According to the discussion, what can be learned by analyzing ancient pottery?

Listen to part of a lecture in an archaeology class.
Professor: Let’s review. Why is pottery such an important subject of archaeological analysis?
Student 1: Well, pottery contains more information than we might think.
Professor: Can you elaborate on that answer?
Student 1: Well, like sudden changes in the style and shape of pottery might help us figure out when certain cultures made contact with each other and borrowed each other’s ideas, designs, even technology.
Professor: Good! So let’s continue by expanding our discussion into the topic of classifying pottery. Classification is simply an attempt to categorize or group the pottery based on specific characteristics.
    We look at ancient Mayan pottery, which as you know by now is my specialty. Archaeologists have traditionally attempted to classify these vessels by using a single classification system, but the complexity, the variation of ancient Mayan pottery, is just too great in my opinion to use only one system.
    I support the use of several systems, as do some of my colleagues who have been researching the Mayan archaeological sites of Mexico and Central America. By utilizing more than one system of classification, we aren’t as likely to neglect important details or lose important information.
Student 2: So I think what you’re saying is when we use a single classification system we can’t label a vessel with lots of details, but when we classify it a lot of different ways, that gives us a more complete picture.
Professor: Yes, and if we’re able to label a large quantity of pottery in several ways, we can more clearly see relationships between them because of having a more complete picture of each one. I mean, everybody in this class is from a different state or country. Nobody’s from exactly the same place, so if I only classify people by where they’re from, I might say that you have nothing in common, but what if I add more layers? Andrew, you’re a skier. Sarah’s also a skier, so if we have a classification for your extracurricular activities, we find you two have something in common: snow skiing!
Student 2: I get it!
Professor: So we begin by determining what classifications will be possible and what classifications will be useful. These would be, in my opinion, the vessel shapes, the surface finish which looks at texture, and finally, what we call "pastes." I’ll explain pastes later. Yes, Andrew?
Student 2: Well, would you limit it to just three classification systems? Shapes, surface finish, and pastes?
Professor: Not necessarily. When we encounter pottery decorated with a lot of detail, we might want to add a classification system for this, too... one we could call ’decoration.’ Let’s now look at my first classification type: pottery shapes. What we need to consider is the basic proportions and size of an object.
Student 1: But, what if the object’s broken?
Professor: Obviously, intact pottery is the best, but if all we have in front of us is a collection of pieces, as long as those pieces are of a reasonable size, we can still classify shapes reliably. We just have to reconstruct the object. Now, even if you’re able to reconstruct and then determine how to classify pottery in terms of its shape, you might be unable to classify its surface finish. For example, with many of the pottery collections found at the archaeological site of Polankay, insufficient surface finish was preserved to make a determination.
    You know, really what we need are comprehensive and accurate illustrations of ancient Mayan pottery. Having drawings of their profiles allows us to compare the shapes of pottery found at different archaeological sites because, well, we can’t personally go through all the locations, but even when archaeologists and art historians do attempt to illustrate every single piece, problems arise.
Student 1: Like three different people might draw the profile of the same pot, but the drawings don’t turn out exactly the same?
Professor: Correct. Illustrating involves some simplification of the pottery and people may have different ideas of which features are important to keep in the drawing and which can be left out. Uh, what else?
Student 1: Well, drawing the profile of every single pot probably takes tons of time, so it could be expensive.
Professor: Uh huh...
Student 1: But, digital photography is so popular and inexpensive now. Why don’t we just give up on drawings and make a collection of photographs? You can’t get more accurate than a photograph.
Professor: That’s a natural question. I’ll get to that in a second.