Part 3 - Seasons & the Celestial Sphere
Part 4 - Conclusion - Teaching Science Inductively
"This course is an unusual combination of elementary science and advanced epistemology."
Part 1 - Sun, Moon & Planets
This course is an unusual combination of elementary science and advanced epistemology.
The science is basic observational astronomy. This is an important and under-appreciated topic in schools today. The scientific revolution began with astronomy, and one cannot understand the progression that led to Newtonian physics unless one first understands astronomy. And that starts with basic observational astronomy.
Now, at this beginning level, there’s almost no mathematics—it’s just a matter of being able to identify and understand what you directly see in the sky. I’ll be talking about the sun, the moon, the visible planets, and the stars—and everyone has seen these objects over the course of their entire lives. Yet most educated, intelligent adults understand little about the observed movements of celestial bodies and have trouble identifying even the brightest stars on the clearest nights. Why?
In two words, my answer is: Bad epistemology. As presented in classrooms and in books today, this material is nearly unintelligible. At the outset, I’ll just mention a few of the basic errors that are made in the standard presentations. The errors, and how to correct them, will be discussed in more detail throughout this course.
First, there is a premature leap to theory. To the extent that observations are discussed at all, they are usually presented as consequences of the theory. Of course, the student has no idea where the theory came from. But the task he is given is to memorize the theory and deduce what the observations must be. This is all backwards; observations come before theory, and learning the observations is easier than deducing them from a theory.
Second, in a related point, there is a premature leap to precise quantification. For example, the student is told that a year is 365.24 days. He may be very fuzzy on the concept “year,” and he may have no idea how it is measured, but he knows that he has to memorize the number 365.24. Again, this is backwards; precise numbers should be introduced only when the student can grasp their meaning and importance. I’ll explain later why I think that this mania for precise numbers is pure Platonism.
Third, in classrooms the material is often presented to students who are too young. A student has to be at a certain level of intellectual maturity in order to understand the regular patterns in the movements of celestial bodies. In my judgment, most of the material we’ll be discussing is about at the sixth grade level. To present it much earlier is a waste of time—the students aren’t ready for it.
Most of you probably suffered through such presentations, although you may have little memory of it, since the experience is not very memorable. So let’s get rid of one issue at the outset. I said that this material is about at the sixth grade level. That doesn’t mean that you should know it; it just means that you would know it if it had been taught properly. But it wasn’t, so there’s nothing to be embarrassed about. I want everybody to feel free to ask ignorant questions.
In order to encourage that freedom, I’ll make a confession. When I passed my Ph.D. qualifying exams in physics, I knew very little of this sixth grade material on observational astronomy. I could use quantum mechanics to calculate the energy levels of an electron in an atom, but I couldn’t look up in the sky and identify and understand what I was seeing. That’s ridiculous, but true. So I challenge any of you to surpass me in the “embarrassing ignorance” category. This class will be more fun if we don’t worry about that.
One more preliminary point: There may be some of you who are astronomy enthusiasts and already know most of the facts I will present. I still think that you’ll get a lot out of the class, but I’ll ask one favor of you; let those who are less knowledgeable answer any basic questions that I raise. We learn more by struggling through a little confusion than by just being told the right answer.
Now let’s get started. And, in trying to get started, we immediately run into a problem. We want to begin with observations, but there are thousands of relevant observations and it’s complicated; the sun, the moon, the planets, and the stars all move differently. A bunch of unrelated observations is useless—it can’t be understood and retained. In part, this is what motivates the rationalistic approach. The rationalist makes a premature leap to theory, which at least allows him to present the topic in a pseudo-integrated way. Of course, the theory itself stands as arbitrary in the student’s mind, so it isn’t a real integration of observations—but at least the student isn’t overwhelmed by an endless list of concrete facts.
So, the question is: How do we not fall into either one of these errors—how do we escape from the disastrous alternative of presenting disintegrated observations or arbitrary theory? This is a crucial question. And there is only one possible approach to answering it: We have to find a way to present the observations in an integrated, pre-theoretical framework. In other words, we have to integrate the observations without introducing theory. Now, this is a tough job; it requires an understanding of epistemology and some creative thinking.
Fortunately, Tom has figured out how to do it in astronomy, and this course is based largely on his ingenious solution to the problem. An essential aspect of his solution is the invention of new teaching devices. The devices are designed to ruthlessly strip away the details, present the essential observations in the correct order, and present them in a way so that they are related to each other in an easily intelligible whole.
The first device is something we call the “sun puppet.” It’s a simple yet remarkably powerful tool for illustrating the most basic facts about observational astronomy. This is where we start. And what celestial body do we start with? We have to start with the sun, which is our source of light and heat, and by far the most prominent and important object in the sky. Maybe we could live without the rest, but we can’t live without the sun.
Now, what do we see the sun doing every day? It comes up in the east, it continues rising in the morning sky until it reaches its highest point at noon, then it descends in the afternoon and finally sets in the west. The sun is our time keeper. We divide the period from one noon to the next into 24 equal intervals; and, on average, the sun is above the horizon for 12 hours and below it for 12 hours.
[Discuss telling time by the sun.] Interestingly, this is not obvious to kids; they require some practice at it. Consider the absurdity of teaching the heliocentric theory to a child who cannot yet point to where the sun is at 10 in the morning or 3 in the afternoon.
Now let’s take the sun puppet for a spin and see what it can really do. We add the moon, and see how it moves relative to the sun. The first thing to point out is that it behaves in pretty much the same way as the sun. It rises in the east, goes across the sky on about the same path, and sets in the west. But, of course, its position changes with respect to the sun, so it’s not moving in the exact same way. In fact, it’s slower; the moon takes almost 25 hours to go around, rather than 24. So it falls behind the sun by almost an hour a day. If we see where the moon is relative to the sun on one day, then we know where it will be the next day or the next week. [Discuss the moon cycle.]
Epistemology break: Is the sun puppet an ingenious way to simplify and relate the observations, or is it a misleading way to over-simplify and inaccurately describe the observations? The fact is that the sun does not always rise directly east or set directly west, it does not always reach the same height in the sky, and it is not always above the horizon for 12 hours. The same is true of the moon—and the variations in the moon’s path depend on both the moon phase and the time of year. So what are we doing here? Are we lying to the poor, misguided students?
No, we aren’t lying. Part of the educator’s job is to present the key facts one at a time, and in the correct order. We can’t learn everything at once; our minds don’t work like that. The sun puppet abstracts entirely from the more complicated phenomenon of the seasons—and by doing so, it provides the foundation that later makes it possible to understand the seasons. And the sun puppet doesn’t lie; it just presents the average day in two-dimensional form. Or, if you wish, you can think of it this way: It describes exactly what you would see if you lived near the equator and observed around the time of the spring or fall equinoxes.
In short, a child has to grasp that the sun and moon travel across the sky in similar, regular patterns before he can grasp the more complicated, seasonal variations in those patterns. So we start with a ruthlessly simplified, two-dimensional presentation.
Now, let’s take a first look at the some other objects in the sky. We want to learn about stars and planets. So which comes first?
There is an argument in favor of the planets. Venus and Jupiter are much brighter than any star; they jump right out of the night sky at you. Sometimes, Mars is also very bright. You might think that after the sun and moon, the most noticeable objects in the sky should be discussed next.
But, if you thought that, you would be wrong. There is a decisive argument in favor of discussing the stars first. The stars move in a simpler way, and the very concept “planet” was arrived at by contrasting the more complex movement of planets with the simple movement of stars. For this reason, the stars have to come first. At this stage, we don’t have to say much about the stars, but we have to say just enough to set the context for the planets.
So, we want to give a very brief introduction to the stars using the sun puppet. Which stars should we choose to talk about? Here there are two criteria. First, we should pick stars that move across the sky on roughly the same path as the sun; this makes it easier to relate them to the sun and illustrate their movement with the sun puppet. Second, we should pick stars that are very easily recognized even by beginning stargazers. As it turns out, there is only one group of stars that satisfies both criteria: It’s the constellation Orion.
This constellation has seven bright stars, including the three in a row making up Orion’s belt. It’s very distinctive; in fact, it’s the first group of stars that my young daughter learned to recognize. And Orion’s belt goes across the sky on exactly the same path that the sun takes in early spring and early fall. It’s absolutely perfect for our purposes.
Notice an interesting point here. In epistemology, the concept “hierarchy” refers to the order in which we have to grasp concepts and generalizations; for instance, we have to grasp low-level concepts like “table” and “chair” before we can grasp the more abstract concept “furniture.” But here we are seeing that there is a parallel to the idea of hierarchy even on the perceptual level; there is sometimes a correct order of learning even when the facts are directly perceivable. And here is how we discover that order.
Imagine I made a mistake and I didn’t start with Orion. Let’s say I chose Aldebaran in the constellation Bull; it is a very bright star that goes across the sky on roughly the same path as the sun. So it seems to fit our criteria. But here is the problem: If you ask me how to find Aldebaran in the sky, I’ll tell you that it’s easy—just look for a bright star to the northwest of Orion. So you need to know Orion first. Every stargazer uses Orion to orient himself and identify the other stars in that area of the sky.
This point can be generalized: Even when it comes to perceptual data, our minds deal with it in a certain way. Our attention is automatically drawn first to those items in the perceptual field that stand out; then, when we deliberately focus on the other items, we view them in relation to the items that stand out. In the case of Orion, it’s the distinctive pattern that jumps out at you: the three stars making up the belt, with the two bright stars above and the two below.
Okay, let’s see how Orion moves across the sky. It’s really pretty simple. The middle of Orion—his belt—really does rise due east, move at a perfectly constant rate across the sky, and set due west. And Orion moves at almost the same rate as the sun; unlike the moon, which is slower, the position of Orion relative to the sun doesn’t seem to change from one day to the next. But if we look over a longer period of time, we notice that it is changing. Orion moves just a little faster than the sun. Imagine that we observe Orion directly overhead at midnight, which happens around Christmas time. That means Orion is opposite the sun. Three months later, Orion will be high in the sky just after sunset. Six months later, we won’t be able to see Orion at all, because it will have caught up with the sun. Three months after that, Orion will be high in the sky just before sunrise. It’s like Orion and the sun are running on a track, but Orion is just a little faster; eventually, Orion laps the sun, but it takes a year. From one summer to the next, Orion goes around one more time than the sun.
The stars move with respect to the sun, but not with respect to each other. That’s why Orion always looks the same—the arrangement of stars that make up his shoulders, his belt, and his feet never changes. Also, Orion never changes position relative to the surrounding constellations (for example, Big Dog, Bull, and Twins). The stars all move together.
Another feature of the stars remains constant, too—their brightness. Rigel is always the brightest star in Orion, Betelgeuse is always the second brightest, and so on. The stars seem eternal and unchanging, which is why the Greeks thought they must be made of some perfect, unearthly material.
For the moment, this is all you need to know about the stars; they move at a perfectly constant rate, revolving around one more time than the sun during a year, and their positions relative to each other and their brightness are unchanging.
Now we are ready for the planets. My first question is: How many planets are there? Well, most of us were taught in school that there are nine planets. Then, recently, Pluto got demoted; he was too small and he moved in a weird way, so he got kicked out of the group. I know that sounds like something that would happen in junior high school. But, in this case, it was justified; Pluto really doesn’t belong with the other, “cool” planets. That leaves us with eight. But there are big differences among these eight. Some of them don’t qualify as planets in a basic course on naked-eye astronomy. Which ones?
First, the fact that we are on a planet—that Earth is a planet—is not available to direct observation. To grasp this fact requires sophisticated measuring instruments, advanced mathematics, and some experimental discoveries in physics. People had been observing the sky and making the distinction between planets and stars for thousands of years, and yet nobody knew that Earth was a planet until the work of Kepler and Galileo about 400 years ago. This is a conclusion from a complex theory, not from direct observation. So, in an introductory course on observational astronomy, the Earth is not a planet. The astounding discovery that we are on a planet has to be saved for later. If presented correctly, this discovery is very dramatic; we’re spinning around at about a 1000 mph and flying through space at 19 miles per second. If we just hand this conclusion to the student at the outset, that’s like reading the last page of a mystery novel at the outset—it ruins the whole story.
Also, Uranus and Neptune don’t qualify; with the naked eye, Uranus is very dim and Neptune can’t be seen at all. These planets were not discovered until the invention of telescopes in the modern era, so they don’t belong in an introductory course on observational astronomy.
That leaves us with the five classical planets: Mercury, Venus, Mars, Jupiter, and Saturn. Now, in what order should we discuss them? In this case, I won’t argue that there is a necessary order, but I do think there is a preferred order. It’s best to start with a planet that is both very bright and moves in a way that is not too radically different than the stars. As it turns out, there is only one such planet: Jupiter.
[Demonstrate the motion of Jupiter using the sun puppet, and then point out that Saturn moves in a similar way. Then demonstrate the motion of Venus, and point out that Mercury moves in a somewhat similar way.] Notice what we are doing here. We are presenting the observable facts in an integrated way (always relative to the sun), but we are not yet offering explanations. The “what” comes before the “why.” [Show them the Falling Apple “planet finder.”]