibit that property everywhere in the map. Quantum mechanics describes a hypothetical single entity - the generic atom, and its shells. It also describes the relation between the wave and particle view.

I first studied this topic while training for nuclear power in 1963. It turns out that the wave-particle duality relates directly to the topic of my dissertation 30 years later - the contracts between infinite divisibility and atomism. For those of you who do not delve deeply into this subject matter, just think about the contrast between counting entities and measuring stuff.

In all cases you speak of, the alleged "territory" is not "the territory" - not the "event level", but an abstraction of interest and relative to the observer. You speak only of maps. We have no direct access to "the territory" - the event level; we only have access to our abstractions from it. We may, however, be interested in lower level abstraction maps.

Making it to an appointment on time is navigating using a map. You made your understanding of your map(1) (appointment calendar) match your understanding of your abstractions from your memory. Both (understandings) are neurological processes, and both institute abstractions - mappings.

Look, for example at the early paragraphs in "Philosophy in the Flesh" discussing "color".
These "maps" just are not similar in structure to the territory. Color, for example, represents a map construct explainable only in terms of both the object and the observer. Similarly with other such cognitive maps. We "understand" and navigate with our maps because we remember not only the so-called "inputs", but the inputs highly correlated with both the "outputs" (what we were doing) and our internal state at the time.

To speak of "characteristics" abstracted ultimately from the environment, to use a general semantics term, constitutes an elementalistic orientation; our memories record what our muscles were doing, what other brain circuits were co-active at the time, as well as our current proprioceptive and enteroceptive state, as a coordinated active neural trace.

You can perform an experiment to directly experience the effect. Close or cover one eye, and turn you gaze extremely in the direction of the close eye. For example, close the left eye and turn your eyes as far to the left as possible.
Find something to look at it that area. Move your eye just a little by looking over the item you see. For example, I'm looking at a wall telephone out of the nose corner of my right eye. I look at the top of it, and then I move my eyes to the bottom of. I appears stable on the wall. It does not appear to move. As I move my eye, the image moves on my retina, but my brain uses the signal sent to the eye to tell it to move to compensate for the apparent motion of the phone image on my retina. The result is that I "see" the phone as being "fixed" is space. It's not "going" anywhere.
Now, fix your gaze on one spot on the item you are looking at and press gently on the outside corner of you eyelid where the eyeball - under the lid, can be felt next to the edge of the eye socket bone. Gently does it. You should notice in the black area to the left of your field of vision a ring-like spot forming, expanding, and shrinking as you apply and release pressure. You should also notice that not only the item you are looking at, but the entire field of vision seems to move. When I press lightly on the lower lid, the field of vision seems to jump up. When I press lightly on the upper lid the field of vision seems to jump down. In both cases, there is the perception of horizontal movement as well. In this case the eyeball is being moved by dint of an external force. There is no "I told you to move 'in this manner' signal coming from the muscle control area of the brain, and that missing signal is not going to the visual processing areas. The visual processing areas get a movement on the retina without the corresponding "I told you to move" signal from the muscle control center. Consequently, movement on the retina without a corresponding muscle control signal means that the object in visual field, in this case, the entire visual field, is actually moving. So we see the object we are looking at, as well as the entire visual field, appear to move. We have received an "elementalistic" motion on the retina signal without any corresponding muscle movement signal.

Movement on the visual field without muscle motion = "external object movement" - perceived as motion.
Movement on the visual field with correlated muscle motion = "actor movement without external object movement" - perceived as stationary.

When I move my eyeball with my finger I "see" motion of the environment (where there is no actual motion).
When I move my eyeball with the eye muscles, I "see" a stationary environment.

The brain's experience of the environment, of objects in the environment records not only what the visual circuits are abstracting, but a construct which is transformed by what I'm doing at the time. This is also correlated with our emotional state. More emotion means more brain circuits are active, and more neurology is used in the memory. That's why we remember emotional events better.

A pattern of chemical and electrical activity in distributed nerve circuits does not show any apparent structural similarity to what we infer exists in the what is going on. Consider the hologram. A flat piece of film with swirling patterns of microscopic wave patterns. But when coherent light shows through it we perceive a three-dimensional image not too different from the image we see when we look at the subject of the hologram. The hologram is a two dimensional mapping of the light patterns in the vicinity of some event. Our brains, in the cortex, a thin folded sheet when stretched out, about the size of a large dinner napkin, records its activity in terms of enhanced synapses that provide the possibility of reactivating not only a particular pattern, but a temporal sequence of patterns that stimulate each other. The playing of a piano piece requires a perfectly timed sequence of memory and motor actions resulting from the correct sequence of neural firings.

A map of "a computer program" is already a map of a map, and a highly abstracted one at that; a map of "family relationships" is already a map of a map, and a highly abstracted one at that. Neither of these is "the territory". Each represents a high level abstraction from "the territory".

You can have a description of your appointment book. This is a map - an abstraction. You can have another description of your appointment book. This is another map - also an abstraction. They can be different. You can specify structural similarity only by identifying items between the two maps, and by indicating relations in each of the maps and identifying these relationships.

X is similar to Y if and only if X and Y have parts x and y such that x maps (m) to y, and relationships among x1, ... xn, map to relationships among y1, ... yn, such that Rx(xi,xj) iff Ry(yi,yj) where yi=m(xi) and yj=m(xj).

Since we have no access to the territory, we can only compare similarities between distinct maps.

If you keep the "purpose" in mind, then you do not have a territory, but a specialized map.

Increasing the similarity of structure requires more and more parts and relationships that correspond, and this means more and more details - finer grained. This is a monotonic increasing function - one with possibly a convergent limit - in which case the map would "become" the territory, through our being unable to distinguish, such as in a very good forgery. As a limit is what we mean by "ideal", we can say that this approach leads to an absurdity. That is why I said in my earlier post, that there is NO ideal map. I redefined "ideal" in that post to be relative to the observer. The "ideal" map is the one that is most helpful to me in my need to navigate at a time and place.

That also means that it is NOT ultra detailed; it must be at an appropriate level of abstraction relative to my perception and intended use.

We CANNOT however, do a backwards mapping an claim that this establishes what the "territory" is.

If M(T) is a useful map, it specifies an abstraction from the territory. But M^-1(T), a subset of T is still an abstraction, and hence a map. It is not "the territory", as "the territory" is that from which ALL maps are abstracted.

A map does not imply, in general, a "corresponding" structure in the territory, because "the map is not the territory", "the map does not cover all the territory", and "the map reflects the map maker". The structure of maps is largely determined by the map maker - his or her abstraction, point of view, needs, preferences, biases, and capabilities. Any two map makers make different maps. "Reliable" maps do not (often) result in unexpected abstractions necessitating their revision during use.

We may "infer" using the principle of regularity based on repeated constructions that we can evaluate as similar that "something" exists in the what is going on that has, when abstracted from by similarly trained humans, allow them to construct similar abstractions. Such an inference is inductive generalization - which is subject to error; it is NOT "truth preserving" deduction as the more precise meaning of "implies" entails.

"All" inductive generalizations are subject to the possibility of eventual disconfirmation, and all our "projections" about "reality" fall into this categorization. We "think" there are "things" "out there" in the "what is going on", and some of us think that we can "know" what those things "are". That, however, steps over the boarder of precise general semantics into the arena of faith.

The best I can work from is a not-yet-disconfirmed model, and that's how I express it. In this arena, that includes the notion that I do not know what is out there; I only project my current model and perceptions.

That we can construct a map in no way implies a structure the map is allegedly about exists. I have lots of maps of unicorns, fairies, chimera, and a host of others "mythical" beings, but theses map cannot "imply" that such things "exist".

For a "current" theory of what it means to be intelligent, read "On Intelligence" by Jeff Hawkins.

"Better" is a value judgement made by an entity which may or may not refer to some formulation of a "standard" passed down by time-binding. As such it reflects relativism.

How would each of you formulate an explanation of "similarity of structure" that is not self-reflexive?

The antecedent of "that" in this post is not apparent to me.