(The multi-month hiatus here on Monomorphic has been due to me working on my thesis. I am now able to, briefly, return to this and other indulgences.)

Life presupposes taking responsibility. It presupposes investing people, objects and matters around you with your concern.

In particular, democratic society presupposes that we all take full, in some sense, responsibility for society itself, its decision making and its future.

However, he who lacks information about some matter cannot take responsibility for it. And thus we often defer to authorities in practice. Authorities allow us to specialise our understanding, which increases our net ability to understand as a collective, assuming that we have sufficiently well functioning interpersonal communication.

There are whole categories of problems that routinely are assigned to specific, predefined authorities and experts; for instance legal matters, constitutional matters, whether some person is mentally ill, medical matters, nuclear and chemical hazards, and so on. Fields where some degree of extensive training is generally required. (However, under the right conditions, these authorities could probably also be called into question by the public opinion.) The opposite is those categories of problems that are routinely assigned to “public opinion” and all of its voices and modulating contraptions and devices, its amplifiers, dampeners, filters, switches and routing mechanisms.

Responsibility aside, in order to maximise an individual’s prospects for life, and by extension society’s prospects for life, it seems important that the individual possess just the right knowledge that they need in their situation. Adding more knowledge is not always a benefit; some kinds of knowledge can be entirely counterproductive. Nietzsche showed this (“On the use and abuse of history for life”), and we can easily apply the idea of computational complexity to see how having access to more information would make it harder to make  decisions.

This is especially true for some kinds of knowledge: knowledge about potential grave dangers, serious threats, monumental changes threatening to take place. Once we have such knowledge we cannot unlearn it, even if it is absolutely clear that we cannot act on it and that we do not have the competence to assess the situation fully. It  takes effort and an act of will to fully disregard a threat on the basis of one’s own insufficient competence.

On the other hand, knowledge about opportunities, about resources, and about problems that one is able to, or could become able to deal with, would generally be helpful and not harmful. However, even this could be harmful if the information is so massive as to turn into noise.

Even disregarding these kinds of knowledge, one of the basic assumptions of democracy – that each individual takes full responsibility for society – seems to be an imperative that is designed never to be fulfilled. An imperative designed to be satisfied by patchworks of individual decisions and “public opinion”, and whatever information fate happens to throw in one’s way. Out of a basic, healthy understanding of their own limitations, individuals generally assume that the democratic imperative to know and to take responsibility was never meant to be taken seriously anyway, but one does one’s best to match one’s peers in appearing to do so.

It seems to me that the questions we must ask and answer are about the proper extent of responsibility, and the proper extent of knowledge, for each individual. For the individual, taking on no responsibility seems detrimental to life; taking on full responsibility for all problems in the world right now, here today, would also be an impossibility. There would be such a thing as a proper extent of responsibility. One’s initial knowledge and abilities would inform this proper extent of responsibility, and the two might properly expand and shrink together, rather than expand and shrink separately.

In a democratic society, in so far as one wants to have one, we should ask: what is the proper level of responsibility that society should expect from each individual, and what level should the individual expect from himself as an ideal?

More generally, empirical studies of how public opinion functions and how democracies function in practice are needed. It is inappropriate to judge and critique democracies based on their founding ideals when the democratic practice differs sharply from those ideals – as inappropriate as it is to critique and judge economies based on the presumption that classical economic principles apply to economic practice in the large.

The assumption that violence is almost always wrong or bad is widespread. But widespread beliefs that usually seem to be beyond questioning can yield interesting ideas when they are dissected and put to the test. Why do we really dislike violence?

If I have to rationalise my intuitive dislike for violence today, on the spot, I would say that violence scares me because of the potentially irreversible effects. If a thug injures me gravely, it might take me a long time to recover my physical abilities, or I might never recover them fully at all. The most irreversible physical injury seems to be death, of course. Violence that is guaranteed to be reversible is somehow a much less scary prospect.

Physical violence is a form of influence that is very rapid, very focussed and that potentially has effects that take a long time to recover from, if recovery is at all possible. If somebody throws a stone at me it is more “injurious” than a light rainfall, even though both situations affect me physically. The stone is more targeted, more intense, more sudden.

What, then, about a more general definition of violence, based on these observations? Suppose that violence is simply sharply focussed influence directed at me from somebody else; not necessarily physical. In this way advertising, music, newspapers can potentially do violence to me. If we also remove the condition that the effect should be sharp and rapid, we can accept slow-acting influence as being violent; the condition is now only that recovery should be relatively slow or impossible. Under this condition, the kind of influence I receive from going to school (education), from watching TV, from advertising, or from random events may indeed be a form of violence, depending, of course, on what my sensitivities to these events are.

Of course we cannot shield ourselves from violence in this broader definition. We must accept it and accept that our identities probably are, partly, the results of such influence.

Physical violence is a form of domination/influence, and it is the most obvious form. It is shockingly easy to notice, a grotesquely rude form of influence. But if all we care about is the effects of violence, the slow or impossible recovery, then we should perhaps also be worried about things that we don’t usually think of as violence. A life free of domination or external influence, however, does not exist.

Reason can be understood as man’s ability to think according to precise rules. Logic is one such set of rules: by using axioms and inference rules, we are able to generate vast arrays of valid statements. For instance, we can attempt to prove mathematical truths, or we can work out how to place furniture in a room, or the quickest way of carrying out five different errands in an afternoon.

Two essential functions of reason are finding solutions and validating solutions. In finding solutions, sometimes we apply reason as a search process, that is, we work through a number of combinations until we find one that works, or until we give up. By deduction we can reduce the size of the search space, and sometimes deduction will lead to a result without any search being necessary at all. In validating solutions, we might obtain the proposed solution from anywhere, possibly from outside reason itself, and then, again it is sometimes a search process: we may attempt to find contradictions that invalidate the proposed solution, and we do not always find them immediately. This would be validation by absence of contradictions, but we might also validate a solution affirmatively by using it in a problem. For instance, we can verify that 7 is the square root of 49 by computing 7*7, and it would be useless to verify it by testing that 7*7 does not equal any of the values 1,2,3…48,50,51,52… infinity.

Reasoning is a slow, tedious process, and it can only consider so many possible solutions in a given amount of time. But it is reliable, and the results of different pieces of reasoning can often be composed to yield a larger, consistent result. But it is clear that our minds have other ways of functioning as well, with other strengths and weaknesses. In particular, it seems that reasoning is essentially a reactive process. It reacts to a given problem with given constraints and rules of inference. But it seems to be unable to create. Creativity appears to always come from extralogical, extra-reasonable places. Creativity in the spontaneous sense of a child drawing a picture with crayons, or a novelist writing a book, or an orator using a particularly persuasive combination of words that captures a fleeting feeling, or a commuter taking a different route home from work, out of curiosity. The distinction is not always clear-cut: a decision like choosing the colour of a wallpaper could be done both using “principles” with which one reasons logically, or using a spur of the moment feeling about what is good. It is clear, though, that the two can interact very productively: often a complex mental activity needs a dialogue between reason and extra-reason, and not just in the sense that extra-reason produces a suggestion that reason validates. This seems to be the danger with excessive reliance on rationality and scientific skepticism, then – it risks shutting out the essential extralogical factor and reducing decision making to searching, or from another viewpoint, it risks invalidating the most powerful search heuristic of all.

It seems as if there is a parallel, of sorts, with modern democracy in this distinction. Democracy at the national level, too, is a reactive form of decision making today. It is true that groups of a small or moderate size sometimes can create things collectively, and when they do, it seems to be the case that the form of the group enables individuals to take turns in influencing the group and being responsible towards it: the individuals make serial contributions that layer on top of each other to form the collective contribution. But voters in a national democracy do not have a format that allows this process to take place across the entire group, and the scale is too great. Those who create proposals are smaller subgroups or elites, and the voters are reduced to playing one of the roles that reason can play: affirm or reject proposals. In fact, not even this, since they are typically not asked to affirm every proposal – they are able to stage a revolution if their discontent becomes tremendously large, and otherwise they only have the ability to voice rejection every four years or so. (The exceptional case where very large groups can create something collectively would be when they share a common sentiment very well, for instance in the event of a national crisis.)

The seat of creativity is ultimately in the individual, and not in the collective. When democracies create agendas, goals, projects and proposals, they are not acting democratically, but channeling individual elements within.

2. Skyscrapers in Ootemachi, Tokyo and the City, London. Buildings belonging mostly to banks and insurance companies. They appear, on some intuitive level, to have been there forever, though most of these buildings can now be built from the ground up in less than a year. It is hard to fathom how they could ever be destroyed, though the work could be done in a matter of months (?) with the right equipment.

3. What is permanent? Anything that we cannot perceive as changeable, we call permanent. But this is a linguistic and epistemological error. The inability to perceive something has led us to declare its absence.

4. The earth. 5.9736 x 10^24 kg of matter, likely fused into a planet about 4.54 billion years ago. The sun will enter a red giant phase in about 5 billion years and swallow or cause tremendous damage to it. The sun is also currently the source of all fossilised energy on earth and the energy used by most life forms on it.

5. A certain class of mathematical proofs often consist in converting facts from one basis (family of concepts) to another. Such proofs often have a hamburger-like structure: first the initial facts are rewritten into a larger, more complex formulation that suits both the assumptions and the conclusion, and then the complex formulation is collapsed in such a way that the desired results come out and the original formulation is lost. The “beef” in such a proof often consists in carrying out the correct rewriting process in the middle.

6. Facebook takes off and becomes enormously popular, in part because it facilitates, on a huge scale, something that human beings want to do naturally. Communication and the need to relate to crowds and individuals could be said to be universal among humans.

An incomplete version of the technology lattice, as suggested in this post, with human desires at the top and the resources available in the universe at the bottom.

7. We can imagine technology as a lattice-like system that mediates between the human being, on one hand, and the universe on the other. As a very rough sketch of fundamental human needs, we could list drives like communication, survival/expansion, power/safety and art. (In fact, an attempt to make some of these subordinate to others would constitute an ethical/philosophical system. Here we do not need such a distinction, and the one I have made is arbitrary and incomplete.) When we place our fundamental drives on one end, and the resources and conditions provided by the universe on another – elements and particles, physical laws and constants – we can begin to guess how new technologies arise and where they can have a place. The universe is a precondition of the earth, which is a precondition of animals and plants, which we currently eat. And food is currently a precondition of our survival. But we can imagine a future in which we are not dependent on the earth for food, having spread to other planets. We can imagine a future in which oil and nuclear power are no longer necessary as energy sources, because something else has taken their place. New possibilities entering the diagram like this adds more structure in the middle – more beef – but the motivating top level and the supplying bottom level do not change perceptibly. (Of course, if they did, beyond our perception, they could be made part of an even larger lattice with a new bottom and top configuration.)

8. Technology is a means to the establishment of permanence, and a re-encoding of human desires into reality.

9. New technologies arise constantly. But can this evolutionary process go on forever? Does the lattice converge towards a final state?

Various technologies have come out of academic experiments, volunteer work and government sponsored research to assist with encrypted communication. PGP/GnuPG and SSH are classic mainstays. Onion routing, as implemented in the TOR system, is an effective way of concealing the true origin and destination of data being sent around. Darknet systems like the I2P project aim to build a complete infrastructure for an entirely new kind of Internet, piggybacking on the old one but with anonymity and encryption as first class fundamental features.

I think we are only at the start of a coming era of political conflicts centered around communications technology, and that more and more issues will have to be ironed out in the coming years and decades. The stakes are high. On one hand control and political stability, on the other hand individual rights and democratic progress. This is not new. One thing that I think is potentially new and interesting though, is how mathematics and computer science ought to become increasingly sensitive and political in the coming years.

Today disciplines like genetics and stem cell research are considered controversial research areas by some people since they touch on the very foundations of what we think of as life. Weapons research of all kinds is considered controversial for obvious reasons, and the development of a weapon on the scale of nuclear bombs would completely shift the global power structure.  One fundamental building block of communications control is the ability to encrypt and to decrypt. These abilities are ultimately limited by the frontiers of mathematical research. Innovations such as the Skein hash function directly affect the cryptographic power balance.

Most of the popular varieties of encryption in use today can be overcome, given that the adversary has sufficient computing power and time. In addition, human beings often compromise their keys, trust the wrong certificates, or act in ways that diminish the security that has been gained. Encryption is not absolute unless the fact that something has been encrypted has been perfectly hidden. Rather, it is a matter of economics, of making it very cheap to encrypt data,and very expensive for unintended receivers to decrypt it.

It is not possible to freeze encryption at a certain arbitrary level, or to restrict the use of it. Computers are inherently general purpose, and software designed for one purpose can almost always be used for another. If the situation is driven to its extreme, we might identify two possible outcomes: either general purpose computers are forbidden or restricted, or uncontrolled, strongly encrypted communication becomes the norm. Christopher Kullenberg has touched on this topic in Swedish.

Those who would rather not see a society where widespread encryption is commonplace would perhaps still want to have what they see as desirable effects of computerisation. In their ideal world they would pick and choose what people can do with computers, in effect giving a list of permitted and prohibited uses. But this is not how general purpose computers work. They are programmable, and people can construct software that does what they want. If the introduction of non-authorised software somehow is prohibited, and all applications must be checked by some authority, applications can still usually be used for purposes they were not designed for. This generality of purpose simply cannot be removed from computers without making them useless – at least that is how it seems today. It seems that it would take a new fundamental model of computation that selectively prohibits certain uses is needed in order to make this happen. (In order to make sure that this kind of discovery is not put to use by the “other camp”, those of us who believe in an open society should try to find it, or somehow establish the fact that it cannot be constructed.)

Mathematics now stands ever more closely connected with political power. Mathematical advances can almost immediately increase or decrease the resistance to information flow (given that somebody incorporates the advances into usable software). The full consequences of this are something we have yet to see.

One of the first schools of thought he brings up is utilitarianism, whose central idea appears to be that the value of an action is placed in the consequences of that action, and not in anything else, such as the intention behind the action, or the idea that there are certain categories of actions that are definitely good or definitely evil. What causes the greatest happiness for the greatest number of people is good, simple as that. From these definitions a huge amount of difficulty follows immediately. For instance, is short-term happiness as good as long-term happiness? How long term is long term enough to be valuable? Is the pleasure of ignorant people as valuable as that of enlightened people? etc. But let’s leave all this aside and try to bring some notion of computability into the picture.

Assume that we accept that “the greatest happiness for the greatest number of people” is a good maxim, and we seek to achieve this. We must weigh the consequences of actions and choices to maximise this value. But can we always link a consequence to the action, or set of actions, that led to it? Causality in the world is a questionable idea since it is a form of inductive knowledge. Causality in formal systems and in the abstract seems valid, since it is a matter of definition, but causality in the empirical, in the observed, seems to always be a matter of correlation: if I observe first A and then B sufficiently many times, I will infer that A implies B, but I have no way of knowing that there are not also other preconditions of B happening (for instance, a hitherto invisible particle having a certain degree of flux). It seems that I cannot reliably learn what causes what, and then, how can I predict the consequences of my actions? Now, suddenly, we end up with an epistemological question, but let us leave this too aside for the time being. Perhaps epistemological uncertainty is inevitable.

I still want to do my best to achieve the greatest happiness for the greatest number of people, and I accept that my idea of what actions cause what consequences is probabilistic in nature. I have a set of rules, A1 => B1, A2 => B2… An => Bn which I trust to some extent and I want to make the best use of them. I have now ended up with a planning problem. I must identify a sequence of actions that maximises that happiness variable. But my brain has limited computational ability, and my plan must be complete by time t in order to be executable. Even for a simple problem description, the state space that planning algorithms must search becomes enormous, and identifying the plan, or a plan, that maximises the value is simply not feasible. Furthermore, billions of humans are planning concurrently, and their plans may interfere with each other. A true computational utilitarian system would treat all human individuals as a single system and find, in unison, the optimal sequence of actions for each one to undertake. This is an absurd notion.

This thought experiment aside, if we are utilitarianists, should we enlist the increased computing power that has recently come into being to help manage our lives? Can it be used to augment (presumably it can not supplant) human intuition for how to make rapid choices from huge amounts of data?

The global idea space is partitioned in various ways. One example would be peoples speaking different languages. English speakers all understand each other, Japanese speakers all understand each other, but there are relatively few people who speak Japanese and English very well. We can understand this situation in an abstract way as two large containers with a narrow passage connecting them.

Similar partitionings occur whenever there are groups of people that communicate a lot among themselves and less with people in other groups. For instance, there would be a partitioning between people who use the internet frequently and people who use it rarely (to some extent similar to a partitioning between young and old people). This partitioning is in fact orthogonal to the language partitioning, i.e. there is an English internet, a Japanese internet, an English non-internet, etc.

The partitioning of the space into containers has effects on the establishment of authorities and the growth of specialised entities inside the containers. The establishment of authorities is in some ways a Darwinist selection process. There can only be one highest authority on philosophy, on history, on art, on mathematics etc. that speaks one given language or acts inside a given container. Or for a more banal example: pop charts and TV programs. (Even though, inside the Anglosphere, each country may still have their own pop chart, they influence each other hugely.) If there are two contenders for the position of highest authority on art in a container, either they have to be isolated from each other somehow, or they must interact and resolve their conflict, either by subordination of one to the other, or by a refinement of their roles so that these do not conflict. As for the specialised entities, the larger the container is, the more space there is for highly niched ideas. This is in fact the “long tail” idea. The Internet is one of the biggest containers to date, and businesses such as Amazon have (or at least had) as their business model to sell not large numbers of a few popular items, but small numbers of a great many niched items. Such long tails can be nurtured by large containers. (In fact this is a consequence of the subordination/refinement when authority contenders have a conflict.)

We may also augment this picture with a directional graph of the flows between containers. For instance, ideas probably flow into Japan from the Anglosphere more rapidly than they flow in the reverse direction. Ideas flow into Sweden from the Anglosphere and from Japan but flow back out of Sweden relatively rarely. Once an idea has flowed into a space like Sweden or Japan from a larger space like the Anglosphere, though, the smaller space can act like a kind of pressure cooker or reactor that may develop, refine, or process the imported idea and possibly send a more interesting product back. A kind of refraction occurs.

In the early history of the internet, some people warned that the great danger of it is that everybody might eventually think the same thoughts, and that we would lose the diversity of ideas. This has turned out to be an unrealised fear, I think, at least as long as we still have different languages. But are languages not enough? Do we need to do more to create artificial partitionings? What is the optimal degree of partitioning, and can we concretely map the flows and containers with some degree of precision?

Much later, when I was a student in London, I was subject to budget constraints and went for the cheapest flight whenever possible. Accordingly I found myself flying with an Irish airline, Ryanair, quite a lot. This enterprise is marked by its grisly yellow and dark blue colour scheme and continuous experimentation in lowered flight standards, comfort and safety, all for the sake of lower prices. For a 1-2 hour flight between England and Sweden it was fully acceptable.

Recently I have been flying between Japan and Sweden quite a bit. The intercontinental flight can last more than ten hours, and takes on quite a different character from short flights. Some of the essential absurdities of any flight journey become increasingly difficult to ignore during this time period.

Firstly, there is the fact that the airplane that more than a hundred passengers ride in is a sealed off, highly fragile, mobile cross-section of society and a habitat for human beings. Airplanes need continuous replacement, draining and replenishment of food, waste, excrement, water, fuel and electricity. The air pressure and temperature inside the cabin are artificially maintained. The similarities with an imagined future biodome on the moon are not a few. What happens if an airplane has to land on a tiny island in the middle of the ocean and doesn’t have enough fuel to fly back, or there is some kind of technical problem? All of these buffered flows which the airplane must always replenish would be interrupted, and our very lives are hooked up to those flows.

In addition, hundreds of people are placed very close to each other for an extended period of time with minimal lateral separation (although there is some longitudinal separation in the form of seat rows). A certain neuroticism is provoked. We become hyper-aware of our neighbours and what they do, what they talk about, how they dress and what habits they have. We try our best not to notice. And this lattice, this packing of people, is surveyed from above by the panoptic eyes of the flight stewards and hostesses. Observation not only from above but also from peers becomes essential in maintaining order in a closed-off society where governmental violence cannot reach and the usual norms might easily be violated. Security breaches are to the greatest possible extent preempted by the pre-flight security theatre, and what remains of risk is contained by observation and observability effects.

This pressurised air and pressurised micro-society is spiced up, or muddled, slightly by the increasingly confused roles of the stewards and hostesses. In the jet set era, the air hostess was an object of attraction, an apple of the eyes of businessmen, an icon of liberty who had authority but no doubt also a certain intoxicating effect which helped to pacify. Today she is more clearly authoritarian, but the old role has not quite been erased from people’s minds. Something oedipal threatens to take place. Is this person who serves me food a nurse, a security guard, a mother as well as a possible lover? The neuroticism of the family extended into international airspace. All authority figures merged into one. Male stewards only slightly less confusing.

Fortunately airlines are very happy to serve up small doses of wine and beer to take the edge off the situation. Flying is absurd, but for the moment we have no other way of getting around.

The easiest technologies to understand on an intuitive-emotional basis seem to be those that involve physical processes. Objects rotating, moving, being lifted and displaced, compressed, crushed. Gases and liquids being sent around in conduits, mediating force and energy. In short, the technology that has its foundation in classical mechanics.

If these are easy to get a feel for, it would probably be in part because an understanding of mechanical processes has been of use to us throughout history, and also before the advent of civilisation. An intuitive understanding of things such as momentum, acceleration, gravity has no doubt benefited mankind and its ancestors for a very long time.

It gets trickier when we get to the more recent technologies. Take electricity to be an arbitrary watershed. We have no intuitive idea of what electricity is, apart from the fact we might be afraid of thunder. Electricity has to be taught through the abstract idea of electrons flowing in conduits, a bit like water in pipes (to name one of many images being used).

And then there’s analog and digital electronics, integrated circuits, semiconductors and so on, where intuition has long ago been left behind. We are forced to approach these things in a purely abstract domain.

Yet, when our Mp3 players, game consoles, mobile phones and computers do things for us, we are left with a sense of wonder. Our minds, always looking for stories and explanations, want to associate the impressive effects produced by these devices with some stimuli. With a steam engine, it’s easy to associate the energy with pressure, heat and motion, all of which are well understood on a low level. With a mobile phone, not so much. A lot of very abstract stories have to be used in order to reach anything that resembles an explanation, and still it doesn’t reach the essence of the device, which might be in its interplay between radio transceivers, sound codec chips, a display with a user interface and software to drive it, a central CPU, and so on, together with, of course, the network of physical antennas and their connectivity with other such networks. Is it too much to suppose that the human mind often stops short of the true explanation here? That we associate the effects produced by the device with what we can touch, smell, see and hear?

This is of course the point where many computer geeks worldwide start to feel a certain affection for the materials that make up the machines. Suppose that we are in the 1980′s. Green text on a black terminal background. A particular kind of fixed width font. The clicking of the keyboard. The dull grey plastic used to make the case. All of these things can acquire a lot of meaning that they don’t really have, because the users lack a window (physical and emotional) into the essence of the machine. The ultimate “disconnected machine”, to relate to my field, is software.

This brings up questions such as: how far can we as a species proceed with technology that we cannot understand instinctively, how can we teach such technology meaningfully and include it in democratic debate, and how can we use people’s tendencies to associate sensory stimuli with meaning and effects in a more meaningful way? – for instance, when we design hardware and software interfaces.

Flood-it, a color filling game. This version was made by Lab Pixies for the iPhone, but many others exist.

There’s a veritable torrent of little games constantly being released for the iPhone. One of the more likable ones is Flood-It, which I’ve been playing recently. The premise is extremely simple: you start off with a grid divided into squares of different, randomized colors. You are given a tool that works a bit like the bucket fill in a picture editor. At each turn, the player chooses a color to fill the grid with, starting from the upper left corner. The monochromatic area slowly grows, and the aim is to fill the entire grid with a single color within a limited number of turns.

A recent analysis showed that finding an optimal solution to games like Flood-It is a NP-hard problem. In addition, deciding whether the game can be solved in n steps for some n is NP-complete. The analysis relies on a reduction of Flood-It to an instance of the SCS problem (shortest common superstring). (It’s important to note that what is NP-complete is deciding whether a particular board can be solved in a certain number of steps, not solving the game with a bounded number of steps. This can be done in polynomial time.) For those who need a summary, ACM Communications had an excellent review of the state of the P/NP problem in September last year.

For a NP-hard problem H, there exists a polynomial time reduction of any problem in NP to H, meaning that if we can solve H in P-time, we can solve any problem in NP in P-time. Many optimization problems in society rely on approximate solutions to difficult problems: routing traffic, assembling DNA sequences from partial subsequences, mathematical theorem proving… On the hypothesis that evolution has turned people into efficient solvers of hard problems (i.e. we have good heuristics in our brains from birth and from experience), we ought to pay people to play these games on their phones, but map real problems into game instances, so that people effectively work while they’re playing. We ought to design games that act as front-ends for real combinatorial problems.

A computer game, as we understand it, can be defined as a very smooth learning curve, and if we only “play” very tricky instances of combinatorial problems, the game would probably present too much of a barrier to new players. So maybe the best way of executing this kind of scheme would be that a majority of all game instances do not represent real problems, but mere training or verification of already solved problems — but every once in a while, a real problem pops up. The player should still get paid though.

A double benefit would be blurring the line between work time and  play time, what is useful and what is useless — I think this line is often artificially constructed. Has technology ever before given us the possibility to literally turn work into play?

Acknowledgements. I am indebted to Christian Sommer for showing me the complexity analysis of Flood-it.

The Flood-It game, easy difficulty setting, with the player having made some progress.