The kinetics of an intelligence explosion - Superintelligence: Paths, Dangers, Strategies - Nick Bostrom

Superintelligence: Paths, Dangers, Strategies - Nick Bostrom (2014)

Chapter 4. The kinetics of an intelligence explosion

Once machines attain some form of human-equivalence in general reasoning ability, how long will it then be before they attain radical superintelligence? Will this be a slow, gradual, protracted transition? Or will it be sudden, explosive? This chapter analyzes the kinetics of the transition to superintelligence as a function of optimization power and system recalcitrance. We consider what we know or may reasonably surmise about the behavior of these two factors in the neighborhood of human-level general intelligence.

Timing and speed of the takeoff

Given that machines will eventually vastly exceed biology in general intelligence, but that machine cognition is currently vastly narrower than human cognition, one is led to wonder how quickly this usurpation will take place. The question we are asking here must be sharply distinguished from the question we considered in Chapter 1 about how far away we currently are from developing a machine with human-level general intelligence. Here the question is instead, if and when such a machine is developed, how long will it be from then until a machine becomes radically superintelligent? Note that one could think that it will take quite a long time until machines reach the human baseline, or one might be agnostic about how long that will take, and yet have a strong view that once this happens, the further ascent into strong superintelligence will be very rapid.

It can be helpful to think about these matters schematically, even though doing so involves temporarily ignoring some qualifications and complicating details. Consider, then, a diagram that plots the intellectual capability of the most advanced machine intelligence system as a function of time (Figure 7).

A horizontal line labeled “human baseline” represents the effective intellectual capabilities of a representative human adult with access to the information sources and technological aids currently available in developed countries. At present, the most advanced AI system is far below the human baseline on any reasonable metric of general intellectual ability. At some point in future, a machine might reach approximate parity with this human baseline (which we take to be fixed—anchored to the year 2014, say, even if the capabilities of human individuals should have increased in the intervening years): this would mark the onset of the takeoff. The capabilities of the system continue to grow, and at some later point the system reaches parity with the combined intellectual capability of all of humanity (again anchored to the present): what we may call the “civilization baseline”. Eventually, if the system’s abilities continue to grow, it attains “strong superintelligence”—a level of intelligence vastly greater than contemporary humanity’s combined intellectual wherewithal. The attainment of strong superintelligence marks the completion of the takeoff, though the system might continue to gain in capacity thereafter. Sometime during the takeoff phase, the system may pass a landmark which we can call “the crossover”, a point beyond which the system’s further improvement is mainly driven by the system’s own actions rather than by work performed upon it by others.1 (The possible existence of such a crossover will become important in the subsection on optimization power and explosivity, later in this chapter.)


Figure 7 Shape of the takeoff. It is important to distinguish between these questions: “Will a takeoff occur, and if so, when?” and “If and when a takeoff does occur, how steep will it be?” One might hold, for example, that it will be a very long time before a takeoff occurs, but that when it does it will proceed very quickly. Another relevant question (not illustrated in this figure) is, “How large a fraction of the world economy will participate in the takeoff?” These questions are related but distinct.

With this picture in mind, we can distinguish three classes of transition scenarios—scenarios in which systems progress from human-level intelligence to superintelligence—based on their steepness; that is to say, whether they represent a slow, fast, or moderate takeoff.


A slow takeoff is one that occurs over some long temporal interval, such as decades or centuries. Slow takeoff scenarios offer excellent opportunities for human political processes to adapt and respond. Different approaches can be tried and tested in sequence. New experts can be trained and credentialed. Grassroots campaigns can be mobilized by groups that feel they are being disadvantaged by unfolding developments. If it appears that new kinds of secure infrastructure or mass surveillance of AI researchers is needed, such systems could be developed and deployed. Nations fearing an AI arms race would have time to try to negotiate treaties and design enforcement mechanisms. Most preparations undertaken before onset of the slow takeoff would be rendered obsolete as better solutions would gradually become visible in the light of the dawning era.


A fast takeoff occurs over some short temporal interval, such as minutes, hours, or days. Fast takeoff scenarios offer scant opportunity for humans to deliberate. Nobody need even notice anything unusual before the game is already lost. In a fast takeoff scenario, humanity’s fate essentially depends on preparations previously put in place. At the slowest end of the fast takeoff scenario range, some simple human actions might be possible, analogous to flicking open the “nuclear suitcase”; but any such action would either be elementary or have been planned and pre-programmed in advance.


A moderate takeoff is one that occurs over some intermediary temporal interval, such as months or years. Moderate takeoff scenarios give humans some chance to respond but not much time to analyze the situation, to test different approaches, or to solve complicated coordination problems. There is not enough time to develop or deploy new systems (e.g. political systems, surveillance regimes, or computer network security protocols), but extant systems could be applied to the new challenge.

During a slow takeoff, there would be plenty of time for the news to get out. In a moderate takeoff, by contrast, it is possible that developments would be kept secret as they unfold. Knowledge might be restricted to a small group of insiders, as in a covert state-sponsored military research program. Commercial projects, small academic teams, and “nine hackers in a basement” outfits might also be clandestine—though, if the prospect of an intelligence explosion were “on the radar” of state intelligence agencies as a national security priority, then the most promising private projects would seem to have a good chance of being under surveillance. The host state (or a dominant foreign power) would then have the option of nationalizing or shutting down any project that showed signs of commencing takeoff. Fast takeoffs would happen so quickly that there would not be much time for word to get out or for anybody to mount a meaningful reaction if it did. But an outsider might intervene before the onset of the takeoff if they believed a particular project to be closing in on success.

Moderate takeoff scenarios could lead to geopolitical, social, and economic turbulence as individuals and groups jockey to position themselves to gain from the unfolding transformation. Such upheaval, should it occur, might impede efforts to orchestrate a well-composed response; alternatively, it might enable solutions more radical than calmer circumstances would permit. For instance, in a moderate takeoff scenario where cheap and capable emulations or other digital minds gradually flood labor markets over a period of years, one could imagine mass protests by laid-off workers pressuring governments to increase unemployment benefits or institute a living wage guarantee to all human citizens, or to levy special taxes or impose minimum wage requirements on employers who use emulation workers. In order for any relief derived from such policies to be more than fleeting, support for them would somehow have to be cemented into permanent power structures. Similar issues can arise if the takeoff is slow rather than moderate, but the disequilibrium and rapid change in moderate scenarios may present special opportunities for small groups to wield disproportionate influence.

It might appear to some readers that of these three types of scenario, the slow takeoff is the most probable, the moderate takeoff is less probable, and the fast takeoff is utterly implausible. It could seem fanciful to suppose that the world could be radically transformed and humanity deposed from its position as apex cogitator over the course of an hour or two. No change of such moment has ever occurred in human history, and its nearest parallels—the Agricultural and Industrial Revolutions—played out over much longer timescales (centuries to millennia in the former case, decades to centuries in the latter). So the base rate for the kind of transition entailed by a fast or medium takeoff scenario, in terms of the speed and magnitude of the postulated change, is zero: it lacks precedent outside myth and religion.2

Nevertheless, this chapter will present some reasons for thinking that the slow transition scenario is improbable. If and when a takeoff occurs, it will likely be explosive.

To begin to analyze the question of how fast the takeoff will be, we can conceive of the rate of increase in a system’s intelligence as a (monotonically increasing) function of two variables: the amount of “optimization power”, or quality-weighted design effort, that is being applied to increase the system’s intelligence, and the responsiveness of the system to the application of a given amount of such optimization power. We might term the inverse of responsiveness “recalcitrance”, and write:


Pending some specification of how to quantify intelligence, design effort, and recalcitrance, this expression is merely qualitative. But we can at least observe that a system’s intelligence will increase rapidly if either a lot of skilled effort is applied to the task of increasing its intelligence and the system’s intelligence is not too hard to increase or there is a non-trivial design effort and the system’s recalcitrance is low (or both). If we know how much design effort is going into improving a particular system, and the rate of improvement this effort produces, we could calculate the system’s recalcitrance.

Further, we can observe that the amount of optimization power devoted to improving some system’s performance varies between systems and over time. A system’s recalcitrance might also vary depending on how much the system has already been optimized. Often, the easiest improvements are made first, leading to diminishing returns (increasing recalcitrance) as low-hanging fruits are depleted. However, there can also be improvements that make further improvements easier, leading to improvement cascades. The process of solving a jigsaw puzzle starts out simple—it is easy to find the corners and the edges. Then recalcitrance goes up as subsequent pieces are harder to fit. But as the puzzle nears completion, the search space collapses and the process gets easier again.

To proceed in our inquiry, we must therefore analyze how recalcitrance and optimization power might vary in the critical time periods during the takeoff. This will occupy us over the next few pages.


Let us begin with recalcitrance. The outlook here depends on the type of the system under consideration. For completeness, we first cast a brief glance at the recalcitrance that would be encountered along paths to superintelligence that do not involve advanced machine intelligence. We find that recalcitrance along those paths appears to be fairly high. That done, we will turn to the main case, which is that the takeoff involves machine intelligence; and there we find that recalcitrance at the critical juncture seems low.

Non-machine intelligence paths

Cognitive enhancement via improvements in public health and diet has steeply diminishing returns.3 Big gains come from eliminating severe nutritional deficiencies, and the most severe deficiencies have already been largely eliminated in all but the poorest countries. Only girth is gained by increasing an already adequate diet. Education, too, is now probably subject to diminishing returns. The fraction of talented individuals in the world who lack access to quality education is still substantial, but declining.

Pharmacological enhancers might deliver some cognitive gains over the coming decades. But after the easiest fixes have been accomplished—perhaps sustainable increases in mental energy and ability to concentrate, along with better control over the rate of long-term memory consolidation—subsequent gains will be increasingly hard to come by. Unlike diet and public health approaches, however, improving cognition through smart drugs might get easier before it gets harder. The field of neuropharmacology still lacks much of the basic knowledge that would be needed to competently intervene in the healthy brain. Neglect of enhancement medicine as a legitimate area of research may be partially to blame for this current backwardness. If neuroscience and pharmacology continue to progress for a while longer without focusing on cognitive enhancement, then maybe there would be some relatively easy gains to be had when at last the development of nootropics becomes a serious priority.4

Genetic cognitive enhancement has a U-shaped recalcitrance profile similar to that of nootropics, but with larger potential gains. Recalcitrance starts out high while the only available method is selective breeding sustained over many generations, something that is obviously difficult to accomplish on a globally significant scale. Genetic enhancement will get easier as technology is developed for cheap and effective genetic testing and selection (and particularly when iterated embryo selection becomes feasible in humans). These new techniques will make it possible to tap the pool of existing human genetic variation for intelligence-enhancing alleles. As the best existing alleles get incorporated into genetic enhancement packages, however, further gains will get harder to come by. The need for more innovative approaches to genetic modification may then increase recalcitrance. There are limits to how quickly things can progress along the genetic enhancement path, most notably the fact that germline interventions are subject to an inevitable maturational lag: this strongly counteracts the possibility of a fast or moderate takeoff.5That embryo selection can only be applied in the context of in vitro fertilization will slow its rate of adoption: another limiting factor.

The recalcitrance along the brain-computer path seems initially very high. In the unlikely event that it somehow becomes easy to insert brain implants and to achieve high-level functional integration with the cortex, recalcitrance might plummet. In the long run, the difficulty of making progress along this path would be similar to that involved in improving emulations or AIs, since the bulk of the brain-computer system’s intelligence would eventually reside in the computer part.

The recalcitrance for making networks and organizations in general more efficient is high. A vast amount of effort is going into overcoming this recalcitrance, and the result is an annual improvement of humanity’s total capacity by perhaps no more than a couple of percent.6 Furthermore, shifts in the internal and external environment mean that organizations, even if efficient at one time, soon become ill-adapted to their new circumstances. Ongoing reform effort is thus required even just to prevent deterioration. A step change in the rate of gain in average organizational efficiency is perhaps conceivable, but it is hard to see how even the most radical scenario of this kind could produce anything faster than a slow takeoff, since organizations operated by humans are confined to work on human timescales. The Internet continues to be an exciting frontier with many opportunities for enhancing collective intelligence, with a recalcitrance that seems at the moment to be in the moderate range—progress is somewhat swift but a lot of effort is going into making this progress happen. It may be expected to increase as low-hanging fruits (such as search engines and email) are depleted.

Emulation and AI paths

The difficulty of advancing toward whole brain emulation is difficult to estimate. Yet we can point to a specific future milestone: the successful emulation of an insect brain. That milestone stands on a hill, and its conquest would bring into view much of the terrain ahead, allowing us to make a decent guess at the recalcitrance of scaling up the technology to human whole brain emulation. (A successful emulation of a small-mammal brain, such as that of a mouse, would give an even better vantage point that would allow the distance remaining to a human whole brain emulation to be estimated with a high degree of precision.) The path toward artificial intelligence, by contrast, may feature no such obvious milestone or early observation point. It is entirely possible that the quest for artificial intelligence will appear to be lost in dense jungle until an unexpected breakthrough reveals the finishing line in a clearing just a few short steps away.

Recall the distinction between these two questions: How hard is it to attain roughly human levels of cognitive ability? And how hard is it to get from there to superhuman levels? The first question is mainly relevant for predicting how long it will be before the onset of a takeoff. It is the second question that is key to assessing the shape of the takeoff, which is our aim here. And though it might be tempting to suppose that the step from human level to superhuman level must be the harder one—this step, after all, takes place “at a higher altitude” where capacity must be superadded to an already quite capable system—this would be a very unsafe assumption. It is quite possible that recalcitrance falls when a machine reaches human parity.

Consider first whole brain emulation. The difficulties involved in creating the first human emulation are of a quite different kind from those involved in enhancing an existing emulation. Creating a first emulation involves huge technological challenges, particularly in regard to developing the requisite scanning and image interpretation capabilities. This step might also require considerable amounts of physical capital—an industrial-scale machine park with hundreds of high-throughput scanning machines is not implausible. By contrast, enhancing the quality of an existing emulation involves tweaking algorithms and data structures: essentially a software problem, and one that could turn out to be much easier than perfecting the imaging technology needed to create the original template. Programmers could easily experiment with tricks like increasing the neuron count in different cortical areas to see how it affects performance.7 They also could work on code optimization and on finding simpler computational models that preserve the essential functionality of individual neurons or small networks of neurons. If the last technological prerequisite to fall into place is either scanning or translation, with computing power being relatively abundant, then not much attention might have been given during the development phase to implementational efficiency, and easy opportunities for computational efficiency savings might be available. (More fundamental architectural reorganization might also be possible, but that takes us off the emulation path and into AI territory.)

Another way to improve the code base once the first emulation has been produced is to scan additional brains with different or superior skills and talents. Productivity growth would also occur as a consequence of adapting organizational structures and workflows to the unique attributes of digital minds. Since there is no precedent in the human economy of a worker who can be literally copied, reset, run at different speeds, and so forth, managers of the first emulation cohort would find plenty of room for innovation in managerial practices.

After initially plummeting when human whole brain emulation becomes possible, recalcitrance may rise again. Sooner or later, the most glaring implementational inefficiencies will have been optimized away, the most promising algorithmic variations will have been tested, and the easiest opportunities for organizational innovation will have been exploited. The template library will have expanded so that acquiring more brain scans would add little benefit over working with existing templates. Since a template can be multiplied, each copy can be individually trained in a different field, and this can be done at electronic speed, it might be that the number of brains that would need to be scanned in order to capture most of the potential economic gains is small. Possibly a single brain would suffice.

Another potential cause of escalating recalcitrance is the possibility that emulations or their biological supporters will organize to support regulations restricting the use of emulation workers, limiting emulation copying, prohibiting certain kinds of experimentation with digital minds, instituting workers’ rights and a minimum wage for emulations, and so forth. It is equally possible, however, that political developments would go in the opposite direction, contributing to a fall in recalcitrance. This might happen if initial restraint in the use of emulation labor gives way to unfettered exploitation as competition heats up and the economic and strategic costs of occupying the moral high ground become clear.

As for artificial intelligence (non-emulation machine intelligence), the difficulty of lifting a system from human-level to superhuman intelligence by means of algorithmic improvements depends on the attributes of the particular system. Different architectures might have very different recalcitrance.

In some situations, recalcitrance could be extremely low. For example, if human-level AI is delayed because one key insight long eludes programmers, then when the final breakthrough occurs, the AI might leapfrog from below to radically above human level without even touching the intermediary rungs. Another situation in which recalcitrance could turn out to be extremely low is that of an AI system that can achieve intelligent capability via two different modes of processing. To illustrate this possibility, suppose an AI is composed of two subsystems, one possessing domain-specific problem-solving techniques, the other possessing general-purpose reasoning ability. It could then be the case that while the second subsystem remains below a certain capacity threshold, it contributes nothing to the system’s overall performance, because the solutions it generates are always inferior to those generated by the domain-specific subsystem. Suppose now that a small amount of optimization power is applied to the general-purpose subsystem and that this produces a brisk rise in the capacity of that subsystem. At first, we observe no increase in the overall system’s performance, indicating that recalcitrance is high. Then, once the capacity of the general-purpose subsystem crosses the threshold where its solutions start to beat those of the domain-specific subsystem, the overall system’s performance suddenly begins to improve at the same brisk pace as the general-purpose subsystem, even as the amount of optimization power applied stays constant: the system’s recalcitrance has plummeted.

It is also possible that our natural tendency to view intelligence from an anthropocentric perspective will lead us to underestimate improvements in sub-human systems, and thus to overestimate recalcitrance. Eliezer Yudkowsky, an AI theorist who has written extensively on the future of machine intelligence, puts the point as follows:

AI might make an apparently sharp jump in intelligence purely as the result of anthropomorphism, the human tendency to think of “village idiot” and “Einstein” as the extreme ends of the intelligence scale, instead of nearly indistinguishable points on the scale of minds-in-general. Everything dumber than a dumb human may appear to us as simply “dumb”. One imagines the “AI arrow” creeping steadily up the scale of intelligence, moving past mice and chimpanzees, with AIs still remaining “dumb” because AIs cannot speak fluent language or write science papers, and then the AI arrow crosses the tiny gap from infra-idiot to ultra-Einstein in the course of one month or some similarly short period.8 (See Fig. 8.)

The upshot of these several considerations is that it is difficult to predict how hard it will be to make algorithmic improvements in the first AI that reaches a roughly human level of general intelligence. There are at least some possible circumstances in which algorithm-recalcitrance is low. But even if algorithm-recalcitrance is very high, this would not preclude the overall recalcitrance of the AI in question from being low. For it might be easy to increase the intelligence of the system in other ways than by improving its algorithms. There are two other factors that can be improved: content and hardware.

First, consider content improvements. By “content” we here mean those parts of a system’s software assets that do not make up its core algorithmic architecture. Content might include, for example, databases of stored percepts, specialized skills libraries, and inventories of declarative knowledge. For many kinds of system, the distinction between algorithmic architecture and content is very unsharp; nevertheless, it will serve as a rough-and-ready way of pointing to one potentially important source of capability gains in a machine intelligence. An alternative way of expressing much the same idea is by saying that a system’s intellectual problem-solving capacity can be enhanced not only by making the system cleverer but also by expanding what the system knows.


Figure 8 A less anthropomorphic scale? The gap between a dumb and a clever person may appear large from an anthropocentric perspective, yet in a less parochial view the two have nearly indistinguishable minds.9 It will almost certainly prove harder and take longer to build a machine intelligence that has a general level of smartness comparable to that of a village idiot than to improve such a system so that it becomes much smarter than any human.

Consider a contemporary AI system such as TextRunner (a research project at the University of Washington) or IBM’s Watson (the system that won the Jeopardy! quiz show). These systems can extract certain pieces of semantic information by analyzing text. Although these systems do not understand what they read in the same sense or to the same extent as a human does, they can nevertheless extract significant amounts of information from natural language and use that information to make simple inferences and answer questions. They can also learn from experience, building up more extensive representations of a concept as they encounter additional instances of its use. They are designed to operate for much of the time in unsupervised mode (i.e. to learn hidden structure in unlabeled data in the absence of error or reward signal, without human guidance) and to be fast and scalable. TextRunner, for instance, works with a corpus of 500 million web pages.10

Now imagine a remote descendant of such a system that has acquired the ability to read with as much understanding as a human ten-year-old but with a reading speed similar to that of TextRunner. (This is probably an AI-complete problem.) So we are imagining a system that thinks much faster and has much better memory than a human adult, but knows much less, and perhaps the net effect of this is that the system is roughly human-equivalent in its general problem-solving ability. But its content recalcitrance is very low—low enough to precipitate a takeoff. Within a few weeks, the system has read and mastered all the content contained in the Library of Congress. Now the system knows much more than any human being and thinks vastly faster: it has become (at least) weakly superintelligent.

A system might thus greatly boost its effective intellectual capability by absorbing pre-produced content accumulated through centuries of human science and civilization: for instance, by reading through the Internet. If an AI reaches human level without previously having had access to this material or without having been able to digest it, then the AI’s overall recalcitrance will be low even if it is hard to improve its algorithmic architecture.

Content-recalcitrance is a relevant concept for emulations, too. A high-speed emulation has an advantage not only because it can complete the same tasks as biological humans more quickly, but also because it can accumulate more timely content, such as task-relevant skills and expertise. In order to tap the full potential of fast content accumulation, however, a system needs to have a correspondingly large memory capacity. There is little point in reading an entire library if you have forgotten all about the aardvark by the time you get to the abalone. While an AI system is likely to have adequate memory capacity, emulations would inherit some of the capacity limitations of their human templates. They may therefore need architectural enhancements in order to become capable of unbounded learning.

So far we have considered the recalcitrance of architecture and of content—that is, how difficult it would be to improve the software of a machine intelligence that has reached human parity. Now let us look at a third way of boosting the performance of machine intelligence: improving its hardware. What would be the recalcitrance for hardware-driven improvements?

Starting with intelligent software (emulation or AI) one can amplify collective intelligence simply by using additional computers to run more instances of the program.11 One could also amplify speed intelligence by moving the program to faster computers. Depending on the degree to which the program lends itself to parallelization, speed intelligence could also be amplified by running the program on more processors. This is likely to be feasible for emulations, which have a highly parallelized architecture; but many AI programs, too, have important subroutines that can benefit from massive parallelization. Amplifying quality intelligence by increasing computing power might also be possible, but that case is less straightforward.12

The recalcitrance for amplifying collective or speed intelligence (and possibly quality intelligence) in a system with human-level software is therefore likely to be low. The only difficulty involved is gaining access to additional computing power. There are several ways for a system to expand its hardware base, each relevant over a different timescale.

In the short term, computing power should scale roughly linearly with funding: twice the funding buys twice the number of computers, enabling twice as many instances of the software to be run simultaneously. The emergence of cloud computing services gives a project the option to scale up its computational resources without even having to wait for new computers to be delivered and installed, though concerns over secrecy might favor the use of in-house computers. (In certain scenarios, computing power could also be obtained by other means, such as by commandeering botnets.13) Just how easy it would be to scale the system by a given factor depends on how much computing power the initial system uses. A system that initially runs on a PC could be scaled by a factor of thousands for a mere million dollars. A program that runs on a supercomputer would be far more expensive to scale.

In the slightly longer term, the cost of acquiring additional hardware may be driven up as a growing portion of the world’s installed capacity is being used to run digital minds. For instance, in a competitive market-based emulation scenario, the cost of running one additional copy of an emulation should rise to be roughly equal to the income generated by the marginal copy, as investors bid up the price for existing computing infrastructure to match the return they expect from their investment (though if only one project has mastered the technology it might gain a degree of monopsony power in the computing power market and therefore pay a lower price).

Over a somewhat longer timescale, the supply of computing power will grow as new capacity is installed. A demand spike would spur production in existing semiconductor foundries and stimulate the construction of new plants. (A one-off performance boost, perhaps amounting to one or two orders of magnitude, might also be obtainable by using customized microprocessors.14) Above all, the rising wave of technology improvements will pour increasing volumes of computational power into the turbines of the thinking machines. Historically, the rate of improvement of computing technology has been described by the famous Moore’s law, which in one of its variations states that computing power per dollar doubles every 18 months or so.15 Although one cannot bank on this rate of improvement continuing up to the development of human-level machine intelligence, yet until fundamental physical limits are reached there will remain room for advances in computing technology.

There are thus reasons to expect that hardware recalcitrance will not be very high. Purchasing more computing power for the system once it proves its mettle by attaining human-level intelligence might easily add several orders of magnitude of computing power (depending on how hardware-frugal the project was before expansion). Chip customization might add one or two orders of magnitude. Other means of expanding the hardware base, such as building more factories and advancing the frontier of computing technology, take longer—normally several years, though this lag would be radically compressed once machine superintelligence revolutionizes manufacturing and technology development.

In summary, we can talk about the likelihood of a hardware overhang: when human-level software is created, enough computing power may already be available to run vast numbers of copies at great speed. Software recalcitrance, as discussed above, is harder to assess but might be even lower than hardware recalcitrance. In particular, there may be content overhang in the form of pre-made content (e.g. the Internet) that becomes available to a system once it reaches human parity. Algorithm overhang—pre-designed algorithmic enhancements—is also possible but perhaps less likely. Software improvements (whether in algorithms or content) might offer orders of magnitude of potential performance gains that could be fairly easily accessed once a digital mind attains human parity, on top of the performance gains attainable by using more or better hardware.

Optimization power and explosivity

Having examined the question of recalcitrance we must now turn to the other half of our schematic equation, optimization power. To recall: Rate of change in Intelligence = Optimization power/Recalcitrance. As reflected in this schematic, a fast takeoff does not require that recalcitrance during the transition phase be low. A fast takeoff could also result if recalcitrance is constant or even moderately increasing, provided the optimization power being applied to improving the system’s performance grows sufficiently rapidly. As we shall now see, there are good grounds for thinking that the applied optimization power will increase during the transition, at least in the absence of a deliberate measures to prevent this from happening.

We can distinguish two phases. The first phase begins with the onset of the takeoff, when the system reaches the human baseline for individual intelligence. As the system’s capability continues to increase, it might use some or all of that capability to improve itself (or to design a successor system—which, for present purposes, comes to the same thing). However, most of the optimization power applied to the system still comes from outside the system, either from the work of programmers and engineers employed within the project or from such work done by the rest of the world as can be appropriated and used by the project.16 If this phase drags out for any significant period of time, we can expect the amount of optimization power applied to the system to grow. Inputs both from inside the project and from the outside world are likely to increase as the promise of the chosen approach becomes manifest. Researchers may work harder, more researchers may be recruited, and more computing power may be purchased to expedite progress. The increase could be especially dramatic if the development of human-level machine intelligence takes the world by surprise, in which case what was previously a small research project might suddenly become the focus of intense research and development efforts around the world (though some of those efforts might be channeled into competing projects).

A second growth phase will begin if at some point the system has acquired so much capability that most of the optimization power exerted on it comes from the system itself (marked by the variable level labeled “crossover” in Figure 7). This fundamentally changes the dynamic, because any increase in the system’s capability now translates into a proportional increase in the amount of optimization power being applied to its further improvement. If recalcitrance remains constant, this feedback dynamic produces exponential growth (see Box 4). The doubling constant depends on the scenario but might be extremely short—mere seconds in some scenarios—if growth is occurring at electronic speeds, which might happen as a result of algorithmic improvements or the exploitation of an overhang of content or hardware.17 Growth that is driven by physical construction, such as the production of new computers or manufacturing equipment, would require a somewhat longer timescale (but still one that might be very short compared with the current growth rate of the world economy).

It is thus likely that the applied optimization power will increase during the transition: initially because humans try harder to improve a machine intelligence that is showing spectacular promise, later because the machine intelligence itself becomes capable of driving further progress at digital speeds. This would create a real possibility of a fast or medium takeoff even if recalcitrance were constant or slightly increasing around the human baseline.18Yet we saw in the previous subsection that there are factors that could lead to a big drop in recalcitrance around the human baseline level of capability. These factors include, for example, the possibility of rapid hardware expansion once a working software mind has been attained; the possibility of algorithmic improvements; the possibility of scanning additional brains (in the case of whole brain emulation); and the possibility of rapidly incorporating vast amounts of content by digesting the Internet (in the case of artificial intelligence).24

Box 4 On the kinetics of an intelligence explosion

We can write the rate of change in intelligence as the ratio between the optimization power applied to the system and the system’s recalcitrance:


The amount of optimization power acting on a system is the sum of whatever optimization power the system itself contributes and the optimization power exerted from without. For example, a seed AI might be improved through a combination of its own efforts and the efforts of a human programming team, and perhaps also the efforts of the wider global community of researchers making continuous advances in the semiconductor industry, computer science, and related fields:19


A seed AI starts out with very limited cognitive capacities. At the outset, therefore, Image is small.20 What about Image and Image? There are cases in which a single project has more relevant capability than the rest of the world combined—the Manhattan project, for instance, brought a very large fraction of the world’s best physicists to Los Alamos to work on the atomic bomb. More commonly, any one project contains only a small fraction of the world’s total relevant research capability. But even when the outside world has a greater total amount of relevant research capability than any one project, Imagemay nevertheless exceed Image, since much of the outside world’s capability is not be focused on the particular system in question. If a project begins to look promising—which will happen when a system passes the human baseline if not before—it might attract additional investment, increasing Image. If the project’s accomplishments are public, Image might also rise as the progress inspires greater interest in machine intelligence generally and as various powers scramble to get in on the game. During the transition phase, therefore, total optimization power applied to improving a cognitive system is likely to increase as the capability of the system increases.21

As the system’s capabilities grow, there may come a point at which the optimization power generated by the system itself starts to dominate the optimization power applied to it from outside (across all significant dimensions of improvement):


This crossover is significant because beyond this point, further improvement to the system’s capabilities contributes strongly to increasing the total optimization power applied to improving the system. We thereby enter a regime of strong recursive self-improvement. This leads to explosive growth of the system’s capability under a fairly wide range of different shapes of the recalcitrance curve.

To illustrate, consider first a scenario in which recalcitrance is constant, so that the rate of increase in an AI’s intelligence is equal to the optimization power being applied. Assume that all the optimization power that is applied comes from the AI itself and that the AI applies all its intelligence to the task of amplifying its own intelligence, so that Image = I.22 We then have


Solving this simple differential equation yields the exponential function


But recalcitrance being constant is a rather special case. Recalcitrance might well decline around the human baseline, due to one or more of the factors mentioned in the previous subsection, and remain low around the crossover and some distance beyond (perhaps until the system eventually approaches fundamental physical limits). For example, suppose that the optimization power applied to the system is roughly constant (i.e. Image + Imagec) prior to the system becoming capable of contributing substantially to its own design, and that this leads to the system doubling in capacity every 18 months. (This would be roughly in line with historical improvement rates from Moore’s law combined with software advances.23) This rate of improvement, if achieved by means of roughly constant optimization power, entails recalcitrance declining as the inverse of the system power:


If recalcitrance continues to fall along this hyperbolic pattern, then when the AI reaches the crossover point the total amount of optimization power applied to improving the AI has doubled. We then have


The next doubling occurs 7.5 months later. Within 17.9 months, the system’s capacity has grown a thousandfold, thus obtaining speed superintelligence (Figure 9).

This particular growth trajectory has a positive singularity at t = 18 months. In reality, the assumption that recalcitrance is constant would cease to hold as the system began to approach the physical limits to information processing, if not sooner.

These two scenarios are intended for illustration only; many other trajectories are possible, depending on the shape of the recalcitrance curve. The claim is simply that the strong feedback loop that sets in around the crossover point tends strongly to make the takeoff faster than it would otherwise have been.


Figure 9 One simple model of an intelligence explosion.

These observations notwithstanding, the shape of the recalcitrance curve in the relevant region is not yet well characterized. In particular, it is unclear how difficult it would be to improve the software quality of a human-level emulation or AI. The difficulty of expanding the hardware power available to a system is also not clear. Whereas today it would be relatively easy to increase the computing power available to a small project by spending a thousand times more on computing power or by waiting a few years for the price of computers to fall, it is possible that the first machine intelligence to reach the human baseline will result from a large project involving pricey supercomputers, which cannot be cheaply scaled, and that Moore’s law will by then have expired. For these reasons, although a fast or medium takeoff looks more likely, the possibility of a slow takeoff cannot be excluded.25