What Can We Really Know?

source: sections from pp30-44 -- Part I: constructed Knowledge -- text title: constructing science in middle and secondary school classroom - dale r. baker and michael d. pilburn of arizona state u -- allyn and bacon 1997

We all think that there must be things about nature that are true. We should be able to figure those out. And if we knew those truths, we would understand how the world works. They might be hard to discover, but we could approach them in a series of increasingly accurate approximations. At least, that's how most of us feel about it. Modern scientist first began to doubt this in the early part of the twentieth century. Because of a number of experimental results that we will talk about later, they began to wonder what they really could know.
These were not obscure people, minor scientists. A group of famous individuals including Albert Einstein and Sigmund Freud, asked whether absolute knowledge was possible or if all that we could ever hope for was relative knowledge. We are not going to answer that age-old question in this chapter. It's stuff for philosophers and logicians to argue about. But the fact that such prominent scientists could ask that question should concern us. We might be especially concerned if we are science teachers.

Why is this particularly important for teachers? The answer is simple. Science educators no longer believe in the model of instruction that is based on the passing of knowledge from teacher to student. We have ample evidence that this transmission model just doesn't work.

It is widely accepted that people build their own knowledge. The act of teaching is one of helping people with this process. That would be an almost impossible task for a teacher who didn't understand how it worked. We think that you need a theory about knowledge to be a good teacher. The theory of knowledge that has touched science education most pro- foundly during the last two decades is called constructivism. It addresses exactly those questions that we have just raised. It offers very practical and sound advice to teachers about their roles in the education of students. It also provides a general platform from which all of us can gain a better understanding of our own knowledge

The Origins of Knowledge

The Subject-Object Question
One of the most enduring questions ever asked is whether there is a real world out there beyond our minds. And if so, can we find out about it through organized inquiry? That seems simple. Yes! Of course there is a real world, and we know it through our interactions with it. We sense it, we manipulate it, we create theories about it, and we make successful predictions about it. Thus, it must exist and it can be known. But beware. The problem isn't as straightforward as it might seem.

Our minds have an odd way of filtering our experience and making something that never was there in the first place. We don't just passively receive information. We operate on it and transform it.

A good example is the size of the moon. Despite the fact that the moon's angular diameter, or apparent size, never changes, most people think that the moon is much larger when it's near the horizon than when it's high in the sky. It just looks that way. They usually explain this by saying that light from the moon has to go through more atmosphere when it is on the horizon, so its image is magnified. In fact, the apparent size of the moon is exactly the same when it is on the horizon as when it is high in the sky. The fact that it looks bigger on the horizon is the result of a well-known optical illusion, called the 'moon illusion." How could something like that happen? People not only saw something that wasn't there, but they created an elaborate theoretical explanation to account for it. Everything makes perfectly good sense. The only problem is that none of it is true. Even the initial observation was incorrect.
The Importance of Schemata (aka = prior knowledge?)

The answer comes from the field of Gestalt psychology. It depends on the fact that the information we receive from our environment is usually either incomplete or contradictory in some important ways. No matter. Our minds are perfectly able to fill in the gaps. In fact, if they couldn't we would have a very hard time getting along with our lives. But more than one interpretation is usually possible, and two people can see different things. Consider the drawing of a cube on a sheet of paper in Figure 2.1 (Leyden note: these are optical illusions). One person might see it pointing down and to the right, another up and to the left. In fact, you can probably make it switch back and forth yourself. Your mind takes the ambiguous information contained on a two-dimensional sheet of paper and converts it to a three-dimensional object.
This brings up a couple of points that we want you to consider carefully.
We will probably come back to them again and again, because they are central to the idea we are proposing about where knowledge comes from. The first is that neither person is right. What you see in Figure 2.1 isn't a three-dimensional cube. It is just a bunch of lines on a two-dimensional sheet of paper. The other is that both people are right, because it depends on how you look at it. How you look at it has a lot to do with your prior experience with cubes and with perspective drawings. Perspective drawing is actually a late event in the history of art. Remember Egyptian paintings? They were very flat. When perspective drawing was first discovered, artists actually had machines to help them find things like vanishing points. Would someone who didn't know about perspective drawing see a cube? Probably not. You can only make those lines into a cube if you have prior knowledge that directs your interpretation. There are many names for this prior knowledge, but we will call it a schema. No schema, no cube. By the way, the shape in the lower right-hand comer, if you haven't figured it out yet, is the head of a hammer. And the third picture is a famous optical illusion that can be seen either as a vase or two faces.

The Question of Reality
Sometimes people think that optical illusions are just funny tricks and that they really don't have much to do with the underlying nature of knowledge. But doubts about the meaning of reality extend well beyond the simple issue of the limitations of human perceptual ability. The existence of the physical world is difficult to logically demonstrate. Could you prove that you really existed? The French mathematician Rene' Descartes solved the problem by saying, 'I think, therefore I am." Teaching Note 2.1. is about a robot called Cutie, who tried to answer a similar question about itself.(Leyden note: have omited Cutie / QT discussion)
Even if we accept the fact of our own existence, there is still a problem that is awfully hard to solve. What is the relationship between the observer and the observed? Between us and the world out there? Denying the existence of all reality makes science a futile exercise in self-indulgence with no reasonable outcome. On the other hand, any claim that the world can be known exactly is unrealistic. Between these two positions lie a number of possibilities. Interesting though this discussion has been, you probably felt that it had little to do with science. Now we want to talk about some real cases in the history of science and try to make some of those connections for you.

Probably the earliest well-documented scientific schema was the one proposed by the group of Greek philosophers who were followers of Pythagoras of Samos (sixth century BC.). The Pythagoreans thought that some truths could be discovered without observing the real world. That kind of knowledge is called a priori, or 'before the fact."

The Nature of A Priori
A priori are a little difficult to understand, so let us give you an example.
In set theory, there is a basic principle that the size of a larger set of objects is the sum of the sizes of all of the smaller subsets of the larger set.
So all M&M's are green or red or brown, and so forth, and the total number of M&M's is equal to the sum of the numbers of all the different colored M&M's. Teaching Note 2.2 suggests some ways that you can investigate how people think about this question.
Probably the earliest well-documented scientific schema was the one proposed by the group of Greek philosophers who were followers of Pythagoras of Samos (sixth century B.C.). The Pythagoreans thought that some truths could be discovered without observing the real world. That kind of knowledge is called a priori, or "before the fact."

The Rise of Empiricism
One of the most famous critics of a priori knowledge was Galileo Galilei (1564-1642). He was the first person to report using a telescope to observe the night sky. He saw the Milky Way and learned that it was made of stars. He was the first to see the moons of Jupiter, the phases of Venus, and the mountains of the moon. Galileo was also firmly committed to the importance of observation in science. He rejected the notion of a priori knowledge.
He believed that no theory was acceptable if it was inconsistent with what was observed.
Such a position is called empiricism.

The play The Life of Galileo by Berthold Brecht has a wonderful scene that makes this point. A prince from the East has come with his teachers to hear what Galileo has discovered. Galileo points to a telescope in the comer of the room by a window and tells the prince to look through it. The telescope is pointed at the four largest moons of Jupiter: lo, Callisto, Ganymede, and Europa. After consulting with his teachers, the prince tells Galileo that he cannot look through the telescope. His teachers tell him that what he would see would only be illusion. After all, they already know what is true. They could see nothing through a telescope that would change their minds. As they leave, the prince apologizes to Galileo for not looking through his telescope. Galileo hoped that seeing the moons of Jupiter would shake the prince's confidence in Ptolemy's geocentric model of the universe. After all, it was visible proof that not everything went around the earth. But the prince accepted his teachers arguments that the real world was only illusion. In 1610 Galileo published The Starry Messenger, describing his discoveries. In that book, he admitted publicly his acceptance of the theories of Copernicus. The earth moves! Facing criticism from the church, Galileo wrote to the Grand Duchess Christina arguing for freedom of inquiry, but in 1616 the Vatican's Holy Office issued an edict against the teaching of Copernicanism. Sixteen years later, Galileo wrote "Dialogue of the Great World Systems" in support of the Copernican system. For this heresy he was condemned, in 1633, to life imprisonment. He remained under house arrest until his death in 1642, the year of Isaac Newton's birth. Teaching Note 2.3 suggests a way to involve your students in the scientific questions surrounding Galileo's trial.

Logical Positivism

In the early part of the twentieth century a group of mathematicians and philosophers who had created modern prepositional logic and mathematical philosophy modified empiricism and established a new model for the practice of science.
They proposed that science should proceed by the testing of theories.
The method of logic would be used to generate hypotheses that had implications about nature. Observations would provide the evidence for testing these hypotheses, and the rules of deductive logic would provide the rules for reaching conclusions.
They further specified that no hypothesis could be rejected unless it had been falsified. In its most extreme form, this is known as logical positivism.
Some version of positivism is what is usually represented in modern textbooks as the "scientific method." By the late nineteenth and beginning of the twentieth century, the method was so widely accepted and applied that few people would even think of challenging it.

Science in a Postpositivist Time
By the end of the nineteenth century, it was generally believed that absolute knowledge was possible. One point of view was that if we knew everything about the rules that governed the behavior of something like an electron and everything about the past history of a particular electron, we could predict the motion of that electron perfectly forever in the future. That's a powerful idea, if true. A prominent scientist could tell an audience that if we had known enough biology, we could have predicted the existence of a giraffe. Although we might never be able to actually learn that much, the idea was at least feasible in theory. If we ever got to that point, we could write the last books and close down our laboratories; we wouldn't have to practice science any more. Positivists also held that the process of science had a direction. Theory was like a pyramid, with each scientist refining the work of those before. Thus, Newton could make his famous claim that "if I have seen farther, it is because I have stood upon the shoulders of giants."
(Leyden note: he was saying 'hang around smart people.")
Events in the first half of the twentieth century, especially in physics, challenged the validity of positivism and even of empiricism itself. Even more unexpectedly, they raised questions about what kind of knowledge could be obtained as the result of scientific inquiry.
Physicists uncovered serious problems with the process of observation.
The experiment influenced the result! For example, measuring the motion of an electron changed its position, and measuring its position changed its motion. It was impossible to simultaneously know both. Werner Heisenberg (1901-1976) summarized this in his uncertainty principle. Today most scientists are willing to accept the idea that experimental results are determined by the design of experiments.
Light is a good example. Under certain conditions it appears to have wave-like properties, whereas under others it can best be interpreted as consisting of particles in motion. From a positivist point of view, the solution to such a dilemma is to falsify one of the hypotheses. That is just what physicists tried to do about light, but they were unsuccessful. No matter how hard they tried, neither the wave nor the particle hypothesis could be rejected.

The matter was resolved, as far as possible, by Niels Bohr (1885- 1962), with his principle of complementarity. Although light looked like a wave under certain experimental conditions and like a particle under others, it was neither a wave nor a particle. It was something else. The true nature of light could not be determined, because the result obtained was a product of the experiment that was conducted.7 That idea should be familiar to you by now. As with the cube in Figure 2.1, as with Ptolemy and Copernicus, both views are right, and neither is right. That may make you a little uncomfortable, but it is the way things are.

Events of the twentieth century have presented us with a dilemma. We now know that the connection between theory and observation is a loose one. Multiple theories can be generated from a single set of observations, and an entire millennium of inquiry, as with motion, may consist of a succession of theories that are nothing more than alternative visions seen through the lens of different schemata. What kind of science do we have then? If theories can be both right and wrong at the same time, what about absolute knowledge? Is it possible any more? If all we can produce are artifacts of our encounters with nature, and if we can never possess absolute truth, then why continue the scientific endeavor? The responses of scientists to this dilemma varied. One group, led by Percy Bridgman, answered that all we could talk about was what we did and what happened. Theory was no longer possible. Others continued their work, but none ever viewed it again in quite the same way.

Most people who study knowledge describe its origin as more like a spiral than like a pyramid. You all know the old saying "What goes around comes around." That seems to be the case with scientific knowledge. We have to reject the idea that each new theory is just a more perfect version of the previous one. Instead, each new theory completely rebuilds the world as we know it. Newton's world and Einstein's were so different that it is hard to believe they existed in the same continuum. That's because the world in which each theory is built is a different world. We seem to be big on old sayings, but there is one to the effect that "No person steps twice in the same stream." What does that mean? It means that no person is ever the same twice and that streams are always changing. A big question is whether new world views call for new theories, or it is the other way around. We haven't gotten into that because not a lot has been written about it. We do know, however, that the historian Lynn White Jr. argued that the iron stirrup changed the course of Western civilization.9
(Leyden note: the stirrup was a WEAPON. Well, it enabled people to kill people without getting off their 'high horse' and exposed to the other guy's sword. With stirrups - you stand up on your horse and kill -- and speed away.)
The romantic in us would like to believe that science has changed the course of Western culture, but we don't really have any evidence to support the idea. We also have to admit that many people today, while admitting that science has shaped our culture, don't like that idea very much. They think that science has gotten us all in a lot of trouble.

Where does that leave us? Right where physics is now. We believe in a real world out there, but we have to admit that we can never know exactly what it is like. We know that our vision is shaped by our minds and by our culture. That can never be changed. But that is all right. Science is a human endeavor, and it is nice to see the humanity in it. We feel the same way about science that we do about art and literature. It is a human creation with all of the flaws that implies. We want you to remember this and take it with you as you read the next two chapters. We think it will help you understand the ideas that people have about science and maybe even to be a little more supportive of them.