Tuesday, October 27, 2009


Are You Living In a Computer Simulation?

Nick Bostrom (born Niklas Boström in 1973) is a Swedish philosopher at the University of Oxford known for his work on existential risk and the Anthropic principle. He holds a PhD from the London School of Economics (2000). He is currently the director of The Future of Humanity Institute at Oxford University.

In addition to his writing for academic and popular press, Bostrom makes frequent media appearances in which he talks about transhumanism-related topics such as cloning, artificial intelligence, superintelligence, mind uploading, cryonics, nanotechnology, and the simulation argument.

In 1998, Bostrom co-founded (with David Pearce) the World Transhumanist Association (which has since changed its name to Humanity+). In 2004, he co-founded (with James Hughes) the Institute for Ethics and Emerging Technologies. Bostrom currently serves as the Chair of both organizations. In 2005 he was appointed Director of the newly created Oxford Future of Humanity Institute. Bostrom is the 2009 finalist in philosophy for and potential first ever recipient of the Eugene R. Gannon Award for the Continued Pursuit of Human Advancement.

Are You Living In a Computer Simulation?

Department of Philosophy, Oxford University


Many works of science fiction as well as some forecasts by serious technologists and futurologists predict that enormous amounts of computing power will be available in the future. Let us suppose for a moment that these predictions are correct. One thing that later generations might do with their super-powerful computers is run detailed simulations of their forebears or of people like their forebears. Because their computers would be so powerful, they could run a great many such simulations. Suppose that these simulated people are conscious (as they would be if the simulations were sufficiently fine-grained and if a certain quite widely accepted position in the philosophy of mind is correct). Then it could be the case that the vast majority of minds like ours do not belong to the original race but rather to people simulated by the advanced descendants of an original race. It is then possible to argue that, if this were the case, we would be rational to think that we are likely among the simulated minds rather than among the original biological ones. Therefore, if we don’t think that we are currently living in a computer simulation, we are not entitled to believe that we will have descendants who will run lots of such simulations of their forebears. That is the basic idea. The rest of this paper will spell it out more carefully.

Apart from the interest this thesis may hold for those who are engaged in futuristic speculation, there are also more purely theoretical rewards. The argument provides a stimulus for formulating some methodological and metaphysical questions, and it suggests naturalistic analogies to certain traditional religious conceptions, which some may find amusing or thought-provoking.

The structure of the paper is as follows. First, we formulate an assumption that we need to import from the philosophy of mind in order to get the argument started. Second, we consider some empirical reasons for thinking that running vastly many simulations of human minds would be within the capability of a future civilization that has developed many of those technologies that can already be shown to be compatible with known physical laws and engineering constraints. This part is not philosophically necessary but it provides an incentive for paying attention to the rest. Then follows the core of the argument, which makes use of some simple probability theory, and a section providing support for a weak indifference principle that the argument employs. Lastly, we discuss some interpretations of the disjunction, mentioned in the abstract, that forms the conclusion of the simulation argument.


A common assumption in the philosophy of mind is that of substrate-independence. The idea is that mental states can supervene on any of a broad class of physical substrates. Provided a system implements the right sort of computational structures and processes, it can be associated with conscious experiences. It is nor an essential property of consciousness that it is implemented on carbon-based biological neural networks inside a cranium: silicon-based processors inside a computer could in principle do the trick as well.

Arguments for this thesis have been given in the literature, and although it is not entirely uncontroversial, we shall here take it as a given.

The argument we shall present does not, however, depend on any very strong version of functionalism or computationalism. For example, we need not assume that the thesis of substrate-independence is necessarily true (either analytically or metaphysically) – just that, in fact, a computer running a suitable program would be conscious. Moreover, we need not assume that in order to create a mind on a computer it would be sufficient to program it in such a way that it behaves like a human in all situations, including passing the Turing test etc. We need only the weaker assumption that it would suffice for the generation of subjective experiences that the computational processes of a human brain are structurally replicated in suitably fine-grained detail, such as on the level of individual synapses. This attenuated version of substrate-independence is quite widely accepted.

Neurotransmitters, nerve growth factors, and other chemicals that are smaller than a synapse clearly play a role in human cognition and learning. The substrate-independence thesis is not that the effects of these chemicals are small or irrelevant, but rather that they affect subjective experience only via their direct or indirect influence on computational activities. For example, if there can be no difference in subjective experience without there also being a difference in synaptic discharges, then the requisite detail of simulation is at the synaptic level (or higher).


At our current stage of technological development, we have neither sufficiently powerful hardware nor the requisite software to create conscious minds in computers. But persuasive arguments have been given to the effect that if technological progress continues unabated then these shortcomings will eventually be overcome. Some authors argue that this stage may be only a few decades away. Yet present purposes require no assumptions about the time-scale. The simulation argument works equally well for those who think that it will take hundreds of thousands of years to reach a “posthuman” stage of civilization, where humankind has acquired most of the technological capabilities that one can currently show to be consistent with physical laws and with material and energy constraints.

Such a mature stage of technological development will make it possible to convert planets and other astronomical resources into enormously powerful computers. It is currently hard to be confident in any upper bound on the computing power that may be available to posthuman civilizations. As we are still lacking a “theory of everything”, we cannot rule out the possibility that novel physical phenomena, not allowed for in current physical theories, may be utilized to transcend those constraints that in our current understanding impose theoretical limits on the information processing attainable in a given lump of matter. We can with much greater confidence establish lower bounds on posthuman computation, by assuming only mechanisms that are already understood. For example, Eric Drexler has outlined a design for a system the size of a sugar cube (excluding cooling and power supply) that would perform 10^21 instructions per second. Another author gives a rough estimate of 10^42 operations per second for a computer with a mass on order of a large planet. (If we could create quantum computers, or learn to build computers out of nuclear matter or plasma, we could push closer to the theoretical limits. Seth Lloyd calculates an upper bound for a 1 kg computer of 5*10^50 logical operations per second carried out on ~10^31 bits. However, it suffices for our purposes to use the more conservative estimate that presupposes only currently known design-principles.)The amount of computing power needed to emulate a human mind can likewise be roughly estimated. One estimate, based on how computationally expensive it is to replicate the functionality of a piece of nervous tissue that we have already understood and whose functionality has been replicated in silico, contrast enhancement in the retina, yields a figure of ~10^14 operations per second for the entire human brain. An alternative estimate, based the number of synapses in the brain and their firing frequency, gives a figure of ~10^16-10^17 operations per second. Conceivably, even more could be required if we want to simulate in detail the internal workings of synapses and dendritic trees. However, it is likely that the human central nervous system has a high degree of redundancy on the mircoscale to compensate for the unreliability and noisiness of its neuronal components. One would therefore expect a substantial efficiency gain when using more reliable and versatile non-biological processors.

Memory seems to be a no more stringent constraint than processing power. Moreover, since the maximum human sensory bandwidth is ~10^8 bits per second, simulating all sensory events incurs a negligible cost compared to simulating the cortical activity. We can therefore use the processing power required to simulate the central nervous system as an estimate of the total computational cost of simulating a human mind.

If the environment is included in the simulation, this will require additional computing power – how much depends on the scope and granularity of the simulation. Simulating the entire universe down to the quantum level is obviously infeasible, unless radically new physics is discovered. But in order to get a realistic simulation of human experience, much less is needed – only whatever is required to ensure that the simulated humans, interacting in normal human ways with their simulated environment, don’t notice any irregularities. The microscopic structure of the inside of the Earth can be safely omitted. Distant astronomical objects can have highly compressed representations: verisimilitude need extend to the narrow band of properties that we can observe from our planet or solar system spacecraft. On the surface of Earth, macroscopic objects in inhabited areas may need to be continuously simulated, but microscopic phenomena could likely be filled in ad hoc. What you see through an electron microscope needs to look unsuspicious, but you usually have no way of confirming its coherence with unobserved parts of the microscopic world. Exceptions arise when we deliberately design systems to harness unobserved microscopic phenomena that operate in accordance with known principles to get results that we are able to independently verify. The paradigmatic case of this is a computer. The simulation may therefore need to include a continuous representation of computers down to the level of individual logic elements. This presents no problem, since our current computing power is negligible by posthuman standards.

Moreover, a posthuman simulator would have enough computing power to keep track of the detailed belief-states in all human brains at all times. Therefore, when it saw that a human was about to make an observation of the microscopic world, it could fill in sufficient detail in the simulation in the appropriate domain on an as-needed basis. Should any error occur, the director could easily edit the states of any brains that have become aware of an anomaly before it spoils the simulation. Alternatively, the director could skip back a few seconds and rerun the simulation in a way that avoids the problem.

It thus seems plausible that the main computational cost in creating simulations that are indistinguishable from physical reality for human minds in the simulation resides in simulating organic brains down to the neuronal or sub-neuronal level. While it is not possible to get a very exact estimate of the cost of a realistic simulation of human history, we can use ~10^33 - 10^36 operations as a rough estimate. As we gain more experience with virtual reality, we will get a better grasp of the computational requirements for making such worlds appear realistic to their visitors. But in any case, even if our estimate is off by several orders of magnitude, this does not matter much for our argument. We noted that a rough approximation of the computational power of a planetary-mass computer is 10^42 operations per second, and that assumes only already known nanotechnological designs, which are probably far from optimal. A single such a computer could simulate the entire mental history of humankind (call this an ancestor-simulation) by using less than one millionth of its processing power for one second. A posthuman civilization may eventually build an astronomical number of such computers. We can conclude that the computing power available to a posthuman civilization is sufficient to run a huge number of ancestor-simulations even it allocates only a minute fraction of its resources to that purpose. We can draw this conclusion even while leaving a substantial margin of error in all our estimates.
· Posthuman civilizations would have enough computing power to run hugely many ancestor-simulations even while using only a tiny fraction of their resources for that purpose.


The basic idea of this paper can be expressed roughly as follows: If there were a substantial chance that our civilization will ever get to the posthuman stage and run many ancestor-simulations, then how come you are not living in such a simulation?

We shall develop this idea into a rigorous argument. Let us introduce the following notation:

The actual fraction of all observers with human-type experiences that live in simulations is then

Writing f1 for the fraction of posthuman civilizations that are interested in running ancestor-simulations (or that contain at least some individuals who are interested in that and have sufficient resources to run a significant number of such simulations), and N1 for the average number of ancestor-simulations run by such interested civilizations, we have
and thus:
Because of the immense computing power of posthuman civilizations, N1 is extremely large, as we saw in the previous section. By inspecting (*) we can then see that at least one of the following three propositions must be true:


We can take a further step and conclude that conditional on the truth of (3), one’s credence in the hypothesis that one is in a simulation should be close to unity. More generally, if we knew that a fraction x of all observers with human-type experiences live in simulations, and we don’t have any information that indicate that our own particular experiences are any more or less likely than other human-type experiences to have been implemented in vivo rather than in machina, then our credence that we are in a simulation should equal x:

This step is sanctioned by a very weak indifference principle. Let us distinguish two cases. The first case, which is the easiest, is where all the minds in question are like your own in the sense that they are exactly qualitatively identical to yours: they have exactly the same information and the same experiences that you have. The second case is where the minds are “like” each other only in the loose sense of being the sort of minds that are typical of human creatures, but they are qualitatively distinct from one another and each has a distinct set of experiences. I maintain that even in the latter case, where the minds are qualitatively different, the simulation argument still works, provided that you have no information that bears on the question of which of the various minds are simulated and which are implemented biologically.

A detailed defense of a stronger principle, which implies the above stance for both cases as trivial special instances, has been given in the literature. Space does not permit a recapitulation of that defense here, but we can bring out one of the underlying intuitions by bringing to our attention to an analogous situation of a more familiar kind. Suppose that x% of the population has a certain genetic sequence S within the part of their DNA commonly designated as “junk DNA”. Suppose, further, that there are no manifestations of S (short of what would turn up in a gene assay) and that there are no known correlations between having S and any observable characteristic. Then, quite clearly, unless you have had your DNA sequenced, it is rational to assign a credence of x% to the hypothesis that you have S. And this is so quite irrespective of the fact that the people who have S have qualitatively different minds and experiences from the people who don’t have S. (They are different simply because all humans have different experiences from one another, not because of any known link between S and what kind of experiences one has.)

The same reasoning holds if S is not the property of having a certain genetic sequence but instead the property of being in a simulation, assuming only that we have no information that enables us to predict any differences between the experiences of simulated minds and those of the original biological minds.

It should be stressed that the bland indifference principle expressed by (#) prescribes indifference only between hypotheses about which observer you are, when you have no information about which of these observers you are. It does not in general prescribe indifference between hypotheses when you lack specific information about which of the hypotheses is true. In contrast to Laplacean and other more ambitious principles of indifference, it is therefore immune to Bertrand’s paradox and similar predicaments that tend to plague indifference principles of unrestricted scope.

Readers familiar with the Doomsday argument may worry that the bland principle of indifference invoked here is the same assumption that is responsible for getting the Doomsday argument off the ground, and that the counterintuitiveness of some of the implications of the latter incriminates or casts doubt on the validity of the former. This is not so. The Doomsday argument rests on a much stronger and more controversial premiss, namely that one should reason as if one were a random sample from the set of all people who will ever have lived (past, present, and future) even though we know that we are living in the early twenty-first century rather than at some point in the distant past or the future. The bland indifference principle, by contrast, applies only to cases where we have no information about which group of people we belong to.

If betting odds provide some guidance to rational belief, it may also be worth to ponder that if everybody were to place a bet on whether they are in a simulation or not, then if people use the bland principle of indifference, and consequently place their money on being in a simulation if they know that that’s where almost all people are, then almost everyone will win their bets. If they bet on not being in a simulation, then almost everyone will lose. It seems better that the bland indifference principle be heeded.

Further, one can consider a sequence of possible situations in which an increasing fraction of all people live in simulations: 98%, 99%, 99.9%, 99.9999%, and so on. As one approaches the limiting case in which everybody is in a simulation (from which one can deductively infer that one is in a simulation oneself), it is plausible to require that the credence one assigns to being in a simulation gradually approach the limiting case of complete certainty in a matching manner.


The possibility represented by proposition (1) is fairly straightforward. If (1) is true, then humankind will almost certainly fail to reach a posthuman level; for virtually no species at our level of development become posthuman, and it is hard to see any justification for thinking that our own species will be especially privileged or protected from future disasters. Conditional on (1), therefore, we must give a high credence to DOOM, the hypothesis that humankind will go extinct before reaching a posthuman level:

One can imagine hypothetical situations were we have such evidence as would trump knowledge of fp. For example, if we discovered that we were about to be hit by a giant meteor, this might suggest that we had been exceptionally unlucky. We could then assign a credence to DOOM larger than our expectation of the fraction of human-level civilizations that fail to reach posthumanity. In the actual case, however, we seem to lack evidence for thinking that we are special in this regard, for better or worse.

Proposition (1) doesn’t by itself imply that we are likely to go extinct soon, only that we are unlikely to reach a posthuman stage. This possibility is compatible with us remaining at, or somewhat above, our current level of technological development for a long time before going extinct. Another way for (1) to be true is if it is likely that technological civilization will collapse. Primitive human societies might then remain on Earth indefinitely.

There are many ways in which humanity could become extinct before reaching posthumanity. Perhaps the most natural interpretation of (1) is that we are likely to go extinct as a result of the development of some powerful but dangerous technology. One candidate is molecular nanotechnology, which in its mature stage would enable the construction of self-replicating nanobots capable of feeding on dirt and organic matter – a kind of mechanical bacteria. Such nanobots, designed for malicious ends, could cause the extinction of all life on our planet.

The second alternative in the simulation argument’s conclusion is that the fraction of posthuman civilizations that are interested in running ancestor-simulation is negligibly small. In order for (2) to be true, there must be a strong convergence among the courses of advanced civilizations. If the number of ancestor-simulations created by the interested civilizations is extremely large, the rarity of such civilizations must be correspondingly extreme. Virtually no posthuman civilizations decide to use their resources to run large numbers of ancestor-simulations. Furthermore, virtually all posthuman civilizations lack individuals who have sufficient resources and interest to run ancestor-simulations; or else they have reliably enforced laws that prevent such individuals from acting on their desires.

What force could bring about such convergence? One can speculate that advanced civilizations all develop along a trajectory that leads to the recognition of an ethical prohibition against running ancestor-simulations because of the suffering that is inflicted on the inhabitants of the simulation. However, from our present point of view, it is not clear that creating a human race is immoral. On the contrary, we tend to view the existence of our race as constituting a great ethical value. Moreover, convergence on an ethical view of the immorality of running ancestor-simulations is not enough: it must be combined with convergence on a civilization-wide social structure that enables activities considered immoral to be effectively banned.Another possible convergence point is that almost all individual posthumans in virtually all posthuman civilizations develop in a direction where they lose their desires to run ancestor-simulations. This would require significant changes to the motivations driving their human predecessors, for there are certainly many humans who would like to run ancestor-simulations if they could afford to do so. But perhaps many of our human desires will be regarded as silly by anyone who becomes a posthuman. Maybe the scientific value of ancestor-simulations to a posthuman civilization is negligible (which is not too implausible given its unfathomable intellectual superiority), and maybe posthumans regard recreational activities as merely a very inefficient way of getting pleasure – which can be obtained much more cheaply by direct stimulation of the brain’s reward centers. One conclusion that follows from (2) is that posthuman societies will be very different from human societies: they will not contain relatively wealthy independent agents who have the full gamut of human-like desires and are free to act on them.

The possibility expressed by alternative (3) is the conceptually most intriguing one. If we are living in a simulation, then the cosmos that we are observing is just a tiny piece of the totality of physical existence. The physics in the universe where the computer is situated that is running the simulation may or may not resemble the physics of the world that we observe. While the world we see is in some sense “real”, it is not located at the fundamental level of reality.

It may be possible for simulated civilizations to become posthuman. They may then run their own ancestor-simulations on powerful computers they build in their simulated universe. Such computers would be “virtual machines”, a familiar concept in computer science. (Java script web-applets, for instance, run on a virtual machine – a simulated computer – inside your desktop.) Virtual machines can be stacked: it’s possible to simulate a machine simulating another machine, and so on, in arbitrarily many steps of iteration. If we do go on to create our own ancestor-simulations, this would be strong evidence against (1) and (2), and we would therefore have to conclude that we live in a simulation. Moreover, we would have to suspect that the posthumans running our simulation are themselves simulated beings; and their creators, in turn, may also be simulated beings.

Reality may thus contain many levels. Even if it is necessary for the hierarchy to bottom out at some stage – the metaphysical status of this claim is somewhat obscure – there may be room for a large number of levels of reality, and the number could be increasing over time. (One consideration that counts against the multi-level hypothesis is that the computational cost for the basement-level simulators would be very great. Simulating even a single posthuman civilization might be prohibitively expensive. If so, then we should expect our simulation to be terminated when we are about to become posthuman.)

Although all the elements of such a system can be naturalistic, even physical, it is possible to draw some loose analogies with religious conceptions of the world. In some ways, the posthumans running a simulation are like gods in relation to the people inhabiting the simulation: the posthumans created the world we see; they are of superior intelligence; they are “omnipotent” in the sense that they can interfere in the workings of our world even in ways that violate its physical laws; and they are “omniscient” in the sense that they can monitor everything that happens. However, all the demigods except those at the fundamental level of reality are subject to sanctions by the more powerful gods living at lower levels.

Further rumination on these themes could climax in a naturalistic theogony that would study the structure of this hierarchy, and the constraints imposed on its inhabitants by the possibility that their actions on their own level may affect the treatment they receive from dwellers of deeper levels. For example, if nobody can be sure that they are at the basement-level, then everybody would have to consider the possibility that their actions will be rewarded or punished, based perhaps on moral criteria, by their simulators. An afterlife would be a real possibility. Because of this fundamental uncertainty, even the basement civilization may have a reason to behave ethically. The fact that it has such a reason for moral behavior would of course add to everybody else’s reason for behaving morally, and so on, in truly virtuous circle. One might get a kind of universal ethical imperative, which it would be in everybody’s self-interest to obey, as it were “from nowhere”.

In addition to ancestor-simulations, one may also consider the possibility of more selective simulations that include only a small group of humans or a single individual. The rest of humanity would then be zombies or “shadow-people” – humans simulated only at a level sufficient for the fully simulated people not to notice anything suspicious. It is not clear how much cheaper shadow-people would be to simulate than real people. It is not even obvious that it is possible for an entity to behave indistinguishably from a real human and yet lack conscious experience. Even if there are such selective simulations, you should not think that you are in one of them unless you think they are much more numerous than complete simulations. There would have to be about 100 billion times as many “me-simulations” (simulations of the life of only a single mind) as there are ancestor-simulations in order for most simulated persons to be in me-simulations.

There is also the possibility of simulators abridging certain parts of the mental lives of simulated beings and giving them false memories of the sort of experiences that they would typically have had during the omitted interval. If so, one can consider the following (farfetched) solution to the problem of evil: that there is no suffering in the world and all memories of suffering are illusions. Of course, this hypothesis can be seriously entertained only at those times when you are not currently suffering.

Supposing we live in a simulation, what are the implications for us humans? The foregoing remarks notwithstanding, the implications are not all that radical. Our best guide to how our posthuman creators have chosen to set up our world is the standard empirical study of the universe we see. The revisions to most parts of our belief networks would be rather slight and subtle – in proportion to our lack of confidence in our ability to understand the ways of posthumans. Properly understood, therefore, the truth of (3) should have no tendency to make us “go crazy” or to prevent us from going about our business and making plans and predictions for tomorrow. The chief empirical importance of (3) at the current time seems to lie in its role in the tripartite conclusion established above. We may hope that (3) is true since that would decrease the probability of (1), although if computational constraints make it likely that simulators would terminate a simulation before it reaches a posthuman level, then out best hope would be that (2) is true.

If we learn more about posthuman motivations and resource constraints, maybe as a result of developing towards becoming posthumans ourselves, then the hypothesis that we are simulated will come to have a much richer set of empirical implications.


A technologically mature “posthuman” civilization would have enormous computing power. Based on this empirical fact, the simulation argument shows that at least one of the following propositions is true: (1) The fraction of human-level civilizations that reach a posthuman stage is very close to zero; (2) The fraction of posthuman civilizations that are interested in running ancestor-simulations is very close to zero; (3) The fraction of all people with our kind of experiences that are living in a simulation is very close to one.

If (1) is true, then we will almost certainly go extinct before reaching posthumanity. If (2) is true, then there must be a strong convergence among the courses of advanced civilizations so that virtually none contains any relatively wealthy individuals who desire to run ancestor-simulations and are free to do so. If (3) is true, then we almost certainly live in a simulation. In the dark forest of our current ignorance, it seems sensible to apportion one’s credence roughly evenly between (1), (2), and (3).

Unless we are now living in a simulation, our descendants will almost certainly never run an ancestor-simulation.

From: http://www.simulation-argument.com/simulation.html

Saturday, October 24, 2009



Gödel, Escher, Bach: An Eternal Golden Braid (commonly GEB) is a Pulitzer Prize-winning book by Douglas Hofstadter, described as "a metaphorical fugue on minds and machines in the spirit of Lewis Carroll”.

On its surface, GEB examines logician Kurt Gödel, artist M. C. Escher and composer Johann Sebastian Bach, discussing common themes in their work and lives. At a deeper level, the book is a detailed and subtle exposition of concepts fundamental to mathematics, symmetry, and intelligence.

Through illustration and analysis, the book discusses how self-reference and formal rules allow systems to acquire meaning despite being made of "meaningless" elements. It also discusses what it means to communicate, how knowledge can be represented and stored, the methods and limitations of symbolic representation, and even the fundamental notion of "meaning" itself.

In response to confusion over the book´s theme, Hofstadter has emphasized that GEB is not about mathematics, art, and music but rather about how cognition and thinking emerge from well-hidden neurological mechanisms. In the book, he presents an analogy about how the individual neurons of the brain coordinate to create a unified sense of a coherent mind by comparing it to the social organization displayed in a colony of ants.


GEB takes the form of an interweaving of various narratives. The main chapters alternate with dialogues between imaginary characters, inspired by Lewis Carroll's "What the Tortoise Said to Achilles", in which Achilles and the Tortoise discuss a paradox related to modus ponens. Hofstadter bases the other dialogues on this one, introducing characters such as a Crab, a Genie, and others. These narratives frequently dip into self-reference and metafiction.

Word play also features prominently in the work. Puns are occasionally used to connect ideas, such as "the Magnificrab, Indeed" with Bach's Magnificat in D; " SHRDLU, Toy of Man's Designing" with Bach's Jesu, Joy of Man´s Desiring; and "Typographical Number Theory", or "TNT", which inevitably reacts explosively when it attempts to make statements about itself. One Dialogue contains a story about a genie (from the Arabic "Djinn") and various "tonics" (of both the liquid and musical varieties), which is of course entitled "Djinn and Tonic".

One dialogue in the book is written in the form of a crab canon, in which every line before the midpoint corresponds to an identical line past the midpoint. The conversation still makes sense due to uses of common phrases which can be used as either greetings or farewells ("Good day") and the positioning of lines which, upon close inspection, double as an answer to a question in the next line.


GEB contains many instances where objects and ideas speak about or refer back to themselves (cf. recursion and self-reference). For instance, TNT is an illustration of Gödel´s incompleteness theorem. There is also a phonograph which destroys itself by playing a record entitled "I Cannot Be Played on Record Player X" (this being an analogy to Gödel's incompleteness theorem), an examination of canon form in music, and a discussion of Escher's lithograph of two hands drawing each other. To describe such self-referencing objects, Hofstadter coins the term "strange loop", a concept he examines in more depth in his follow-up book I Am a Strange Loop.

To escape many of the logical contradictions brought about by these self-referencing objects, Hofstadter discusses Zen Koans. He attempts to show the reader how to perceive reality outside the normal confines of their own experience and embrace such paradoxical questions by rejecting the premise — a strategy also called “unasking”.

Call stacks are also discussed in GEB, as one dialogue describes the adventures of Achilles and the Tortoise as they make use of "pushing" and "popping" tonics. Entering a picture in a book would count as "pushing", entering a picture in a book within a picture in a book would have caused a double "pushing", and "popping" refers to an exit back to the previous layer of reality. The Tortoise humorously remarks that a friend of his (a weasel) performed a "popping" while in their current state of reality and has never been heard from since; the implied question is, "Did the friend simply cease to exist, or has the friend achieved a higher state of reality?" Also, since the reader is "pushed" into the world of Tortoise and Achilles, would the friend have ascended to the same level of reality in which the readers of GEB reside? Subsequent sections discuss the basic tenets of logic, self-referring statements, ("typeless") systems, and even programming.

One puzzle (in the dialogue "Aria with Diverse Variations") is a speculation concerning an author who writes a book and chooses to end the story without actually stopping the text. That an author cannot make a sudden ending (with regard to the story) come as a surprise, when the fact that there are only a few pages left in the book is obvious to the reader. Such an author might wrap up the main point, and then continue writing, but drop clues to the reader that the end has already passed, such as wandering and unfocused prose, misstatements, or contradictions.


The book is filled with puzzles. An example of this is the chapter entitled "Contracrostipunctus", which combines the words acrostic and contrapunctus (counterpoint). In a dialogue between Achilles and the Tortoise, the author hints that there is a contrapuntal acrostic in the chapter that refers both to the author (Hofstadter) and Bach. This can be found by taking the first word of each paragraph, to reveal: Hofstadter's Contracrostipunctus Acrostically Backwards Spells "J. S. Bach". This is only the acrostic. The counterpoint acrostic is found by taking the first letters of the acrostic (in bold) and reading them backwards to get "J. S. Bach" (as the acrostic itself claims).

Art of fugue(Contrapunctus XIV)


Although Hofstadter claims the idea of translating his book "never crossed [his] mind" when he was writing it, when approached with the idea by his publisher he was "very excited about seeing [the] book in other languages, especially … French". He knew, however, that "there were a million issues to consider" when translating, since the book relies not only on word-play but "structural puns" as well—writing where the form and content of the work mirror each other (such as the "Crab Canon" dialogue, which reads almost exactly the same forwards as backwards).

Hofstadter gives one example of translation trouble in the paragraph "Mr. Tortoise, Meet Madame Tortue", saying translators "instantly ran headlong into the conflict between the feminine gender of the French noun tortue and the masculinity of my character, the Tortoise". Hofstadter decided to translate the French character as "Madame Tortue", and the Italian version as "signorina Tartaruga". Because of other troubles translators might have retaining the meaning of the book, Hofstadter "painstakingly went through every last sentence of GEB, annotating a copy for translators into any language that might be targeted".

Translation also gave Hofstadter a way to add new meaning and puns. For instance, in Chinese, the subtitle is not a translation of an Eternal Golden Braid, but a seemingly unrelated phrase Jí Yì Bì (集异璧, literally "collection of exotic jades") which is homophonic to GEB in Chinese. Some material regarding this interplay is to be found in Hofstadter's later book Le Ton beau de marot, which is mainly about translation.

BlooP and FlooP

BLooP and FLooP are simple programming languages designed by Douglas Hofstadter to illustrate a point in his book Gödel, Escher, Bach. BLooP is a non-Turing-complete programming language whose only control flow structure is a bounded loop. This language can only express primitive recursive functions. FLooP is identical except that it supports unbounded loops; it is a Turing-complete language. These can be regarded as primitive models of computation.

BLooP examples

Note: The only variables are output (the return value of the procedure) and cell(i) (an infinite array of integers). The only operators are ⇐ (assignment), + (addition), × (multiplication), < (less-than), > (greater-than) and = (equals).

Factorial function:

Subtraction function (this is not a built-in operation):

From Wikipedia

Saturday, October 17, 2009

Henry Markram


Henry Markram, Project Director of the Blue Brain Project, Director of the Center for Neuroscience & Technology and co-Director of EPFL's Brain Mind Institute, obtained his B.Sc. (Hons) from Cape Town University, South Africa under the supervision of Rodney Douglas and his Ph.D from the Weizmann Institute of Science, Israel, under the supervision of Menahem Segal. During his PhD he discovered a link between acetylcholine and memory mechanisms by showing that acetylcholine modulates the primary receptor linked to synaptic plasticity.

He went to the USA as a Fulbright Scholar at the National Institutes of Health (NIH), where he studied ion channels on synaptic vesicles. He then went as a Minerva Fellow to the Laboratory of Bert Sakmann at the Max Planck Institute, Heidelberg, Germany, where he discovered calcium transients in dendrites evoked by sub-threshold activity, and by single action potentials propagating back into dendrites. He also began studying the connectivity between neurons, describing in great detail how layer 5 pyramidal neurons are interconnected.

He was the first to alter the precise millisecond relative timing of single pre- and post-synaptic action potentials to reveal a highly precise learning mechanism operating between neurons -- now reproduced in many brain regions and known as spike timing-dependent synaptic plasticity (STDP). These experiments were carried out in 1993, four years before publication. Although there were some correlation-sensitive findings before, this was the first study that manipulated single pre- and post-synaptic spike times to monitor the effect of synaptic changes.

He was appointed assistant professor at the Weizmann Institute for Science, Israel, where he started systematically dissecting out the neocortical column. He discovered that synaptic learning can also involve a change in synaptic dynamics (called redistribution of synaptic efficacy) rather than merely changing the strengths of connections. He also revealed a spectrum of new principles governing neocortical microcircuit structure, function, and emergent dynamics. Based on the emergent dynamics of the neocortical microcircuit he and Wolfgang Maass developed the theory of liquid computing, or high entropy computing.

In 2002 he moved to EPFL as full professor and founder/director of the Brain Mind Institute and Director of the Center for Neuroscience and Technology. At the BMI, in the Laboratory for Neural Microcircuitry, Markram has continued to unravel the blueprint of the neocortical column, building state-of-the-art tools to carry out multi-neuron patch clamp recordings combined with laser and electrical stimulation as well as multi-site electrical recording ,chemical imaging and gene expression. Markram has received numerous awards and published over 75 papers.

About the Blue Brain Project

The cerebral cortex, the convoluted "grey matter" that makes up 80% of the human brain, is responsible for our ability to remember, think, reflect, empathize, communicate, adapt to new situations and plan for the future. The cortex first appeared in mammals, and it has a fundamentally simple repetitive structure that is the same across all mammalian species.

The brain is populated with billions of neurons, each connected to thousands of its neighbors by dendrites and axons, a kind of biological "wiring". The brain processes information by sending electrical signals from neuron to neuron along these wires. In the cortex, neurons are organized into basic functional units, cylindrical volumes 0.5 mm wide by 2 mm high, each containing about 10,000 neurons that are connected in an intricate but consistent way. These units operate much like microcircuits in a computer. This microcircuit, known as the neocortical column (NCC), is repeated millions of times across the cortex. The difference between the brain of a mouse and the brain of a human is basically just volume - humans have many more neocortical columns and thus neurons than mice.

This structure lends itself to a systematic modeling approach. And indeed, the first step of the Blue Brain project is to re-create this fundamental microcircuit, down to the level of biologically accurate individual neurons. The microcircuit can then be used in simulations.

What the Blue Brain Project is not

The Blue Brain Project is an attempt to reverse engineer the brain, to explore how it functions and to serve as a tool for neuroscientists and medical researchers. It is not an attempt to create a brain. It is not an artificial intelligence project. Although we may one day achieve insights into the basic nature of intelligence and consciousness using this tool, the Blue Brain Project is focused on creating a physiological simulation for biomedical applications.

Building the microcircuit

Modeling Neurons

Neurons are not all alike - they come in a variety of complex shapes. The precise shape and structure of a neuron influences its electrical properties and connectivity with other neurons. A neuron's electrical properties are determined to a large extent by a variety of ion channels distributed in varying densities throughout the cell's membrane. Scientists have been collecting data on neuron morphology and electrical behavior of the juvenile rat in the laboratory for many years, and this data is used as the basis for a model that is run on the Blue Gene to recreate each of the 10,000 neurons in the NCC.

Modeling connections

To model the neocortical column, it is essential to understand the composition, density and distribution of the numerous cortical cell types. Each class of cells is present in specific layers of the column. The precise density of each cell type and the volume of the space it occupies provides essential information for cell positioning and constructing the foundation of the cortical circuit. Each neuron is connected to thousands of its neighbors at points where their dendrites or axons touch, known as synapses. In a column with 10,000 neurons, this translates into trillions of possible connections. The Blue Gene is used in this extremely computationally intensive calculation to fix the synapse locations, "jiggling" individual neurons in 3D space to find the optimal connection scenario.

Modeling the column

The result of all these calculations is a re-creation, at the cellular level, of the neocortical column, the basic microcircuit of the brain. In this case, it's the cortical column of a juvenile rat. This is the only biologically accurate replica to date of the NCC - the neurons are biologically realistic and their connectivity is optimized. This would be impossible without the huge computational capacity of the Blue Gene. A model of the NCC was completed at the end of 2006.
In November, 2007, The Blue Brain Project officially announced the conclusion of Phase I of the project, with three specific acheivements:

1. A new modeling framework for automatic, on-demand construction of neural circuits built from biological data

2. A new simulation and calibration process that automatically and systematically analyzes the biological accuracy and consistency of each revision of the model

3. The first cellular-level neocortical column model built entirely from biological data that can now serve as a key tool for simulation-based research

Simulating the microcircuit

Once the microcircuit is built, the exciting work of making the circuit function can begin. All the 8192 processors of the Blue Gene are pressed into service, in a massively parallel computation solving the complex mathematical equations that govern the electrical activity in each neuron when a stimulus is applied. As the electrical impulse travels from neuron to neuron, the results are communicated via inter-processor communication (MPI). Currently, the time required to simulate the circuit is about two orders of magnitude larger than the actual biological time simulated. The Blue Brain team is working to streamline the computation so that the circuit can function in real time - meaning that 1 second of activity can be modeled in one second.

Interpreting the results

Running the Blue Brain simulation generates huge amounts of data. Analyses of individual neurons must be repeated thousands of times. And analyses dealing with the network activity must deal with data that easily reaches hundreds of gigabytes per second of simulation. Using massively parallel computers the data can be analyzed where it is created (server-side analysis for experimental data, online analysis during simulation).

Given the geometric complexity of the column, a visual exploration of the circuit is an important part of the analysis. Mapping the simulation data onto the morphology is invaluable for an immediate verification of single cell activity as well as network phenomena. Architects at EPFL have worked with the Blue Brain developers to design a visualization interface that translates the Blue Gene data into a 3D visual representation of the column. A different supercomputer is used for this computationally intensive task. The visualization of the neurons' shapes is a challenging task given the fact that a column of 10,000 neurons rendered in high quality mesh (see picture) accounts for essentially 1 billion triangles for which about 100GB of management data is required. Simulation data with a resolution of electrical compartments for each neuron accounts for another 150GB. As the electrical impulse travels through the column, neurons light up and change color as they become electrically active. See some clips of the column in action.

A visual interface makes it possible to quickly identify areas of interest that can then be studied more extensively using further simulations. A visual representation can also be used to compare the simulation results with experiments that show electrical activity in the brain. This calibration - comparing the functioning of the Blue Brain circuit with experiment, improving and fine-tuning it - is the second stage of the Blue Brain project, expected to be complete by the end of 2007.

What's next for the Blue Brain Project?

Phase I marks the completion of a proof-of-principle simulation-based research process that has resulted in a cellular-level model of the neocortical column. We have achieved biological fidelity such that the model itself now serves as a primary tool for evaluating the consistency and relevance of neurobiological data, while providing guidance for new experimental efforts. These new data will serve to further refine the neocortical column model. The assembled process allows neuroscientists to investigate scientific questions by integrating the available experimental data and evaluating hypotheses of network dynamics and neural function.

The completion of phase I provides the basis now for increasing the resolution of the models down to the molecular level and expanding the size of the models towards the whole brains of mammals.

In the future, information from the molecular and genetic level will be added to the algorithms that generate the individual neurons and their connections, and thus this level of detail will be reflected in the circuit's construction. The simulations can be used to explore what happens when this molecular or genetic information is altered -- situations such as a genetic variation in particular neurotransmitters, or what happens when the molecular environment is altered via drugs.

The project will continue to expand and will necessarily involve additional scientists and research groups from around the world.