This is a followup to a post more than an year ago, titled Probability, Randomness, Non-Determinism, Approximation – the subtle distinctions. Again a very scientific or academic post to explain the words above which are frequently used out of context, even by professors.
As a college student, my classmates always used the phrase, “Theory vs. Practical”. Because I was a good coder (even if I say so myself), I was always branded as the”practical-oriented guy as opposed to a theoretician. I admit I wasn’t a theoretician, but the real title that I deserved was an applied scientist, not a “practical-oriented guy” (whatever the hell that means).
1. Theoretical vs Descriptive: Most people use the two terms interchangebly and it really gets on my nerves. Have you ever heard someone talk about theoretical questions vs. practical questions about Java/C/C++? What people really mean are descriptive vs. problem-statement questions. All questions are very much practical questions since they don’t deal with thought-experiments.
A question like, “Explain threading classes in Java”, is not a theoretical question, but a descriptive question. You’re being asked to describe how threading works in Java, not to present a theory about how you think it works. There’s no theory involved here. There’s no model that you present about how it may work, and then verify experimentally or empirically. It’s a fact. It works. You know how it works. You’re being asked to describe it. This like saying “Why is the Mona Lisa so popular?” is a theoretical question (unless of course some psychoanalyst presents a theoretical model about it).
This terminology probably comes from a natural extension of mathematical sciences developed by people without a lot of imagination. Mathematics may have three questions about the pythagoras theorem:
a) State the pythagoras theorem and prove it
b) Given a triangle with ….. find the hypotenuse.
c) Explain how the pythagoras theorem is used in various problems.
The first being theoretical in the sense you’re asked to present a theory and so as to not take it at face value, prove it (thereby demonstrating an understanding of theory). The second being a problem-statement where you’re asked to apply the pythagoras theorem to solve a problem. The third question is descriptive where you’re asked for an explanation or a description, but not the theory itself.
This distinction is very important when we may have a question with two interpretations – one theoretical, and the other descriptive. One question that comes to mind is, “Why is the sky blue?”
a. The theoretical interpretation asks for your understanding of theory behind it. It is not only asking you to state the theory but to demonstrate an understanding of it, so that you may apply the theory elsewhere or develop it forther.
b. The descriptive interpretation may take many forms of an answer. Today is a clear and sunny day withthout clouds, and therefore the sky is blue. This describes certain things, but makes to rigorous scientific attempt at modelling it.
2. Applied vs. Practical: Another one of those things that bother me. I see many people who don’t want to spend time understanding theory, find they can do things, and claim they’re “applied”. Conversely, I find many applied scientists are labelled as “practical-oriented guys”. 
Again, this demonstrates a gross misunderstanding of how science works.
An applied scientist has a firm understanding of theory. They just don’t develop theory, but they are not unaware of it. Application of theory requires a deep understanding of it to begin with. An applied person isn’t necessarily the one who can hold a test tube with a steady hand and perform a qualitative analysis on it themselves. A lab practicioner, on the other hand, may not have much understanding of theory, but they would be able to do this in their stride.
The closest analogy I can think of is a mechanic vs. an automobile engineer. A mechanic really doesn’t understand the theory behind the distance between the two electrodes in a spark plug, or they may not be able to determine the barometric pressure in a car’s tyres for optimal performance. They can however, do these things. An automobile engineer may not have developed the theory of fluid mechanics, and tensile strength of bonding between rubber molecules in the tyres, but they certainly understand it. Given sufficient parameters, they can determine the optimal pressure in the tyre. They are applying theory, but not developing it.
In the computing world, this is seen altogether too often. We see programmers who have memorized a lot of syntax and function calls and go around claiming theory is not important. We do see better programmers who have a firm theoretical understanding of Turing Machines or Regular grammars but may not have developed these concepts. And we see people who are developing new types of “machines” and “grammars”. Although not apparent at first sight, there is a significant difference between the three.
The theoretician is the guy who thought up Regular Grammar and Context-Free Grammar. The applied computer scientist who knows when to use a regular expression, and when to use a recursive-descent parser. The practician is someone who remembers a million function calls but won’t be able to decide whether a grammar is regular or context-free. Having been told to use a certain grammar, they may be able to code the parser.
3. Theoretical vs. Applied: After the point above , this becomes easy to see. Scientists understand theory. They understand science. They have a firm basis for whatever they do. They are decision makers. They can decide whether or not a certain type of string can be matched with a regular expression, or whether it needs a more sophisticated parser like an RDP. There is a common misconception that theoreticians are ones who study theory, and applied scientists don’t understand theory. Part of this comes due to the confusion between scientists and engineers.
Theoreticians develop theory. They are ones who propose theory. Given that the sky is blue, they develop a model for “why is it blue?” Taking into account empirical data, experimental results, etc. they propose a theory (not a description). A theory models behaviour of stuff in the sky that produces the color blue – it promotes understanding of how things work. It’s only a theory if it explains all the factors responsible and is proven (until then, it’s a conjecture.)
Applied Scientists then use this theory to create blue elsewhere. If I put a lot of atmospheric gasses in a room, and provided just as much light as the sun, can I produce blue? An applied scientist will interpret the theory and answer questions. Or they may tell you what color the sky would look like on Mars or Venus or Pluto. That’s why I distinguish between theory and description – a descriptive answer to “Why is the sky blue?” would not allow one to predict how the sky would look like on Venus, only a theoretical answer would. They may also verify theory by designing experiments (not necessarily perform experiments). They can tell you what happens when you mix the “blue liquid” and the “red liquid” in a test tube without ever having done it.
The practitioner won’t be able to tell you what’s going to happen. If something goes wrong, they won’t be able to extrapolate what may be the cause. They won’t be able to tell you exactly how an experiment would need to be designed so as to isolate the cause of a certain phenomenon – say something like determining the existence of ether.
