When is theoretical computer science useful?

Question

In class, we learned about the halting problem, Turing machines, reductions, etc. A lot of classmates are saying these are all abstract and useless concepts, and there's no real point in knowing them (i.e., you can forget them once the course is over and not lose anything).

Why is theory useful? Do you ever use it in your day-to-day coding?

Answer 1

True story:

When I got my first programming job out of graduate school, the guys that owned the company that I worked for were pilots. A few weeks after I was hired, one of them asked me this question:

There are 106 airports in Arkansas. Could you write a program that would find the shortest rout necessary to land at each one of them?

I seriously thought he was quizzing me on my knowledge of the Traveling Salesman Problem and NP-Completeness. But it turns out he wasn't. He didn't know anything about it. He really wanted a program that would find the shortest path. He was surprised when I explained that there were 106-factorial solutions and finding the best one was a well-known computationally intractable problem.

So that's one example.

Answer 2

When I graduated from college, I assumed that I was on par with everyone else: "I have a BS in CS, and so do a lot of other people, and we can all do essentially the same things." I eventually discovered that my assumption was false. I stood out, and my background had a lot to do with it--particularly my degree.

I knew that there was one "slight" difference, in that I had a "B.S." in CS because my college was one of the first (supposedly #2 in 1987) in the nation to receive accreditation for its CS degree program, and I graduated in the second class to have that accreditation. At the time, I did not think that it mattered much.

I had also noticed during high school and in college that I did particularly well at CS--much better than my peers and even better than many of my teachers. I was asked for help a lot, did some tutoring, was asked to help with a research project, and was allowed to do independent study when no one else was. I was happy to be able to help, but I did not think much about the difference.

After college (USAFA), I spent four years in the Air Force, two of which were applying my CS degree. There I noticed that very few of my coworkers had degrees or even training related to computers. The Air Force sent me to five months of certification training, where I again found a lack of degrees or training. But here I started to notice the difference--it became totally obvious that many of the people I encountered did not REALLY know what they were doing, and that included the people with training or degrees. Allow me please to illustrate.

In my Air Force certification training were a total of thirteen people (including me). As Air Force officers or the equivalent, we all had BS degrees. I was in the middle based on age and rank (I was an O-2 amongst six O-1s and six O-3s and above). At the end of this training, the Air Force rubber-stamped us all as equally competent to acquire, build, design, maintain, and operate ANY computer or communication system for ANY part of the Department of Defense.

However, of the thirteen of us, only six had any form of computer-related degree; the other seven had degrees ranging from aeronautics to chemistry/biology to psychology. Of the six of us with CS degrees, I learned that two had never written a program of any kind and had never used a computer more than casually (writing papers, playing games, etc.). I learned that another two of us had written exactly one program on a single computer during their CS degree program. Only one other person and myself had written more than one program or used more than one kind of computer--indeed, we found that we two had written many programs and used many kinds of computers.

Towards the end of our five-month training, our class was assigned a programming project and we were divided into four groups to separately undertake it. Our instructors divided up the class in order to spread the "programming talent" fairly, and they assigned roles of team lead, tech lead, and developer. Each group was given a week to implement (in Ada) a full-screen, text-based user interface (this was 1990) for a flight simulator on top of an instructor-provided flight-mechanics library. I was assigned as tech lead for my team of four.

My team lead (who did not have a computer degree) asked the other three of us to divide up the project into tasks and then assigned a third of them to each of us. I finished my third of the tasks by the middle of that first day, then spent the rest of the day helping my other two teammates, talking to my team lead (BSing ;^), and playing on my computer.

The next morning (day two), my team lead privately informed me that our other two teammates had made no progress (one could not actually write an "if" statement that would compile), and he asked me to take on their work. I finished the entire project by mid-afternoon, and my team spent the rest of the day flying the simulator.

The other guy with the comparable CS degree was also assigned as a tech lead for his team, and they finished by the end of day three. They also began flying their simulator. The other two teams had not finished, or even made significant progress, by the end of the week. We were not allowed to help other teams, so it was left at that.

Meanwhile, by the middle of day three, I had noticed that the flight simulator just seemed to behave "wrong". Since one of my classmates had a degree in aeronautics, I asked him about it. He was mystified, then confessed that he did not actually know what made a plane fly!?! I was dumbfounded! It turns out that his entire degree program was about safety and crash investigations--no real math or science behind flight. On the other hand, I had maybe a minor in aeronautics (remember USAFA?), but we had designed wings and performed real wind tunnel tests. Therefore, I quietly spent the rest of the week rewriting the instructor-provided flight-mechanics library until the simulator flew "right".

Since then, I have spent nearly two decades as a contractor and occasionally as an employee, always doing software development plus related activities (DBA, architect, etc.). I have continued to find more of the same, and eventually I gave up on my youthful assumption.

So, what exactly have I discovered? Not every one is equal, and that is okay--I am not a better person because I can program effectively, but I am more useful IF that is what you need from me. I learned that my background really mattered: growing up in a family of electricians and electrical engineers, building electronics kits, reading LITERALLY every computer book in the school/public libraries because I did not have access to a real computer, then moving to a new city where my high school did have computers, then getting my own computer as a gift, going to schools that had computers of many different sizes and kinds (PCs to mainframes), getting an accredited degree from a VERY good engineering school, having to write lots of programs in different languages on different kinds of computers, having to write hard programs (like my own virtual machine with a custom assembly language, or a Huffman compression implementation, etc.), having to troubleshoot for myself, building my own computers from parts and installing ALL the software, etc.

Ultimately, I learned that my abilities are built on a foundation of knowing how computers work from the electrical level on up--discrete electronic components, circuitry, subsystems, interfaces, protocols, bits, bytes, processors, devices, drivers, libraries, programs, systems, networks, on up to the massive enterprise-class conglomerates that I routinely work on now. So, when the damn thing misbehaves, I know exactly HOW and WHY. And I know what cannot be done as well as what can. And I know a lot about what has been done, what has been tried, and what is left relatively unexplored.

Most importantly, after I have learned all that, I have learned that I don't know a damned thing. In the face of all that there is potentially to know, my knowledge is miniscule.

And I am quite content with that. But I recommend that you try.