Sandwich Engineering is one of the hottest research topics in today's world. Every tech influencer on social media has been talking about it, and it is now an indisputable fact that if you do not learn how to make a sandwich, your job will soon be replaced by the world's most professional sandwich makers.
So, stay tuned and do not miss out this great opportunity. The future belongs to those who know how to leverage the full power of sandwiches; they are the ones who will dominate the tech industry within the next couple of years. Sandwich engineering is the future, and those who recognize its potential are the ones who will lead this new era of groundbreaking innovation.
This series will present you with an overview of this brand new field of study called "Sandwich Engineering", and how it is going to revolutionize the industry, offer cutting-edge solutions to startups, help passionate individuals succeed, achieve world peace, save our planet, make everything diverse, fulfilling, mindful, sustainable, and... whatever.
In order to understand the basics of sandwich engineering, one must first learn how a sandwich should be defined. A sandwich is the result of combining the following sequence of things and stacking them together:
(1) A piece of bread, and
(2) Something which goes inside the sandwich, and
(3) Another piece of bread.Graphically speaking, this kind of composition can be depicted in the form of the diagram shown below.
What this image tells us is pretty straightforward. First of all, it asks the question, "What is a sandwich?" Then, it proceeds to claim (with the help of an arrow) that a sandwich is the result of combining a piece of bread (i.e. "Bread"), something which goes in between (i.e. "..."), and another piece of bread (i.e. "Bread").
In other words, the diagram states that we can make a sandwich by putting a bread AND something else AND another bread together in the same place. This process of combining multiple things into a single composite object (in this case, a sandwich) can be achieved by joining these three ingredients with the word "AND".
One should also be able to define a more specific type of sandwich. For example, a "ham sandwich" is a sandwich in which the middle ingredient is known to be a slice of ham.
What about a broader type of sandwich, such as "meat sandwich"? Its definition is not as specific as that of a ham sandwich because we are not exactly sure what sort of meat will be placed inside of it. In case of ambiguity like this, though, we are free to specify the ingredient as a list of options. Such a list can be denoted by the word "OR".
Here, we have two major constructs in our grammar - "AND" and "OR". Whenever we put multiple things together and let them coexist, we use the word "AND". Whenever we put only one among the multitude of things available, we use the word "OR".
The problem with the above illustration, though, is that it is now starting to look a bit messy. It contains far too many arrows and words, and thus it is quite difficult for us to grasp what is going on in the picture. Therefore, it is important for us to split each part of the sandwich and turn it into its own encapsulated definition. This is our first step toward abstraction.
Let us revisit the definition of "meat sandwich". Instead of listing all the alternatives when describing the "meat" ingredient (such as ham, bacon, etc), we may as well simply put the word "meat" in the place where the chosen piece of meat will be inserted.
If anyone asks what the word "meat" is supposed to represent, we will then present him with the full definition of the word "meat", which is shown below.
The key point here is that we are deferring our explanation of the word "meat" up until the moment at which it is being asked.
In the same vein, one may also treat the word "bread" as an abstract concept by endowing it with an encapsulated definition. For instance, one could define "bread" as a selection of one of the following choices: "bun", "toast", "biscuit", or "English muffin". This makes sense because every one of them can be classified as "bread".
If you fully expand our definition of "meat sandwich" by replacing all of its abstract components with their full definitions, then, you will see something like this:
As you can tell, this diagram looks a bit too bloated. It contains too many details, so it is neither easy to draw nor easy to read. This is why we ought to abstract out some of its parts to keep things simple.
Abstraction can be done on multiple levels as well. For example, nothing prevents us from turning "sausage" into its own abstract definition, such as the one displayed below.
This will let us replace the "sausage" part of the definition of meat with the listing of different types of sausages.
... which, in turn, will imply that the full definition of "meat sandwich" should look something like this:
Here, "meat" is the abstraction of what goes inside a meat sandwich (in general), and "sausage" is the abstraction of what goes inside a meat sandwich as soon as we decided to put a sausage in it. These are two different levels of abstraction, and they unwrap themselves one by one, as we specify our choices of ingredients.
As we keep stretching this kind of reasoning, we will eventually find ourselves reaching the most extreme edge cases in which the idea of infinity is involved. There are two of them - one which represents the concept of "anything", and the other one which represents the concept of "everything".
Whenever someone says "anything", he is referring to any one of the infinitely many things we can ever imagine. This is the equivalent of the "OR" relation among the infinity of things.
Whenever someone says "everything", he is referring to every one of the infinitely many things we can ever imagine. This is the equivalent of the "AND" relation among the infinity of things.
With these two ends of the spectrum in mind, we should be able to imagine a "sandwich" as an object which comprises two pieces of bread and "anything" between them.
And of course, this "anything" is an abstract entity which defines itself as an arbitrary choice among infinitely many options.
A sandwich is a sandwich as long as there is anything between two pieces of bread, and we do not care what it is; it could be a piece of meat, vegetable, mashed potato, glass, metal, antimatter, black hole, or whatever. There are infinitely many choices available, which makes "anything" the most general form of existence we are ever able to define.
What we can learn from the above example is the fact that abstraction comes in different degrees of generalization. Some forms of abstraction are either more general or more concrete than others.
For example, "sandwich" is the most general kind of all sandwiches because its definition allows us to choose absolutely anything for its core ingredient. In other words, it covers the widest range of choices we can ever imagine.
"Meat sandwich", on the other hand, is less general than "sandwich" because the range of choices of its core ingredient is more restricted. Instead of just "anything", we are forced to choose something which is able to be classified as "meat".
"Ham sandwich" is even less general than "meat sandwich" because its range of choices is way more restricted. Instead of enjoying the freedom of choosing any type of meat, we are forced to choose a slice of ham as its core ingredient.
In the context of set theory, we should be able to arrange the aforementioned three categories of sandwich as a sequence of subset relations. Here, "meat sandwich" is a subset of "sandwich" because the former is more specific than the latter, and "ham sandwich" is a subset of "meat sandwich" because the former is more specific than the latter.
Each of these subset relations, in a way, can be considered a categorical branch in the taxonomy of sandwiches.
From a graphical point of view, it should be fairly straightforward to construct the family tree of sandwiches in terms of such branches.
As you get closer to the tree's root, you will encounter more and more general categories of sandwich. As you get closer to the tree's individual leaves, you will encounter more and more specific categories of sandwich.
(Will be continued in Chapter 2)