"Teaching Physical Concepts Beyond the
Boundaries of 'Standard Culture' and Language"
Prepared by Anne Dalke
Additions, revisions, extensions are encouraged in the Forum
Participants: Peter Beckmann, Sharon Burgmayer, Laura Cyckowski, Anne Dalke, Wil Franklin, Paul Grobstein, Rachel Horton, Elizabeth Logue, Selene Platt, Betsy Reese, Sandy Schram and Scott Silverman.
Peter opened the conversation by saying that this was a difficult topic to talk about. There's lots of very practical science going on, which helps us importantly in everyday life, but only a highly selective set of scientist-priests understands that science. These "priests" communicate largely in mathematics--and when they use English (or another common language), "it's still just a shorthand for the mathematics." There is no "physical understanding" of any of these concepts in the general culture. The overriding thesis of Peter's presentation was that the educational system has to address this problem.
Peter began with the assumption that the group accepted the thesis--for conversation purposes, if not for any deeper ones--that "we are mammalian bipeds wandering through the world, trying to make sense of our reality by doing what evolution has equipped us to do: modeling the things we see, hear, taste, smell and feel. That our descriptions (of these colors and sounds, etc.) are invented in our brains is a basic assumption now shared by members of any educated group. There is also a great realm of other things we don't experience through our senses, which play an important part in our lives; these things occur on time and distance scales outside our realm. They include a few subjects so exotic that Peter was the only one present who could "even mumble about them," and there are few people on campus who are able to teach them. One example is the electrons in graphine molecules (a form of one-dimensional graphite), which have no mass. A second is the work of string theorists, who are "making no physical headway," but inventing incredibly new mathematics. Since Peter prepared his notes for this talk, a third example emerged, in an article that described the improvements in our ability to measure time distances--to such minute levels that the meaning of time itself has been brought into question. "Time is not modeled in any physical theory."
To give us some perspective on these matters, Peter described "the invention of the human concept of gravity," described by Newton in the Principia in the 1680's. Here's the history, as Peter told it: on one end of Cambridge campus, the projectile scientists (who were well funded by the military) had developed some very good and accurate laws about how the material world worked (for instance, in the absence of air resistance, all things will drop at the same rate). They had every right to say that they had discovered some universal laws (which is "what science is all about"). At other end of the campus, the unfunded astronomers were working on another set of interesting ideas about planet rotations and distances, designing "beautiful rules" and formulas that worked for them all. "Strolling between the two groups," Newton came up with the "absurd notion" that these descriptions of earthly and planetary things were linked. Newton made this connection, not by making observations, but by showing that the mathematics being used on both sides of campus was identical. He invented the concept of a force--but before that, he had to invent the calculus, in order to make the measurements (although his Principia includes no calculus; he was afraid of being embarrassed, of being found to have made mistakes in the mathematics).
Nothing in the daily routine of anyone living in the 17th century would have suggested what Newton sorted out; but when he did, gravity was born. For a period of 50 years, few people understood it; only slowly did it filter into the culture. Over the next 100 years, this concept of the "attraction of two things" gradually moved into the sphere of what Peter fondly thinks of as the "Sandra Berwind concept of culture." Most people came to understand that, when they dropped something, "it was being attracted to the earth." Contemporary "cocktail party discussion of gravity" is basically accurate. Our times are different from Newton's: we now try to educate everyone, not just the elite. And we no longer have the luxury of moving slowly in this process. Calculus, which was once introduced in the middle of the college years, is now taught in 11th grade; eventually it will reach kindergarten--but we should be teaching field theory in kindergarten now.
Peter then offered "a contemporary example of something outside the cultural circle." All science has a procedure whereby we say that "there is stuff," and "stuff is doing things." Can we agree that we have this compartmentalization in our culture--in other words, that we separate the attributes of an entity from what the entity is doing? This is how evolution has made us conceptualize the world: everything is either an attribute or an action. An effect is part of the action. Interactions between particles are actions, not attributes. A "property" or "attribute" describes something that holds true in all instances; it is intrinsic to the physical phenomenon. Is the distinction between attributes and action one of time? Are attributes instantaneous, while actions take place sequentially (what we call "dynamical")? Field theorists don't refer to forces of nature; they "let them be things." In the world of science, fundamental particles can turn into each other: protons can turn into neutrons, up quarks can become down quarks. You can change the attribute, but the distinction between an attribute and a dynamic still holds. Peter deflected the question of whether an attribute is a property of reality or a story of reality: "I really don't care if particular features are characteristic of reality, or stories descriptive of it." Answering that question would take us back to Bohr's assertion that "there is only the story," and to Einstein's refusal to accept that description. But the debate about the nature of reality is irrelevant to the point Peter was pursuing, which has to do with the translation from special to general knowledge.
Peter then asked us to imagine a particle that "has two different attributes instantaneously: it simultaneously has an attribute that is not itself." In response to the charge that this description was "too vague," he refined it: the particle has "a single attribute that is double-valued," that is, simultaneously possesses two values for a single attribute. Under many circumstances, it would actually "contradict the mathematics" not to have both aspects simultaneously. Several examples were offered (and rejected): the two simultaneous values of the square root of 4 (2 and -2); a wave and a particle; bodies that are both separate and connected. We couldn't guess the phenomenon that Peter was describing, although it drew on "borderline trivial mathematics," taught on the sophomore level. The "priests in the temples" know what Peter is describing, but they deny the knowledge to others. They refuse to teach it, saying that it can only be represented by mathematics, and is too difficult. Is this because scientists "want to keep the power," or because they are "too lazy" to figure how to translate what they understand into the language of those less educated and/or less mathematically adept?
What Peter was describing was "proton spin," an attribute of elementary particles that results in the capacity to do Magnetic Resonance Imaging. Technicians can use it to make observations, then manipulate them on computer programs, in order to produce 3-dimensional pictures, which doctors can then use to diagnose disorders. The process involves 2x2 matrices, which are teachable to 5-15 year-olds. Behind every MRI machine makers are physicists writing the code to translate the activity to the everyday world. Peter's claim is that this can be brought "inside the culture." We have to try to teach these concepts in elementary school--or our technological society will fall apart. The priests say they "only have the mathematics for this, and don't know how to make it practical"--but Newton probably thought the same thing. Science taught to younger children "has to be hands-on: physical experiments where they can see the results. It has to be something they can really do." Peter is proposing not only that we find ways to bring into culture, at a very early level, the understandings that are currently expressed in mathematics, but the math itself. For young children, teaching those concepts has to be connected to reality--and no one, so far, has really been successful in this mission. Peter "went out on a limb" to "add one more footnote" to his presentation: the claim that there is math that is independent of reality. This is what made Galileo's work blasphemous: he was revising the description of reality.
We now have a "ton of technology" available to extend, on both large and small scales, our sense of distance and time. The microscope, for instance, has allowed us to see physical things that are now in our culture: "a cell is meaningful, and teachable." Is there a limit to this process, to talking (for example) "about stuff below the physical light limits," stuff for which there "will never be a physical representation"? There is an interesting challenge: we have learned how to bring large-scale observations into the culture, but there may be a special problem about small-scale phenomenon, which we haven't learned how to handle. How can young people grasp quantum mechanisms, the action of stuff in mathematics, not the real world? Children are not the only ones "suffering from arrested development," who find it difficult to understand ideas such as "entanglement."
A "devil's advocate" also cautioned against attempts to introduce concepts earlier in the educational system. Kids' need for hands-on work will lead teachers to make analogies ("it's like a spinning top") which will be incorrect--and then have to be untaught. Perhaps we should not jump so quickly to "bridge the dimensionality gap." Perhaps children just need to be helped to see that there's a difference in how things behave, on different levels. Alternatively, one might take a phenomenon which exists "inside the cultural circle," help children become comfortable with it, teach them to use mathematics to describe it. Then move them on to something else, teach them the math dealing with that...slowly getting closer and closer to the boundary, until they realize that they have reached a level of mathematics which doesn't have a physical representation. (An example was offered of teaching children about the internet. They quickly understand the implications--that they can use the computer to get any kind of information. What they don't understand is that that information does not reside in their computer; they need to learn the technology of calls and responses over the network. But they have something they can see and use as a start.)
Discussion turned to the question of whether, in moving from outside to inside the cultural realm, the bridge always needs to be mathematical. In general, specialized understandings result from observations not accessible to the world @ large. New understandings, related to the new observations, emerge; these are also not accessible the lay person. How to move such ideas from the "priesthood" into general understanding? How to move the boundary outward? One way, based on the belief that new understandings are always mathematical in character, involves "expanding the turf" by teaching math. Begin with what is familiar; once students are happy with the mathematics, they will accept, without noticing, that they are doing math about stuff they can't see, feel or touch.
But the problem of moving from specialized observations and descriptions is a more general problem--and it was claimed that its solution does not have to depend on mathematics. For example, the theory of evolution is a fully non-mathematical set of concepts, based on a set of observations outside the normal realm, across different time scales. It was enormously difficult to bring that realm into culture--but it was not a math problem. We're getting better at making such observations more generally accessible, particularly those from long time scales. It seems more problematic to "go the other way." And sometimes what seems like success is really "the wrong picture." For example, consider the infrared pictures of the universe and the sun now widely available. Of course we can't see any of this: the colors are computer-generated, in relation to intensities and wave lengths. How to teach these concepts more accurately? How can we educate people how to teach, beyond their breadth?
But: do we really need to teach these concepts to everyone? Discussion turned to "illiterates who raise children"--a shorthand for the wide spectrum of human knowledge that is not held by scientist-priests. Do we "need to know everything" (for instance) about what goes into the meal we are eating in a restaurant? Or do we just want "an exchange," a "trusting relationship" with those who cook for and serve us? Who decides what is valuable to transmit? Perhaps physics is not as important as the knowledge of raising kids. Other cultures have other ways of understanding things; is our quantum understanding a long way 'round, through western rationalism and mathematics, to understanding that other cultures already have at an intuitive level? In Spanish, there are two forms of the verb "to be," one describing a "permanent attribute," the other indicating time passing. The same distinctions are available in some Native American languages, which are inherently equipped to handle quantum mechanics: the "sun comes up from the sea," for instance; sun and sea are not described as independent identities. Inuits also have ice "doing this, doing that"; they mix up attributes and behavior.
Isn't mathematics just one idiom for expressing a relationship to the cosmos, "one particular sort of model of the cosmos," which is politically problematic? It's "imperialistic" to demand that other peoples "shift their vocabulary" to employ that of science. Should we be creating technologies destructive of others' sense of their relation to the cosmos? Do we all have to learn to use the technologies of Western science, and to acquire the language necessary to articulate and manipulate them? Must we all have a relation to infinity based on science? Cultural sensitivity is necessary. This process of dissemination could destroy people's capacity to live in other ways.
However, this is a powerful technology, which dominates the planet. More people must understand these concepts if our technological society is to survive. We don't really want a smaller and smaller percentage of our population to control all the scientific information. These technologies will move forward, whether we want them to or not. Some degree of public awareness is preferable. It's also the case that bringing scientific concepts into the culture "in cartoon ways" makes it easily mis-useable (think of how evolution is being used now in ways that further intelligent design). The key point remains: how can we take specialized knowledge, based on a set of observations not accessible to everybody, and make it knowledge that belongs to the general culture? Specialized knowledge, by definition, is a way of describing set of observations that most people don't have. We have evolved some useful guidelines for bringing it into the culture
- bring it in as a story (not as a description of reality)
- make the observations accessible to the culture at large (if you don't, will be perceived as a description of reality).
When Peter's sons were younger, he regularly visited their 2nd-5th grade classes, in order to teach particle physics. He shared ideas with the children by having them enact molecules. They were atoms. They learned about fractures and light. About quarks coming together to make neutrons and protons. About pressure and temperature. When "they were the molecules" (for instance), they were able to understand that temperature is molecular speed. They learned solid state physics--although it wasn't 'til years later, in 8th grade, that they actually "got what a molecule is."
The discussion continues on the on-line forum, and will resume in person on April 7, when Deepak Kumar will talk about "Rethinking Computer Science Education."
Return to Brown Bag Series on Rethinking Science Education