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**A Socratic Dialogue on Theoretical Computer Science**

This dialogue takes place between 23:00 and 24:00 at the counter of the bar in a trendy night club. Alice and Bob have just met and they are sipping a glass of wine. The ice has already been broken and they try to find out more about each other.

**Bob:**I am a physicist. What do you do?

**Alice:**I am a computer scientist.

**Bob:**You are the first woman computer scientist I have met! There aren't many women who like to program or fix computers for a living, aren't there?

**Alice:**Well, actually I am a

*theoretical*computer scientist.

**Bob:**(Not hiding a look of surprise on his face.) You must be joking! This surely is a contradiction in terms. There is little that is as practical as, and less theoretical than, computer science! Pardon me for saying so, but, as a scientist myself, I have some level of familiarity with computers, and I know from my daily experience that these machines have dramatically changed many aspects of my work and of my life. I really could not live without my iPod!

I have also read that what we are witnessing today is just the beginning of a digital revolution and that a population of 'effectively invisible' computers around us is embedded in the fabric of our homes, shops, vehicles, farms and some even in our bodies. However, computing is just a technology, not a science.

**Alice:**(With a smile on her face and sipping her wine.) You are not alone in thinking so. However, the information-technology revolution is a glaring example of how results from

*basic scientific research*, having its roots in subjects such as mathematical logic and computability theory, which once looked very abstract and remote from actual application, lead to technological innovations that cause far-reaching transformations to our society. Because of computer science, logic is the most applied branch of mathematics today.

**Bob:**I am not easily convinced. What is Theoretical Computer Science (TCS)?

**Alice:**Let me rest on the shoulders of giants and quote Oded Goldreich and Avi Wigderson, two of the foremost (theoretical) computer scientists of our time:

TCS is the fundamental scientific discipline that aims at understanding general properties of computing, be it natural, man-made, or imaginary.

In fact, in some sense, the whole world of computing arose from Alan Turing's analysis of an imaginary computing device (the Turing machines you might have heard of) that he invented in order to understand the notion of mechanical computation. That imaginary device eventually gave birth to the computers of today and to the software that drives them. So computers arose as the answer to man's quest to understand computation, something that is around us in nature and in our artifacts.**Bob**: Yes, I am aware that Nature itself "computes". It is not uncommon these days to see theoretical physicists discuss the information content of black holes or of the universe itself, or the feasibility and power of quantum computation or other computing principles from the physical world. But tell me, how do theoretical computer scientists work? What contributions has the field given to science?

**Alice:**(Her face becoming brighter with joy.) Research in TCS often starts from the desire to understand the properties of some notion of computation. In particular, we are interested in characterizing what algorithmic problems can be solved, in theory or in practice, using the chosen notion of computation. You know, computers look very powerful, and indeed they are. (Bob nods.) However, they are not omnipotent and there are many precisely formulated problems that they will

*never*be able to solve. Characterizing the notion of computational process and showing the existence of unsolvable problems was one of the early breakthroughs of TCS around 1936, long before any computer existed! Since then, we have learned a lot about the notion of computational complexity of problems. Have you ever watched the TV show Numb3rs?

**Bob:**(Smiling) Sure, there is a cool physicist in it who walks around with Charlie Eppes.

**Alice:**(Smiling back) Good. Then you might recall that Charlie Eppes every now and again tries to solve the "P vs NP" problem. This is a problem from computer science that is one of the most fundamental mathematical problems of our time. It is one of the Millennium Problems of the Clay Mathematics Institute (in fact, it is the first such problem) and is the only one amongst them that, apart from its intrinsic scientific interest, has profound practical applications and even philosophical implications!

**Bob:**(Taken aback) What does that problem have to do with philosophy?

**Alice:**(Sensing victory) Well, there is a strong sense in which the solution of that problem would allow us to automate efficiently the creative process of finding solutions to a plethora of computational problems in many areas of science. Some people like to say that the "P vs NP" problem can be rephrased as asking whether creativity can be efficiently automated. People in my community tend to believe that the answer is no and that some computational problems are intrinsically hard to solve. Do you shop on line?

**Bob**: Sure I do, just like anyone else.

**Alice:**In fact, every time you submit your credit card number for an on-line purchase, you are implicitly trusting that a very basic mathematical problem, the time-honoured decomposition of a number into its prime factors, is computationally hard. The whole of cryptography is a very active branch of TCS.

**Bob:**Now you really have to tell me more. What are the typical questions people like you work on?

**Alice:**I am glad you asked, but I do not want to bore you too much.

**Bob:**(Laughing) Well the night is still young, and I feel that we are on the same wavelength. So, go ahead.

**Alice:**Well, some of my colleagues still work on understanding what can be possibly computed in principle or with certain bounds on the amount of the resources at our disposal. You know, some problems can in principle be solved using a computer, but in practice this would require more time than the age of the universe. Others develop increasingly sophisticated algorithms for solving computational problems. These are the algorithms that, for instance, allow you to search for a lot of the information you need using Google in less than no time, schedule many of the aspects of the daily life of our city as well as the timetable of the classes that we took at university. Do you drive a car?

**Bob:**Sure, but not tonight. (Laughs)

**Alice:**Well, the functioning of many of your car's features relies on the algorithms these colleagues of mine develop as well as on the analysis techniques that others have proposed for making models of the behaviour of the ABS system in your car, say, for describing its expected properties and for checking that the system affords the properties on your wish list. You do expect your car's airbag to inflate immediately after a crash, do you? (Alice smiles.)

**Bob:**Sure I do! (He smiles back.)

**Alice:**Then it's on the work of people like me your trust is based. And we haven't even started talking about computational learning theory, information theory, global computing and the design of the internet markets you use and inhabit. Did you know that thanks to innovations in learning theory developed by theoretical computer scientists automated search and data selection methods have become indispensable in a growing number of fields including yours? Computers can "learn"! And I have not yet told you about the theory of programming languages and the study of methods for describing what programs do when they compute.....

**Bob**: I think I need a little fresh air. Let's get out of here and take a walk. I am ready to hear your stories, but not in this noisy place.

Alice and Bob collect their jackets and head out. A full moon was lighting the sky and heard Alice ask: "Do you know that coding theory allows us to perform error-free transmission of information to and fro the spacecrafts that we send out to explore the solar system and beyond? Coding theory is also a very active area of TCS...."