In my previous post, I concluded by mentioning that while inheritance hierarchies represent knowledge that is obtained through deductive reasoning, delegation allows us to build taxonomies dynamically from instances through inductive reasoning. In this post, I’d like to explore this idea further and examine how we build our own taxonomies during the process of learning.
Suppose a young child named Marisa visits the zoo for the first time. All she knows is that she will see animals there. As she enters the zoo, she sees a Komodo Dragon named Stanley prominently displayed near the entrance. All she knows at this point is that Stanley is an animal. She can see that Stanley has no hair and is told that he is cold-blooded, though she doesn’t quite know what that means yet. If she were building an animal taxonomy in her mind, it may look like this:
Next, Marisa and her family walk over to the elephant habitat, where she sees Clyde the elephant. Marisa notices that Clyde has a little bit of hair and is told that he is warm-blooded, but her attention is really drawn to Clyde’s trunk and tusks.
Marisa is quite excited by what she is seeing. As she glances around in all directions, she notices a very tall animal with a very long neck. She is told that his name is Jerry and he is also warm-blooded. After Marisa adds Clyde and Jerry to her taxonomy, it looks like this:
As Marisa’s parents talk with her about the animals she has seen, Marisa learns that Stanley is a reptile, Clyde is an elephant and Jerry is a giraffe. This requires Marisa to refactor her taxonomy by adding new concepts that represent classes of animals. After this refactoring, here is her new taxonomy:
What has happened is that Clyde, Jerry and Stanley have each been given a prototype of their own. These new prototypes have as their prototype Animal, which used to be the prototype for the three animals Marisa has seen thus far. Also, the properties that belonged to those three animals have been pulled up into their prototypes. I refer to this process of taxonomy refactoring as promotion. The promotion process creates a prototype that is a copy of the object being promoted. Afterwards, the object simply references that prototype.
It’s important to note that at this time, if you asked Marisa to describe an elephant, giraffe or reptile, she wouldn’t describe a generic animal that fits the type, she would describe Clyde, Jerry or Stanley. Her taxonomy is based on the particular animals she knows. This is reflected by the promotion process I described above. The prototypes Elephant, Giraffe and Reptile were created by copying Clyde, Jerry and Stanley, respectively. So the process of building taxonomies through inductive reasoning that is being illustrated here is a good analogy for how we internally represent information we’ve learned.
Now suppose that Marisa learns that elephants and giraffes have some things in common. They are both warm-blooded and have hair. She also learns that such animals are called mammals. This requires another refactoring of Marisa’s taxonomy using the process of promotion:
Notice that the properties that Elephant and Giraffe have in common have been pulled up into Mammal and the properties that they don’t have in common stay with them. When promoting multiple objects into a common prototype, only the properties possessed by of all the objects can be pulled into the prototype. This is consistent with the notion of prototypes as types or supertypes in a taxonomy, which is how we’re considering them here.
Marisa is fascinated by Clyde and spends a fair amount of time at the elephant enclosure. After a few minutes, she sees two more elephants named Chloe and Claire, who look very much like Clyde except that they don’t have tusks. This causes Marisa to rethink her concept of an elephant. Obviously, not all elephants have tusks, but her current Elephant prototype does. Marisa adds Chloe and Claire to her taxonomy. They could have Elephant as their prototype and override the hasTusks property, but that would make them one-offs and Marisa suspects that there may be many elephants that don’t have tusks as well as many that do. So she refactors her taxonomy to look like this:
A couple of things have happened here. First, Marisa created two new concepts representing types of elephants through the promotion process. After that step, she has two elephant types that are prototypes of the three elephants she knows. But the hasTusks property still resides with the top-level Elephant prototype. That doesn’t look right since not all elephants have tusks. So Marisa applies a process called distribution to push the hasTusks property from Elephant down into ElephantWithTusks. The distribution process pushes down properties that are possessed by some of a prototype’s immediate instances but not others. In this case, ElephantWithoutTusks already had the hasTusks property (with the value false) by virtue of promotion, but ElephantWithTusks didn’t, so hasTusks (with the value true) is pushed into ElephantWithTusks.
The resulting taxonomy Marisa has in her mind is a fairly rich taxonomy that classifies the five animals she has seen in the zoo. She built this taxonomy from the ground up through inductive reasoning. We have seen how she can refactor her taxonomy when she sees new animals that don’t conform to it. Every item shown in the taxonomy is a simple object. The items represented by the rectangles are objects that serve as prototypes.
The code supporting this example is available on GitHub.