Decisions about what to believe and how to act are informed by knowledge. The quality of these decisions impacts our lives as individuals and as a society. Bad decisions about beliefs and actions create unhappy societies. Good decisions about beliefs and actions help create happy societies.
Knowledge informs good decisions. But almost all decisions must be made on the basis of incomplete knowledge. A blind person who understands the limitations associated with blindness is equipped to act more wisely than a blind person who, used to seeing, keeps on pretending that he can see when he really cannot. It is not knowledge alone that we need, but an understanding of where our blindspots are. We need to understand what we do know, what we do not, what we can and cannot know. And we need to understand how to act accordingly.
What do we know? How do we know it? Wherein lies our certainty? What we propose to argue here is that when we say "know" we mean "presume to know" or "know on the basis of certain assumptions that we trust." And that many of the assumptions that we trust are not necessarily trustworthy. Yet we trust them because the alternative requires more investigatory and reasoning power than most of us have the time or energy to employ.
To make matters worse, we have come to understand that certain things are ultimately unknowable. We have to make do on partial knowledge, no matter how smart or well-informed we might be. So we make decisions with what we have. This is often the most suitable course of action, but it presumes that we are open to change; we do not simply keep on making the same bad mistakes over and over in the face of compelling evidence that we are doing just that. Not if there is a better alternative.
Our goal here is to develop a framework about knowledge. We will work first develop the ideas on which our definition of knowledge rests. We will define knowledge. We will talk about what we can know with some certainty. Then we will look at a brief history of knowledge. In it we will discover that there are a number of things we know we cannot know. Finally, we will touch on the issue of making decisions in the absence of adequate knowledge. It's a topic that could not be completely treated in a huge encyclopedic volume of work; but we will give it a few meager paragraphs.
Plato firmly fixed the notion of two parallel universes within our culture: the real, material universe; and the ethereal, ideal universe. There was much merit in the idea because it suggested a mental representation of the real and it suggested that this representation is not identical to the real. Furthermore, it suggested that when a man created a thing, he was inspired by some ideal for that thing. Today we might call that a design.
Plato's idea had problems though. He imagined an ideal bed. In his model, all beds were failed approximatons of some singular ideal bed. All beds in Plato's take on things fall short of their ideal. All differences in beds might be attributed then to how they differ from the ideal. It may be true that all beds are less than ideal, but not for the reason Plato assumed. His notion is rendered nonsense if one imagines that each sleeper has subtly different needs. Ideal comfort derives from different needs in sleeping surface. Ideal decoration qualtiies derive from different tastes and decorating environments. The idea of a single ideal bed is nonsense.
A similar sort of argument goes for blue as an instantiation of blueness. Aristotle is quoted by Aquinas as suggesting that all instances of blue inherit from some ideal "blueest object." Hume understood both the strengths and the weaknesses of Plato's two notions. He proposed two similar categories. One he called fact. Fact deals with matter. Consider a golden dubloon. It has mass, and size, and shape. One can see its features and feel them. These things are facts about this material object, he suggested. They are independently verifiable.
Distinct from matters of fact are "relationahips of ideas." A triangle is defined as planar closed figure with three straight edges. The triangle is a relationship of ideas. It relates the ideas of line and plane to the figure triangle. Go look in nature, and you will find no real triangles. You might find representations of triangles, but the triangle is an idealization, an idea. The triangle is a figure from geometry, and geometry is one of the ideal examples of a pursuit that exists entirely in the "relationship of ideas." There are applications of geometry to navigation, design, surveying, and so on; but geometry itself lives in the world of "relationships of ideas." Geometry is an abstraction. And when it is applied to other problems involving real, factual things, it can be seen as being representational of those things.
If one has a plot plan for a lot upon which one is to build a house, one employs a surveyor to make sure that an expensive construction project is not compromised by virtue of having some part of the construction be on another's property. Geometry is an abstract tool brought to bear on this very concrete, factual problem. Geometry is but one of a large number of tools in the relationship of ideas. All of logic lives there. So, too does algebra, trigonometry, calculus, set theory, group theory, topology, and a vast array of other things that start with "why" and end in "y."
We can look at this world of relationships and imagine that another yet another way of looking at it is by thinking about what happens inside our brains. The processes in our brains are all carried out by creating relationships. There is not a single neuron for "car." There is an area of the brain that represents the word car. And an area of the brain that represents some visual ideas about car. And there may be some bits of the brain that connect these ideas to car-related ideas; color, horsepower, gas mileage, fast, fun ride, or outta gas, broken.
The brain uses a sprawling relational system to represent the ideas that are integral to and closely associated with car. In other words, with our own brains, the car is expressed as a relationship of ideas. It is a different sort from a mathematical function, perhaps, but it is definitely a relationship. One of the reasons Hume's notions seem strange and foreign to us is that we rarely are called upon to make the distinctions he makes. But it is a necessary starting point in considering knowledge. The reason is that our mental images and abstractions of the physical world depend at least in part upon sensation, perception, and interpretation.
Our ideas about the world depend upon interaction with the world through sensation. The way the ideas organize in our minds may be mediated by language, culture, education, and other factors. But fundamentally, knowledge is a kind of mental representation of fact. It is a kind of bridge that spans the gap between the ideal and the real. And the better the knowledge, the more robust and durable is that bridge.
Plunge your hands in a basin of icewater. What happens? Your hands feel cold. Why? The technical reason has to do with the low temperature of the water and with water's superior ability to carry heat from the surface of your skin. It transports heat energy through the skin, via conduction, and this loss of heat lowers the temperature of the hands. Before long, the hands feel cold, uncomfortable.
The sensation of cold is a "pure" sensation. That is, there is very little mental moderation or abstraction of the sense. There are two good reasons for this. One is that it is evidently not difficult to accomplish, the sensation of cold. All sorts of reactions change speed with temperature, so making good thermal sensation is not a difficult trick for biology to accomplish. The second reason is that it is quite useful to eliminate interpretation of cold sensation because interpretation is subject to mistake, and thermal challenges are frequently mortal challenges in nature. Thus the sensation of heat and cold are unmoderated sensations. The body senses them directly and when conditions are unfavorable, it gets our attention.
Two people may sit in the same room. One may be hot, the other cold. This demonstrates that the sensation of being hot or cold is a kind of relationship between the person sensing the environment and the environment itself. The perception of being warm or cold is a subjective one. It is affected by one's specific conditions; age, metabolism, weight, dress, and adapations to prevailing conditions.
People who live in northern climates and spend time outdoors may frequently find an environment warm that people used to tropical climates will find cold, because of adaptations to their respective environments. The feeling of thermal comfort is a judgment about the thermal environment. It is subjective, but never wrong. Propositions such as "this room is cold" may not evaluate to "true" in any meaningful sense.
I might know that I feel cold in this room. You might know that you feel warm in this room. Is the room too warm? Is the room too cold? Is this a meaningful way to think of it? Or is the question "what is the best means of making everyone comfortable?" That question has nothing to do with the truth of any propositions about the room's temperature.
We introduce this question because when making propositions about real world facts, the notions of “true” and ‘false” are frequently unhelpful. True and false are notions of logic that belong to "relationships of ideas" not to fact. It is a discussion taken up later.
Taste behaves much like the sensation of warmth and coldness. We have four simple tastes and most of the chemical substances that stimulate taste sensation stimulate only one of the four sensory receptors. And it is so in everyone. Some people taste things more intensely than others, owing to the fact that they have more taste receptors. But sensations of sweetness, saltiness, sourness, and bitterness are directly wired into our brains. And because there is no overlap in their sensory range, there is no conceptualizing required to report one of these sensations.
Once again, there are compelling reasons for this; the four fundamental flavors serve four fundamentally different functions. Sweet informs the body of digestibility of vegetable matter, available energy. Salt informs the body of a vital compound whose balance in body chemistry is of paramount importance and whose availability in some environments is low. Sour seems to be associated with certain special nutrients such as vitamin C. Bitter’s function is to prevent us from eating the wrong plant matter; most poisonous plant alkaloids have bitter flavors. The argument for bitter, then, is much like the argument for cold sensation. It is a sense that requires little interpretation and is linked closely to avoiding hazards that threaten survival.
The fundamental flavors in taste are simple, but taste involves smell. And smell is highly complex. There are evidently at least sixteen or twenty five fundamental smells, with the whole language of odor built upon that. So when one eats food one experiences all the odors, all the tastes, and the textures as well. The fact that we have food experts suggests that this system is complex and can create highly nuanced effects. It may not take a great deal of interpretation to detect the single- valued inputs, but it might take a considerable amount of attention to grasp all of the interrelationships between the inputs. That can require a goodly bit of interpretation.
Most of our sensation requires some interpretation. This interpretation is sometimes performed automatically by the nervous system as an integral part of sensation, and it is sometimes performed at some higher conceptual level.
Color sensation provides some very interesting insights into the interactions between sensation, perception, and interpretation. Light is made up of photons, and each photon has a characteristic wavelength. Photons that we perceive as red have wavelengths close to 600 nm. Those we percieve as green have wavelengths close to 540 nm. Those we perceive as blue have wavelengths close to 450 nm. Surfaces that reflect or emit photons soly in these wavelengths will appear to be that color.
Our eyes have specialized color receptors tuned to each of these three primary colors. Red light stimulates red receptors, but it does not stimulate green or blue ones, for instance. Yellow light stimulates both green and red receptors. Aqua light stimulates both blue and green receptors.
It is no great surprise, then, that every known culture has words for colors. But it is a surprise that the words vary from culture to culture. Some cultures have no word for yellow. Most have no word for orange. In some cultures blue and green have the same word. In others aqua is identified either as blue or green. And even many native English speakers will be hard pressed to distinguish puce from fuchsia or ochre from sienna.
At first blush, it seems simple. We all sense the same colors; but we categorize them differently. Our language establishes the categorical tags. Our cultural practices establish the categorical definitions and boundaries of those definitions. A language that fails to distinguish blue from green, for instance, is unlikely to have a special word for aqua. People who have no reason to distinguish between twenty eight earthtones will never bother distinguishing sienna from ocher, not because they are physically incapable of making the distinction, but because it is not required.
I remember as a schoolboy standing on a promontory at the Cape of Good Hope, overlooking the point at which the Atlantic Ocean touched the Indian Ocean. I was certain that the deep blue of the Atlantic was blue. But I remember thinking that the Indian Ocean was green. I distinctly remember that it was almost impossible to distinguish one from the other, so if the Indian Ocean actually was a different color, it was a subtle aqua tint of blue. By green standards, it had nothing to do with green.
Some recent articles in Science News suggest that how we physically perceive color depends to some degree on our acculturation. There is some interaction between what we learn about color categorization and what our apparent capacities are at distinguishing colors, even when the factor of language has been removed. Probably we are required to make careful distinctions the boundaries of color categories, but make less careful distinctions near the center of color regions. Once we have a lifetime of practice doing this, our brains may simply be trained to ignore certain information to the point that we cannot perceive it anymore. This is quite telling. It suggests a profoundly deep interaction between what we are capable of perceiving and how we are acculturated. This is a topic we intend to take up again.
A topic we have already mentioned is the distinction between asserting that a thing is a certain way, and asserting what is perceived. Imagine a stone. It is shiny and it is orangy brown. In some languages it might be called rust colored. In others, orange. In still others, brown. Languages that only have primary colors and black might call it black. Now, imagine we illuminate the stone under ultraviolet light. Under this light, it emits an eerie green glow. What color is the stone? One can set up careful measurements and define precisely the spectral intensity of the photons emitted and reflected from the surface under any sort of illumination. In a scientific sense we can define the color of the stone with incredible accuracy. But the act of summarizing all of this information as a single color risks losing most of the information. The only reason this would be acceptable is if most decisions people make are not critically dependent upon color. Or, more specifically, upon a complete characterization of a surface's interaction with light.
The same cannot be said about other sorts of visual data. A visual scene may be composed of tens or hundreds of megabytes of data, but the visual system has already begun abstracting that data by the time the visual signal has reached the visual cortex. The signal has already been processed to supply information about edges and lines, regions of high contrast, regions of order, and of confusion.
In digital photography terms, it has been compressed. But in the terms of our discussion, it has been abstracted. And the abstraction rules will typically be to identify objects and place abstract tokens for them at various places in the visual field. If we are highly artistic sorts, the tokens might reasonably well represent the actual objects. If we are intuitive sorts, the tokens might not represent many of the salient visual features of the object.
This is a salient point. The visual system, unless it is hard pressed by its user, does not represent very much of a visual field literally. It identifies areas in the field of vision that have interest, and those that do not. Interesting areas it represents with carefully derived rule-based representations of objects. The balance it fills with fills rather reckless representations.
The lollypop tree is not what a child literally sees. But it may be a fair representation of what she perceives. No child who looks at a lollypop tree and a real one would confuse the two, it is just that the child's mind represents the tree as an abstract and simple object, not as a complex three dimensional one with gazillions of limbs and leaves. The depiction is a depiction not of what the child sees but of how that visual perception is represented in the mind. The visual system is constantly called upon to take hugely massive amounts of data and reduce what is seen to what is meaningful. And the only way to do that is to throw out most of what is there, to decide what is of interest, and to represent that as parsimoniously as possible.
That this happens is clear from stories of people who were born without vision, lived for roughly two decades blind, but then had sight restored. There have been only a few such cases, but what happens is not what one might first assumes would happen. The assumption is that once a person is equipped with all the requisite organs, sight becomes normal and vision becomes normal. What actually happens is slightly different. At first the visual world seems rich, colorful interesting. And this impression is extremely attractive and entertaining.
But people who have been blind all their lives have committed much of the regions of the brain that is usually used to interpret visual data over to other tasks. So images, for all their powerful attractions are overwhelming. They present too much information. The brain tries to process it all. And the person becomes weary. In the end, vision becomes an interesting curiousity, but it does not become a dependable sense. And the reason is that the information is not being appropriately abstracted and ignored.
Because it is called upon to process so much information so quickly, the visual system takes a lot of shortcuts. Each of these is subject to some mode of trickery. Michael Bach has spent a good deal of time cataloguing tricks that exploit deficiencies in visual perception and he presents his findings in this catalogue of optical illusions. Sound data is inherently smaller than visual data, by two or so orders of magnitude. Yet it still constitutes a challenge to the perceptive mind. Again, the methods that the aural system uses resemble some of those of the visual system.
Sounds, too, are automatically filtered and recognized noises are frequently replaced with representative tokens. A trained musician might have a highly refined sense of sound and may have very robust ways of hearing and representing sounds within her mind. A person who has never heard a violin, however, may have difficulty distinguishing the sound of one from another; they would be represented in his mind the same way. Anyone who has heard the group Zap Mama will be intrigued by the abilities of some of the members to hear and reliably reproduce noises in ways most westerners would be hard pressed to do. Some of the group's members grew up in the Congolese jungle and refined their sense of hearing and sonic interpretation outside the field of language in ways that might only be done if one spent twenty years of near-silence living in a jungle and depending upon its sounds for one's survival.
Yet for all humans speech is a central quality, an imperative social act. Because speech is so important, humans have single neurons that fire when a particular phoneme is heard. All the filtering and processing that takes place before this point may then be discarded and ignored, provided other aural clues such as pitch and tone and clues about emphasis have been registered as well. In short, language processing discards most of the sonic signal. It replaces that with reconstructive rules, rules that capture all that the listener perceives. If that person is a trained actor, the nuances of accent and stress may be accurately registered. If the person is a counsellor, nuances about emotional condition may also be registered.
But in all of these cases, it is an abstraction of the signal that is stored in the mind. That abstraction is the perception. This is important, because when humans encounter rare events, they frequently lack the capacities to interpret these events correctly.
Interpretation is a mental act that takes perceptions and organizes them in ways that are potentially useful to some purpose. An interpretive process in the mind may assemble a collection of perceived edges in a visual field and produce the output "snake" or "lion" or "pizza" or "homework." What happens next may depend upon other interpretations lurking in the mind. If hunger is one of them, then pizza may have special meaning. If an important social engagement is pressing, then homework may have special meaning. If one is at a zoo, then lion may have a different meaning than if one is walking alone on a narrow path across the grassy African plain. In all of these examples interpretation is integrally tied to expectation. We tend to accurately percieve things that are reasonably well expected, but less accurately perceive things that are completely unexpected.
Interpretation is a difficult subject because it occurs in so many contexts. And it crosses perceptive bounds. For example; an infant when given a plastic cube the size of an orange may look at it, feel all of its sides, put it in his mouth and taste it, and so on. The cube is represented in his mind by sensations of sight and touch. And the mind corellates those sensations. Correlated sensations have special powers on the mind. When we see and hear something, we remember much more effectively than when we only see or only hear. Some factor about simultaneity of sensation impresses the mind in a distinct way. There is reason to believe that language enables the process of making sense of correlated sensory input.
Helen Keller noted that the world seemed an impenetrable tangle of sensations until she learned her first word, water. Then she suddenly had an insatiable thirst for language, because it untangled that sensory jumble. Language allows us to create simple tokens that represent complex things. And this is precisely what we are equipped to do in visual and aural processing. Language, however, allows us to tokenize things that are not purely sensory. It allows us to tokenize ideas, relationships, actions, and so on.
It is reasonable to assume that language we learn first is most closely related to objects and sensations. My own informal study of French suggests that all I can remember of the language is stuff that strikes me as being really important. "Je suis fatigue," translates idiomatically to "Oh, I'm feeling kinda tired." And "Il peu," translates literally to "It stinks" or idomatically to "Eeew!" Thirty or fifty hours of sitting in front of "French in Action" and that's what I can remember. But in both cases it is because the action of the actors in saying these things perfectly matched the sense of the language. The lingual tokens attached to my memory because the communicated in French what I already percieved.
Perhaps most amazing to me is the ability of animals to sense, perceive, and interpret three dimensional data in real time. Consider the housefly. It has a brain that is probably too tiny to skewer with a sewing needle, yet in real time it percieves a threat, readies, and flies at the very last moment along a trajectory that frequently saves its life. It does not learn this behavior from thousands of hours of flight training. It is born with all of these capacities, it lives for some days, and it dies.
How is it that the common housefly is so able to perceive the three dimensional world and motions that threaten it? There is, of course, the evolutionary answer. Animals, almost all of them, either eat other animals or are eaten by them. Every animal, or one of its close evolutionary ancestors, was predator or prey. And every animal that spends much time above the ground relies to some extent on visual acuity to survive. Site and the ability to sense motion are survival necessities for animals.
Another part of the answer might be found in a paper by Smith et al. in Gazzaniga's Neurosciences (1990.) It is a paper describing research on young children. Children sat in front of computer screens and were shown images of things moving. The moving objects were simple objects, triangles or circles or squares, perhaps. They purposefully did not resemble animals or people. When the objects were stationary the children attributed to them the qualities of inanimate objects. When the objects moved in simple oscillitor motion like that of a pendulum or a tree waving in the wind, the children also imagined that the objects were inanimate. But when the objects moved in other ways, the children attributed to them qualities of animate objects.
If we think about the snake-charmer whose charm to the snake has less to do with his clever music than it does to his carefully choreographed harmonic oscillaion, we imagine that the snake interprets motion as does the fly and the three year old.
We also imagine that if nature has solved the problem of motion so effectively and compactly in the fly and the cobra, there is hardly any reason why the same problem may not be solved as compactly in other animals. The response of young children to motion, in fact, suggests this very thing.
If we imagine that humans carry a tiny knot of neurons that interpret the three dimensional world and the motions in it using approximately the same information as the fly, then much can be explained. A person is walking in the woods. His visual system detects a motion. The little flyspeck of an interpretive system interprets the motion as that of an animal and sends out a big, loud alarm. But the visual signal is interpreted in other parts of the brain in other ways. And on the basis of their analysis, there is nothing there; no recognizable animal to account for the motion. What happens next? The brain has produced conflicting interpretations of a sensory event. One interpretation is that there is an animate motion, cause for alarm. Another interpretation is that there is no animal to account for it.
One possible interpretation would be that the motion was caused by an invisible animate force. What is the term we use for invisible animate forces? A spirit. Another possibility, is for one to construct a fictitious animal to account for the motion. A third possiblity is, lacking an explanation for the sensation, one ignores the data. Interestingly, all of these responses seem to have history in human interpretation. It is also interesting that, as the practice of monotheistic religion spread and as the ideas of the enlightenement became engrained in European culture, sightings of spirits and mythical animals became ever less frequent. The seventeenth century witch trials dealt a kind of death blow to the whole notion. It would seem that ever since then, we see differently.
Our culture prevents us from inventing the same sorts of mythical figures that our mind once served up. To some degree this is what knowledge does. Proper knowledge of the world around us changes our perceptions and it changes our intepretations of our perceptions. This is the purpose of knowledge, to help us interpret our perceptions in the most useful ways possible. It starts with making the most useful categorical assignments, proceeds by noticing useful relationships among categories, and by making useful distinctions within categories. And it is sometimes refined by application of carefully crafted mathematical models, diagrams, or other sorts of descriptive models.
At this point we have discussed how the mind is engaged in sensing the external world and how it organizes the sensory information in compact and robust ways. The details of the process are not all well known, but what is important to understand is that a great deal of abstraction takes place. And, as a result, most of what we see and hear, taste, touch, and smell, is lost forever. We have only a vague impression that captures some tiny fraction of the original information.
The river of the unknown is bounded on two banks. On one bank is fact. It is solid and discoverable, but unknown. On the opposite bank is is the mind, the relationships of ideas within it. Connecting these extremes is a bridge. Its main structure is sensation and perception. But these are narrow and slippery, hazardous for foot traffic. Intepretation is the road deck and railing. It allows enough traffic between both sides that the facts may be ascertained correctly, and that they are appropriate to the need at hand. The completed bridge, including both terminals and the traffic it carries constitutes knowledge.
The mind is a representational machine. It represents the world in an abstract form using relationships. Some representations of the world are more accurate than others. Artists, for instance, may be much more skilled at abstracting overall shapes and relevant details about the world, they are trained to make distinctions about what we see that most people do not. They understand the interplay between shape and light and shadow. Their minds develop rules for abstracting objects and textures that are suggestive of sensory data without actually replicating it. Thus they exploit our automatic perceptive processes.
Physicists look at falling objects differently than people who have not studied physics. Expert mechanics understand the nuances of automobile design, the sorts of things that fail, and the symptoms of failure very well. They have detailed mental models. Our representations of the world reflect our level of knowledge in a particular area of expertise. In a very real sense, then, knowledge about the real world is a proper correspondence between the actual way the world is and our mental models of it.
Similarly, knowledge about the abstract world is a proper correspondence between the way we manipulate objects and relationships in an abstract world, and the way the abstract world is constructed. In chess, for instance, nothing about the game is about the pieces. Everything is about the relationships of position. Set up a chess board with a position from an actual chess game. Show it quickly to a novice and to an expert. Then have each reconstruct the positions of the pieces. The novice will get much of it wrong. The chess master will get most of it right. Now, try the same thing by putting the pieces on the board in a random way. The novice will get much of it wrong. So, too will the chess master. Why? because in the first case his experience of the game allows him to percieve the relationships between the pieces. He remember these relationships and uses them to reconstruct the position of the board. But when there is not real game, the relationships are nonsensical. He must remember in a different way, the same way as the novice. So, in the practice of chess, knowledge or expertise involves a detailed understanding of the positional relationships. This is what good players learn.
Knowledge is
These are not exclusive; the first item is a kind of simplified subset of the second. There are a lot of interesting observations that can be made about knowledge defined in this way. One observation is that the notions of true and false are not very helpful.
Knowledge is better understood in terms of how useful it is. Take, for example, the notion that the earth is spherical. This knowledge would have proven of some use to astronomers and cartographers long before it was generally known, but it really became of great relevance once there was interest and motivation to promote trade between Europe and Asia in the absence of secure land routes. The idea that the earth is spherical, at that point, became highly relevant in a way it had not previously been. It was useful knowledge. But to the average land owner, a person or a household, the inaccuracies of representing land boundaries on a flat piece of paper present no problems whatsoever. But the earth is not exactly, precisely spherical. It is flattened a bit here or there. Nor is it ideally smooth. So even the idea that it is spherical is not strictly true.
Cast into the terms that Hume used, knowledge of the fact, factual knowledge is a proper or useful correspondence between fact and our mental representation of it - the relationships of ideas that represent it in our minds. If we represent fact badly in our minds, we act on it badly. If we interpret a lion as a pizza or mistake our wife for a hat, ill consequences can ensue. Our minds must be capable of making these distinctions clearly.
Much of learning is, therefore, about making useful distinctions. Some kinds of problems are solved by means other than distinctions. Some are solved by generalization or synthesis. Such methods can be powerful because they can unify a vast number of seemingly disparate phenomena into a single line of analysis and study. We will talk about the work Newton did on gravitation a little later. His work is among the world's most shining examples of synthesis.
So far we have introduced the two extremes that are connected by the bridge of knowledge and we have shed some small amount of light on the way these extremes are connected by sensation, perception, and interpretation. In the next segment we will take a whirlwind tour of knowledge with the hope of seeing some examples of things that work and of things that do not.
Copyright: Stephen R. Brubaker, 2007. All Rights Reserved