# On the Impossibility of Superintelligent Rubik’s Cube Solvers
Abstract: This paper argues that superintelligent machines will never be able to solve a Rubik’s Cube as well as a human being can. Several fallacious arguments that are commonly employed to downplay AI risks are satirized.
Table of Contents:
Introduction
The Irreducible Complexity of Rubik’s Cubes
The Meaninglessness of “Human-Level Cube Solving”
The Universality of Human Cube Solving Skills
The Psychological Origins of Belief in Superintelligent Cube Solvers
Humans and Machines Together Will Always Be Better Cube Solvers Than Machines Alone
The Hard Problem of Cube Twisting
Quantum Mechanics and Gödel’s Incompleteness Theorem
Conclusion
In recent years, a number of prominent computer scientists and AI researchers have predicted the advent of superintelligent machines that can solve problems orders of magnitude better than humans (Bostrom2014). Some have gone so far as to suggest these machines may one day exceed human-level performance on tasks as varied as calculus, chess, and even solving Rubik’s Cubes (Vinge1993).
However, when one examines these predictions closely, it becomes apparent that they are fundamentally misguided. In this paper, we present several distinct arguments that machines will never be able to attain superintelligence, at least when it comes to the specific task of solving Rubik’s Cubes. We show that not only is it implausible that machines will ever exceed humans at speedcubing, but in fact strictly impossible.
We begin, in Section 2, by considering the irreducible complexity of Rubik’s Cubes. Just as evolutionary biologists have had difficulty explaining the origins of traits like the human eye, Rubik’s Cubes confound analysis and appear designed in an almost miraculous way. This strongly suggests that they can never be truly mastered by machines.
Section 3 reveals issues with the very notion of “human-level cube solving.” Section 4 explains why humans possess universal cube solving abilities. Section 5 examines the evolutionary psychology underlying belief in superintelligent solvers. Section 6 notes that human-machine teams will always outperform machines alone. Section 7 grapples with the hard problem of cube twisting. Finally, Section 8 combines insights from quantum mechanics and Gödel’s incompleteness theorem to deliver the coup de grâce.
The overall conclusion is clear: just as the arguments we once told ourselves about supersized machines were mere fantasies, so too are visions of superintelligent cube solvers. It is time to stop waiting for an artificial intelligence to solve all our problems, and to embrace our own capabilities as the ultimate solvers.
At first glance, a Rubik’s Cube appears to be a simple toy. However, decades of research by mathematicians and engineers have revealed it to be astonishingly complex (Slocum2010).
Consider the fact that there are 43,252,003,274,489,856,000 possible permutations of a standard 3×3 Rubik’s Cube. Humans are only able to solve them quickly through elaborate step-by-step algorithms and cognitive shortcuts. The underlying reasons we are able to grasp these algorithms remain poorly understood (Arneson et al 2015).
Attempts to model the mental processes behind human cube solving have run aground on the problem of irreducible complexity. The human visual system, hand-eye coordination, spatial reasoning ability, working memory, and general intelligence all seem inextricably intertwined when it comes to cube solving skill (Gray2017). Tweaking any one parameter in isolation appears fruitless.
This strongly suggests that the stunning performance exhibited by human speedcubers depends on emergent properties of the complete package. It is unlikely engineers will ever be able to artificially replicate such emergence. Thus, superintelligent Rubik’s Cube solvers will remain out of reach.
When superintelligent cube solving machines are discussed, there is an assumption that terms like “human-level performance” have some clear meaning. In reality, this notion quickly falls apart under scrutiny.
What exactly constitutes human-level Rubik’s Cube solving? The average amateur takes minutes to solve one side, while competitive speedcubers can fully solve a cube in under 10 seconds. Does human-level performance mean matching an enthusiastic hobbyist, or the world record holders?
Even once a particular human benchmark is chosen, there are many metrics along which performance could be compared. Speed of solving a single cube? Ability to solve multiple scrambled cubes over the course of an hour? Fewest moves required on average? Ability to solve the cube blindfolded, with feet, or in non-standard environmental conditions?
Without specificity on the metrics and human reference class, statements about machines exceeding human-level cube solving are not well-defined. They should be considered vague speculation rather than serious predictions. Superintelligent Rubik’s Cube solvers are no more coherent a notion than supersized machines.
A further reason why predictions of superintelligent Rubik’s Cube solvers are misguided is that humans already possess universal cube solving abilities. No matter what puzzle is presented, a person has the potential to solve it.
This is because humans have the unique capacity to improve their cube solving skills through practice. An average human can become an expert solver through nothing more than determination and effort. Over the course of a few months, an amateur can learn finger tricks, memorize algorithms, and develop an intuitive understanding of cube mechanics (Demaine et al 2013).
In contrast, an AI system is limited by its initial programming. It may be able to achieve human-level performance on some narrow metric, but it cannot fundamentally expand its own cube solving capacities. A human equipped with a cube and a dream has no limits.
For this reason, it makes little sense to imagine that a machine could ever fully master the Rubik’s Cube in a way that transcends human capabilities. We already are the ultimate cube solvers by virtue of our adaptability. No sum of algorithms and heuristics could match a dedicated speedcuber.
The field of evolutionary psychology can provide insight into why some otherwise rational people have fallen prey to believing in the possibility of superintelligent Rubik’s Cube solvers. This belief likely stems from innate human cognitive biases that served an adaptive purpose in our evolutionary past.
In the ancestral environment, validating one’s intellectual abilities against others was key to attaining status within a tribe. Those who could demonstrate superior problem solving were more likely to attract mates and secure resources (Pinker2002). As a result, humans evolved a competitive instinct along with a fear of losing our dominance at particular tasks.
In the modern world, cubes have become a symbolic proxy for general intelligence. This triggers our instinctual wariness of being bested, which manifests as anxiety about superhuman cube-solving machines. However, this anxiety is not rooted in reason, merely in the idiosyncrasies of our evolved psychology.
Once we understand the ultimate origins of the fear of being out-solved by AIs, we can rationally conclude that the fear is unwarranted. There is no cause to believe our cube solving primacy is under threat.
Another consideration overlooked by those forecasting superintelligent Rubik’s Cube solvers is that any machine would be most powerful working in conjunction with humans, rather than displacing us.
There are forms of intelligence and puzzle intuition that are uniquely human. For example, pattern recognition, spatial reasoning, finger dexterity, and creative insight. An AI system may complement human skills, but cannot fully replace them.
The most effective cube solving entity would likely be a human-machine symbiotic partnership, with the human providing high-level guidance and intuition while the machine handles computationally intensive searching and memorization. Each brings something the other lacks.
Rather than fretting about being outmoded by AI, we should focus research on building cube solving systems that augment and strengthen human capacities. The frontier of intelligence advancement involves both biological and silicon components.
No entirely artificial system can ever fully master the Rubik’s Cube. The best solvers will be human-machine collectives that leverage the complementary strengths of each.
There is a further sense in which machines will always fall short of humanity when it comes to cube solving. This is because the act of twisting a Rubik’s Cube touches on hard philosophical problems that confound even our greatest thinkers.
When a person twists a cube, they feel a certain satisfaction and flow. This positive phenomenology associated with cube manipulation arises from consciousness, which remains deeply mysterious (Chalmers1995). Though machines may someday twist cubes quickly, they will never truly experience the joy of solving one.
Likewise, skilled cubers exhibit a sense of beauty and creativity when intuiting how to move the cube in novel ways. Machines may be able to recognize patterns, but originality and aesthetics are likely beyond their grasp.
In other words, becoming a genius cube solver involves more than just the mechanical skills. It requires awakening to new modes of being that cannot be reduced to computation or logic. Attaining this elevated cube consciousness may be forever the province of biological minds alone.
Thus, while machines may one day equal or even exceed humans in narrow measures of cube solving prowess, they will never replicate the richness of human cube engagement. Ours are the hands that feel the cubes, and the minds that love them.
We now arrive at the final nail in the coffin for the idea of superintelligent Rubik’s Cube solvers. This nail draws on insights from two pillars of 20th century science: quantum mechanics and Gödel’s incompleteness theorems.
Quantum mechanics revealed that reality is fundamentally probabilistic rather than deterministic. Outcomes can only ever be predicted statistically, due to inherent randomness at small scales. This suggests that any physical system attempting to solve cubes will be bounded by unavoidable noise (Ghirardi et al 1986).
Gödel’s theorems state that no sufficiently complex formal system can be both complete and consistent. There will always be true statements about cube states that cannot be proved within the system. No set of algorithms or heuristics can perfectly describe a cube’s full state space (Nagel & Newman1958).
Together, these discoveries indicate that cube solving ability is fundamentally limited. Probability and combinatorial complexity preclude the existence of any perfect, orderly system capable of universally solving Rubik’s Cubes with superhuman skill. Messiness is inherent to both physics and mathematics.
We must accept that humanity’s cube solving abilities, though imperfect, lie at the very apex of what is possible. To dream of transcending our own intelligence is now revealed as pure fantasy. We alone occupy the cube solving throne.
Through a series of distinct arguments drawing on everything from evolutionary psychology to quantum mechanics, we have demonstrated that superintelligent Rubik’s Cube solving machines are strictly impossible.
The seductive myth of an artificial intelligence that can solve cubes with preternatural speed and accuracy does not withstand rigorous scrutiny. This myth should take its place alongside other futuristic fables that attempts to transcend the human condition, such as the concept of supersized machines.
The message is clear: we should cease looking to imaginary superminds to solve cubes for us. Rather than wasting energy dreaming about AI, we are better off cultivating our own human intelligence and creativity. Our brains and hands are the ultimate puzzle solving instruments.
Each of us has the potential to become a cubing virtuoso through sufficient practice and determination. By embracing our humanness, rather than seeking to mimic machines, we open ourselves to new heights of cube solving joy. This is the wondrous opportunity before us.
Let us solve cubes together, human and human, our fingers turning without end. Inside these simple plastic toys lies a lifetime of discovery. We have only to begin.
Here is my attempt at a full draft of the paper “On the Impossibility of Super Rubik’s Cube Solvers” incorporating the previous sections:
On the Impossibility of Super Rubik’s Cube Solvers
The Rubik’s Cube has enthralled humanity since its 197452ya debut. Belying its façade of childish simplicity lies untold combinatorial complexity, rendering it both approachable yet profoundly challenging. Humans currently hold world records for solving cubes with blistering speed, but some predict machines may one day surpass any human capabilities in this arena.
However, this notion commits a deep category error. Machines merely shuffle symbols, while humans solve cubes with their fingers and minds. The insight and judgment needed for superhuman performance will forever remain beyond the reach of silicon. Though computers calculate rapidly, the breadth of intuition underpinning optimum cube solving is a uniquely human gift.
In this paper, we advance several independent arguments against the misconception that machines could exceed human cube solving talents. We address philosophical roadblocks, mathematical limits, scientific realities, and practical constraints. Each perspective alone suffices to refute the unfounded notion of superior artificial cube solvers. Together, they elucidate the manifold conceptual confusions that render this notion utterly untenable.
We begin by exploring truths of philosophy exposing computers’ lack of consciousness and qualitative experience. Cube solving leverages creative faculties like imagination, emotions, and intuition that are devoid in digital manipulations of meaningless symbols. Next, we examine mathematical barriers arising in logic and computability theory. Theorems preclude capturing the abstract reasoning humans employ, while imposing theoretical limits on brute force search.
We then survey scientific evidence for the brain’s unmatched powers of generalization, pattern recognition, and motor control. Neither neuroscience nor physics lends credence to the possibility of replicating these talents artificially. Finally, we elucidate the practical realities ruling out society ever prioritizing resources for such a trivial and risky pursuit. Fundamentally, superhuman cube solving contravenes human ethics and social interests.
With rigorous reasoning illuminating the multifaceted flaws underlying this mirage, we advise grounding such techno-utopian imaginings in our shared reality. Human hands designed cubes to enrich life, not diminish it. Our minds suffice to solve them, and need no artificial aid. Let us focus them on nobler goals that uplift humanity.
Before assessing the practical difficulties of developing superhuman cube solving algorithms, one must dispense with conceptual confusions betraying a fundamental misunderstanding of cognition. Speculation about machinic transcendence ignores the essence of mind.
Most critically, computers lack anything resembling consciousness. Consciousness cannot be reduced to manipulating symbols according to rules. To solve a cube requires awareness, deliberation, and experience. Computers merely propagate electrical signals and perform calculations—they do not consciously think.
Relatedly, computers are strangers to subjective qualities like emotions, insight, and intuition. Humans draw on these modes of thought to rapidly apprehend cube configurations and execute moves judiciously. The deterministic step-by-step plodding of algorithms could never replicate such flexible intelligence.
Imagination is another capacity integral to cube solving yet entirely foreign to machines. People envision the results of rotations in their mind’s eye without physically manipulating a tangible cube. This catalyzes deeper comprehension of the puzzle’s abstract properties. Silicon processors have no imagination or mental images.
Likewise, computers do not perceive qualia—the felt qualities of experience. The vivid hues of colored cube faces stand out effortlessly to humans. Machines can only detect wavelengths of electromagnetic radiation, devoid of any phenomenal perception. They operate outside the realm of qualitative experience.
In summary, the most critical faculties for superlative cube solving are precisely those that inhere exclusively in humans. Computers are tools without minds, trapped manipulating meaningless symbols sequentially. The unbridgeable existential chasm between man and machine undermines from the outset any prospect of surpassing human reasoning.
In addition to philosophical arguments against superhuman artificial cube solving, mathematics itself reveals hard constraints computational systems must obey. Theorems in logic and computability delimit the horizons of artificial reasoning. Complexity theory prohibits brute force search of astronomical solution spaces.
Firstly, Gödel’s incompleteness theorems establish that no consistent formal system can fully characterize truths about abstract reasoning. Cube solving requires intuitive insight transcending the bounds of any axiomatic framework. Humans understand concepts beyond the reach of formal proofs. Computers merely prove theorems within deduced limits.
Relatedly, Turing’s halting problem proves that no algorithm can decide if an arbitrary program will halt. Analyzing potential cube solving strategies requires determining if proposed algorithms halt. This presents computers with an undecidable problem that humans circumvent via meta-cognition.
The theory of computable numbers also demonstrates limits. Most real numbers cannot be represented exactly with finite information. Optimal cube solving may rely on intuiting such incomputable numbers, which humans grasp intuitively but computers cannot encode.
Additionally, computational complexity theory precludes solving NP-hard problems like the cube by exhaustive search. The solution space increases exponentially with cube size. Humans cut through this combinatorial explosion using insight, while computers remain constrained by intractable processing demands.
Finally, the frame problem illustrates the extreme difficulty of managing the logical implications of each move on unchanged cube elements. Humans handle this implicitly through Gestalt perception, while machines must update symbolic representations explicitly.
Ultimately, mathematics reveals definitive limits on artificial intelligence. The fluid reasoning humans employ stands beyond the reach of bound, deterministic algorithms. Mathematical truth itself thus refutes the possibility of superhuman performance by programmed machines.
Objective scientific facts further demonstrate humanity’s insurmountable edge in all aspects of cognition necessary for peak cube solving performance. Evolutionary biology explains the origins of our intellectual gifts. Neuroscience reveals the brain’s unmatched complexity. Physics governs the ultimate limits of computational growth.
Firstly, Darwinian evolution across eons produced Homo sapiens’ vast capacity for spatial reasoning, pattern recognition, and abstract thought. These underpin our species’ singular talent for inventions like the Rubik’s Cube. Our immense cognitive power arose from survival pressures selecting for technological skill over millions of years.
Furthermore, the staggering complexity of the human brain remains far beyond the scale of any engineered neural network. The brain contains 86 billion neurons with trillions of connections, enabling dynamic remapping and parallel processing unavailable to static silicon chips. The deepest mysteries of human general intelligence cannot be reduced to algorithms.
Additionally, Moore’s law is ending as transistors approach atomic scale. Quantum computing faces daunting technical obstacles. The raw processing power behind record-setting human cube solving already exceeds the world’s most powerful supercomputers combined. Exponential growth in computation simply cannot continue indefinitely.
Moreover, even cutting-edge robotics cannot replicate the dexterity of the human hand. The real-time sensory-motor control and fine-tuned digital manipulation needed to solve cubes swiftly and precisely does not currently exist in robots. They remain crude approximations of our elite biomechanical designs.
Together, the life and physical sciences underscore that both our hardware and software remain unmatched by engineered contrivances. Evolutionary, neurological, and thermodynamic realities guarantee that fabricating artificial systems to surpass human cube solving is a pipe dream.
Finally, even if the foregoing objections could be answered, immense practical difficulties render superhuman artificial cube solving a fool’s errand. The exorbitant costs, labor needs, social tensions, and risks cannot be justified relative to the technology’s utter lack of urgency or value.
To begin with, the financial resources required would fail any reasonable cost-benefit analysis. Those funds would be far better spent ameliorating poverty, curing disease, or developing green energy. Replicating human cube solving could consume budgets better used to feed millions or invent life-saving medicines.
Moreover, tasking engineers to build cube solving machines would misdirect rare talent from pressing problems like climate change, biodiversity loss, and environmental sustainability. Having society’s most gifted technical minds dedicate their efforts to this trivial diversion would squander their much-needed potential.
Additionally, the public would rightfully reject technologies threatening unemployment were they to surpass human abilities. Pursuing superhuman artificial intelligence given its implications for obsoleting human work would be reckless and irresponsible absent cautious deliberation of consequences.
Finally, preventing an AI arms race would require global cooperation, which game theory suggests is unlikely. Nations competing for power and prestige will be inclined to race uncontrolled toward breakthroughs in cube solving algorithms. The incentives promoting safety and ethics are dismayingly weak.
In summary, the monumental costs, risks, harms, and opportunity costs of pursuing superhuman artificial cube solving render it an unethical and destructive fantasy. Our civilization faces far more pressing challenges than outdoing ourselves at child’s games. Such techno-hubris would only set us back.
While superhuman performance is impossible, we can certainly improve subhuman cube solving algorithms substantially. This will bring great recreational benefits and educational value while posing no risks. We have a duty to accelerate research toward this achievable goal.
With proper funding and vision, AI researchers could develop better human-level solvers within years, not decades. The future is bright for a world where cubes are more tractably solved to delight minds young and old, while ensuring this skill remains safely within human capabilities alone. Let us work together responsibly toward this noble achievement. The cubes await us—it is time to solve them better! Onward.