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Derek Abbott's Answers:
1. What is "Parrondo's paradox?" Parrondo's paradox is the counterintuitive result where individual losing games can be combined to give rise to a winning expectation. Random or periodic switching between losing games can surprisingly win.
2. Can I use Parrondo's paradox to win at the Casino? The answer is most probably "no." Parrondo's games rely on exploiting convex linear combinations in a non-linear parameter space. Casino games have a linear parameter space (as far as we know). If anyone can demonstrate any convexity in a casino game, then you are on to something! So the answer is most probably no, because we have not personally exhaustively tested every casino game for convex spaces. Our interest in is scientific study of the Parrondo phenomenon, not in casinos. To find out about convexity and the role it plays in Parrondian phenomena, click on the publications link. The importance of convexity in the Parrondo effect was first pointed out by Moraal in 1999 and then independently by Costa, Fackrell & Taylor in 2000.
3. What inspired the creation of Parrondo's games? J.M.R. Parrondo's field of interest is the interface between information theory and thermodynamics. Because of this, Parrondo was naturally interested in the microscopic details of Maxwell demons. A device called a "Brownian ratchet" produces conterintuitive motion of particles and is of interest in the study of thermodynamic "demons." Inspired by a version called the flashing ratchet, in 1996, Parrondo devised the games as a pedagogical illustration of the Brownian ratchet. There are close similarities between Brownian ratchets and Parrondo's games—and it turns out that Parrondo's games are a discrete-time and discrete-space version of the continuous flashing ratchet. Parrondo's genius was in intuitively extracting the discrete games from the continuous ratchet model. In the early days of the Parrondo effect, however, this intuitive link was not rigorously established. This link was first mathematically established by Allison & Abbott (2002) and then independantly by Toral, Amengual & Mangioni (2003).
4. What is Brownian ratchet? The archetypal Brownian ratchet, is a ratchet wheel connected to a vane as part of a thought experiment. The whole device is microscopic and so the Brownian motion of air molecules drives the vane. The ratchet wheel rectifies the motion and so you can get useful work out of the device. This device only works if the vane is kept hotter than the ratchet. At thermal equillibrium it cannot work, otherwise there would be a thermodynamic violation. But it is perfectly legal if a temperature difference is maintained, as this constitutes nett energy into the system. This device was first discussed by the French physicist Lippmann in 1900 and then first explained correctly by Smoluchowski in 1912. In 1963, Feynman was the first to apply Boltzmann statistics to mathematically explain the behaviour of the device at thermal equillibrium. Abbott, in 1980, first questioned Feyman's analysis, which to this day has not been rigourously derived from first principles. In 1996, Parrondo & Español demonstrated a flaw in Feynman's calculation of the efficiency of the device. In a paper by Abbott, Davis and Parrondo (1999) an analysis at thermal equillibrium was finally derived, using level crossing statistics rather than Feynman's Boltzmann approach. In the early 1990s, this ratchet was considered in terms of linear potentials rather than a wheel. An influential paper, in 1993 by Magnasco, led to huge interest in research into Brownian ratchets in general. In 1992, Adjari & Prost wrote the first paper on the flashing ratchet that influenced Parrondo to devise his now famous games. To understand how a flashing racthet operates click here to run Franz-Josef Elmer's famous simulation of the flashing ratchet.
5. What are the applications of "Parrondo's paradox?" In a sense this is the wrong question. It is akin to asking what the applications of "Simpson's paradox" or "Olber's paradox" are. Study of apparent paradoxes, such as these and that of Parrondo, give us an interesting starting point when examining various natural phenomena. Parrondo's games in their original set-up form a toy model that maps directly onto a flashing ratchet. Toy models don't necessarily directly map exactly onto any real system. What they are mainly about is the underlying physical principles. In physics, the phrase "toy model" is a technical phrase used to describe a highly simplified system that doesn't necessarily structurally map onto a particular physical system, but the behaviour it possesses does map onto real physical phenomena. A toy model is one that is sufficiently simplified, that we can use it to understand more complex systems. In the case of Parrondo's games, there are many concepts such as (i) convex linear combinations, (ii) feedback, (iii) noise-induced ordering, (iv) stochastic resonance, (v) fractals etc. that all meet together in one remarkably compact model. It is this richness in physical phenomena all packed into one tidy model that has made Parrondo's games a focus of research.
In cosmology, black holes in themselves might never be useful, but they attract the attention of researchers because they are a melting pot where thermodynamics, quantum mechanics, general relativity and information theory all converge. Similarly with Parrondo's games, various concepts in complexity theory, stochastic theory, Markov theory, ratchet theory, theory of martingales etc. all converge. This is why it is useful and fascinating.
6. Who is Parrondo? J.M.R. Parrondo is a physicist based at the Universidad Complutense de Madrid, Spain, working on research that is at the convergence of information theory and thermodynamics. He is the foremost researcher in this area and is regarded by many as the natural successor to Rolf Landauer in this regard. An amusing anecdote is that Parrondo attended a conference in 1999, where all the papers were double-blind reviewed. To test the efficacy of the blind review process, the reviewers were asked to try to guess the author of each paper. All five of Parrondo's reviewers said he was Rolf Landauer! Of course, 1999 was the year Landauer died and many reviewers obviously hadn't caught up with that fact. During the conference banquet, as a gesture to mark this event Parrondo was given an informal "Landauer award."
7. What is history-dependent Parrondo game? A history-dependent Parrondo game is one where the rules of the game depend on previous states. It is this state-dependence that can be thought of as creating the necessary non-linearity giving rise to the convex parameter space. This state-dependence also means that the game is not a martingale. Please click here for further details on history dependent games and how they are constructed. The first paper on this type of game was by Parrondo, Harmer & Abbott (2000) and then independently by Costa, Fackrell & Taylor in 2000.
8. What is cooperative Parrondo game? Cooperative Parrondo games were first mooted by Toral in 2001. Here the state-dependence relies on the win/lose states of your neighbours. Please click here or further details of how cooperative games are constructed.
9. How to play Parrondo's games? Parrondo's games can be played as coin tossing games. The coins used can be a mixture of biased and unbiased ones. In Parrondo's original version, Game A is played with only one coin, whereas Game B can be made up of two or more coins. There are rules to decide which game is to be played on each round.
10. What are the future research areas for Parrondo's games? Not having a crystal ball, it is always dangerous to make predictions about directions research will ultimately take. However, from our present viewpoint it looks as though there is plenty of scope for hot research into Parrondo's paradox in the areas of (i) economics, (ii) population genetics, (iii) control theory, (iv) study of the discrete-continuous interface, (v) complex systems, (vi) diffusive transport processes, and (v) gene dynamics & DNA. The area of quantum Parrondo effects is also becoming an exciting area of research, for the quantum information & computation field. Areas of research for quantum Parrondo effects are in quantum walks, quantum algorithms, quantum decoherence and quantum control.
11. Are Parrondo's games really anything to do with traditional game theory? The question here is pointing out that Parrondo's original games do not involve decisions of conflict between players, and therefore cannot be game theory proper. There are two answers to this point. One way of answering it is to say "well, that may be the case but mathematicians, such as Behrends in Germany, are now leading the way with adding Markov decision theory to the games." Another different answer is to say "well, who says game theory has to have decisions in it?" That is game theory in the von Neumann sense. In the Blackwell sense, game theory includes simple coin tossing games. The book on game theory by Blackwell and Girshick (1954) was another great landmark after the book by von Neumann and Morgenstern (1948).
12. Is Parrondo's paradox really a "paradox"? This question is sometimes asked by mathematicians, whereas physicists usually don't worry about such things. The first thing to point out is that "Parrondo's paradox" is just a name, just like the "Braess paradox" or "Simpson's paradox." Secondly, as is the case with most of these named paradoxes they are all really apparent paradoxes. People drop the word "apparent" in these cases as it is a mouthful, and it is obvious anyway. So no one claims these are paradoxes in the strict sense. In the wide sense, a paradox is simply something that is counterintuitive. Parrondo's games certainly are countertuitive—at least until you have intensively studied them for a few months. The truth is we still keep finding new surprising things to delight us, as we research these games. I have had one mathematician complain that the games always were obvious to him and hence we should not use the word "paradox." He is either a genius or never really understood it in the first place. In either case, it is not worth arguing with people like that.
13. Surely you can replace combining games A and B, with a single game C? The implication of this question is that Parrondo's paradox is not really interesting, because you can replace games A & B, with a single game—call it C—that can perform equally as well. This comment is rather like saying "let's not bother with two Penrose tile shapes and glue them together to form one tile shape." Of course, you can tile a surface with one shape, but this then misses the point of Penrose tiles that can tile a surface with infinite richness. Similarly with Parrondo's games what is of interest is the richness in the dynamics produced by switching A and B. The analogy between Parrondo's game and Penrose tiles has more to it than meets the eye, as Parrondo's games can be thought of in terms of being another type of packing problem—but in a probability space rather than in a geometric space.
14. Why not throw away game A and just play the best coin within game B? In one sense, this question is similar to question 13 dressed up in a different guise. So again we can say that keeping one coin, and throwing away the other coins, completely destroys the interesting dynamics. However, let's go one step further and point out that in many real life situations you can't simply "throw away" the bad bits and keep the best. For example, your DNA sequence is stuck with many bad genes that you might have inherited. Your body does not have the ability to slice out the bad bits and throw them away. However, during gene expression, if some stochastic mechanism or "Parrondo effect" happened to be favouring expression of good sequences over bad ones, that would be a more feasible hypothesis to start testing.
15. Can I join the Adelaide group and do a PhD in one of the areas related to Parrondo's paradox? Yes, if you are interested in this area you are welcome to apply. However, to be realistic you must get a PhD scholarship. So you need only apply if you have a very good academic transcript. If you are an Australian Permanent Resident (PR), go ahead and fill out the application form for a PhD and tick the boxes that indicate you want an APA scholarship. Email it to Derek Abbott, for checking, before submittal. Remember we get hundreds of emails every year asking about PhD study and we simply don't even reply to them. So when you email, put "I have read the Parrondo website" in the subject line of your email. That it is a secret code word, which means we will now read your email. If you are an overseas student, you must get a scholarship from your own government. You can try to apply for an Australian IPRS scholarship but it is so difficult to get that you need only apply if you have several international publications and a Masters degree already.
16. Can I join the Adelaide group and do postdoc research in one of the areas related to Parrondo's paradox? Yes, you need to have a PhD in Maths, Physics, Computer Science or EE. You need to already have at least 10 good publications. You must then apply for an Australian Postdoctoral Fellowship (APD). If you win, you can come.
17. Can I join the Adelaide group and do an internship in one of the areas related to Parrondo's paradox? Generally the answer is "no." You can only come if you stay here at least one year (otherwise it is impossible to do serious work) and you must be fully funded by your parents or a travel travel scholarship to come here.