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?
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.
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.
Sure, it's useful.
Imagine a developer working on a template engine. You know the sort of thing...
Blah blah blah ${MyTemplateString} blah blah blah.
It starts out simple, with a cheeky little regular expression to peform the replacements.
But gradually the templates get a little more fancy, and the developer includes features for templatizing lists and maps of strings. To accomplish that, he writes a simple little grammar and generates a parser.
Getting very crafty, the template engine might eventually include a syntax for conditional logic, to display different blocks of text depending on the values of the arguments.
Someone with a theoretical background in CS would recognize that the template language is slowly becoming Turing complete, and maybe the Interpreter pattern would be a good way to implement it.
Having built an interpreter for the templates, a computer scientist might notice that the majority of templating requests are duplicates, regenerating the same results over and over again. So a cache is developed, and all requests are routed through the cache before performing the expensive transformation.
Also, some templates are much more complex than others and take a lot longer to render. Maybe someone gets the idea to estimate the execution of each template before rendering it.
But wait!!! Someone on the team points out that, if the template language really is Turing complete, then the task of estimating the execution time of each rendering operating is an instance of the Halting Problem!! Yikes, don't do that!!!
The thing about theory, in practice, is that all practice is based on theory. Theoretically.
The things I use most:
computational complexity to write algorithms that scale gracefully
understanding of how memory allocation, paging, and CPU caching work so I can write efficient code
understanding of data structures
understanding of threading, locking, and associated problems
As to that stuff on Turing machines etc. I think it is important because it defines the constraints under which we all operate. Thats important to appreciate.
it's the difference between learning algebra and being taught how to use a calculator
if you know algebra, you realize that the same problem may manifest in different forms, and you understand the rules for transforming the problem into a more concise form
if you only know how to use a calculator, you may waste a lot of time punching buttons on a problem that is either (a) already solved, (b) cannot be solved, or (c) is like some other problem (solved or unsolved) that you don't recognize because it's in a different form
pretend, for a moment, that computer science is physics... would the question seem silly?
A friend of mine is doing work on a language with some templates. I was asked in to do a little consulting. Part of our discussion was on the template feature, because if the templates were Turing complete, they would have to really consider VM-ish properties and how/if their compiler would support it.
My story is to this point: automata theory is still taught, because it still has relevance. The halting problem still exists and provides a limit to what you can do.
Now, do these things have relevance to a database jockey hammering out C# code? Probably not. But when you start moving to a more advanced level, you'll want to understand your roots & foundations.
Although I don't directly apply them in day-to-day work, I know that my education on formal computer science has affected my thinking process. I certainly avoid certain mistakes from the onset because I have the lessons learned from the formal approaches instilled in me.
It might seem useless while they're learning it; but I bet your classmate will eventually comes across a problem where they'll use what they were taught, or at least the thinking patterns behind it...
Wax on... Wax off... Wax on... Wax off... What does that have to do with Karate, anyways?
At one job I was assigned the task of improving our electrical distribution model's network tracing algorithm as the one they were using was too slow. The 3-phase network was essentially three n-trees (since loops aren't allowed in electrical networks). The network nodes were in the database and some of the original team couldn't figure out how to build an in-memory model so the tracing was done by successive depth SELECTs on the database, filtering on each phase. So to trace a node ten nodes from the substation would require at least 10 database queries (the original team members were database whizzes, but lacked a decent background in algorithms).
I wrote a solution that transformed the 3 n-tree networks of nodes from the database into a data structure where each node was stored once in a node structure array and the n-tree relationship was converted to three binary trees using doubly-linked pointers within the array so that the network could be easily traced in either direction.
It was at least two orders of magnitude faster, three on really long downstream traces.
The sad thing was that I had to practically teach a class in n-trees, binary trees, pointers, and doubly-linked lists to several of the other programmers who had been trained on databases and VB in order for them to understand the algorithms.
It's a classic dichotomy, between "how" and "what". Your classmates are looking at "how" to program software, and they're very focused on the near focus; from that perspective, the perspective of implementation, it seems like knowing things like halting states and Turing machines are unimportant.
"How" is very little of the actual work that you get expected to do with Computer Science, though. In fact, most successful engineers I know would probably put it at less than 20 percent of the actual job. "What" to do is by far more important; and for that, the fundamentals of Computer Science are critical. "What" you want to do relates much more to design than implementation; and good design is... well, let's just call it "non-trivial".
"There are two ways of constructing a software design: One way is to make it so simple that there are obviously no deficiencies, and the other way is to make it so complicated that there are no obvious deficiencies. The first method is far more difficult." - C.A.R. Hoare
Good luck with your studies!
I think understanding the fundamental models of computation is useful: sure you never need to be able to translate a Turing machine into a register machine in practice, but learning how to see that two very different problems are really instances of the same concept is a critical skill.
Most knowledge is not "practical", but helps you connect dots in ways that you cannot anticipate, or gives you a richer vocabulary for describing more complex ideas.
It's not the specific problems that you study that matters, it's the principles that you learn through studying them. I use concepts about algorithms, data structures, programming languages, and operating systems every day at my job. If you work as a programmer you'll make decisions all the time that affect system performance. You need to have a solid foundation in the fundamental abstract concepts in order to make the right choices.
After i graduated from CS I thought similarly: the whole bunch of theories that we studied are completely useless in practice. This proved to be right for a short period of time, however the moment you deal with complex tasks, theory is definitely MORE VALUABLE than practice. every one after few years of coding can write some programs that "work" but not every one is able to understand how. no matter what most of us will deal at a certain point with performance issues, network delays, precission, scalability etc. At this stage the theory is critical. in order to design a good solution when dealing with complex systems is very important to know how the memory management works, the concepts of process and threads, how memory is assigned to them, or efficient data structures for performance and so on.
One time for example i was working on a project including plenty of mathematical calculations and at a certain point our software failed. while debugging i figured out that after some mathematical operation i received a number as DOUBLE of a value 1.000000000002 but from the mathematical perspective couldnt be > 1 which at some later stage in the program was giving the legendary NaN exception. i spent some time to figure this out but if i had paid more attention to the "approximation of Double and Float" lesson i would have not wasted that time.
If you work in a company that does groundbreaking work, it is important to be able to communicate to architects and developers what the benefits are. There is a lot of hype about all kinds of technologies and positioning yourself can be difficult. When you frame your innovation in scientific and theoretical terms you are definitely at an advantage and customers sense you are the real thing. I can tell folks: there is a new way to deal with state, encoding and nondeterminism (i.e. complexities) and you can definitely be more productive than you are today.
If you take the long view in your career learning about theory will give you depth, the depth you need to grow. The return on investment in learning your 5th or 6th programming language will be a lot less then learning your 2nd and 3rd. Exposure to theory will give you a sense for real engineering, about where the degrees of freedom are and how you can make the right trade-offs.
The important concepts 1) State, 2) Encoding, 3) Nondeterminism. If you don't know them they will not help you. What theory should provide you with is the big picture and a sense of how basic concepts fit together. It should help you hone your intuition.
Example: some of the answers above mention the halting problem and Turing machines. When I came across Turing's paper in college I did not feel enlightened at all. One day I came across Goedel's incompleteness theorem and Goedel numbering in particular. Things started to make a lot of sense. Years later I read about Georg Cantor at a bookstore. Now I really started to understand Turing machines and the halting problem. Try for yourself and look up "Cantor's Diagonal Argument" on Wikipedia. It is one of the most awesome things intellectually you will ever encounter.
Food for thought: A typical Turing machine is not the only way to design a state transition machine. A Turing machine with two rather than one tape would give you a lot more speed for a number of algorithms. http://www.math.ucla.edu/~ynm/papers/eng.ps
You can expose yourself to these insights more efficiently then I did by reading this book. Link at the bottom of this post. (At the very least, check out the table of contents on Amazon to get a taste of what this is all about):
I found the book by Rosenberg sensational. http://www.amazon.com/The-Pillars-Computation-Theory-Nondeterminism/dp/0387096388 If you have only one book on theory IMHO this should be the one.
I do not use it on a daily basis. But it gave me a lot of understanding that helps me each day.
I found that all I need for daily bliss from the CS theoretical world is the utterance of the mantra "Low coupling and High Cohesion". Roger S. Pressman made it scholarly before Steve McConnell made it fashionable.
Ya, I generally use state diagrams to design the shape and flow of the program.
Once it works in theory, I start coding and testing, checking off the states as i go.
I find that they are also a useful tool to explain the behavior of a process to other people.
Simple. For example: if I'm using RSACryptoServiceProvider I'd like to know what is that and why I can trust it.
Because C++ templates are actually some kind of lambda calculus. See www.cs.nott.ac.uk/types06/slides/michelbrink_types_06.pdf
I'm studying for my Distributed algorithms course now. There is a chapter about fault tolerance and it contains some proofs on the upper bound for how many processes can fail (or misbehave) so that the distributed algorithm can handle it correctly.
For many problems, the bound for misbehaving processes is up to one third of total number of processes. This is quite useful in my opinion because you know that it's pointless to try to develop a better algorithm (under given assumptions).
Even if theoretical courses aren't going to be used directly, it might help you think better of something.
You don't know what your boss is going to ask you to do, you may have to use something that you thought it won't be benefical, as Jeffrey L Whitledge said.
To be honest, I sort of disagree with a lot of the answers here. I wrote my first compiler (for fun; I really have too much coffee/free time) without having taken a course in compilers; basically I just scanned the code for another compiler and followed the pattern. I could write a parser in C off the top of my head, but I don't think I could remember how to draw a pushdown automaton if my life depended on it.
When I decided I wanted to put type inference in my toy (imperative) programming language, I first looked over probably five papers, staring at something called "typed lambda calculus" going what.... the.... ****....? At first I tried implementing something with "generic variables" and "nongeneric variables" and had no idea what was going on. Then I scrapped it all, and sat there with a notebook figuring out how I could implement it practically with support for all the things I needed (sub-typing, first-class functions, parameterized types, etc.) With a couple days of thinking & writing test programs, I blew away more than a weeks worth of trying to figure out the theoretical crap.
Knowing the basics of computing (i.e. how virtual memory works, how filesystems work, threading/scheduling, SMP, data structures) have all proved HIGHLY useful. Complexity theory and Big-O stuff has sometimes proved useful (especially useful for things like RDBMS design). The halting problem and automata/Turing Machine theory? Never.
I know this is old, but my short reply to those who claim that theory is 'useless' and that they can practice their profession without it is this:
Without the underlying theory, there is no practice.
Why is theory useful?
Theory is the underlying foundation on top of which other things are built. When theory is applied, practice is the result.
Consider computers today. The common computer today is modeled and built on top of the Turing Machine, which, to keep it simple, is an abstract/theoretical model for computation. This theoretical model lies at the foundation of computing, and all the computing devices we use today, from high-end servers to pocket phones, work because the underlying foundation is sound.
Consider algorithm analysis. In simple terms, algorithm analysis and time-complexity theory have been used to classify problems (e.g. P, NP, EXP, etc) as well as how the algorithms we have behave when trying to solve different problems in different classes.
Suppose one of your friends gets a job at some place X and, while there, a manager makes a few simple requests, such as these examples:
Ex 1: We have a large fleet of delivery vehicles that visit different cities across several states. We need you to implement a system to figure out what the shortest route for each vehicle is and choose the optimal one out of all the possibilities. Can you do it?
Thinking the theory is 'useless' your friends don't realize that they've just been given the Traveling Salesman Problem (TSP) and start designing this system without a second thought, only to discover their naive attempt to check all the possibilities, as originally requested, is so slow their system is unusable for any practical purposes.
In fact, they have no idea why the system works at an "acceptable" level when checking 5 cities, yet becomes very slow at 10 cities, and just freezes when going up to only 40 cities. They reason that it's only "2x and 8x more cities than the 5 city test" and wonder why the program does not simply require "2x and 8x more time" respectively...
Understanding the theory would've allowed them to realize the following, at least at a glance:
It's the TSP
The TSP is NP-hard
Their algorithm's order of growth is O(n!)
The numbers speak for themselves:
+--------------+-------+-----------------------------------------------------------------+
| No. Cities | O(N!) | Possibilities |
+--------------+-------+-----------------------------------------------------------------+
| 5 | 5! | 120 |
| 10 | 10! | 3,628,800 |
| 40 | 40! | 815,915,283,247,897,734,345,611,269,596,115,894,272,000,000,000 | <-- GG
+--------------+-------+-----------------------------------------------------------------+
They could've realized at the outset that their system was not going to work as they imagined it would. The system was later considered impractical and cancelled after a significant amount of time, effort, and other resources had been allocated to, and ultimately wasted on, the project --and all because thought "theory is useless".
So after this failure, the managers think "Well, maybe that system was underestimated; after all, there're a LOT of cities in our country and our computers are simply not as fast as we need them to be for our recently cancelled system to have been a success".
The management team blames slow computers as the cause of the project's failure. After all, they're not experts in CS theory, don't need to be, and those who're supposed to be the experts on the topic and could've informed them, didn't.
But they have another project in mind. A simpler one actually. They come the week later and ask say the following:
Ex 2: We have only a few servers and we have programmers who keep submitting programs that, due to unknown reasons, end up in infinite cycles and hogging down the servers. We need you to write a program that will process the code being submitted and detect whether the submitted program will cause an infinite cycle during its run or not, and decide whether the submitted program should be allowed to run on this basis. Can you do it?
Your dear friend accepts the challenge again and goes to work immediately. After several weeks of work, there're no results, your friend is stressed, and doesn't know what to do. Yet another failure... your friend now feels "dumb" for not having been able to solve this "simple problem"... after all, the request itself made it sound simple.
Unfortunately, your friend, while insisting that "theory is useless" didn't realize that the, allegedly simple, request was actually an intractable problem about decidability (i.e. the halting problem itself), and that there was no known solution for it. It was an impossible task.
Therefore, even starting work to solve that particular problem was an avoidable and preventable mistake. Had the theoretical framework to understand what was being requested been in place, they could've just proposed a different, and achievable, solution... such as implementing a monitoring process that can simply kill -SIGTERM <id> of any user process (as per a list of users) that monopolizes the CPU for some arbitrary/reasonable interval under certain assumptions (e.g. we know every program run should've terminated within 10 minutes, so any instance running for 20+ minutes should be killed).
In conclusion, practice without the theory is like a building without a foundation. Sooner or later, the right amount of pressure from the right angle will make it collapse in on itself. No exceptions.
Do you ever use it in your day-to-day coding?
Yes, but not directly. Rather, we rely on it indirectly. The caveat here is that different theoretical concepts will be more or less applicable depending on the problem domain you happen to be working on.
Surely, we:
use computers daily, which relies on computational models (e.g. turing machines)
write code, which relies on computability theory (e.g. what's even computable) and lambda calculus (e.g. for programming languages)
rely on color theory and models (e.g. RGB and CMYK color models) for color displays and printing, etc.
Euler's theorems in computer graphics so that matrices can be built to rotate objects about arbitrary axes, and so on...
It's a fact that someone who simply use a plane to travel doesn't need to understand the theory that even allowed planes to be built and fly in the first place... but when someone is expected to build said machines and make them work... can you really expect a good outcome from someone who doesn't understand even the principles of flight?
Was it really a coincidence that, for most of history, no one was able to build a flying machine (and a few even died testing theirs) until the Wright brothers understood certain theoretical concepts about flight and managed to put them into practice?
It's no coincidence. We have a lot of working technology today because the people who built them understood, and applied, the theoretical principles that allowed them to work in the first place.
I guess it depends on which field you go into.