So far, I have explained several ways of manufacturing sandwiches.
While these may sound a bit too technical, the underlying notion is not complicated at all. All we need to do is execute a sequence of actions which, when carried out in the right order, will manifest themselves in whichever types of sandwiches we want.
Let me go back to our previous example. We have seen that, by running a conveyor belt with a bread dispenser, a cheese dispenser, and another bread dispenser, we are able to produce a queue of cheese sandwiches.
The series of events you are witnessing here (i.e. (1) addition of bread, (2) addition of cheese, and (3) another addition of bread) can also be illustrated as a path inside the "tech tree" of sandwiches, like the one shown below.
Here, you should be able to see that the tech tree depicts all sorts of alternative ways in which a sandwich can be manipulated. The act of stacking the 3 ingredients of a cheese sandwich (i.e. bread, cheese, and bread), then, translates to the act of walking down the path which is highlighted above.
The thing is, however, that there are types of sandwiches which cannot be produced simply by stacking a bunch of ingredients.
For instance, what shall we do if we want a grilled cheese sandwich, rather than just a boring, squishy kind of sandwich with a slice of cold cheese in it?
In order to craft such a hot and crispy work of culinary arts, we need a more advanced equipment called "toaster" on our conveyor belt. Its job is to toast anything which passes through it.
For example, passing a cheese sandwich through a toaster will toast all of its 3 ingredients - the bottom bread, the cheese, and the top bread. Both pieces of bread will become pieces of toast (because "toasted bread" is the same thing as "toast" in our language), and the slice of cheese will become a slice of toasted cheese.
Now, you see that our definitions are beginning to get a bit complicated. For the sake of preserving our sanity, therefore, let us clarify things a bit before moving on.
First of all, a stack made out of a piece of bread, a slice of cheese, and another piece of bread is called a "cheese sandwich". We all agree on this, right?
And the truth is, such a stack would've been referred to as a "ham sandwich" if the slice of cheese were replaced by a slice of ham. And it would've been referred to as an "avacado sandwich" if the slice of cheese were replaced by a slice of avacado.
In general, therefore, we must be able to say that if "X" is surrounded by two pieces of bread (where "X" can be anything), the whole thing should be called an "X sandwich".
What happens when we replace the two pieces of bread with two pieces of toast? Common sense tells us that we should call it an "X toast sandwich" instead of just "X sandwich".
So, it is reasonable to state that if there is a slice of cheese between two pieces of toast, we ought to call it a "cheese toast sandwich" instead of just "cheese sandwich".
There are somewhat trickier scenarios, though. What if we put a slice of toasted cheese between two pieces of (regular) bread? Or, in contrast, what if we put a slice of toasted cheese between two pieces of toast?
The way to resolve any potential source of confusion here, is to apply a general set of definitions instead of just making guesses. For this purpose, let such recall that:
(1) If "X" is surrounded by two pieces of bread, it must be called "X sandwich".
(2) If "X" is surrounded by two pieces of toast, it must be called "X toast sandwich".
Now try substituting the "X" with "toasted cheese". If you do, you will see how the aforementioned two sandwiches should be worded, from a purely literal viewpoint.
Obviously, though, we should admit that an expression such as "toasted cheese toast sandwich" is way too verbose. Typically, we just call such a thing as a "grilled cheese". Although it does not include some of the core descriptive words such as "sandwich" or "toast", we all know that it denotes a toast sandwich with toasted cheese in it.
What we are seeing here is an example of "sandwich type aliasing".
Since "toasted cheese toast sandwich" is too long, we have decided to use the term "grilled cheese" instead to indicate the same exact thing which "toasted cheese toast sandwich" aims to express. In this case, we say that "grilled cheese" is an alias of "toasted cheese toast sandwich".
And, when you look at the definition of "grilled cheese" in the form of a diagram (see the image below), you will see that an alias is just an extra reference (arrow) which is attached to the original term. We may also refer to such a thing as a "synonym".
Now that we are clearly aware of what "grilled cheese" is supposed to mean, let us come back to its manufacturing process.
First of all, we know that stacking a piece of bread, a slice of cheese, and another piece of bread will yield a "cheese sandwich", right? This process can be established by setting up 3 dispensers in a row.
And then, we turn this "cheese sandwich" into a "grilled cheese" by letting it pass through a toaster.
An alternative way of imagining this whole process is to think of it as a path within the sandwich's tech tree. Each time we are taking a step in the assembly line of a grilled cheese, we are moving from one location in the tech tree to another. The image below, for instance, clearly reveals that we could reach the position of "grilled cheese" after 4 moves.
Here is where things start to get way more interesting. As you may have noticed already, the richness of our tech tree is determined by the diversity of modifications which can be applied to the sandwich. If the only option we had were to simply keep stacking pieces of bread and nothing else, our tech tree would have looked too bland due to the presence of nothing but a single linear path.
Once we equip ourselves with a multitude of alternative choices (e.g. "+bread", "+cheese", "toast", etc), on the other hand, the tree branches itself into a rich taxonomy of sandwich recipes.
And, speaking of recipes, here is one more concept I would like to introduce for the sake of providing our future sandwich craftsmen with additional insight. It starts with the notion that each path within the tech tree can be defined as a unique recipe for a sandwich.
As you can clearly tell already, a "grilled cheese" is just a toast sandwich with a slice of toasted cheese in it.
It is important to note, however, that its recipe is something different, and thus should be represented a bit differently.
A grilled cheese itself is undoubtedly made up of a piece of toast, a slice of toasted cheese, and another piece of toast. The recipe for a grilled cheese, on the other hand, is made up of a sequence of the following 4 instructions:
(1) Add a piece of bread, and
(2) Add a slice of cheese, and
(3) Add a piece of bread, and
(4) Toast it.
These four steps are the "ingredients" of the recipe; they exist as a stack not in our physical space where we can touch and view things, but in the space of events (aka "possibility space"). They are part of our imperative knowledge, as opposed to declarative knowledge.
(Will be continued in Chapter 8)